Stable Delay of Arbitrary
Radio-Frequency
Waveforms over Optical
Fibers
Assaf Ben-Amram
Submitted in partial fulfillment of the requirements for the Master's
Degree in the Faculty of Engineering, Bar-Ilan University
Ramat-Gan, Israel 2015
This work was carried out under the supervision
of Prof. Avi Zadok from the Faculty of
Engineering, Bar-Ilan University
ACKNOWLEDGEMENTS
Now that the work is done, I can gladly say that the last two years were worth it. The
knowledge and experience I gained throughout this research are highly valuable and
useful. However, it could only happen with the help and guidance of many
individuals whom I mention next.
First and foremost, my full gratitude goes to my advisor, Prof. Avi Zadok. He warmly
welcomed me to his research group and gave me the opportunity to work with him.
Besides sharing his great knowledge and experience with me, he also patiently
guided me during this research and always treated me as equals, which is absolutely
not to be taken for granted. The writing of this thesis could not be completed
without his constant and endless support. His friendliness to his group members
induced a comfort environment that made the research process much less stressful.
For these and more, I am truly grateful.
Special thanks are given to Yoni Stern, who taught and guided me from the very
beginning of my way through the Master's degree. Most of my experience in working
with lab equipment is the result of his patient and close guidance. Yoni also helped
me understand the theoretical background of this research with his great
knowledge, and always answered kindly to any of my questions. I would like to thank
him for all his help and patience.
I would also like to thank all of Avi's former and current group members for sharing
their experience, their wise advises and support: Dr. Arkady Rudnitsky, Dvir Munk,
Eyal Preter, Idan Bakish, Nadav Arbel, Orel Shlomi, Raphi Cohen, Ran Califa, Shahar
Levi, Yair Antman and Yosef London.
I would like to express my great appreciation to the Faculty of Engineering at Bar-Ilan
University, and especially to Mrs. Dina Yeminy, for all her help and support from the
beginning of my Bachelor's degree till now.
Last but not least, I'm grateful for my loving and supporting parents and family that
encouraged me during the past two years, and express my gratitude to my lovely
wife Tzofia and my adorable daughter Noam. Thank you all!
TABLE OF CONTENTS
LIST OF FIGURES
GLOSSARY
NOTATIONS
LIST OF PUBLICATIONS
ABSTRACT ................................................................................................................................................. I
1. INTRODUCTION .............................................................................................................................. 1
1.1. MICROWAVE PHOTONICS ................................................................................................................ 1
1.1.1. BACKGROUND .......................................................................................................................... 1
1.1.2. RADIO-OVER-FIBER................................................................................................................... 3
1.1.3. VARIABLE OPTICAL DELAY LINES................................................................................................. 5
1.1.3.1. MOTIVATION .................................................................................................................................. 5
1.1.3.2. IMPLEMENTATION EXAMPLES OF VARIABLE ODLS ......................................................................... 6
1.2. STABLE RADIO-OVER-FIBER DISTRIBUTION ........................................................................................ 8
1.2.1. ENVIRONMENTAL EFFECTS ON OPTICAL FIBERS ............................................................................ 8
1.2.2. THE NEED FOR STABILIZED OUTPUT PHASE .................................................................................. 9
1.2.3. CURRENT SOLUTIONS FOR RADIO-OVER-FIBER DISTRIBUTION ...................................................... 10
1.3. HIGH-RESOLUTION BRILLOUIN SENSING ......................................................................................... 12
1.3.1. STIMULATED BRILLOUIN SCATTERING (SBS) .............................................................................. 12
1.3.2. HIGH-RESOLUTION DISTRIBUTED FIBER-OPTIC SENSORS BASED ON SBS ANALYSIS ......................... 14
1.3.2.1. BRILLOUIN OPTICAL TIME DOMAIN ANALYSIS .............................................................................. 14
1.3.2.2. BRILLOUIN OPTICAL CORRELATION DOMAIN ANALYSIS ................................................................ 15
1.4. LINEAR FREQUENCY MODULATED WAVEFORMS .............................................................................. 17
1.5. OBJECTIVES OF RESEARCH ............................................................................................................. 19
2. RESEARCH METHODOLOGY ......................................................................................................... 21
2.1. PRINCIPLE OF OPERATION ............................................................................................................. 21
2.2. STABILIZATION USING TWO LASER SOURCES ................................................................................... 24
2.3. SCHEMATIC ILLUSTRATION OF THE EXPERIMENTAL SETUP ................................................................. 25
2.4. THE CORRECTION FACTOR ............................................................................................................. 28
3. EXPERIMENTAL SETUPS ............................................................................................................... 31
3.1. OPEN LOOP MEASUREMENTS WITH A SINGLE LASER SOURCE ............................................................ 31
3.1.1. STAGE 1: OBSERVATION OF THE CHROMATIC DISPERSION EFFECTS ............................................... 31
3.1.2. STAGE 2: CHARACTERIZATION OF THE RELATIONS BETWEEN WAVELENGTH, RF PHASE SHIFTS AND DC
VOLTAGE ...………………………………………………………………………………………………………………………………………… 35
3.2. CLOSED-LOOP, STABLE DISTRIBUTION OF A RF SINE WAVE .............................................................. 37
3.3. CLOSED-LOOP, STABLE DISTRIBUTION OF AN ARBITRARY RF WAVEFORM ........................................... 39
4. EXPERIMENTAL RESULTS ............................................................................................................. 46
4.1. OPEN LOOP MEASUREMENTS WITH A SINGLE LASER SOURCE ............................................................ 46
4.1.1. STAGE 1: OBSERVATIONS OF THE CHROMATIC DISPERSION EFFECTS ............................................. 46
4.1.2. STAGE 2: CHARACTERIZATION OF THE RELATIONS BETWEEN THE WAVELENGTH, PHASE SHIFTS AND DC
VOLTAGE …………………………………………………………………………………………………………………………………………… 47
4.2. CLOSED-LOOP, STABLE DISTRIBUTION OF A RF SINE WAVE .............................................................. 49
4.3. CLOSED-LOOP, STABLE DISTRIBUTION OF AN ARBITRARY RF WAVEFORM ........................................... 53
5. STABILIZED DELAY WITHIN HIGH-RESOLUTION BRILLOUIN ANALYSIS .................................. 59
5.1. B-OCDA EXPERIMENTAL SETUP .................................................................................................... 59
5.2. EXPERIMENTAL RESULTS ............................................................................................................... 62
6. DISCUSSION AND SUMMARY ...................................................................................................... 66
6.1. SUMMARY OF RESULTS ................................................................................................................. 66
6.2. LIMITATIONS AND FUTURE WORKS................................................................................................. 67
REFERENCES .......................................................................................................................................... 69
בעברית תקציר א .…….…………………….……………………………….…………………………………………………
LIST OF FIGURES
Figure 1: The basic concept of a MWP system [1] ................................................. 2
Figure 2: General RoF system structure [27]. The optical carrier and sidelobes are
transmitted over optical fibers from the central station to base stations, and after
detection to the air by microwave antennas. ODN: Optical Distribution Network, CS:
Central Station, BS: Base Station .......................................................................... 4
Figure 3: A phased array antennas structure scheme. The steering of the beam is
achieved by differential phase shifts between the array elements [29]. ................... 6
Figure 4: A fiber-optic prism feeding phased array antenna elements for the steering
of the scanning beam [1]. EOM: Electro-optic Modulator ....................................... 7
Figure 5: The phase stabilized downlink transmission scheme [74]. The reference
signal is mixed with its replica after round-trip travel and the outcome signal changes
the wavelength of the tunable laser. MZM: Mach-Zehnder modulator, PolM:
polarization modulator, BPF: bandpass filter ....................................................... 11
Figure 6: An example for a phase-coded B-OCDA setup. Note the 25 km-long fiber
delay line that is placed prior to the fiber under test [63]. .................................... 17
Figure 7: Illustration of the PSLR, ISLR and resolution of the impulse response of an
LFM waveform [29]........................................................................................... 19
Figure 8: Experimental setup for the realization of a long, stabilized fiber-optic delay
of arbitrary RF waveforms. BPF: bandpass filter, PC: polarization controller ........... 26
Figure 9: An illustration of the setup used in the observation of the chromatic
dispersion effects. LPF: low-pass filter, EDFA: erbium doped fiber amplifier ........... 31
Figure 10: Radio frequency spectrum of the waveform generated by the microwave
generator without the LPF. ................................................................................ 32
Figure 11: Radio frequency spectrum of the waveform generated by the microwave
generator, with use of the LPF. .......................................................................... 33
Figure 12: Optical power spectral density of an optical carrier modulated by a 3 GHz
sine wave......................................................................................................... 34
Figure 13: An illustration of the setup used in the characterization of the relations
between wavelength, RF phase shift and mixer DC voltage. LPF: low-pass filter, EDFA:
erbium doped fiber amplifier, DVM: digital voltmeter .......................................... 35
Figure 14: An illustration of the setup used in the closed feedback, phase stabilized
delay of an RF sine wave ................................................................................... 38
Figure 15: An illustration of the setup for the stabilized delay of an arbitrary RF
waveform. LPF: low-pass filter, EDFA: erbium doped fiber amplifier, DVM: digital
voltmeter, BPF: band-pass fiter .......................................................................... 40
Figure 16: RF power spectral density of a LFM waveform at the output of the delay
line. ................................................................................................................. 43
Figure 17: Measured optical power spectral density of the delayed waveform. An
optical bandpass filter was used to retain one optical carrier that was modulated by
the control tone (right-hand peak), and reject a second optical carrier which was
modulated by the user's RF waveform. ............................................................... 44
Figure 18: RF power spectral density of the control sine wave following two-way
propagation along the fiber delay line. ............................................................... 44
Figure 19: A 3 GHz control sine wave, detected following two-way propagation in a
8.8 km-long dispersive fiber delay line. Each trace corresponds to a different
wavelength of the tunable optical carrier, in 0.1 nm increments. The change in group
delay between successive acquisitions is about 30 ps. .......................................... 46
Figure 20: (left) Output phase of a 3 GHz control sine wave following two-way
propagation in a 8.8 km long delay fiber, as a function of tunable laser wavelength,
(right) DC reading of the mixing between the delayed control sine wave and its
reference replica, as a function of the tunable laser source wavelength. ................ 48
Figure 21: The DC voltage at the output of the mixer as a function of time, in open
feedback loop operation. .................................................................................. 49
Figure 22: Closed loop, phase stabilized two-way delay of a 3 GHz sine wave over 8.8
km of fiber. (top): DC voltage obtained by the mixing the delayed sine wave with its
reference replica, as a function of time. (bottom): wavelength setting commands to
the tunable laser source, as a function of time. ................................................... 50
Figure 23: Persistence traces of the output 3 GHz control sine wave, following two-
way delay in 8.8 km of fiber, accumulated over 10 minutes of operation at 0.5
second intervals, with (left) and without (right) closed loop feedback. ................... 51
Figure 24: Persistance traces of the 3 GHz control sine wave foolowing delay over 8.8
km of fiber: feedback loop open and no external heating of the delay fiber (top left);
feedback loop open during the heating of the fiber by a halogen lamp (top right);
feedback loop closed during ongoing heating (bottom left); and feedback loop closed
following the removal of the heating lamp and during the cooling down of the delay
fiber (bottom right). .......................................................................................... 52
Figure 25: The DC voltage at the output of the mixer as a function of time, during the
four stages of the experiment described in Figure 24. .......................................... 53
Figure 26: The DC voltage at the output of the mixer as a function of time, during 2
minutes of open feedback loop operation. .......................................................... 54
Figure 27: Wavelength of the tunable laser source of the RF control sine wave
(green) and of the LFM signal (blue), as a function of time during two minutes of
closed-loop operation. ...................................................................................... 55
Figure 28: The DC voltage at the output of the mixer as a function of time during
closed-loop operation. ...................................................................................... 55
Figure 29: Persistence traces of the compressed shapes of LFM waveforms, sampled
at the output of the fiber delay over 2 minutes, without (top) and with (bottom)
closed-loop wavelength control. ........................................................................ 57
Figure 30: Schematic illustration of a phase-coded Brillouin optical correlation-
domain analysis (phase-coded B-OCDA) setup, incorporating a stabilized fiber-optic
delay line in the path of the Brillouin signal wave. Solid lines denote fiber paths,
dashed lines represent RF cable paths, and dashed-dotted, black lines correspond to
DC control signals. Blue color represents paths and components related to the
sensing functionality, whereas green paths and components are part of the delay
stabilization module. The 'Wavelength control' module is described in detail in Fig.
15. Details of the 'Pump wave processing' module are not shown, for better clarity
(see [64]). ........................................................................................................ 60
Figure 31: Top – Wavelength of the control channel (left-hand axis), and the implied
thermal drift in the path length of the 25 km-long delay line (right-hand axis), as a
function of time. Thermal drift on the order of 10 cm is observed. Bottom –
Measured Brillouin gain as a function of frequency offset between pump and signal,
and of time. The phase-coded B-OCDA setup was adjusted to monitor the Brillouin
gain spectrum in a 2 cm-wide hot-spot. The delay of the Brillouin signal was free-
running, without closed-loop feedback to the wavelength of the sensor laser. The
Brillouin gain spectrum changed after 10 minutes, from that of the hot-spot to that
of the fiber under test at room temperature. ...................................................... 63
Figure 32: Top – Wavelength of the Brillouin sensor laser source (left-hand axis), and
the implied thermal drift in the path length of the 25 km-long delay line (right-hand
axis), as a function of time. Thermal drift on the order of 9 cm is observed. Bottom –
Measured Brillouin gain as a function of frequency offset between pump and signal,
and of time. The phase-coded B-OCDA setup was adjusted to monitor the Brillouin
gain spectrum in a 2 cm-wide hot-spot. Unlike Fig. 31, the delay of the Brillouin signal
was stabilized through closed-loop feedback to the wavelength of the sensor laser.
The Brillouin gain spectrum remained that of the hot-spot throughout the
measurements. ................................................................................................ 64
Figure 33: Measured Brillouin frequency shifts as a function of time. The phase-
coded B-OCDA setup was adjusted to monitor the location of a 2 cm-wide hot-spot.
Thermal drift in a 25 km-long delay line incorporated in the setup leads to incorrect
interrogation after 10 minutes of free-running operation (blue). Delay drift is
overcome with closed-loop, stabilized delay (red). ............................................... 65
GLOSSARY
AM Amplitude Modulator
AWG Arbitrary Waveform Generator
B-OCDA Brillouin Optical Time Domain Analysis
B-OTDA Brillouin Optical Correlation Domain Analysis
BPF Band Pass Filter
BS Base Station
CFBG Chirped Fiber Bragg Grating
CS Central Station
CW Continuous Wave
DBG Dynamic Brillouin Grating
DC Direct Current
DSP Digital Signal Processing
DVM Digital Voltmeter
EDFA Erbium-Doped Fiber Amplifier
EMI Electro-Magnetic Interference
EOM Electro-Optic Modulator
FBG Fiber Bragg Grating
FIR Finite Impulse Response
FWHM Full Width Half Maximum
IF Intermediate Frequency
IIR Infinite Impulse Response
I/Q In-phase and Quadrature
ISLR Integrated Side-Lobe Ratio
LCFBG Linearly-Chirped Fiber Bragg Grating
LFM Linear Frequency-Modulated
LO Local Oscillator
LPF Low Pass Filter
LTE Long Term Evolution
MWP Microwave Photonics
MZM Mach-Zehnder Modulator
NLFM Nonlinear Frequency-Modulated
ODL Optical Delay Line
ODN Optical Distribution Network
OFDM Orthogonal Frequency-Domain Multiplexing
PAA Phased-Array Antenna
PC Polarization Controller
PolM Polarization Modulator
PSD Power Spectral Density
PSLR Peak-to-Side-Lobe Ratio
RF Radio Frequency
RoF Radio-over-Fiber
SBS Stimulated Brillouin Scattering
SMF Single Mode Fiber
SNR Signal to Noise Ratio
SOA Semiconductor Optical Amplifier
TLS Tunable Laser Source
TTD True Time Delay
WDM Wavelength Division Multiplexing
NOTATIONS
A Complex envelop of a wave z Distance
0,g g SBS gain parameters mZ Distance between correlation
, Angular frequency peaks
B Brillouin gain line SN Total number of symbols in
P Optical power phase sequence
0, ,f f Frequency sT Phase symbol duration
Lifetime
T Duration of LFM signal
Temperature
B Bandwidth of a signal
,t Time
Instantaneous phase
L Length
n Refractive index
c Speed of light
L Linear thermal expansion
Coefficient
D Chromatic dispersion
Coefficient
Optical wavelength
0,V V Voltage parameters
Correction factor
S Dispersion slope parameter
LIST OF PUBLICATIONS
Journal papers:
1. A. Ben-Amram, Y. Stern, Y. London, Y. Antman and A. Zadok, "Stable closed-loop
fiber-optic delay of arbitrary radio-frequency waveforms," submitted to Optics
Express, 2015 (in review).
Conference papers:
1. A. Ben-Amram, Y. Stern and A. Zadok, " Fiber-optic distribution of arbitrary
radio-frequency waveforms with stabilized group delay," in Proc. of Conference
on Lasers and Electro-Optics (CLEO) 2015, (OSA, 2015), paper JTh2A.54.
2. A. Ben-Amram, Y. Stern, Y. Antman, Y. London and A. Zadok, "Stabilized Fiber-
Optic Delay of Arbitrary Waveforms with Application in Distributed Sensors,"
accepted for presentation in IEEE Microwave Photonics Topical Meeting,
Paphos, Cyprus, Oct. 2015.
I
ABSTRACT
Microwave photonics (MWP) is an area of research that merges between the
optical and radio-frequency (RF) domains. MWP techniques provide many potential
advantages over the processing of signals in the electrical domain, such as broad
bandwidth, long reach with low attenuation, and immunity against electro-magnetic
interference. One important application of MWP is the fiber-optic implementation of
variable RF delay lines, which are critical components in beam steering within
phased-array radar systems. Another significant application is the transmission of RF
signals from cellular and wireless networks over long distances using optical fibers,
or radio-over-fiber (RoF). RoF extends the reach and coverage of such networks.
Various precision applications require that the time delay of RF waveforms
over long fibers remains stable. Examples include the distribution of local oscillators
in large antenna arrays, and the testing and calibration of radar systems. Recently
another application emerged for long stable delay, as part of distributed sensors of
strain and temperature based on Brillouin scattering. Such sensors address cm-scale
segments along many km of fiber. Unfortunately, delay along optical fibers changes
when exposed to variations in the surrounding temperature. A change of 1 ºC
modifies the optical path length by 0.75 cm per 1 km of standard optical fiber.
Presently available solutions are either too complicated for implementation in most
radar and sensor systems, or provide insufficient stability.
The method employed in this thesis relies on chromatic dispersion in order to
compensate for thermal delay drifts. This basic principle was independently
II
proposed by our group and in parallel by a group from the Beijing University of Posts
and Telecommunication. A single tunable laser source is modulated by both a control
RF sine wave and the input RF waveform to be delayed. Following distribution along
a fiber, the RF phase of the output control tone is tracked and used for identifying
delay drifts. The wavelength of the tunable laser source is then adjusted in a closed
feedback loop, so that delay variations due to chromatic dispersion and
environmental changes cancel out. However, the initial embodiment relied the
separation between input and control waveforms in the RF domain, hence their
spectra were required to be non-overlapping. This restriction is difficult to
accommodate in systems that support broadband waveforms, such as high-
resolution fiber sensing protocols.
In this work, I introduce and demonstrate a significant extension of the
stabilization technique. Rather than use a single source, the control RF tone and the
input waveform modulate two separate tunable laser sources with different
wavelengths. Feedback provided by the output phase of the delayed control tone is
used to adjust the wavelengths of both sources, to obtain a stable delay of both
waveforms. The two waveforms were separated in the optical domain, therefore no
restrictions were imposed in their RF spectra. The attainable performance of the
stabilized delay line is analyzed, and tradeoffs between the range of temperature
variations that can be accommodated and residual delay uncertainty are identified. A
figure of merit is proposed, and an upper bound on performance is established in
terms of the specifications of the laser sources used.
III
Three main experiments are demonstrated in as part of this work. First, the
stable distribution of the control sine wave over 9 km of fiber is demonstrated with
residual delay variations of ±4 ps. Second, the stable distribution of broadband,
linearly frequency-modulated (LFM) waveforms, which are employed in many radar
systems, is demonstrated over the same distance. Residual delay variations are
reduced from 200 ps in open-loop operation to 20 ps in closed-loop operation,
limited by the timing jitter of our sampling oscilloscope. Last, the stable interrogation
of a 2 cm-wide local hot spot in high-resolution distributed Brillouin analysis is
achieved, in the presence of thermal delay drifts that are several times larger.
Correct interrogation could not be performed under free-running conditions.
The experimental results demonstrate the applicability of the proposed
stabilization technique to the processing of broadband microwave signals as part of
more complicated systems. The method could be further extended to the active
mitigation of acoustic and mechanical vibrations, with broader-bandwidth feedback.
Introduction 1
1. INTRODUCTION
1.1. MICROWAVE PHOTONICS
1.1.1. BACKGROUND
Over the past thirty years, the research field that merges between analog
radio-frequency (RF) and microwave signals with photonic means, known as RF-
photonics or microwave-photonics (MWP) [1], has been a very productive one [1, 2].
In MWP systems, an optical carrier wave is modulated by the electrical signal of
interest. After modulation, the optical signal propagates through optical fibers and
devices, and finally the electrical signal is reconstructed by photo-detection. MWP
processes have several potential advantages over their all-RF equivalents [1]: optical
fibers provide a low propagation loss regardless of the microwave frequency; optical
fibers have an ultra-broad transmission bandwidth of several THz; electro-magnetic
interference (EMI) has little effect on optical fibers; use of several optical carriers can
provide for parallel processing, etc. When taking into account all these advantages,
MWP setups could prove as improved optical versions of current RF systems, or
perform tasks that currently cannot be carried out in the RF domain. The basic
concept of a MWP system is illustrated in Figure 1.
Amongst the many potential applications of MWP available in the research
literature, a relatively simple one, which is already being used in analog links for the
defense sector [1], is that of antenna remoting. In order to connect between, for
example, an end unit of a radar system and a central office, an optical fiber can be
used as a transmission link. Fibers provide an attractive alternative for electrical
Introduction 2
cable paths: waveforms can propagate over tens of km without amplifiers along the
way, and with group velocity dispersion that is much smaller than that of RF cables.
Another commonly discussed application is that of MWP filters, implementing both
finite-impulse-response (FIR) and infinite-impulse-response (IIR) RF transfer
functions in optical media [3]. Other applications include the photonic generation of
arbitrary and ultra-wideband RF signals [4, 5]; the photonic implementation of
advanced RF modulation formats [6]; and analog-to-digital conversion using
photonic devices [7].
Figure 1: The basic concept of a MWP system [1].
The field of MWP continues to produce exciting advances. Examples of the
last 2-3 years include, among many others: in-phase and quadrature (I/Q) detectors
for radars [8]; analog distribution networks [9]; generation of arbitrary waveforms
and arbitrary filter transfer functions [10, 11, 12, 13, 14, 15, 16, 17]; and integrated
MWP transmitters and receivers on a single chip [10, 17, 18, 19, 20].
Introduction 3
In this work I focus on two main applications of MWP: distribution of radio
waveforms over optical fibers, and long stabilized optical delay lines. Both are
introduced next.
1.1.2. RADIO-OVER-FIBER
In many scenarios, where cellular wireless reception cannot be provided or
when long distances must be covered, data of wireless networks is distributed over
cables instead. As the demand for large data transmission bandwidth over wireless
access networks increases continuously, RF coaxial cables can no longer support the
necessary transmission. One important solution, introduced several years ago, is the
distribution of RF signals from wireless networks over long optical fibers, or radio-
over-fiber (RoF) [1, 21, 22]. The basic concept of RoF networks is that RF signals
modulate the optical carrier in the central station. The optical carrier and sidebands
are then transmitted over optical fibers to remote base stations. After detection at
the base station, the reconstructed RF signals are radiated by microwave antennas. A
general RoF system structure is illustrated in Figure 2. RoF networks benefit from the
low propagation loss and broadband bandwidth of the optical fibers and extend the
reach and coverage of wireless communication networks.
Introduction 4
Figure 2: General RoF system structure [27]. The optical carrier and sidelobes are transmitted over optical fibers from the central station to base stations, and after
detection to the air by microwave antennas. ODN: Optical Distribution Network, CS: Central Station, BS: Base Station, PD: Photo-Detector, RN: Remote Node, MT: Mobile
Terminal.
RoF networks are incorporated in satellite communication, mobile radio
communication, and other wireless network systems [23]. For example, the long
term evolution (LTE) technology standard for wireless communication systems,
published in 2011, relies on optical fibers to connect between the base stations and
the central stations [24]. The research in RoF in recent years focuses on increasing
the carrying capacity using technologies such as wavelength division multiplexing
(WDM), orthogonal frequency-domain multiplexing (OFDM) [23, 25], or a
combination of both [26]. A full-duplex RoF link for optical/wireless integration
based on analog RoF for the uplink transmission and digital RoF for the downlink was
implemented in [27]. Objectives of ongoing research include cost reduction,
increased bandwidth, better simplicity and higher transmission power [28]. In one
example, the modulation depth in RoF links was enhanced by a ring resonator notch
filter that removed the optical carrier [29].
Introduction 5
1.1.3. VARIABLE OPTICAL DELAY LINES
1.1.3.1. MOTIVATION
The delay of RF waveforms is required as part of the testing and calibration of
many radar systems, and in the emulation of remote targets within testing facilities.
One way to accomplish the necessary delay relies on high rate digital signal
processing (DSP) for generating replicas of an input waveform. The capabilities of
DSP advance continuously. However, even today, state-of-the-art analog to digital
converters and DSP elements cannot reach tens-of-GHz rates with sufficient vertical
resolution, that is separation between adjacent quantization levels. Therefore, the
delay of waveforms based on propagation over long optical fibers, referred to as
optical delay lines (ODLs), represents an attractive alternative. Many principles and
technologies are common to ODLs and RoF networks. The separation between them
is somewhat arbitrary, and it is made based on context, system considerations and
the types of waveforms being transmitted.
In the applications above the delays are typically fixed. However, much
attention was also given over the last thirty years to the optical implementation of
variable RF delay lines [4]. Variable RF delay lines play a major role in radar systems
based on phased-array antennas (PAAs), in which beam steering relies on the proper
interference between the radiation patterns from individual antenna elements, as
illustrated in a Figure 3 [30]. Each individual antenna within the array radiates
equally to all directions. When the signals feeding the antennas are in-phase, the
intensity peak of the interference pattern is formed perpendicular to the aperture.
When the signals are phase-shifted from one another, the interference pattern is
Introduction 6
reconstructed at a different angle governed by the incrementing phases, causing an
effective tilt of the beam. PAAs are faster and more reliable than mechanical beam
steering elements [31, 32].
Figure 3: A phased array antennas structure scheme. The steering of the beam is achieved by differential phase shifts between the array elements [30].
The steering of beams using incremental phase delays is adequate for single-
frequency or narrow-bandwidth transmission. When broadband radar signals are
used, incremental phase delays are not enough to avoid spatial dispersion of the
beam. Variable group delay elements, often referred to as true time delays (TTDs),
must be used instead [33]. Variable optical delay lines can provide, in principle, the
necessary TTDs.
1.1.3.2. IMPLEMENTATION EXAMPLES OF VARIABLE ODLS
A switching matrix between fibers of different lengths provides a simple form
of an ODL. In a series of works by Tur and coauthors [34, 35, 36], discrete ODLs were
realized through wavelength-selective switching among different paths. The quality
Introduction 7
of the delayed waveforms, in terms of distortion, was excellent. However, it is
difficult to vary the delay values continuously in such networks. The principle was
extended in networks of many fibers, each connected to a series of fiber Bragg
gratings (FBGs) set for different reflectivity wavelengths [37, 38]. Continuous delay
tuning was achieved by linearly-chirped FBGs (LCFBGs) in conjunction with tunable
laser sources (TLSs) [39]. Other approaches include so-called fiber prisms [40, 41],
consisted of an array of both highly-dispersive and non-dispersive segments, as
illustrated in Figure 4, and slow light-based techniques using stimulated Brillouin
scattering (SBS) in fibers [42, 43, 44, 45, 46, 47], or propagation in semiconductor
optical amplifiers (SOAs) [48, 49]. A large number of delay resolution points was
achieved by a combination of a switching matrix together with FBGs and tunable
laser sources [50].
Figure 4: A fiber-optic prism feeding phased array antenna elements for the steering of the
scanning beam [1]. EOM: Electro-optic Modulator, PD: Photo-Detector.
In a recent series of works by Ofir Klinger et al. of our group [51, 52, 53, 54],
ODL setups were adjusted to specifically accommodate linear frequency -modulated
Introduction 8
(LFM) and nonlinear frequency-modulated (NLFM) waveforms, which are common in
many radar systems. These types of waveforms are introduced in detail later in this
chapter. Long delay variations of over 100 ns were obtained. However, the setup
cannot support most other types of RF signals.
The key metric of variable MWP TTD elements is the product of the
waveform bandwidth that can be supported, multiplied by the range of delay
variations, subject to the constraints of sufficient signal quality (known as the 'delay-
bandwidth product'). Many ODL implementations struggle to reach delay-bandwidth
products above the order of unity. Recent state-of-the-art examples of ODLs include
a 7-bit compact silicon-based reconfigurable optical TTD providing a delay of 1.27 ns
with a 10 ps resolution [55]; a continuously tunable ODL based on micro-ring
resonators providing a delay of 100 ps with 168 GHz bandwidth [56]; moveable
mirrors based on dynamic Brillouin gratings (DBGs) providing the delay of 1 Gbit/s
data by as much as 10 ns [57]; and lastly, systems based on nonlinear wavelength
conversion and dispersive propagation, that achieved delay variations of micro-
seconds and supported 10 Gbit/s data [58].
1.2. STABLE RADIO-OVER-FIBER DISTRIBUTION
1.2.1. ENVIRONMENTAL EFFECTS ON OPTICAL FIBERS
Transmission over optical fibers provides many potential advantages as noted
above. One drawback, however, is the sensitivity of fibers to numerous
environmental parameters, first and foremost to temperature [59]. Instabilities in
the phase of an RF signal reconstructed at the output of a long fiber-optic delay line
Introduction 9
stem from the thermo-optic properties of silica. The group delay in silica fibers
changes by 7.5 ppm per C. Therefore, a change of 1 C in the surrounding
temperature is analogous to the lengthening or shortening of every 1 km of fiber by
an extra 0.75 cm. These delay variations may add up to many cm over long fibers. On
the other hand, an RF signal of 3 GHz, for example, corresponds to a wavelength of
10 cm. Thus, the phases of RF waveforms at the output of a long free-running delay
line might become completely arbitrary. The problem worsens with higher RF, and
with increase in the extent of delay (length of fiber).
1.2.2. THE NEED FOR STABILIZED OUTPUT PHASE
The importance of a stabilized output phase is apparent, for instance, in the
case of PAAs that was mentioned above. When the relative phases between
neighboring elements fluctuate, the transmitted beam becomes spatially distorted.
RF phase stability is also necessary in the testing and calibration of radars; in the
emulation of distant targets; in the distribution of local oscillator microwave tones
among multiple sites, such as in large radio-astronomical arrays [60]; in microwave
generation within electro-optic oscillators [61]; in optical coherence tomography
based on CFBGs and ODLs [62]; and in certain types of lidars [63].
Recently, the significance of stable delay of modulated sequences, carried
over tens of km of fiber, has been also highlighted in the context of distributed fiber-
optic sensors that are based on Brillouin scattering analysis [64, 65]. This particular
application is pursued in our group as well, hence a stabilized delay represented a
pressing need of specific setups. High-resolution Brillouin sensors, and the effects of
delay propagation instability in such setups, are addressed later in this chapter.
Introduction 10
1.2.3. CURRENT SOLUTIONS FOR RADIO-OVER-FIBER DISTRIBUTION
Early attempts to overcome the instability of the output RF phase relied, for
example, on the passive thermal isolation of a 32 km long fiber inside a container
[66]. However the stability that can be achieved using passive means is restricted. As
discussed in subsequent chapters, the extent of thermal stability that is needed for
supporting GHz-frequency signals over many km is on the order of 1e-3 C. Some
approaches rely on all-optical phase-locked loops to provide stabilization on the
scale of the optical wavelength. These ultra-precision delay lines are used in particle
accelerators and colliders [67, 68]. Other solutions rely on a heterodyne
optoelectronic delay-locked loop [69]; adjusting the phase of a laser by pump
modulation and cavity length control [70]; and DSP compensation [71]. Most of
these techniques deal with phase drifts within the optical domain, which makes the
compensation systems extremely complicated, and are not suitable for incorporation
in radar systems.
The solution path proposed in this research relies on chromatic dispersion in
the delay fiber to compensate for the thermo-optic variations in path length. The
approach employs a closed feedback loop that offsets the wavelength of the tunable
laser source, onto which the RF signal is modulated, so that path length variations
due to the thermo-optic effect and chromatic dispersion cancel out. The approach
was suggested in parallel by our group and, initially unknown to us, by the group of
Prof. Kun Xu at the Beijing University of Posts and Telecommunication [72, 73, 74,
75]. In their setup, which is illustrated in Figure 5, the desired RF waveform of the
user and an internal control tone jointly modulate the output of a single tunable
Introduction 11
laser. Following propagation along the fiber, the two waveforms are detected and
separated by RF filters. The output phase of the control tone is then monitored and
used to drive the feedback loop and adjust the source wavelength to obtain a stable
path length [75].
Figure 5: The phase stabilized downlink transmission scheme [75]. The reference signal is mixed with its replica after round-trip travel and the outcome signal changes the
wavelength of the tunable laser. MZM: Mach-Zehnder modulator, PolM: polarization modulator, BPF: bandpass filter, WTL: wavelength tunable laser, PD: photo-detector,
BC: bias controller, EDFA: erbium doped fiber amplifier, CIR: circulator, OSC:
oscilloscope, SA: spectrum analyzer.
The system reported in [75] supports a broad range of user waveforms,
however it requires that the RF spectra of the user waveform and of the control tone
do not overlap. This restriction is not easily met in high-resolution Brillouin analysis
setups, which involve broadband sequence modulation. The setup therefore is not
directly applicable to Brillouin sensing, and significant modifications are necessary.
Introduction 12
1.3. HIGH-RESOLUTION BRILLOUIN SENSING
1.3.1. STIMULATED BRILLOUIN SCATTERING (SBS)
Stimulated Brillouin scattering (SBS) is a nonlinear optical effect that can
couple between two optical waves along a standard fiber [76]. In SBS, a relatively
intense pump wave interacts with a counter-propagating signal wave, which is
typically weaker and detuned in frequency. The combined intensity to the two waves
stimulates, through electrostriction, an acoustic wave. The frequency of the acoustic
wave equals the difference between the optical frequencies of the pump and signal
waves, and its wavenumber is the sum of their wavenumbers. Through photo-
elasticity, the acoustic wave leads to a travelling index grating, which scatters the
light waves. The travelling grating can couple optical power between the counter-
propagating pump and signal waves. Effective coupling requires that the difference
between the central frequencies of the two waves should closely match the Brillouin
frequency shift of the fiber 11B GHz (for standard single-mode fibers at 1550 nm
wavelength) [76, 77].
SBS requires the lowest power threshold among all nonlinear mechanisms in
standard silica fibers [78], which makes it very attractive for all-optical signal
processing [15, 43, 79, 80], and sensing [81, 82, 83] applications. In most of the
applications and throughout this work, the power of the pump is strong enough so
that it is barely affected by the amplification of the probe, a regime known as that of
an undepleted pump [76]. For this case, the complex envelop of the pump wave
Introduction 13
pumpA is considered as constant, and the complex envelop of the probe wave probeA
is exponentially amplified along the fiber:
( ) (0)exp ( )2probe probe probe
zA z A g
(1)
In equation (1) above, 1( ) mprobeg defines the complex gain function,
probe is the frequency of the probe wave and z is the distance the probe wave
travelled along the fiber. The complex gain function, for a continuous-wave (CW)
pump laser, is of Lorentzian shape [76, 84]:
2
0( )
1 2
pump
probe
pump probe B B
g Ag
j
(2)
Here, the frequency of the pump is pump , 2 30 Mrad/sB denotes the
narrow inherent linewidth of the SBS process, and 1
0 W mg
is the gain coefficient
at the peak of the Brillouin gain line. In case the pump wave is modulated to obtain a
broadened power spectral density (PSD) pump pumpP , the complex gain function is
given by a convolution of the pump PSD with the SBS line shape [43]:
0
( )1 2
pump
probe pump
pump probe B B
g Pg d
j
(3)
The value of B varies with both temperature and mechanical strain. Hence,
a mapping of the local Brillouin gain spectrum along standard fibers is being used in
distributed sensing of both quantities for 25 years [85, 86, 87].
Introduction 14
1.3.2. HIGH-RESOLUTION DISTRIBUTED FIBER-OPTIC SENSORS BASED ON
SBS ANALYSIS
1.3.2.1. BRILLOUIN OPTICAL TIME DOMAIN ANALYSIS
One of the major challenges facing Brillouin sensing technology is reaching
cm-scale spatial resolution. The most widely employed measurement protocol is that
of Brillouin optical time domain analysis, or B-OTDA [85], proposed initially by
Horiguchi and coworkers 25 years ago. B-OTDA relies on SBS amplification of a CW
signal by counter-propagating pump pulses. Since the pump pulses are limited to a
certain time frame, the SBS effect only occurs when and where the pulses exist along
the fiber. Therefore, the SBS gain of the signal wave is time dependent, and spatial
distinction is achieved through temporal analysis. At every section of the fiber, if the
frequency difference between the pump pulse and the signal wave equals to the
local value Brillouin frequency shift B , SBS amplification takes place. When strain is
applied, for example, in some sections, it changes the Brillouin frequency shift so
that B , which in turn leads to a decrease in the SBS amplification.
The spatial resolution of this fundamental scheme is limited to the duration
of the pump pulses, which is in turn restricted to the acoustic lifetime 1 B ~ 5
ns, or longer. Consequently, currently available commercial equipment provides a
spatial resolution on the order of 1 m, with 50 km range. Much effort is being
dedicated to resolution enhancement in B-OTDA, using elaborate schemes for the
shaping and control of pump pulses. A detailed account of these efforts is beyond
the scope of this research, which is focused on microwave photonics. State of the art
Introduction 15
B-OTDA setups reported in the literature reach 2 km range with 2 cm resolution [88],
or 5 km range with 5 cm resolution [89].
1.3.2.2. BRILLOUIN OPTICAL CORRELATION DOMAIN ANALYSIS
In the late 90's, Hotate and coworkers proposed a different sensing technique
known as Brillouin optical correlation domain analysis, or B-OCDA [64, 90]. B-OCDA
reaches higher spatial resolution than that of B-OTDA, on the scale of few mm [91].
B-OCDA relies on the broadband modulation of the Brillouin pump and signal waves,
so that their complex envelopes are in correlation only within discrete and narrow
peaks along the fiber. Hotate's initial method was to frequency-modulate both the
pump and signal waves by a common sine wave function over a broad frequency
range. By that, the difference between their instantaneous frequencies remained
fixed at B in specific, narrow segments only. Only in those positions could the SBS
effect be built.
The first demonstrations provided mm-scale resolution. However, multiple
periodic correlation peaks were generated, effectively limiting the number of
resolution points that could be unambiguously interrogated to only a few hundreds.
Similarly to B-OTDA, the unambiguous measurement range of B-OCDA was
continuously extended over the last 15 years, using more elaborate frequency
modulation protocols. A full account of these efforts is outside the present
discussion.
Recently, our research group and coworkers proposed to jointly modulate the
pump and signal waves with a phase code in order to increase the number of
Introduction 16
resolution points [92]. The phase codes employed are binary sequences, designed to
exhibit low correlation sidelobes. Using this method, the resolution is determined by
the duration of an individual bit, whereas the separation between neighboring,
periodic peaks is set by the length of the code, which could be chosen arbitrarily. By
slightly changing the bit duration, the positions of all the peaks (except for the zero-
order one) are effectively scanned along the fiber under test. Modulation rates can
be as high as 12 Gbit/s, yielding a resolution of 9 mm [65]. The phase-coded B-OCDA
principle was recently extended by our group to the analysis of a 2.2 km-long fiber
with a spatial resolution of 2 cm [64].
One difficulty that is associated with the setup is the need for a deliberate
delay imbalance between the paths that lead the pump and signal waves towards
the opposite ends of the fiber under test. This imbalance is necessary to guarantee
that high-order correlation peaks are in overlap with the test fiber. The delay must
be several times longer than the fiber under test itself, reaching 60 km in some
experiments. An example for a B-OCDA setup is illustrated in Figure 6.
Introduction 17
Figure 6: An example for a phase-coded B-OCDA setup. Note the 25 km-long fiber delay line that is placed prior to the fiber under test [63]. PC: polarization controller, EDFA: erbium doped fiber
amplifier.
The proper function of B-OCDA requires that the path lengths leading the two
waves towards the correlation peaks remain stable to within 1 cm over 1-2 hours.
The requirement is the same as that of a fiber-optic delay lines with a stabilized
phase of the output RF waveform. Solutions developed towards stabilize microwave-
photonic delay lines could be highly instrumental in high-resolution Brillouin sensor
setups.
1.4. LINEAR FREQUENCY MODULATED WAVEFORMS
A group of signals that is widely employed in radar systems is that of linear
frequency-modulated (LFM) waveforms. A LFM signal of duration T , bandwidth B
and central radio frequency 0f can be expressed as:
2
0 0( ) cos 2 rectLFM
B tA t A f t t
T T
(4)
Introduction 18
Here rect( ) equals 1 for 1 2 , and zero elsewhere. The instantaneous
frequency ( )f t of the LFM waveform is obtained from the derivative of its
instantaneous phase ( )t , which is the argument of the cosine in equation (4):
2
0 0
1( ) 2
2
d B Bf t f t t f t
dt T T
(5)
It can be deduced from equation (5) that the instantaneous frequency of LFM
signals is time dependent, sweeping across a broad bandwidth over relatively long
durations. The broad bandwidth of the LFM waveform provides high ranging
resolution, whereas their long duration leads to a high overall energy which helps
improve the signal-to-noise ratios (SNRs) of the measurements.
Equation (5) reveals another advantage of LFM signals: the equivalence
between temporal delays and frequency offsets. This quality is used in ranging
measurements: the delayed echoes that are reflected from a target are mixed with a
replica of the transmitted waveform. The beating between the two is centered at an
intermediate frequency that is directly proportional to the distance to the target.
The same property was used in MWP TTDs of these waveforms [51].
LFM signals are of constant amplitude, and are simply generated and
processed. The post-detection processing of LFM signals is carried out by a cross-
correlation of a LFM reference signal and the detected waveform. The result of the
cross-correlation is referred to as the impulse response function. It is characterized
by a strong and narrow main-lobe peak and low side-lobes.
Introduction 19
Three figures of merit define the quality of the impulse response function, as
illustrated in Figure 7: the peak-to-side-lobe ratio (PSLR) is the ratio between the
power of the main-lobe peak and the power of the highest side-lobe peak; the
integrated side-lobe ratio (ISLR) is the ratio between the integrated energy within
the full-width-half-maximum (FWHM) of the main-lobe and the integrated energy
elsewhere; and the resolution simply defined by the FWHM of the main-lobe. The
first two are measured in dB, and the last is measured in seconds.
Figure 7: Illustration of the PSLR, ISLR and resolution of the impulse response of an LFM waveform [29]. PSLR: pick to side-lobe ratio, ISLR: integrated side-lobe ratio.
In this work, we use the stabilized, long fiber-optic delay of LFM signals in
proof-of-concept experiments.
1.5. OBJECTIVES OF RESEARCH
The main goals of this work are: 1) to stabilize the output timing and phase of
arbitrary RF signals, following their MWP delay over long optical fibers; and 2) to
employ the solution in high-resolution Brillouin analysis of fixed fiber positions over
an extended period of time. The proposed solution relies on the cancellation of
thermo-optic path length drift by chromatic dispersion as noted above. Unlike [75],
Introduction 20
however, the user waveform and the control tone will be modulated onto separate
tunable laser sources. The separation between the two waveforms will be carried
out in the optical domain, so that all restrictions on the RF spectra of the two signals
are removed. The research program consisted of the following tasks:
1) Preliminary tests to examine the relations between the RF phase shift and the
wavelength of the tunable laser. The design of a proper control feedback
loop. The generation of an error signal, and its application in controlling the
transmission wavelength of a tunable laser diode.
2) The demonstration of a stabilized output phase of a single-tone RF sine wave
at the output of closed-loop fiber-optic delay line.
3) The extension of the setup to support a user waveform and a control tone,
modulated onto two separate lasers. The stabilization of the delay of the user
waveform based on a feedback provided by a control sine wave that is
carried over a separate laser source.
4) The stabilization of the output phase of arbitrary RF signals, such as
broadband LFM waveforms.
5) The incorporation of the stabilized delay line within a high-resolution
Brillouin analysis setup, and the demonstration of its added value.
Experimental Setups 21
2. RESEARCH METHODOLOGY
As was discussed in the previous chapter, the temperature of the
surroundings of an optical fiber changes its optical path length. Due to the thermo-
optic properties of the silica, the group delay along the fiber changes by 7.5 ppm per
C. These changes lead to phase variations in delayed RF tones. On the other hand, a
travelling signal in an optical fiber experiences delay variations that stem from
chromatic dispersion. In this work, a method for cancelation of the temperature-
induced phase variations by dispersion-induced delay variations is proposed.
2.1. PRINCIPLE OF OPERATION
Let us assume a delay line of length L which is exposed to a temperature
change T . The 'nominal' delay of the signal in the optical fiber is nL
c , where
1.45n is the group index of light in the fiber, and c is the speed of light. The
variations of the delay as a result of T are:
1 1 1 1T
n L n n LL T T T
n T L T c n T L T
(6)
In equation (6) above 1
7.5 /n
nppm C
n T
is the thermo-optic
coefficient of silica fibers, 1
0.5 /L
Lppm C
L T
is their linear thermal expansion
coefficient, and 1LT
.
Experimental Setups 22
On the other hand, the change in delay due to an offset of the optical carrier
wavelength by a certain is given by:
( ) ( ) ( )D
cD L D
n (7)
In equation (7) above, ps nm kmD is the chromatic dispersion coefficient
of the optical fiber. It is assumed for the moment that the central wavelengths of the
two laser sources, that of the user waveform and that of the control tone, are
sufficiently close so that the same value of chromatic dispersion coefficient applies
to both. Subject to this condition, the same wavelength correction can be applied to
both sources. Even if this condition is not met, knowledge of the fiber dispersion
slope parameter could provide for the necessary correction in wavelength increment
between the two sources (this issue is addressed in subsequent sections).
Comparison between (6) and (7) reveals the range of temperatures variations
that can be compensated by a tunable laser of scanning range :
( )cDT
n
(8)
For a standard SMF-28 fiber, whose chromatic dispersion parameter is
17 ps nm kmD , and for a tunable laser source with a wavelengths scanning
range of 100 nm, the supported temperature span would be 50 C .
The residual phase uncertainty of the compensated delay line is related
to the radio frequency of the input waveform f , the fiber dispersion, and the
residual uncertainty of the laser source wavelength :
Experimental Setups 23
1
2DL
f
(9)
Using equation (9), we can set a performance bound on the extent of the
nominal delay and the maximal radio frequency that can be supported by a given
fiber of known dispersion, and a given laser source of known wavelength instability,
subject to a constraint of maximum tolerable residual phase error:
1
2 2 2
n nf
fDL fDc Dc
(10)
Equation (10) suggests that a longer delay and a higher radio frequency
would require better wavelength stability. The relation also suggests a tradeoff
between the delay-bandwidth product and the range of temperature variations that
can be supported: The former requires an optical fiber with low chromatic
dispersion, whereas the latter requires an optical fiber that is highly dispersive (see
equation (8)). For instance, the use of a tunable source with wavelength instability of
1 pm and a standard SMF-28 fiber, would allow for the delay of signals with phase
stability of one angular degree only when the delay-bandwidth product f does not
exceed 610 . The tradeoff can be expressed in terms of a figure of merit, which sets a
bound on the nominal delay of the fiber, the range of temperature variations, and
the delay variations that are attainable (in units of C):
maxmax
1 1FoM T N
(11)
Experimental Setups 24
Here max is the tuning range of the laser source. Equation (11) highlights
the significance of the tunable laser quality, in term of its "effective number of
wavelength resolution points" maxN
, in setting upper bound on the
performance of the stabilized fiber delay line. Tunable lasers with a scanning range
of 100 nm and wavelength resolution of 1 pm, or about 100,000 wavelength
resolution points, are readily available. Such sources could support a stabilized fiber-
optic delay line with a figure of merit of about 1.5e10 C.
The RF bandwidth of the input waveform is restricted by dispersion-induced
fading. Assuming double-sideband, small-signal modulation, one can show that the 3
dB RF bandwidth of delayed distribution is given by [93, 94]:
3
2
1 1 2 1
2 3 2 3 2dB
nf
L D D
(12)
Here 2
2 2D
c , in units of ps2/km. The bandwidth limitation for a 25
km-long, standard single-mode fiber delay line is about 7 GHz.
2.2. STABILIZATION USING TWO LASER SOURCES
The stabilization principle relies on the transmission of a single-tone wave,
which is referred to as the control signal, along with the user's waveform. After a
round-trip, the control signal is mixed with its local replica. The DC level, which is
filtered out of the mixer's output, represents the variations of the output RF phase of
the control tone. The phase stabilization is carried out by changing the wavelength of
the tunable laser source in increments that are determined by the DC level and a
Experimental Setups 25
correction factor. This correction factor is linearly proportional to the dispersion
parameter (more about the correction factor is provided later in this chapter).
In previous arrangements both RF signals, the control tone and that of the
user, modulated a single tunable laser source. When using this configuration, it is
possible to stabilize the output phase of the user's waveform only when the two
signals can be separated in the RF domain with no overlap between them.
Consequently, this configuration might be unsuitable for broadband waveforms.
In this work we propose a method that uses two tunable laser sources in two
different wavelengths. Each RF signal, the control tone and that of the user,
modulates a different laser source. If the separation between the wavelengths of the
two laser sources is large, the dispersion parameters of the fiber may not be the
same for both, and each laser source would require a different correction factor. The
two correction factors would be related by a simple linear relation, which is
governed by the dispersion slope parameter of the fiber. In using this scheme, the
phase of an arbitrary RF signal can be stabilized based on the feedback provided by
tracking the phase of an independent RF control tone, without any restriction on its
spectrum.
2.3. SCHEMATIC ILLUSTRATION OF THE EXPERIMENTAL SETUP
A schematic illustration of experimental setup for the stabilized fiber-optic
delay of arbitrary RF waveforms is shown in Figure 8. The generic description is given
here to help clarify the stabilization principle, whereas a more detailed account will
be provided in the next chapter. Solid black lines denote optical fiber paths, green
Experimental Setups 26
lines indicate radio frequency signal paths that are part of the control circuitry, red
lines correspond to the path of the user's signal to be delayed, and dashed black
lines indicate DC signals of the control feedback loop. The setup is modular: the
feedback loop can be disconnected, and either of the two RF inputs, that of the
intended user and the control sine wave, may be switched on and off independently.
A control sine wave modulates the upper tunable laser source whose
wavelength is denoted as 𝜆1. A replica of the RF control sine wave is retained at the
near end of the fiber, to be used as reference. The input RF waveform to be delayed
modulates the lower tunable laser source whose wavelength is denoted as 𝜆2. The
nominal wavelengths of the two lasers must be sufficiently distinct to allow for
convenient optical filtering. The two signals are combined at the input of the fiber
delay line.
Amplitude
Modulator
User RF
RF splitter
RF control
(sine wave)
RF mixer
Feedback
Tunable laser 𝝀𝟏
Wavelength
control
Control
sine wave
Reference voltage
Amplitude
Modulator Tunable laser 𝝀𝟐
PC
PC
1 2
3
Det. 2
BPF 𝝀𝟏
Fiber
mirror
Det. 1
User RF
BPF 𝝀𝟐
2:1 1:2
Figure 8: Experimental setup for the realization of a long, stabilized fiber-optic delay of arbitrary RF waveforms. BPF: bandpass filter, PC: polarization controller.
Experimental Setups 27
At the far end of the fiber delay line the optical signal is split in two. One copy
of the signal is filtered by an optical bandpass filter (BPF) to retain only the
waveform of the user and eliminate the control sine wave, and is then detected by a
photo-receiver (Det. 1). The filtered signal serves as the stabilized RF output of the
setup, to be used by a larger system such as a Brillouin fiber sensor, if necessary. The
output of the second coupler branch is retransmitted back along the fiber delay line
by a fiber mirror.
Back at the transmitter end of the fiber link, the returning optical waveform
is filtered by a second BPF whose central wavelength is set to 𝜆1 to retain the control
sine wave only, and detected by a second photo-receiver (Det. 2). The sine wave,
having propagated through a two-way delay, is mixed with its reference replica in a
RF mixer, generating a DC voltage. The voltage depends on the RF phase differential
between the two sine wave copies, ranging from a maximal positive value when the
two are in-phase, through zero value for a 90 phase differential, and maximum
negative value for a 180 phase difference. Therefore, the stabilization of the DC
output of the mixer at any given value guarantees the phase stability of the control
sine wave.
The DC reading is used as the input of a negative feedback loop mechanism,
which modifies the operating wavelength of both laser diodes in attempt to retain
the DC value of choice. For convenience, our experiments aim to maintain zero
voltage, since this working point provides a linear relation between phase drift and
correction voltage (see also below). The phase stabilization of the control sine wave
is reached through a compensation of thermal drifts by chromatic dispersion. It
Experimental Setups 28
invariably guarantees the phase stabilization of the user waveform as well at the
output of Det. 1, irrespective of any particular properties of that waveform.
In most applications, the waveform of the user must be transmitted to a
remote location. Therefore it propagates only one-way along the fiber delay line. The
control sine wave, on the other hand, propagates back and forth since its reference
replica is retained at the transmitter end.
2.4. THE CORRECTION FACTOR
The DC voltage V is sampled by a computerized setup controlling the
tunable laser sources, and a command for setting their wavelengths to new values is
sent at pre-determined time intervals based on their present operating wavelength,
the sampled voltage and the correction ratio:
next prev V (13)
The correction factor α between the DC voltage reading and the necessary
wavelength increment correction can be deduced from equation (13):
V V
(14)
The first term on the right-hand side is related to the length of the fiber, its
dispersion parameter, and the radio-frequency of the control sine wave. According
to (7) and (9):
1 nm
2 radRFf DL
(15)
Experimental Setups 29
The second term on the right-hand side of equation (14) refers to the change
in the phase per DC voltage. The output voltage follows a sine wave dependence of
the phase difference between the delayed and local replicas of the RF tones. As
mentioned earlier, we look to stabilize a phase difference of 90 between the two RF
inputs of the mixer. Denoting the residual phase error with respect to 90 as , we
may write:
0( ) sin( )V V (16)
Here 0V is the maximum reading of the mixer output voltage. Hence, in the
vicinity of zero residual phase error:
0 0( ) cos( ) ( ) ( )dV V d V d (17)
We therefore find that the second term on the right-hand side of equation
(14) is simply given by the magnitude of the sinusoidal variations of the mixer
output:
0
1 rad
mVV V
(18)
The numerical values of both terms are calibrated using simple experimental
procedures. Bringing (15) and (18) together:
0
1 1( )
2 ( )RFV f LV D
(19)
Two correction factors are necessary in our stabilization protocol, one for
each tunable laser source. Since the wavelengths of the two are typically separated
Experimental Setups 30
by about 10 nm, the different dispersion coefficient of the fiber at each wavelength
must be taken into consideration:
2 1 2 1( ) ( ) ( )D D S (20)
Here S is the dispersion slope parameter of the fiber. For standard SMF-28
fiber it is given by 20.092[ps nm km]S . For instance, if the separation between
the wavelengths of the laser sources is 10 nm, a difference between dispersion
coefficients of 0.92 ps nm kmD must be taken in consideration when setting
the two correction factors 1 2( , ) in equation (18).
Residual delay variations stem from uncertainties in both the setting of
wavelengths and in the measurement of voltage. The wavelength setting error in
1 was ±30 pm, corresponding to of about ±5 ps over 9 km. The standard
deviation of the noise V in voltage measurements was on the order of ±5 mV,
corresponding to delay variations 02V fV on the order of ±2.5 ps.
Experimental Setups 31
3. EXPERIMENTAL SETUPS
3.1. OPEN LOOP MEASUREMENTS WITH A SINGLE LASER
SOURCE
The preliminary experiments we conducted are divided into two stages. In
the first we observed the effect of chromatic dispersion on the output phase of a RF
sine wave, and in the second we examined the relations between the DC level at the
mixer output, the phase shift of the RF output waveform and the wavelength of the
tunable laser source.
3.1.1. STAGE 1: OBSERVATION OF THE CHROMATIC DISPERSION EFFECTS
Real-time
Scope
Signal
Generator
LPF -
𝑓𝑐 = 3.3𝐺𝐻𝑧
Tunable laser
𝜆1 = 1550 𝑛𝑚 Amplitude
Modulator
Fiber
mirror
Amplifier +40dB
Det. 1
EDFA
Figure 9: An illustration of the setup used in the observation of the chromatic dispersion effects. LPF: low-pass filter, EDFA: erbium doped fiber amplifier.
Experimental Setups 32
The purpose of the first experiment was to modulate a tunable laser source
by a RF sine wave, and measure the RF phase shifts at the output of a long fiber-
optic delay line due to chromatic dispersion. The setup for this experiment is shown
in detail in Figure 9. Black lines denote optical fiber paths and green lines indicate
radio frequency signal paths. A sine wave of 3 GHz frequency and 27 dBm power was
generated by a high frequency microwave generator. The frequency of the sine wave
was chosen according to the bandwidth limitations of the RF amplifiers and the
photo-detector that are part of the setup. At the output of the signal generator a
low-pass filter (LPF) with cut-off frequency 3.3cf GHz was placed, in order to
prevent aliasing. This LPF also blocked off harmonic distortions, as shown in Figures
10 and in Figure 11.
Figure 10: Radio frequency spectrum of the waveform generated by the microwave generator without the LPF.
Experimental Setups 33
Figure 11: Radio frequency spectrum of the waveform generated by the microwave generator, with use of the LPF.
After the LPF, the RF sine wave was split in two paths: one was used to drive
an electro-optic amplitude modulator (AM), which was placed at the output of a
tunable laser diode source (see next). The other replica of the sine wave was
sampled by a 6 GHz bandwidth real-time oscilloscope and used as a timing
reference.
The light source used in the experiment was a continuous wave (CW) tunable
laser diode at the 1550 nm wavelength range, with 8 dBm output power. The output
of the laser passed through a polarization controller (PC) and connected to the AM.
The PC was needed for matching the state of polarization of the laser light with that
of the modulator. The optical carrier and the two modulation side-bands propagated
through a magneto-optical fiber circulator and into an 8.8 km-long optical fiber delay
line that was wrapped around a spool. Figure 12 shows the optical carrier and
modulation side-lobes as measured by an optical spectrum analyzer (OSA). The fiber
Experimental Setups 34
delay line was terminated by a fiber mirror, which in this particular experiment was a
bare cleaved facet. The Fresnel relative power reflectivity of facet is about -14 dB
(4%).
Figure 12: Optical power spectral density of an optical carrier modulated by a 3 GHz sine wave.
Following a round-trip in the fiber delay line and back through the circulator,
the optical signal was amplified by a programmable erbium doped fiber amplifier
(EDFA) from an optical power of -29 dBm to 0 dBm. It is important to keep the
output power of the EDFA below 0 dBm in order to prevent damage of the photo-
receiver. The output of the EDFA was then detected by a fast photo-receiver with a
rise-time of 35 ps, denoted as Det. 1, and amplified by a RF amplifier that provided a
total gain of 40 dB. The output of the amplifier was sampled by a second channel of
the real-time digitizing oscilloscope. The oscilloscope was connected by the internal
communication network of the laboratory to a personal computer.
Experimental Setups 35
The timing of the reference signal channel was held steady by the internal
trigger of the oscilloscope, whereas the timing of the delayed waveform in the other
channel could vary across the screen. The wavelength of the tunable laser source
was tuned by a matlab code within the range of 1550-1551 nm, in increments of 0.1
nm, every 2 seconds. The time interval between measurements was defined by the
minimal time required to save data on the oscilloscope. The RF phase difference
between the reference sine wave and the delayed replica, for each wavelength step,
was measured on the oscilloscope.
3.1.2. STAGE 2: CHARACTERIZATION OF THE RELATIONS BETWEEN
WAVELENGTH, RF PHASE SHIFTS AND DC VOLTAGE
DVM
Signal
Generator
LPF - 𝑓𝑐 = 3.3𝐺𝐻𝑧
Tunable laser
𝜆1 = 1550 𝑛𝑚 Amplitude
Modulator
Fiber
mirror
Amplifier +40dB
Det. 1
EDFA
Attenuator -16dB
Mixer
IF
LO RF
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
Figure 13: An illustration of the setup used in the characterization of the relations between wavelength, RF phase shift and mixer DC voltage. LPF: low-pass filter, EDFA:
erbium doped fiber amplifier, DVM: digital voltmeter.
Experimental Setups 36
The purpose of this experiment was to characterize the relations between
the wavelength of the tunable laser source and the phase shift of a delayed RF sine
wave, and the corresponding DC voltage reading that is obtained by mixing the
delayed RF sine wave and the reference tone. That DC reading is later used as
feedback for the tunable laser wavelength adjustment.
The setup for this experiment is illustrated in Figure 13. It is very similar to
the previous one of Figure 9, except for a few additions. The cleaved facet at the end
of the delay line was replaced by a fiber mirror with 99% power reflectivity.
Following two-way delay, photo-detection and amplification of the RF sine wave, the
output of the RF amplifier was connected to the RF input port of a RF mixer. The
reference replica of the same RF tone was attenuated by a 16 dB RF attenuator and
connected to the local oscillator (LO) input port of the same mixer. The purpose of
the attenuator was to make sure that the amplitudes of both sine waves are equal at
the input ports of the mixer. The output of the RF mixer is the product between the
two sine waves, and can be written as:
1 2
1 2 1 2 1 2 1 2( ) cos ( ) cos ( )2
mix
A AV t C t t (21)
Here, 1,2A , 1,2 and 1,2 are the amplitudes, frequencies and instantaneous
phases of the two sine waves, respectively. C denotes a proportionality constant
that is determined by the responsivity of the detector, RF amplification and
efficiency of the mixer. In this particular case, the frequencies of both sine waves
were equal, hence the right-hand cosine term in (20) becomes a DC voltage. Two
cascaded LPFs with a cut-off frequency 0 2.25f GHz were placed at the output
Experimental Setups 37
port of the mixer, in order to block-off the signal at the doubled frequency.
Consequently, the signal measured by a digital voltmeter (DVM) was:
1 2( ) cos ( )
2
A AV t C t (22)
In (21), ( )t denotes the difference between the instantaneous phases of
the two sine waves.
Similarly to the previous experiment, we used a matlab code to change the
wavelength of the tunable laser source within the range of 1550-1551 nm, in
increments of 0.1 nm and every 0.5 seconds. For each step we observed the RF
phase shift between the two sine waves on the oscilloscope, and simultaneously the
DC voltage. The results provided the necessary correction factor that was used later
in the conversion of residual phase errors to wavelength offsets of tunable lasers
(see Chapter 2).
3.2. CLOSED-LOOP, STABLE DISTRIBUTION OF A RF SINE WAVE
The purpose of this stage in the experiment was to distribute a single-tone RF
sine wave over a fiber-optic delay line, measure the DC voltage that represents
phase shifts as above, and use this voltage in a closed feedback loop that changes
the wavelength of the laser source and maintains a stable output RF phase of the
sine wave.
The setup for this experiment is illustrated in Figure 14. The dashed black
lines indicate DC signals of the control feedback loop. The setup was that of the
previous stage, except for the feedback loop that was added after the DVM. The
Experimental Setups 38
conversion factor between measured voltage and necessary wavelength correction
was extracted in the previous experimental phase. Both the DVM and the tunable
laser source were connected to a computer.
Using a LabVIEW code, we implemented a closed feedback loop according to
equation (12), which is repeated here for convenience:
next prev V (23)
Every half a second, the LabVIEW code issued a set of commands to measure
the DC voltage and set the tunable laser source to a new wavelength. The feedback
loop was designed to maintain zero DC voltage, which corresponds to a stabilized
DVM
Signal
Generator
LPF - 𝑓𝑐 = 3.3𝐺𝐻𝑧
Tunable laser
𝜆1 = 1544 𝑛𝑚 Amplitude
Modulator
Fiber
mirror
Amplifier +40dB
Det. 1
EDFA
Attenuator -16dB
Mixer
IF
LO RF
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
Figure 14: An illustration of the setup used in the closed feedback, phase stabilized delay of an RF sine wave. EDFA: erbium doped fiber amplifier, LPF: low-pass filter, DVM: digital
voltmeter.
Experimental Setups 39
relative phase of 90º. This feedback loop repeated itself automatically, until
terminated manually or until the wavelength of the tunable laser source drifted by
more than 5 nm.
3.3. CLOSED-LOOP, STABLE DISTRIBUTION OF AN ARBITRARY
RF WAVEFORM
The purpose of this experiment was to transmit a RF sine wave as the control
signal over one optical wavelength, and an arbitrary RF waveform, referred to as the
user's waveform, on a different optical carrier. The tracking of the output RF phase
of the control signal provided the necessary feedback for adjusting the wavelengths
of both optical carriers, and stabilizing the delays and output phases of both.
The setup for this experiment is illustrated in Figure 15. Red lines correspond
to the path of the user's signal to be delayed. On the upper branch, a CW tunable
laser source was initiated to a wavelength of 1527.5 nm, denoted here as 1 , and to
an output power of 5 dBm. The output of the laser source was connected to a PC
and then to an electro-optic AM. A RF LFM signal was generated using an arbitrary
waveform generator (AWG). The LFM signal was defined by a pulse duration of
5T s , a central frequency of 0 1.75f GHz and a bandwidth of 500B MHz .
The central frequency of the LFM signal was chosen according to the bandwidth of
the photo-receiver we have in our disposal.
Experimental Setups 40
Real-time
Scope
Mixer
LO
IF
RF
DVM
Signal
Generator
LPF - 𝑓𝑐 = 3.3𝐺𝐻𝑧
Amplitude
Modulator
Tunable laser
𝜆2 = 1544 𝑛𝑚
Arbitrary
Waveform
Generator
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
Attenuator -12dB
Amplifier +40dB
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
Tunable laser
𝜆1 = 1527.5 𝑛𝑚
2:1 Amplitude
Modulator 1:2
Fiber
mirror
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
Amplifier +30dB
Optical BPF
𝜆1 = 1527.5 𝑛𝑚
Det. 1
EDFA
Amplifier +40dB
Optical BPF
𝜆2 = 1544 𝑛𝑚
Det. 2
EDFA
LPF - 𝑓𝑐 = 3.3𝐺𝐻𝑧
LPF - 𝑓𝑐 = 2.25𝐺𝐻𝑧
Correlation
processing
Figure 15: An illustration of the setup for the stabilized delay of an arbitrary RF waveform. LPF: low-pass filter, EDFA: erbium doped fiber amplifier, DVM: digital
voltmeter, BPF: band-pass fiter.
Attenuator -16dB
Experimental Setups 41
The AWG used for this setup has a maximal sampling rate of 5 Gsample/s.
The output of the AWG was split into two paths. The signal in one path was used as a
reference signal for the post-detection correlation processing of the delayed
waveform, and was therefore connected directly to the real-time oscilloscope.
The RF LFM waveform in the other path was filtered by a LPF with a cut-off
frequency 2.25cf GHz in order to prevent aliasing. The filtered waveform was
attenuated by a -12 dB RF attenuator, and then amplified by a fixed-gain 40 dB
broadband RF amplifier. The attenuator was required to prevent saturation of the
amplifier. Following amplification, the waveform passed through another LPF with a
cut-off frequency of 2.25cf GHz to ensure that only the LFM signal at the correct
central frequency is used in modulation of the laser source, with no copies at other
frequencies. At that point, the power of the LFM signal was 7 dBm. Lastly, the
processed LFM waveform was used to modulate the light at the output of the laser
source via the electro-optic AM.
Going down to the lower branch of the setup, a second CW tunable laser
source was initiated to a wavelength of 1544 nm, denoted as 2 , and an output
power of 8 dBm. The wavelengths of both laser sources were chosen arbitrarily;
however, they must be a separated but at least 4 nm to allow for their proper
separation by the optical band-pass filters (BPFs) available to us.
Similarly to previous setups, a sine wave of 3 GHz frequency and 27 dBm
power was generated by a high frequency microwave generator. This sine wave was
split into two paths: one copy was attenuated by a -16 dB RF attenuator and then
Experimental Setups 42
connected to the LO input port of a RF mixer, as the reference signal for phase
stabilization, and the other copy was filtered by a LPF with a cut-off frequency of
3.3cf GHz and used to modulate the second tunable laser source through a
second electro-optic AM.
Next, both optical carriers and their side-lobes were combined by a 50/50
optical coupler, and directed through a magneto-optical fiber circulator into an 8.8
km-long fiber delay line. At the far end of the delay line, the combined signals were
split by a 50/50 optical splitter. One copy of the both modulated carriers was
reflected back by a 99% reflectivity fiber mirror.
The other copy of the signal, with an optical power of -15 dBm, was amplified
by a programmable EDFA to an output power of 8 dBm and filtered by a 4 nm-wide
tunable optical band-pass filter (BPF) with 1 as its central wavelength, to retain only
the optical carrier with the user's waveform, which in our particular case was the
LFM signal. The filtered waveform was detected by a fast photo-receiver with a rise-
time of 35 ps, denoted as Det. 1. The output power of the EDFA was chosen to
maximize the signal power, without reaching the upper limit of the photo-receiver
dynamic range.
The reconstructed, delayed LFM signal was amplified by a 30 dB RF amplifier,
since the electrical output power of the detector was too low for further processing.
The transfer function of the optical BPFs in our disposal provided a rejection ratio of
about 20 dB, hence the amplified RF waveform was filtered yet again with a LPF with
a cut-off frequency of 2.25cf GHz , to remove residual cross-talk of the control
Experimental Setups 43
sine wave. Lastly, the output LFM waveform was sampled by the real-time
oscilloscope for further off-line processing. Figure 16 shows the LFM waveform at
the output of LPF prior to the oscilloscope.
Figure 16: RF power spectral density of a LFM waveform at the output of the delay line.
The reflected copy of the optical waveforms traveled back through the fiber
delay line and then through the circulator. The overall optical power of the
waveforms at the circulator output was -23 dBm. The waveforms were then
amplified by another programmable EDFA to an output power of 5 dBm, and filtered
by a second 4 nm-wide tunable optical BPF with a central wavelength of 2 to retain
only the control sine wave. The output of the BPF as measured by the OSA is shown
in Figure 17. The filtered signal was detected by another fast photo-receiver with a
rise-time of 12 ps, denoted as Det. 2, and was then amplified by a 40 dB RF amplifier.
Following the amplifier, the signal was connected to the RF input port of the RF
mixer. Figure 18 shows the filtered RF sine wave prior to the mixer.
Experimental Setups 44
Figure 17: Measured optical power spectral density of the delayed waveform. An optical bandpass filter was used to retain one optical carrier that was modulated by the control tone (right-hand peak), and reject a second optical carrier which
was modulated by the user's RF waveform.
The RF mixer multiplied the delayed sine wave with its reference replica. The
output of the mixer was filtered twice by LPFs with cut-off frequencies of
Figure 18: RF power spectral density of the control sine wave following two-way propagation along the fiber delay line.
Experimental Setups 45
2.25cf GHz , and 3.3cf GHz , in order to retain only the DC voltage component,
as explained in detail in the previous sub-section.
A LabVIEW code was used to interrogate the DVM readings of the DC voltage.
The correction factor between DC voltage and the necessary wavelength offsets to
the laser diode of the control waveform was known from previous experiments. The
corresponding correction factor for the tunable laser of the LFM waveform was
extrapolated based on the dispersion slope parameter of the delay fiber, using
equation (19). New wavelength settings were sent to both tunable laser sources by
the LabVIEW code, and the process repeated itself until termination.
In parallel to the tracking of the control sine wave and the setting of
wavelengths, the timing of the delayed LFM waveform at the far end of the delay
line was monitored by its cross-correlation with its reference replica (see in Chapter
1 for compression of LFM waveforms). The timing of the main lobe peak was used as
a measure of the effective delay of the waveform. A properly stabilized delay line
manifests in reduced timing jitter of the compressed main lobe. The smallest jitter
we could observe corresponds to the timing inaccuracy of the sampling oscilloscope,
which is on the order of ±1 ppm of the acquisition trace duration.
Experimental Results 46
4. EXPERIMENTAL RESULTS
4.1. OPEN LOOP MEASUREMENTS WITH A SINGLE LASER
SOURCE
4.1.1. STAGE 1: OBSERVATIONS OF THE CHROMATIC DISPERSION EFFECTS
Figure 19 shows the delayed control sine wave following propagation along
the fiber delay line, for 10 wavelengths of the tunable laser diode source. The
wavelength was changed by 0.1 nm increments between successive acquisitions. The
wavelength variations translate into group delay variations and changes to the
output RF phase, according to the chromatic dispersion of the delay fiber. Each 0.1
nm wavelength increment corresponds to a delay variation of about 30 ps, in good
agreement with the predictions of equation (7).
Figure 19: A 3 GHz control sine wave, detected following two-way propagation in a 8.8 km-long dispersive fiber delay line. Each trace
corresponds to a different wavelength of the tunable optical carrier, in 0.1 nm increments. The change in group delay between
successive acquisitions is about 30 ps.
Experimental Results 47
The overall duration of the experiment was about 20 seconds. Variations in
the temperature of the air-conditioned laboratory are limited to 1-2 C over an hour.
Therefore, temperature drifts within the experimental durations were unlikely to
exceed 0.01 C. The corresponding delay changes are below 0.1 ppm, or few ppm at
most. These possible thermal drifts are two orders of magnitude smaller than the
dispersion-induced variations observed in the measurements.
4.1.2. STAGE 2: CHARACTERIZATION OF THE RELATIONS BETWEEN THE
WAVELENGTH, PHASE SHIFTS AND DC VOLTAGE
Figure 20 shows the output phase of a delayed, 3 GHz control sine wave
(left), and the DC voltage obtained at the output of the mixer (right), as a function of
the tunable laser diode wavelength. The phase varies linearly with wavelength
whereas the DC voltage follows a sinusoidal pattern, in agreement with equation
(21). Given the dispersion parameter of the delay fiber and the frequency of the RF
sine wave, the expected delay variation is approximately 300 ps/nm. The change in
delay corresponds to a RF phase variation of about 324 angular degrees per nm. The
observed phase variations were 303 angular degrees per nm. The experimental
duration was sufficiently short to avoid thermal delay drift in between successive
measurements.
Experimental Results 48
Figure 20: (left) Output phase of a 3 GHz control sine wave following two-way propagation in a 8.8
km long delay fiber, as a function of tunable laser wavelength, (right) DC reading of the mixing between the delayed control sine wave and its reference replica, as a function of the tunable laser
source wavelength.
The correction factor α between the DC voltage reading and the necessary
wavelength increment can be deduced from the results of Figure 20. The
term of equation (14) can be calculated based on experimental parameters, but can
also be extracted from the left-hand panel of Figure 20. The slope of the curve
suggests that:
1 1 nm
2 0.84 2 radRFf DL
(24)
The V term (see equation (17)) is simply given by the magnitude of the
DC voltage variations with wavelength:
0
1 1 rad
110 mVV V
(25)
Multiplying the two together, we find:
1550
1 1 pm( ) 1.6
0.84 2 110 mVV
(26)
Experimental Results 49
4.2. CLOSED-LOOP, STABLE DISTRIBUTION OF A RF SINE WAVE
This section describes the experimental, closed-loop stable distribution of a
RF sine wave. First, Figure 21 shows the voltage at the mixer output that was
monitored over 45 minutes with the feedback loop open. Two periods of the DC
voltage were observed over 40 minutes, corresponding to delay variations of 660 ps
or about 7.5 ppm of the nominal delay of the fiber. These delay variations therefore
suggest a temperature change of about 1 ºC. The measurements suggest that
temperature is drifting linearly in time. One can reasonably expect that such slow
drifts in the temperature of an air-conditioned laboratory would be monotonous and
nearly linear. The magnitude 0V of voltage changes in this particular experiment is
200 mV. The results suggest a correction factor of pm
0.8mV
.
Figure 21: The DC voltage at the output of the mixer as a function of time, in open feedback loop operation.
Figure 22 shows the DC voltage at the mixer output (top) and the wavelength
setting commands sent to the tunable laser source (bottom), as a function of time
Experimental Results 50
during over 2 minutes of closed-loop operation. Following the first 5 seconds of
transient operation, the mixer output reaches zero voltage and is held stable with
small-scale oscillations around that value. At the same time, the laser diode
wavelength continues to adjust and compensate for ongoing thermal drifts. As
further, direct illustration of phase stability, Figure 23 shows persistence trace
recordings of the control sine wave at the output of Det. 1, accumulated over 10
minutes following the initial stabilization. The output phase is entirely random for
open-loop operation (right), and is nicely stabilized with the loop closed (left). The
results provide a proof of the proposed stabilization concept.
Figure 22: Closed loop, phase stabilized two-way delay of a 3 GHz sine wave over 8.8 km of fiber. (top): DC voltage obtained by the mixing the delayed sine wave with its reference replica, as a
function of time. (bottom): wavelength setting commands to the tunable laser source, as a function of time.
Experimental Results 51
Figure 23: Persistence traces of the output 3 GHz control sine wave, following two-way delay in 8.8 km of fiber, accumulated over 10 minutes of operation at 0.5 second intervals, with (left) and
without (right) closed loop feedback.
In order to accelerate the thermal drift of the delay, a halogen lamp was
placed in close proximity to the fiber spool. Heat radiated from the lamp introduced
strong temperature gradients over many minutes. Figure 24 shows several
persistence traces of the delayed, control sine wave. First, the feedback loop was
disconnected (top left), and the output was recorded over 7.5 minutes without
deliberate heating. Next, the halogen lamp was brought near the fiber for 2.5
minutes, and the feedback remained disconnected (top right). Then, feedback was
applied, and recording were taken over another 2.5 minutes (bottom left). Last, the
lamp was removed, and the output was recorded for additional 7.5 minutes during
the cooling down of the delay fiber (bottom right). In all panels, traces were acquired
once every 10 seconds. The result show drifts of the output RF phase when the
feedback loop was opened, both with and without the heating of the lamp. The
closed feedback was able to stabilize the output phase, even during the cool-down
transient of the delay fiber.
Experimental Results 52
Figure 24: Persistance traces of the 3 GHz control sine wave following delay over 8.8 km of fiber: feedback loop open and no external heating of the delay fiber (top left); feedback loop open during the heating of the fiber by a halogen lamp (top right); feedback loop closed during ongoing heating (bottom left); and feedback loop closed following the removal of the heating lamp and during the
cooling down of the delay fiber (bottom right).
Figure 25 shows the DC reading as a function of time along the entire
experiment, with the instances of transition between the four stages of the
experiment as described above indicated on the curve. The DC voltage varied
gradually during open loop operation. The rate of the voltage sweep depended on
the rate of the temperature changes, hence sharper voltage transitions were
observed with heating installed. The voltage remained fixed at zero value following
the closing of the loop 10 minutes into the measurements, both with and without
the presence of the lamp.
Experimental Results 53
Figure 25: The DC voltage at the output of the mixer as a function of time, during the four stages of the experiment described in
Figure 24.
4.3. CLOSED-LOOP, STABLE DISTRIBUTION OF AN ARBITRARY
RF WAVEFORM
This section describes the experimental, closed-loop stable distribution of a
LFM waveform as an example for the processing of arbitrary user signals. Similarly to
the previous experiment, we started with the feedback loop open in order to extract
the magnitude of the DC voltage at the output of the mixer for the calibration of the
correction factor. Once again we used the halogen lamp to accelerate the thermal
drift of the delay. Figure 26 shows the DC voltage at the output of the mixer over 2
minutes of open feedback loop operation, indicating a phase change of about 3π. In
this particular experiment the magnitude 0V was 350 mV, hence the correction
factor for the tunable laser source of the RF control sine wave was set to
pm0.6
mV
. Based on the dispersion slope of the delay fiber, the correction
Experimental Results 54
factor for the other tunable laser, that of the user waveform, was adjusted to
1
pm0.54
mV
.
Figure 26: The DC voltage at the output of the mixer as a function of time, during 2 minutes of open feedback loop operation.
Figure 27 shows the wavelengths of the tunable laser source of the RF control
sine wave (green) and of tunable laser source of the LFM signal (blue), as a function
of time during 2 minutes of closed-loop operation in which the halogen lamp was
placed near the delay fiber. Both wavelengths were swept in order to maintain a
stable delay, according to the feedback provided by the control channel. Figure 28
shows the DC voltage reading at the output of the mixer as a function of time.
Following an initial transient of a few seconds, the control voltage remained fixed at
a constant value while the delay fiber was being heated.
Experimental Results 55
Figure 27: Wavelength of the tunable laser source of the RF control sine wave (green) and of the LFM signal (blue), as a function of time during two minutes of closed-loop operation.
Figure 28: The DC voltage at the output of the mixer as a function of time during closed-loop operation.
Unlike previous experiments, the DC voltage reached a value of 11 mV which,
although small, was nevertheless different from zero. This behavior stems from a
combination of comparatively rapid heating, alongside rather slow and simplistic
feedback. As can be seen in Figure 27, the feedback loop changed the wavelengths
of the tunable lasers by approximately 1 nm within 100 seconds. Considering the
dispersion parameter of the fiber, the 1 nm wavelength offset compensated for
thermal drifts of the one-way delay in the 8.8 km-long fiber by approximately 150 ps.
Experimental Results 56
This delay variation represents 3.3 ppm of the 45 µs-long nominal one-way delay, or
an increase of 0.3 ºC in the average temperature of the fiber. In other words, the
thermal drift of the delay during each 0.5 second-long interval was associated with a
wavelength correction of 5 pm, which is in turn equivalent to a voltage drift of about
10 mV.
The feedback procedure relies on a simple proportionality correction, and
does not include any extrapolation of the wavelength correction term based on
previous samples. In addition, the effective loop bandwidth of 2 Hz was very narrow.
Hence the feedback loop could not reconstruct the overall trend of the
instantaneous temperature, or correct for drifts that take place within a sampling
interval. The results demonstrate the limitations of this basic feedback approach. In
this particular experiment, the heating rate of the delay fiber was nearly constant.
Therefore, the shortcoming of the feedback mechanism manifested only in a nearly-
fixed, small bias of the mixer voltage, which leads to the stabilization of the output
waveform to a slightly different delay. This difference in itself is usually insignificant,
as long as no additional delay jitter is induced. However, this drawback might have
more severe implications in cases of rapid temperature changes of non-constant
rates. The problem may be solved by using faster and more careful feedback
protocols.
Lastly, Figure 29 shows persistence traces of the compressed shapes of the
delayed LFM waveforms, sampled every 5 seconds following their one-way
propagation over the fiber delay line. The delayed waveforms were compressed
using off-line matched-filter post-processing. The resolution of the 500 MHz-wide
Experimental Results 57
LFM waveforms following their compression is on the order of 2 ns. The top and
bottom panels show the results of open-loop and closed-loop operation,
respectively. The timing drift of the main lobe peak position is reduced from 200 ps
during open-loop operation to 20 ps with the feedback loop closed. The latter value
is limited by the timing inaccuracy of the digitizing oscilloscope.
Figure 29: Persistence traces of the compressed shapes of LFM waveforms, sampled at the output of the fiber delay over 2 minutes, without (top) and with (bottom) closed-
loop wavelength control.
One of the tunable lasers available to us could only perform a continuous
wavelength sweep over approximately 2 nm. Any discontinuity in the lasers
wavelengths immediately disrupts the closed-loop operation. Therefore, the largest
Experimental Results 58
timing jitter that could be compensated for in the particular experiment was on the
order of 300 ps.
Stabilized Delay Within High-Resolution Brillouin Analysis 59
5. STABILIZED DELAY WITHIN HIGH-RESOLUTION BRILLOUIN ANALYSIS
The purpose of this experiment is to demonstrate the applicability of the
proposed stabilization technique to the processing of broadband microwave signals
as part of more complicated systems. As was mentioned in Chapter 1, high-
resolution B-OCDA systems require a fiber optic delay line of many km in order to
achieve cm resolution measurements. However, thermal delay drifts on the long
fiber might lead to the incorrect interpretation of data and to loss of resolution. The
principles of B-OCDA were addressed in the introduction. In this chapter, I first
describe the phase-coded B-OCDA experimental setup and then proceed to show the
significance of stabilized delay for its proper functions.
5.1. B-OCDA EXPERIMENTAL SETUP
In this section I provide more detail on the resolution and spatial scanning
protocols in phase-coded B-OCDA systems. Both pump and signal optical waves are
coded by a repeating, high-rate binary phase sequence of symbol duration sT and a
period of sN bits. A large number of correlation peaks is typically introduced along
the fiber under test, with a spatial extent 12 sz c n T (which also signifies
resolution), and separation between neighboring peaks of sN z [65, 92, 95]. Post-
detection data analysis protocols are able to simultaneously and unambiguously
interrogate Brillouin interactions taking place at thousands of correlation peaks [65,
95]. One of the main challenges in the realization of phase-coded B-OCDA is the
Stabilized Delay Within High-Resolution Brillouin Analysis 60
spatial scanning of correlation peaks positions. The favored solution path to-date
relies on long fiber delay lines.
Figure 30 shows a schematic illustration of a phase-coded B-OCDA setup,
which includes a stabilized delay line based on the principles of this work. A tunable
laser source at 2 of 1551 nm is used as the common source for Brillouin pump and
signal waves. Light from the laser output is phase-modulated by a repeating binary
sequence ( sN = 211 bits), chosen for its favorable correlation properties [96]. The
symbol duration sT of 200 ps corresponds to a spatial resolution of 2 cm.
Figure 30: Schematic illustration of a phase-coded Brillouin optical correlation-domain analysis (phase-coded B-OCDA) setup, incorporating a stabilized fiber-optic
delay line in the path of the Brillouin signal wave. Solid lines denote fiber paths, dashed lines represent RF cable paths, and dashed-dotted, black lines correspond to
DC control signals. Blue color represents paths and components related to the sensing functionality, whereas green paths and components are part of the delay
stabilization module. The 'Wavelength control' module is described in detail in Fig. 15. Details of the 'Pump wave processing' module are not shown, for better clarity
(see [65]).
The modulated light is split into pump and signal branches, that are linked
through a 200 m long fiber under test to form a fiber loop. The value of B in the
Stabilized Delay Within High-Resolution Brillouin Analysis 61
fiber under test at room temperature is 10.85 GHz. Light in the pump branch is offset
in frequency by an adjustable using an electro-optic single-sideband modulator,
restricted to pulses by an electro-optic amplitude modulator, and amplified by an
EDFA. These components are not shown in Fig. 30, for better clarity and focus on the
current work (see [65] for full detail). Light in the signal branch passes through a 25
km-long delay fiber and enters the fiber under test from the opposite direction. The
signal wave at the output of the fiber under test is filtered by an optical band-pass
filter that retains 2 , detected by a photo-receiver, and sampled for off-line
processing.
The role of the long fiber delay is as follows: The middle of the fiber loop is
defined as the location of equal distances from the splitting point at the phase
modulator output (see Fig. 30), going in clockwise and counter-clockwise directions.
Correlation peaks are introduced at distances 12m s s sZ m N z m N c n T from
the middle of the loop, where m is an integer. The locations mZ of all peaks, with
the exception of the zero-order one, may be moved with slight changes sT to the
symbol duration: m m s sZ Z T T .
Let us denote the highest (lowest) order of correlation peaks that is in
overlap with the fiber under test as maxm ( minm ). A sufficiently long delay imbalance
in the signal path guarantees that max min minm m m . Consequently, the positions
of all correlation peaks within measurement range can be scanned with practically
equal increments, which are set to match the resolution step: mZ z for all
Stabilized Delay Within High-Resolution Brillouin Analysis 62
maxminm m m . The long fiber delay allows for the rapid, all-electrical scanning of
correlation peak positions, with no moving parts and over long ranges [92].
The proper function of the sensing setup requires that the long fiber delay
remains stable to within 1
2sT throughout the duration of the analysis, which might
require 1-2 hours. Stabilization was achieved using the protocol proposed in this
work. Light from a laser diode source of wavelength 1 of 1530 nm was modulated
by a 3 GHz control sine wave and coupled into the signal path. The control channel
was filtered and detected at the output of the fiber under test, and used to adjust
both 1 and 2 as discussed above. In order to test the stability of the setup, a 2 cm-
wide hot-spot was introduced at an arbitrary location along the fiber under test, and
sT was fine-tuned so that one of the correlation peaks was in overlap with the hot-
spot.
In a first experiment, closed-loop feedback was provided only to the
wavelength of the tunable laser of the control signal, whereas the delay of the B-
OCDA signal wave was free-running. In a second experiment, feedback was provided
to the wavelengths of both tunable lasers. In both experiments, the Brillouin gain
spectrum at the position of the hot spot was acquired every 30 s.
5.2. EXPERIMENTAL RESULTS
Figure 31(top) shows the instantaneous setting of 1 during the first
experiment. Intentional heating of the delay line by a halogen lamp began six
minutes into the measurements. Starting at that stage, the wavelength was adjusted
Stabilized Delay Within High-Resolution Brillouin Analysis 63
over a 1.2 nm range (left-hand axis), indicating a thermal drift in path length of over
10 cm (right-hand axis). Figure 31(bottom) shows the Brillouin gain spectra as a
function of time. Ten minutes into the experiment, the measured gain spectrum was
shifted from that of the hot-spot to that of the fiber under test at room temperature.
Thermal delay drift therefore led to an incorrect interpretation of the measurement
data.
In a second experiment, closed-loop feedback was applied to the wavelength
of the sensor laser 2 as well. Figure 32(top) shows the settings of that wavelength
Figure 31: Top – Wavelength of the control channel (left-hand axis), and the implied thermal drift in the path length of the 25 km-long delay line (right-hand
axis), as a function of time. Thermal drift on the order of 10 cm is observed. Bottom – Measured Brillouin gain as a function of frequency offset between pump and signal, and of time. The phase-coded B-OCDA setup was adjusted to monitor
the Brillouin gain spectrum in a 2 cm-wide hot-spot. The delay of the Brillouin signal was free-running, without closed-loop feedback to the wavelength of the sensor laser. The Brillouin gain spectrum changed after 10 minutes, from that of
the hot-spot to that of the fiber under test at room temperature.
Stabilized Delay Within High-Resolution Brillouin Analysis 64
as a function of time. Here too, heating of the delay line started after six minutes,
and the wavelength changes indicate a thermal drift of about 9 cm, or several times
larger than both z and the extent to the hot-spot. This time, however, the
measured Brillouin gain spectrum remained that of the hot-spot.
Figure 32: Top – Wavelength of the Brillouin sensor laser source (left-hand axis), and the implied thermal drift in the path length of the 25 km-long delay line (right-hand axis), as a function of time. Thermal drift on the order of 9 cm is observed. Bottom – Measured Brillouin gain as a function of frequency offset between pump and signal, and of time. The phase-coded B-OCDA setup was adjusted to monitor the Brillouin
gain spectrum in a 2 cm-wide hot-spot. Unlike Fig. 31, the delay of the Brillouin signal was stabilized through closed-loop feedback to the wavelength of the sensor
laser. The Brillouin gain spectrum remained that of the hot-spot throughout the measurements.
Lastly, Fig. 33 shows the experimental estimated B at the position of the
hot-spot as a function of time, for both experiments. The instantaneous adjustments
to 2 were accounted for in the data analysis of the second experiment, as B is
Stabilized Delay Within High-Resolution Brillouin Analysis 65
inversely proportional to the optical wavelength [76]. The stabilization of the delay
line allowed for correct interrogation of the narrow hot-spot in the presence of
thermal drift. Note that the temperature of the hot-spot was not the same in the
two experiments.
Figure 33: Measured Brillouin frequency shifts as a function of time. The phase-coded B-OCDA setup was adjusted to monitor the location of a 2 cm-wide hot-spot. Thermal drift in a 25 km-long delay line incorporated in the setup leads to incorrect
interrogation after 10 minutes of free-running operation (blue). Delay drift is overcome with closed-loop, stabilized delay (red).
Discussion and Summary 66
6. DISCUSSION and SUMMARY
6.1. SUMMARY OF RESULTS
A technique for the distribution of arbitrary RF waveforms over long optical
fiber with a stabilized delay was proposed and demonstrated in this work. The
method is based on the compensation of thermal drifts in the long fiber-optic delay
line using chromatic dispersion. This basic concept was previously reported and
demonstrated in [72, 75]. However, in this work we extended this principle for the
distribution of broadband input RF waveforms alongside the control RF sine wave,
with no spectral restrictions. To that end, we used two tunable laser sources with
different wavelengths: one was modulated by the control RF sine wave and the
other by the arbitrary input waveform. By monitoring the RF phase of the control
sine wave, reconstructed after two-way propagation, the wavelengths of both
tunable laser sources were adjusted in a closed feedback loop to maintain a stable
delay of both waveforms. Since the signals were separated in the optical domain, no
restrictions were imposed on the RF spectrum of the input waveform.
The proposed method was successfully demonstrated in three main
experiments: First, the stable distribution of the control sine wave in closed-loop
operation was reported, with residual delay variations of less than 10 ps. Second, the
stable distribution of broadband LFM waveforms, which are prevalent in many radar
systems as they provide both high SNR and high resolution, had been achieved. In
this experiment the timing drifts in free-running operation were reduced by an order
of magnitude in closed-loop operation. Last, the stable interrogation of a local hot
Discussion and Summary 67
spot in high-resolution distributed Brillouin analysis was demonstrated, in the
presence of thermal delay drifts that were several times larger than its extent. This
demonstrated the applicability of the proposed stabilization technique to the
processing of broadband microwave signals as part of more complicated systems.
6.2. LIMITATIONS AND FUTURE WORKS
The results obtained in this work were limited by several factors. Some of the
limitations are inherent to the stabilization principle. The method relies on chromatic
dispersion, hence the fiber-optic delay line must be sufficiently long so that the delay
variations are appreciable. The same dispersion, however, introduces delay
uncertainties. In extreme conditions, propagation over long dispersive fibers might
distort the temporal envelope profile of broadband waveforms.
Other limitations are related to the specific implementation chosen in our
experiments. One such issue is the choice of the radio-frequency of the control sine
wave. The sensitivity of the feedback mechanism to small-scale delay variations
would improve with higher control tone frequencies. A major restriction is imposed
by the low bandwidth of the feedback loop. The update rate of the tunable lasers
wavelengths was limited by the protocols of their computer-controlled interfaces to
only twice per second. The fundamental limitation on the rate of wavelength
adjustments, on the other hand, is set by the two-way delay along the fiber and may
be as high as tens of KHz. A broader feedback loop may also compensate and
stabilize the effects of structural and acoustic vibrations.
Discussion and Summary 68
Yet another practical restriction has to do with the tuning range of the laser
sources and the bandwidth of optical filters used in the separation between the two
waveforms. As noted earlier, the tuning range of the source restricts the system's
figure of merit. One of the laser sources available to us could only be tuned
continuously over 2-3 nm. Optical bandpass filters impose a similar limitation: when
the laser wavelength is swept beyond their transmission bandwidth, they too must
be adjusted. Our optical filters had a bandwidth of 4 nm, and they could only be
tuned manually. Use of electrically-controlled filters would resolve this problem.
The introduction of the proposed technique into real-world systems can
provide many opportunities. Unlike already existing solutions, the proposed method
provides a stable delay with variations of only few ps, over long fiber-optic delay
many km of fiber and wide range of temperatures. Applications such as beam
forming in phased-array antenna, that rely on the precise phase difference between
neighboring elements, may find the proposed method crucial for maintaining proper
function. The dispersion of the delay fiber can be chosen to emphasize long delay,
high precision or broad temperature range, as expressed in the figure of merit of the
proposed system.
Several topics remain for further academic inquiry. For instance, the
development of a broadband feedback loop that is able to compensate for rapid
changes and sharp gradients in the surrounding temperature, as well as for
structural and acoustic vibrations. Another direction would be the incorporation of
the stabilized delay as a module within a radar test and measurement setup, or
phased array antennas.
References 69
REFERENCES
[1] J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Phot. 1,
319-330 (2007).
[2] P. Candelas, J. M. Fuster, J. Marti and J. C. Roig, "Optically generated electrical-
modulation formats in digital-microwave link applications," Jour. Light. Tech. 21(2),
496-499 (2003).
[3] C. H. Cox and E. I. Ackerman, "Microwave photonics: past, present and future," in
International topical meeting on Microwave photonics, 9-11, Gold Coast, Qld, Sept.
2008.
[4] J. Capmany, B. Ortega and D. Paster, "A tutorial on microwave photonic filters," Jour.
Light. Tech. 24(1), 201-229 (2006).
[5] A. Zadok, D. Grodensky, D. Kravitz, Y. Peled, M. Tur, X. Wu and A. E. Willner, "Ultra-
Wideband Waveform Generation Using Nonlinear Propagation in Optical Fibers," in
Ultra Wideband Communications: Novel Trends - Antennas and Propagation, M. Martin
ed. (InTech 2011).
[6] I. S. Lin, J. D. McKinney and A. M. Weiner, "Photonic synthesis of broadband microwave
arbitrary waveforms applicable to ultra-wideband communication," Micro. Wire. Comp.
Lett. IEEE 15(4), 226-228 (2005).
[7] R. A. Becker, C. E. Woodward, F. J. Leonberger and R. C. Williamson, "Wide-band
electrooptic guided-wave analog-to-digital converters," Proceedings of the IEEE, 72(7),
802-819 (1984).
[8] H. Emami and N. Sarkhosh, "Reconfigurable microwave photonic in-phase and
quadrature detector for frequency agile radar," Jour. Opt. Soci. Am. A 31(6), 1320-1325
(2014).
[9] D. Novak and R. Waterhouse, "Commercial and defense applications of microwave
photonics," Avionics, Fiber-Optics and Photonics Conference, IEEE, San Diego, CA, Oct.
2013.
[10] J. Capmany, G. Li, C. Lim and J. Yao, "Microwave Photonics: Current challenges towards
widespread application," Opt. Exp. 21(19), 22862-22867 (2013).
[11] J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret and S. Sales, "Microwave Photonic
Signal Processing," Jour. Light. Tech. 31(4), 571-586 (2013).
[12] J. Yao, "A Tutorial on Microwave Photonics, Part 1," IEEE Phot. Soc. New. 26, 5-12
References 70
(2012).
[13] L. Li, X. Yi, T. X. H. Huang and R. Minasian, "High-Resolution Single Bandpass Microwave
Photonic Filter With Shape-Invariant Tunability," IEEE Phot. Tech. Lett. 26(1), 82-85
(2014).
[14] C. Wang and J. Yao, "Fiber Bragg gratings for microwave photonics subsystems," Opt.
Exp. 21(19), 22868-22884 (2013).
[15] Y. Stern, K. Zhong, T. Schneider, R. Zhang, Y. Ben-Ezra, M. Tur and A. Zadok, "Tunable
sharp and highly selective microwave-photonic band-pass filters based on stimulated
Brillouin scattering," Phot. Res. 2(4), B18-B25 (2014).
[16] H. Wang, J. Y. Zheng, W. Li, L. X. Wang, M. Li, L. Xie and N. H. Zhu, "Widely tunable
single-bandpass microwave photonic filter based on polarization processing of a
nonsliced broadband optical source," Opt. Lett. 38(22), 4857-4860 (2013).
[17] M. Burla, L. R. Cortés, M. Li, X. Wang, L. Chrostowski and J. Azaña, "Integrated
waveguide Bragg gratings for microwave photonics signal processing," Opt. Exp. 21(12),
25120-25147 (2013).
[18] J. Capmany, S. Sales, I. Gasulla, J. Mora, J. Lloret and J. Sancho, "Innovative concepts in
microwave photonics," Waves 4, 43-58 (2012).
[19] D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales and J. Capmany,
"Integrated microwave photonics," Las. Phot. Rev. 7(4), 506-538 (2013).
[20] P. Munoz, J. Capmany, D. Perez, J. Fandino, J. S. Fandino and J. D. Domenech,
"Integrated microwave photonics: state of the art and future trends," 16th
International Conference on Transparent Optical Networks, IEEE, Graz, Austria, Jul.
2014.
[21] J. Yao, "A Tutorial on Microwave Photonics, Part 2," IEEE Phot. Soc. New. 26, 4-12
(2012).
[22] A. M. J. Koonen and M. G. Larrode, "Perspectives of Radio over Fiber Technologies,"
paper OThP3 in Optical Fiber Communication Conference, (OSA), San Diego, CA, Feb.
2008.
[23] R. Karthikeyan and S. Prakasam, "A Survey on Radio over Fiber (RoF) for Wireless
Broadband Access Technologies," Inter. Jour. Com. Appl. 64(12), 15-19 (2013).
[24] ETSI TS 136 410 V9.1.1, Euro. Telecom. Stan. Inst. May 2011,
http://www.etsi.org/deliver/etsi_ts/136400_136499/136410/09.01.01_60/ts_136410v
090101p.pdf
References 71
[25] A. K. Vyas and N. Agrawal, "Radio over Fiber: Future Technology of Communication,"
Inter. Jour. Emer. Tre. Tech. Com. Sci. 1(2), 233-237 (2012).
[26] M. Morant, J. Pérez and R. Llorente, "Polarization Division Multiplexing of OFDM Radio-
over-Fiber Signals in Passive Optical Networks," Adv. Opt. Tech. 2014, 1-9 (2014).
[27] V. A. Thomas, S. Ghafoor, M. El-Hajjar and L. Hanzo, "A Full-Duplex Diversity-Assisted
Hybrid Analogue/Digitized Radio Over Fibre for Optical/Wireless Integration," IEEE
Comm. Lett. 17(2), 409-412 (2013).
[28] J. Beas, G. Castanon, I. Aldaya, A. Aragón-Zavala and G. Campuzano, "Millimeter-Wave
Frequency Radio over Fiber Systams: A Survey," IEEE Comm. Sur. Tut. 15(4), 1593-1619
(2013).
[29] A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-
Royo, A. Melloni and S. Iezekiel, "Using a Si3N4 Ring Resonator Notch Filter for Optical
Carrier Reduction and Modulation Depth," IEEE Phot. Jour. 5(1), (2013).
[30] Y. Stern, "All-Optical Signal Processing and Analysis of Radio Frequency Waveforms,"
M.S. thesis, Dept. Elect. Eng., Bar-Ilan Univ., Ramat-Gan, Israel.
[31] S. Yegananarayanan and B. Jalali, "Wavelength-selective true time delay for optical
control of phased-array antenna," IEEE Phot. Tech.Lett. 12, 1049-1051 (2000).
[32] W. V. Aulock, "Properties of phase arrays," Proceedings of the IRE 48, 1715-1727
(1960).
[33] B. H. Kolner and D. W. Dolfi, "Intermodulation distortion and compression in an
integrated electrooptic modulator," App. Opt. 26, 3676-3680 (1987).
[34] O. Raz, S. Barzilay, R. Rotman and M. Tur, "Submicrosecond scan-angle switching
photonic beamformer with flat RF response in the C and X bands," Jour. Light. Tech. 26,
2774-2781 (2008).
[35] O. Raz, R. Rotman and M. Tur, "Wavelength-controlled photonic true time delay for
wide-band applications," IEEE Phot. Tech. Lett. 17, 1076-1078 (2005).
[36] R. Rotman, O. Raz and M. Tur, "Analysis of a true time delay photonic beamformer for
transmission of a linear frequency-modulated waveform," Jour. Light. Tech. 23, 4026
(2005).
[37] A. Molony, C. Edge and I. Bennion, "Fibre grating time delay element for phased array
antennas," Elec. Lett. 31, 1485-1486 (1995).
[38] H. Zmuda, R. A. Soref, P. Payson, S. Johns and E. N. Toughlian, "Photonic beamformer
for phased array antennas using a fiber grating prism," IEEE Phot. Tech. Lett. 9, 241-243
References 72
(1997).
[39] J. Cruz, B. Ortega, M. Andres, B. Gimeno, D. Pastor, J. Capmany and L. Dong, "Chirped
fibre Bragg gratings for phased-array antennas," Elec. Lett. 33, 545-546 (1997).
[40] B. Vidal, T. Mengual, C. Ibanez-Lopez and J. Marti, "Optical beamforming network
based on fiber-optical delay lines and spatial light modulators for large antenna arrays,"
IEEE Phot. Tech. Lett. 18, 2590-2592 (2006).
[41] R. D. Esman, M. Frankel, J. Dexter, L. Goldberg, M. Parent, D. Stilwell and D. Cooper,
"Fiber-optic prism true time-delay antenna feed," IEEE Phot. Tech. Lett. 5, 1347-1349
(1993).
[42] A. Zadok, A. Eyal and M. Tur, "Extended delay of broadband signals in stimulated
Brillouin scattering slow light using synthesized pump chirp," Opt. Exp. 14(19), 8498-
8505 (2006).
[43] A. Zadok, A. Eyal and M. Tur, "Stimulated Brillouin scattering slow light in optical
fibers," App. Opt. 50(25), E38-E49 (2011).
[44] K. Y. Song, M. G. Herráez and L. Thévenaz, "Gain-assisted pulse advancement using
single and double Brillouin gain peaks in optical fibers," Opt. Exp. 13, 9758-9765 (2005).
[45] E. Shumakher, N. Orbach, A. Nevet and G. Eisenstein, "On the balance between delay,
bandwidth and signal distortion in slow light systems based on stimulated Brillouin
scattering in optical fibers," Opt. Exp. 14, 5877-5884 (2006).
[46] A. Zadok, S. Chin, L. Thévenaz, E. Zilka, A. Eyal and M. Tur, "Polarization-induced
distortion in stimulated Brillouin scattering slow-light systems," Opt. Lett. 34, 2530-
2532 (2009).
[47] M. D. Stenner, M. A. Neifeld, Z. Zhu, A. Dawes and D. J. Gauthier, "Distortion
management in slow-light pulse delay," Opt. Exp. 13(25), 9995-10002 (2005).
[48] S. Sales, W. Xue, J. Mork and I. Gasulla, "Slow and fast light effects and their
applications to microwave photonics using semiconductor optical amplifiers," IEEE
Tran. Micro. Theo. Tech. 58, 3022-3038 (2010).
[49] F. Öhman, K. Yvind and J. Mørk, "Slow light in a semiconductor waveguide for true-time
delay applications in microwave photonics," IEEE Phot. Tech. Lett. 19, 1145-1147
(2007).
[50] N. A. Riza, M. A. Arain and S. A. Khan, "Hybrid analog-digital variable fiber-optic delay
line," Jour. Light. Tech. 22, 619 (2004).
[51] O. Klinger, "Long Microwave-Photonic Variable Delay of Chirped Waveforms,"
References 73
M.S.thesis, Dept. Elect. Eng., Bar-Ilan Univ., Ramat-Gan, Israe, (2012).
[52] O. Klinger, Y. Stern, F. Pederiva, K. Jamshidi, T. Schneider and A. Zadok, "Continuously
variable long microwave-photonic delay of arbitrary frequency-chirped signals," Opt.
Exp. 37, 3939-3941 (2012).
[53] O. Klinger, Y. Stern, T. Schneider, K. Jamshidi and A. Zadok, "Long Microwave-Photonic
Variable Delay of Linear Frequency Modulated Waveforms," IEEE Phot. Tech. Lett.
24(3), 200-202 (2012).
[54] Y. Stern, O. Klinger, T. Schneider, K. Jamshidi, A. Peer and A. Zadok, "Low-distortion
long variable delay of linear frequency modulated waveforms," IEEE Phot. 4(2), 499-503
(2012).
[55] J. Xie, L. Zhou, Z. Li, J. Wang and J. Chen, "Seven-bit reconfigurable optical true time
delay line based on silicon integration," Opt. Exp. 22(19), 22707-22715 (2014).
[56] J. Xie, L. Zhou, Z. Zou, J. Wang, X. Li and J. Chen, "Continuously tunable reflective-type
optical delay lines using microring resonators," Opt. Exp. 22(1), 817-823 (2014).
[57] Y. Antman, L. Yaron, T. Langer, M. Tur, N. Levanon and A. Zadok, "Experimental
demonstration of localized Brillouin gratings with low off-peak reflectivity established
by perfect Golomb codes," Opt. Exp. 38(22), 4701-4704 (2013).
[58] Y. Wang, C. Yu, L. Yan, A. E. Willner, R. Roussev, C. Langrock, M. M. Fejer, J. E. Sharping
and A. L. Gaeta, "44-ns Continuously Tunable Dispersionless Optical Delay Element
Using a PPLN Waveguide With Two-Pump Configuration, DCF, and a Dispersion
Compensator," IEEE Phot. Tech. Lett. 19(11), 861-863 (2007).
[59] M. Johnson, Optical fibers, cables and systems, 2009.
[60] J. M. Payne and W. P. Shillue, "Photonic techniques for local oscillator generation and
distribution in millimeter-wave radio astronomy," Int.Topical Meeting on Microwave
Photonics (IEEE MWP) 1, 9-12, Nov. 2002.
[61] K. Volyanskiy, J. Cussey, H. Tavernier, P. Salzenstein, G. Sauvage, L. Larger and E.
Rubiola, "Applications of the optical fiber to the generation and to the measurement of
low-phase-noise microwave signals," Jour. Opt. Soci. Am. B 25(12), 2140-2150 (2008).
[62] E. Choi, J. Na, S. Y. Ryu, G. Mudhana and B. H. Lee, "All-fiber variable optical delay line
for applications in optical coherence tomography: feasibility study for a novel delay
line," Opt. Exp. 13(4), 1334-1345 (2005).
[63] G. N. Pearson, K. D. Ridley and D. V. Willetts, "Chirp-pulse-compression three-
dimensional lidar imager with fiber optics," App. Opt. 44(2), 257-265 (2005).
References 74
[64] Y. London, Y. Antman, R. Cohen, N. Kimelfeld, N. Levanon and A. Zadok, "High-
resolution long-range distributed Brillouin analysis using dual-layer phase and
amplitude coding," Opt. Exp. 22, 27144-27158 (2014).
[65] D. Elooz, Y. Antman, N. Levanon and A. Zadok, "High-resolution long-reach distributed
Brillouin sensing based on combined time-domain and correlation-domain analysis,"
Opt. Exp. 22, 6453-6463 (2014).
[66] I. L. Newberg, C. M. Gee, G. D. Thurmond and H. W. Yen, "Long microwave delay fiber
optic link for radar testing," Micro. Sym. Dig., IEEE MTT-S International, 2, 693-696
(1989).
[67] J. M. Byrd, L. Doolittle, A. Ratti, J. W. Staples and R. Wilcox, "Timing distribution in
accelerators via stabilized optical fiber links," Proceeding of LINAC, Knoxville, 577-579
(2006).
[68] V. A. Lebedev, J. Musson and M. G. Tiefenback, "High-precision beam-based rf phase
stabilization at jefferson lab," Proceedings of the 1999 Particle Accelerator Conference,
IEEE, 2, 1183-1185 (1999).
[69] L. Zhang, L. Chang, Y. Dong, W. Xie, H. He and W. Hu, "Phase drift cancellation of
remote radio frequency transfer using an optoelectronic delay-locked loop," Opt. Lett.
36(6), 873-875 (2011).
[70] B. Ning, P. Du, D. Hou and J. Zhao, "Phase fluctuation compensation for long-term
transfer of stable radio frequency over fiber link," Opt. Exp. 20(27), 28447-28454
(2012).
[71] D. Hou, P. Li, C. Liu, J. Zhao and Z. Zhang, "Long-term stable frequency transfer over an
urban fiber link using microwave phase stabilization," Opt. Exp. 19(2), 506-511 (2011).
[72] A. Zhang, Y. Dai, F. Yin, T. Ren, K. Xu, J. Li, Y. Ji, J. Lin and G. Tang, "Stable radio-
frequency delivery by λ dispersion-induced optical tunable delay," Opt. Lett. 38, 2419-
2421 (2013).
[73] Z. Wu, Y. Dai, A. Zhang, K. Xu, J. Li and J. Lin, "Broadband downlink stable radio
frequency phase delivery exploiting fiber chromatic dispersion," Opt. Comm. Net.
(ICOCN), 12th International Conference, IEEE, (2013).
[74] Z. Wu, Y. Dai, F. Yin, K. Xu, J. Li and J. Lin, "Stable radio frequency phase delivery by
rapid and endless post error cancellation," Opt. Lett. 38(7), 1098-1100 (2013).
[75] A. Zhang, Y. Dai, F. Yin, J. Li, T. Ren, K. Xu and G. Tang, "Phase stabilized downlink
transmission for wideband radio frequency signal via optical fiber link," Opt. Exp. 22,
21560-21566 (2014).
References 75
[76] R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
[77] G. P. Agrawal, Nonlinear fiber optics, Springer, 2000.
[78] D. Cotter, "Observation of stimulated Brillouin scattering in low-loss silica fibre at 1.3
μm," Elec. Lett. 18, 495-496 (1982).
[79] A. Zadok, A. Eyal and M. Tur, "Gigahertz-wide optically reconfigurable filters using
stimulated Brillouin scattering," Jour. Light. Tech. 25, 2168-2174 (2007).
[80] Y. Antman, N. Primerov, J. Sancho, L. Thévenaz and A. Zadok, "Localized and stationary
dynamic gratings via stimulated Brillouin scattering with phase modulated pumps,"
Opt. Exp. 20, 7807-7821 (2012).
[81] K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial
resolution by correlation-based continuous-wave technique," IEEE Phot. Tech. Lett. 14,
179-181 (2002).
[82] T. Sperber, A. Eyal, M. Tur and L. Thévenaz, "High spatial resolution distributed sensing
in optical fibers by Brillouin gain-profile tracing," Opt. Exp. 18(8), 8671-8679 (2010).
[83] J. C. Beugnot, M. Tur, S. F. Mafang and L. Thévenaz, "Distributed Brillouin sensing with
sub-meter spatial resolution: modeling and processing," Opt. Exp. 19, 7381-7397
(2011).
[84] Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd and A. E.
Willner, "Numerical study of all-optical slow-light delays via stimulated Brillouin
scattering in an optical fiber," Jour. Opti. Soc. Am. B 22, 2378-2384 (2005).
[85] T. Horiguchi, T. Kurashima and M. Tateda, "A technique to measure distributed strain in
optical fibers," IEEE Phot. Tech. Lett. 2, 352-354 (1990).
[86] M. Niklès, L. Thévenaz and P. A. Robert, "Simple distributed fiber sensor based on
Brillouin gain spectrum analysis," Opt. Lett. 21, 758-760 (1996).
[87] X. Bao and L. A. Chen, "Recent progress in Brillouin scattering based fiber sensors,"
Sensors-Basel, 11, 4152-4187 (2011).
[88] Y. Dong, H. Zhang, L. Chen and X. Bao, "2 cm spatial-resolution and 2 km range Brillouin
optical fiber sensor using a transient differential pulse pair," App. Opt. 51(9), 1229-1235
(2012).
[89] S. M. Foaleng, M. Tur, J. C. Beugnot and L. Thévenaz, "High spatial and spectral
resolution long-range sensing using Brillouin echoes," Jour. Light. Tech. 28(20), 2993-
3003 (2010).
References 76
[90] K. Hotate and T. Hasegawa, "Measurement of Brillouin gain spectrum distribution along
an optical fiber using a correlation-based technique -proposal, experiment and
simulation," IEICE T. Electorn, E83-C(3), 405-412 (2000).
[91] K. Song, Z. He and K. Hotate, "Distributed strain measurement with millimeter-order
spatial resolution based on Brillouin optical correlation domain analysis," Opt. Lett.
31(17), 2526-2528 (2006).
[92] A. Zadok, Y. Antman, N. Primov, A. Denisov, J. Sancho and L. Thévenaz, "Random-access
distributed fiber sensing," Laser Phot. Rev. 6(5), L1-L5 (2012).
[93] J. Wang and K. Petermann, "Small signal analysis for dispersive optical fiber
communication systems," Jour. Light. Tech. 10(1), 96-100 (1992).
[94] R. Rotman, O. Raz and M. Tur, "Small signal analysis for analogue optical links with
arbitrary optical transfer function," Elec. Lett. 40(8), 504-505 (2004).
[95] Y. London, Y. Antman, N. Levanon and A. Zadok, "Brillouin analysis with 8.8 km range
and 2 cm resolution," accepted for presentation in Optical Fiber Sensors (OFS-24)
Conference, Curitiba, Brazil, 2015.
[96] Y. Antman, N. Levanon and A. Zadok, "Low-noise delays from dynamic Brillouin gratings
based on perfect Golomb coding of pump waves," Opt. Lett. 37(24), 5259-5261 (2012).
א
תקציר
-רדיומגנטיים בתדרי רדיו ומיקרוגל באמצעים פוטוניים, או -עיבוד אותות אלקטרו
. לעיבוד אותות באמצעות תחומי ההתמחותשני מחקר המשלב בין תחום הינו ,פוטוניקה
פוטוניקה יתרונות רבים על פני עיבוד ישיר בטכניקות מבוססות התקנים -טכניקות רדיו
וחסינות בפני ,סרט גדול, טווח שידור ארוך עם ניחות נמוך-אלקטרוניים, כדוגמת רוחב
מוש של קווי מיפוטוניקה הוא -ת רדיוומגנטיות. יישום חשוב של טכניק-הפרעות אלקטרו
לאותות בתדרי רדיו באמצעים אופטיים, המשמשים כרכיבים הכרחיים מתכוונניםהשהייה
יישום משמעותי נוסף הוא שידור אותות להטיית אלומות במערכות מכ"ם מרובות אלמנטים.
: ארוכים על גבי סיבים אופטיים טווחיםת לסלולרית ואלחוטי שמקורם בתקשורתבתדרי רדיו
אלו. רשתות תקשורתשל והכיסוי סיב. יישום זה מרחיב את טווחי השידור-יגב-על-רדיו
ההשהייה הזמנית של אותות מחייבים כי יישומים שונים בעלי רמת דיוק גבוהה
מתנדים מקומיים הפצה של דוגמאות לכך כוללות רדיו על גבי סיבים ארוכים תשאר יציבה. ה
רכות מכ"ם. לאחרונה הופיע יישום נוסף וכיול של מע ותבמערכי אנטנה גדולים, ובדיק
וטמפרטורה מחיישנים מפולגים למעוות מכאני , כחלק ארוכה ומיוצבתהשהייה המחייב
של סנטימטרים נדרשים לאבחנה מרחביתאלו חיישנים המבוססים על פיזור ברילואן.
הסיבים הדרך האופטית לאורךהמזל, לרועשל סיב. רבים לאורך קילומטרים בודדים,
לשינויים בטמפרטורת הסביבה. שינוי של מעלת פיםחשו אשר הםהאופטיים משתנה כ
סיב אופטי סטנדרטי. של ס"מ לכל קילומטר 0.75משנה את הדרך האופטית ב אחת צלסיוס
כים מדי למימוש עבור רוב מערכות מסוב לתיקון סחיפות כגון אלו יום כהפיתרונות הקיימים
מספקים את היציבות הנידרשת. או שאינם חיישנים,מכ"ם והה
תיזמון הנובעים השינויי קיזוזזו מבוססת על עבודהב תיהשיטה שבה השתמש
בסיסי הוצע במקביל העיקרון ה. דיספרסיה כרומטיתבסיס על משינויי טמפרטורת הסביבה
קבוצה מאוניברסיטת בייג'ינג ידי-עלבאופן בלתי תלוי על ידי קבוצת המחקר שלנו וו
על ידי כןו ,מקור לייזר מתכוונן בודד מאופנן על ידי אות בקרה סינוסי בתדר רדיו .תלתקשור
ב
התפשטות לאורך הסיב, פאזתבתדר רדיו אותו נרצה להשהות. לאחר שרירותי אות כניסה
תזמון. אורך הגל של ב סחיפות יהוילז ומשמשת המוצא בתדר הרדיו של אות הבקרה נמדדת
תיזמון כתוצאה מדיספרסיה הכך ששינויי ,מעודכן בחוג משוב סגורמקור הלייזר המתכוונן
אולם, התיכנון הראשוני התבסס על ומשינויים סביבתיים. אלו הנובעיםאת יםקזזמכרומטית
הפרדה בין אות הכניסה לאות הבקרה במרחב תדרי הרדיו, ולכן נדרש שלא תהיה חפיפה
סרט, כגון -רכות התומכות באותות רחביבמעלהשגה קשה הזאילוץ . במרחב התדר ביניהם
סיב ברזולוציה גבוהה. נישיחי
בעבודה זו אני מציג ומדגים שיפור משמעותי של טכניקת הייצוב. במקום להשתמש
במקור לייזר בודד, אות הבקרה בתדר הרדיו ואות הכניסה מאפננים שני מקורות לייזר
קבל על ידי פאזת המוצא של אות מתכוונים נפרדים בעלי אורכי גל שונים. המשוב המת
את אורכי הגל של שני מקורות הלייזר, בכדי לקבל ייצוב השהייה משנההבקרה המושהה
התדרים האופטי, ולכן אין מגבלה על האותות מופרדים במרחבעבור שני האותות. שני
ניתוח מפורט של ביצועי השיטה המוצעת מצביע על החפיפה שלהם במרחב תדרי הרדיו.
שרות המתחייבות בין טווח שינויי הטמפרטורה הניתן לקיזוז לבין שגיאות תזמון שיוריות. הפ
הניתוח מוביל להצעת מדד איכות עבור ביצועי מערכת ההשהייה המיוצבת, ולחסם עליון על
הביצועים הניתנים להשגה במגבלות המפרט הטכני של מקורות הלייזר.
מודגמת השהיה ניסוי הראשוןבמעבודה זו. שלושה ניסויים עיקריים מודגמים כחלק
של חוסר יציבות שיוריעם ,ק"מ 9של אות הבקרה הסינוסי על גבי סיב באורך של מיוצבת
סרט, -של אותות בעלי אפנון תדר לינארי רחבפצה מודגמת הניסוי השני בשניות. -פיקו 4±
הסחיפה השיורית אורך. אותו העל גבי סיב בהמצויים בשימוש נרחב במערכות מכ"ם,
שניות בחוג סגור, -פיקו 20 -שניות בחוג פתוח ל-פיקו 200 -מ ההופחת ת האותהשהייב
מדידה הושגה . לבסוף, מכשור המעבדהשגיאת התיזמון של ידי -מוגבלת עלכאשר המדידה
ברילואן מפולג ברזולוציה חיישן ס"מ על ידי 2יציבה של נקודה חמה מקומית ברוחב של
. כדי סחיפה סביבתית מכוונת של השהיה לאורך הסיב בשיעור גבוה פי כמהתוך גבוהה,
.שכזו אינה ניתנת להשגה בחוג פתוחמדידה
ג
עבור עיבוד הייצוב המוצעתשיטת את הישימות של מדגימות תוצאות הניסויים
ניתנת להרחבה עבור שיטה הסרט כחלק ממערכות מורכבות יותר. -אותות מיקרוגל רחבי
סרט גדול -חוג משוב בעל רוחב באמצעות, ות לאורך הסיבואקוסטי ותמכאני ותהפרע ביטול
יותר.
עבודה זו נעשתה בהדרכתו של פרופ' אבי צדוק,
אילן-מהפקולטה להנדסה של אוניברסיטת בר
אותות כלליים יה מיוצבת של יהשה
בתדרי רדיו על גבי סיבים אופטיים
עמרם-בן אסף מוסמך תואר קבלת לשם מהדרישות כחלק מוגשת זו עבודה
אילן-בר אוניברסיטת של להנדסה בפקולטה
תשע"ה גן רמת