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    TRUE-TIME ALL OPTICAL PERFORMANCE

    MONITORING BY MEANS OF OPTICAL CORRELATION

    DISSERTATION

    Presented in Partial Fulfillment of the Requirements for the Degree Doctor

    of Philosophy in the Graduate School of

    The Ohio State University

    By

    Feras M. Abou-Galala, M.S.

    ******

    The Ohio State University2007

    Dissertation Committee:

    Prof. Betty Lise Anderson, Advisor Approved byProf. George ValcoProf. Charles Klein ______________________

    AdvisorGraduate Program inElectrical Engineering

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    ii

    ABSTRACT

    In this dissertation we present a new design of an optical performance monitor

    (OPM) that utilizes optical correlation techniques to produce real-time measurements of

    optical link performance. We also introduce a novel design of temporal optical correlator

    that is based on the White cell. We show the advantages of our method over existing

    techniques and outline how our proposed device can be integrated in next generation all-

    optical Internet networks.

    We build and experimentally demonstrate a proof-of-concept design of an OPM

    using a White cell-based time-integrating optical correlator. The experimental apparatus

    is analyzed and measurements are compared to their theoretical values. Results show that

    our proposed technique produces the expected results with an error margin of less than

    5%. Additionally, we show a detailed power loss analysis (measured) and discuss the

    feasibility and scalability of our method. Measurements prove the design to be promising

    and that it can be scaled without large power losses (less than 7dB).

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    DEDICATION

    Dedicated to my father Moustafa, my mother Fatima,

    my brother Basil and my two sisters Hadeel and Haneen

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    ACKNOWLEDGMENT

    I would like to take this opportunity to thank everyone that helped me out and

    supported me throughout my course of studies. I would like to dedicate special thanks to

    my beloved advisor and mentor, Professor Betty Lise Anderson. Her support and

    continuous encouragement enabled me to be where I am at right now and played a big

    part in making me the person I am now. She was always available to answer questions

    when I needed answers, provide mental support when I was down, and above all be the

    happy and joyful person she is. Again, thank you.

    I would also like to thank all my peers who provided me great insight through our

    discussions and conversations. Special thanks to my optics group members, Dave Rabb,

    Dr. Rashmi Mital, Dr. Carolyn Warnky and Dr. Victor Argueta-Diaz.

    I would specially like to mention that I couldnt have got to this point in my life

    as a human being or as a professional without the support and encouragement from my

    parents and my brother and sisters. Their love guided me through any obstacles that I

    faced and made me a better person. Thank you.

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    v

    VITA

    April 22, 1978Born: Tripoli, Libya

    2000....B.S., Electrical EngineeringUniversity of Qatar. Doha, Qatar

    2003M.S., Electrical and Computer EngineeringThe Ohio State University. Columbus, Ohio

    PUBLICATIONS

    1. D. Rabb, B. L. Anderson, C. M. Warnky, F. Abou-Galala, "Binary White cell truetime delay: demonstration of micro-blocks and folded lens trains as delay elements,"IEEE Journal of Lightwave Technology, Vol. 24-4, pp. 1886-1895, April 2006.

    2. B. L. Anderson, D. J. Rabb, C. M. Warnky, F. M. Abou-Galala, "Binary Optical TrueTime Delay Based on the White Cell: Design and Demonstration," IEEE Journal ofLightwave Technology, July 15, 2005.

    3. B. L. Anderson, A. Durresi, D. Rabb, F. Abou-Galala, "Real-Time All-OpticalQuality of Service Monitoring Using Correlation and a Network Protocol to ExploitIt,"Applied Optics, 42(5) pp. 1121-1130, March 2004.

    4. B. L. Anderson, F. Abou-Galala, D. Rabb, A. Durresi, "All-Optical Quality-of-SignalMonitoring in Real Time," Paper # 5247-8, SPIE ITCom conference and proceedings,September 7-11 2003.

    5. B. L. Anderson, F. Abou-Galala, V. Argueta-Diaz, G. Radhakrishnan, R. L. Higgins,"Optical cross-connect based on tip/tilt micromirrors in a White cell," IEEE Journalof Special Topics in Quantum Electronics, 9(2), pp.579-593, March/April,2003

    FIELDS OF STUDY

    Major Field: Electrical and Computer Engineering

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    TABLE OF CONTENTS

    PageAbstract ..iiDedication .iiiAcknowledgments .ivVita .vList of Tables .....ixList of Figures ........x

    CHAPTER 1 INTRODUCTION..................................................................................... 1

    1.1 Optical Networks ................................................................................................ 11.2 Optical Impairments ........................................................................................... 3

    1.2.1 Linear and non-linear impairments............................................................. 51.2.2 Attenuation.................................................................................................. 71.2.3 Dispersion ................................................................................................... 81.2.4 Noise ......................................................................................................... 101.2.5 Jitter........................................................................................................... 11

    1.3 Link Quality Measurement ............................................................................... 111.4 OPM: Existing Methods .................................................................................. 14

    1.5 OPM: Our Proposal .......................................................................................... 191.6 Physical Implementation................................................................................... 201.7 Routing Protocol based on OPM ...................................................................... 211.8 Document Organization.................................................................................... 25

    CHAPTER 2 THEORY.................................................................................................. 26

    2.1 Introduction....................................................................................................... 262.2 Principal of Correlation .................................................................................... 262.3 Optical Correlation for OPM............................................................................ 28

    2.4 Time-Integrating Optical Correlator (TOC) ..................................................... 292.5 White cell principle........................................................................................... 32

    2.5.1 Beam Propagation in the White Cell ........................................................ 342.5.2 White cell Imaging Conditions................................................................. 36

    2.6 White cell-based TDL....................................................................................... 372.6.1 White cell delay arm ................................................................................. 392.6.2 Design constraints..................................................................................... 402.6.3 Linear White cell-based Tapped Delay Line (TDL)................................. 44

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    2.6.4 Weighting elements and beam summation ............................................... 46

    CHAPTER 3 Simulations and Analysis........................................................................ 49

    3.1 Introduction....................................................................................................... 493.2 Impairment simulations .................................................................................... 49

    3.2.1 Attenuation and Dispersion....................................................................... 503.2.2 Modeling Noise and Jitter......................................................................... 51

    3.3 Simulation Results and Analysis ...................................................................... 533.4 Relating Correlation to BER............................................................................. 55

    3.5 Number of Taps in the TOC ............................................................................. 57

    CHAPTER 4 EXPERIMENTAL IMPLEMENTATION........................................... 59

    4.1 Introduction....................................................................................................... 594.2 Input System ..................................................................................................... 614.3 MEMS setup ..................................................................................................... 684.4 Impairment generation circuitry ....................................................................... 694.5 Linear White cell Design .................................................................................. 714.6 Output Optics.................................................................................................... 75

    4.7 Optical System Simulation ............................................................................... 79

    CHAPTER 5 EXPERIMENTAL RESULTS............................................................... 87

    5.1 Introduction....................................................................................................... 875.2 Apparatus Alignment........................................................................................ 895.3 Correlation Measurements .............................................................................. 1005.4 Impairment Measurements ............................................................................. 105

    5.4.1 Attenuation Measurements ..................................................................... 1055.4.2 Dispersion Measurements....................................................................... 106

    5.4.3 Noise Measurements............................................................................... 1075.4.4 Correlation Measurements Analysis....................................................... 1085.5 Power Loss Analysis....................................................................................... 110

    CHAPTER 6 CONCLUSION...................................................................................... 112

    6.1 Accomplishments............................................................................................ 112

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    6.2 Future Work.................................................................................................... 1136.2.1 Input System Improvements ................................................................... 1136.2.2 White cell-based TOC improvements..................................................... 1146.2.3 Output Summation Improvements.......................................................... 1146.2.4 Correlation Output Measurement Improvements ................................... 115

    APPENDIX A: MATLAB CODE FOR CORRELATION SIMULATIONS 116

    APPENDIX B: RAY MATRIX OPTICS130

    APPENDIX C: MAPLE CODE FOR WHITE CELL DESIGN.134

    REFERENCES....139

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    LIST OF TABLES

    Table............................................................................................................................. Page

    Table 1.1: Test time required to establish a reliable BER measurement for various bit rate

    standards [24] ...................................................................................................................... 12

    Table 2.1: Bounce pattern to produce different amounts of delay.................................... 45

    Table 5.1: Weights of the optical power associated with each arm in the TOC............. 104

    Table 5.3: Power loss measurements of our experimental OPM apparatus ................... 110

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    LIST OF FIGURES

    Figure ........................................................................................................................... Page

    Figure 1.1: Simplified design of next generation all-optical networks............................... 3

    Figure 1.2: DWDM telecommunication channel............................................................... 5

    Figure 1.3: Illustration of the effects of different types of impairments on a square pulse 7

    Figure 1.4: Reproduced from [13], screen shot of an eye diagram taken using a real-time

    scope ................................................................................................................................. 13

    Figure 1.5: Reproduced from [15], Amplitude histogram generated using asynchronous

    (a) and synchronous (b) sampling..................................................................................... 15

    Figure 1.6: Reproduced from [18,26] Block diagram of a APS monitor ......................... 17

    Figure 1.7: Reproduced from [31] Illustration of the frequency spectrum of both the data

    signal and the SC signal.................................................................................................... 18

    Figure 1.8: Reproduced from [49], Performance analysis of DORP against availability-

    based routing protocol....................................................................................................... 24

    Figure 2.1 :N-tap time-integrating optical correlator. Figure shows the correlation output

    between a degraded input and the weighting elements at each tap................................... 30

    Figure 2.2: Two types of tapped delay lines. (a) 1xN splitter followed by N fibers with

    different lengths each providing a different delay. (b) 2x2 couplers/splitters with each

    splitter amounts for a single tap ........................................................................................ 32

    Figure 2.3: The original White cell with three spherical mirrors ..................................... 33

    Figure 2.4a,b,c: Beam propagation in the original White cell .......................................... 34

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    Figure 2.5: Single input bounce pattern on mirror M in the White cell............................ 35

    Figure 2.6: Multiple inputs bounce pattern on mirror M.................................................. 36

    Figure 2.7 : Modification made to original White cell (shown in red)............................. 37

    Figure 2.8: Pixels tip angle and deflected beam angle...................................................... 38

    Figure 2.9: Delay arm showing the image locations produced by each lens.................... 40

    Figure 2.10: White cell-based TDL highlighting the null cell, the switching arm, and the

    delay arm........................................................................................................................... 45

    Figure 3.1a,b: Auto/cross correlation function. (a) Effect of attenuation on the correlation

    function; (b) Effect of dispersion on the correlation function .......................................... 51

    Figure 3.2: Effect of noise and jitter on correlation function. (a) Hundred separate

    correlations are superimposed for 20% noise; (b) Hundred superimposed correlations,

    with jitter varying randomly with standard deviation j = 10% jitter .............................. 52

    Figure 3.3 Measurement of the area of the correlation function that exceeds a certain

    threshold during a specified time interval......................................................................... 54

    Figure 3.4: Area of the correlation function that is greater than 50% threshold and within

    the time window in which the ideal correlation function exceeds 50%. The independent

    variable is jitter, with dispersion as a varying parameter.................................................. 55

    Figure 3.5: (a) Simulated eye diagram. The shaded area is the open area of the eye; (b)

    Variation in the open area of the eye diagram for combined jitter and dispersion........... 56

    Figure 3.6: Effect of number of taps on the correlation functions shape ........................ 57

    Figure 4.1: Experimental apparatus block diagram.......................................................... 61

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    Figure 4.2: Principal of operation of a MZ modulator[51]

    ................................................ 62

    Figure 4.3: MZ Modulator transfer function..................................................................... 63

    Figure 4.4: Cross section of the V-groove fiber array ...................................................... 65

    Figure 4.5: Setup of the input optics and the beam propagation path from v-groove fiber

    array into the White cell.................................................................................................... 66

    Figure 4.6: MEMS pixel close up and the intensity profile of maximum allowed spot size

    ........................................................................................................................................... 67

    Figure 4.7: Subsection Subset of MEMS pixels ............................................................... 68

    Figure 4.8: Circuit schematic of a dispersion generation circuitry................................... 70

    Figure 4.9: Circuit schematic of the noise generation circuitry........................................ 71

    Figure 4.10: White cell-based tapped delay line............................................................... 72

    Figure 4.11: Top view of null cell .................................................................................... 74

    Figure 4.12: Side view of delay arm................................................................................. 74

    Figure 4.13: Output arm location and the equipment used to sum the beams and view the

    correlation output.............................................................................................................. 76

    Figure 4.14: Output optics and mounts, units are in mm.................................................. 77

    Figure 4.15: Internal connection of the common-node SM05PD4B photodiode ............. 78

    Figure 4.16: Optical Simulation of the linear White cell-based TOC, using OSLO ........ 81

    Figure 4.17: Optical Simulations of the input optics used in the TOC design ................. 83

    Figure 4.18: Optical simulation of the output of the White cell part in the TOC............. 84

    Figure 4.19: Optical Simulation of the output optics used in the TOC design................. 85

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    Figure 4.20: Optical Simulation of the entire TOC system.............................................. 86

    Figure 5.1: Layout of the experimental apparatus on the optical table-to scale-.............. 88

    Figure 5.2a: Alignment procedure to establish delay arm optical axis............................. 89

    Figure 5.3: Beam intensity profile of a single beam in the array...................................... 91

    Figure 5.4: Gaussian beam propagation and location of measurement points ................. 92

    Figure 5.5: Imaging arms locations .................................................................................. 93

    Figure 5.6a: Photographic image of the setup showing a top view of the input and output

    optics along with a section of the linear WC setup........................................................... 93

    Figure 5.7: Magnified image of the MEMS pixels captured using an IR CCD camera ... 95

    Figure 5.8a,b: The beam array imaged at the MEMS plane. We see all the even-

    numbered bounces in (a) and the odd-numbered ones in (b)............................................ 96

    Figure 5.9: MEMS pixel matrix showing the locations of pixels used and all

    malfunctioning pixels........................................................................................................ 97

    Figure 5.10: Input pulse signals and their autocorrelation function as a function of time 99

    Figure 5.11a: Oscilloscope screen shot showing the input pulse and the output pulse with

    zero delay........................................................................................................................ 101

    Figure 5.12: Oscilloscope screen shot showing the input pulse and the output

    autocorrelation function.................................................................................................. 103

    Figure 5.13: Measured effect of signal attenuation on the correlation output................ 106

    Figure 5.14: Measured effect of signal dispersion on the correlation output ................. 107

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    Figure 5.15a,b: Comparison between theoretical and experimental results (a) Attenuation

    (b) Dispersion.................................................................................................................. 109

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    1

    CHAPTER 1INTRODUCTION

    1.1 Optical Networks

    The purpose of this dissertation work is to introduce a novel approach for optical

    performance monitoring (OPM) of data links in next generation all-optical networks.

    Our approach introduces a new device that is used to detect signal degradation and/or link

    failure in real-time (tens of picoseconds), where the results could be utilized in real-time

    protection and provisioning of all-optical links. The device is to be deployed in the

    optical domain and be integrated in the design of next generation all-optical networks.

    Currently, the increasing demand in the Internet network for real-time multimedia

    data traffic with high quality of service (QoS) is pushing the limits of existing network

    structure [1,2,16,17,18]. Such demand can be easily noticed in our daily life with services

    such as: Voice over IP (VoIP), Video on Demand (VoD), IP-TV, and other high-

    bandwidth, minimal-delay services. A lot of research has been conducted by the Internet

    Engineering Task Force (IETF) and other organizations to establish new standards for

    future networks that can cope with such continuously increasing demands while

    maintaining a high level of reliability.

    Next generation networks call on a new paradigm of all-optical dynamically

    routed networks, where network links are fully transparent to the data bit rate and format.

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    The network core is envisioned to comprise a mesh of nodes interconnected using all-

    optical switches over optical fiber cables [1]. This requires the elimination of the

    expensive electronic transponders that are used to do the Optical-Electronic-Optical

    (OEO) conversion for signal regeneration and reshaping. The speed and price of

    electronics are considered a bottleneck in next generation designs as they impose an

    upper limit on the network bandwidth and the overall cost effectiveness of a network

    design. Additionally, network domain transparency requires the development of new

    routing and signaling protocols that take into account the physical layer parameters of the

    transmitted optical signal. Several enhancements to standard Internet Protocol (IP)

    routing and signaling protocols (e.g. OSPF*, and RSVP respectively) have taken place in

    order to be capable of handling new optical parameters imposed on the network[17,18,19,2].

    This new paradigm proposes a full layer of optical transparency, where the

    current existing optical core networks are integrated with edge routers that act as a

    gateway for the Internet Service Providers (ISPs) to the core network.

    Figure [1.1] shows a simplified view of next generation Internet networks. The

    network backbone (core of the network) is represented as a transparent cloud consisting

    of pure optical links, which are interconnected via all-optical switches. Edge routers act

    as the interface between the optical physical layer (backbone) and the client IP layer

    (ISPs, clients etc). Other components of all-optical networks such as optical amplifiers

    (OA), optical add drop multiplexers (OADM), wavelength converters and others are not

    shown in this figure for simplicity.

    * OSPF stands for Open Shortest Path First RSVP stands for Resource ReSerVation Protocol

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    Figure 1.1: Simplified design of next generation all-optical networks

    1.2 Optical Impairments

    Physical layer parameters have been ignored in the past in low bandwidth

    networks as they only imposed very minor limitations on the overall network bandwidth

    or the maximum span length that a signal has to travel. This is primarily due to the low

    signal bandwidth and the large channel spacing between the multiplexed transmitted

    signals over a fiber. As the network bandwidth increases, however, the amount of data

    transmitted over a single fiber increases and hence the channel spacing decreases. This

    calls for modulation techniques such as Dense Wavelength Division Multiplexing

    (DWDM), where hundreds (commercially available) and even thousands (theoretically)

    of signals expected in the near future to be carried on a single fiber with each signal being

    modulated at bit rates of 10Gbps to 40Gbps [17,18,19].

    DWDM is becoming the core technology for coping with the rapidly increasing

    demand for bandwidth in the Next Generation Internet. An adverse consequence of

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    boosting network capacity, however, is increasing the chances of large-scale network

    failures [24,25,26]. Therefore, increasing the network capacity demands the increase of the

    network reliability and stability and arises the need to continuously monitor DWDM links

    for any failures or signal degradation. In addition, once a failure is detected, a real-time

    link recovery mechanism has to be put in place either to establish a new data path or to

    recover the lost data.

    DWDM links comprise several essential active optical components. In a DWDM

    link, signals encoded on different wavelengths are first multiplexed onto a single fiber

    using DWDM multiplexers (MUXs). The signal routing function is performed using

    optical cross connects (OXCs) sometimes called optical switches. Optical amplifiers

    (OAs) are placed along the link to increase the overall transmitted length of the optical

    signal. The amplifiers function as power boosters by pumping more photons in the signal

    as it gets attenuated along its path in the optical fiber. Some of the routing functions are

    performed by optical add drop multiplexers (OADMs), which are devices used to change

    the wavelength at which signals are traveling by adding or dropping wavelengths at

    intermediate nodes. They are also used for wavelength conversion routing techniques

    described in [50]. At the receiver end, de-multiplexers (DE-MUXs) are placed to decode

    the transmitted data. DE-MUXs can also be placed at intermediate nodes to assist in

    optical switching functions. Optical performance monitors (OPMs) are expected to be an

    integral part of DWDM links in next-generation Internet networks, where reliability and

    high QoS of high bandwidth optical networks are essential aspects of the networks

    design. Figure [1.2] illustrates a cross section of a DWDM link including its basic

    components arranged along a network link. Additionally we show some locations at

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    5

    which OPMs could be installed. In the figure the red arrow suggests that a portion of the

    transmitted power is tapped and sent to the OPM.

    Figure 1.2: DWDM telecommunication channel

    DWDM networks are usually designed with respect to the maximum span length

    that a signal traverses at a given bit rate. Hence, only physical impairments that would

    limit the maximum span length are considered. Over the last decade a lot of research has

    been conducted in locating the impairments that affect the DWDM signal transmission

    the most and that should be taken into consideration during the network design. In the

    next section we will discuss some of the most prominent types of impairments that have

    been reported.

    1.2.1 Linear and non-linear impairmentsWhen an optical signal is transmitted through a transmission link, usually a fiber,

    it is subjected to several degradation factors or impairments. At a specified bit rate these

    physical impairments limit the number of optical spans (point-to-point links between two

    switching nodes, two active elements, or a mixture of both) that the signal transverses

    throughout the network. Additionally, impairments tend to corrupt the data signal

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    transmitted and make it harder for the receiver to distinguish between a digital 1 and a

    0 and hence introduce errors in the received signal and increase the Bit Error Rate

    (BER).

    Different types of degradation factors or signal impairments have different effects

    on the transmitted optical signal. These effects could be seen as a reduction in the

    signals optical power, noise added to the signal, change in the shape of the optical pulse,

    time displacement, or a combination of these effects.

    Optical physical layer impairments are often divided into two categories, linear

    impairments and non-linear impairments. This classification is based on the dependency

    on the signal power [17,18,19,27,28,29,30,31,32,33], where linear impairments affect individual

    wavelengths and are independent of the transmitted signal power, while non-linear

    impairments are more complex and are very hard to quantify as they depend on a

    combination of factors such as the signal power, number of wavelengths per channel, and

    the channels bandwidth. The effect of linear impairments is dominant and is usually the

    main concern of network designer, although in some situations non-linear effects are

    more pronounced and need to be considered in the design [15,16,17]. In our research we

    concentrate on quantifying and measuring linear impairments as they contribute the most

    to signal degradation. We will always assume that the effect of nonlinear impairments is

    negligible.

    Linear degradation factors can be categorized under four major areas: (i)

    attenuation; (ii) dispersion; (iii) noise; (iv) jitter. Figure [1.3] shows how these different

    factors affect the shape and/or the amplitude of the transmitted signal.

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    Figure 1.3: Illustration of the effects of different types of impairments on a square

    pulse

    Clearly from the figure above, we see that different impairments affect the signal

    differently. Let us further discuss the source(s) of each of the four types shown above

    and elaborate more on how they impose a limitation on optical data transmission.

    1.2.2 AttenuationIn this section we refer to attenuation as the reduction in the optical power of the

    transmitted signal over an optical fiber. The effect is a function of the distance traveled,

    where the longer the distance the higher the attenuation factor. Attenuation in optical

    telecommunications is often referred to as the transmission loss and is measured in units

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    of dB/Km indicating the total loss over power accumulated over a certain length of fiber.

    We can quantify attenuation using the following formula [22]:

    )(

    )(log*10)( 10

    mWPowerInput

    mWPowerOutputdBnAttenuatio = [1.1]

    Note that the signal could get attenuated due to some other factors that we will

    discuss in the following sections such as dispersion and noise. Other types of losses that

    lead to signal attenuations include bending losses in the fiber or fiber bundle and coupling

    losses between fibers at intermediate nodes.

    1.2.3 DispersionDispersion in optical communication is a temporal effect that results in pulse

    spreading in time and is highly present in optical fibers [21]. A group of pulses traveling

    as a bit stream will spread in time such that pulses merge together causing errors at the

    receivers end and impairing the signals transmission. At higher bit rates, more pulses

    are multiplexed on the same fiber with smaller channel spacing between pulses, which

    results in the effect becoming more evident.

    The dispersion effect is caused by different sources including material dispersion,

    waveguide dispersion, and polarization mode dispersion [21]. The first two effects are

    dependent on the refractive index of the transmission medium and the wavelengths

    transmitted in the fiber. Let us consider a transmitted pulse with a finite spectral width

    traveling over a dispersive medium, e.g. an optical fiber. We note that any pulse with a

    finite spectrum will contain multiple frequency components and hence multiple

    wavelengths. In material dispersion, the refractive index seen by different wavelengths

    traveling along the fiber vary and hence result in different travel velocities for different

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    wavelengths causing the pulse to spread in time. Waveguide dispersion is very similar to

    material dispersion as it depends on the propagation constant of the transmission medium,

    which is a function of the signals wavelength. It is, however, a much smaller effect and

    could be ignored. Polarization mode dispersion or PMD happens when one of the two

    polarization components of the optical field traveling down the fiber lags behind the other

    component resulting in a spreading in the overall pulse shape.

    Let us examine one of these dispersion sources more carefully, namely material

    dispersion. Material dispersion is a dominant effect in optical fiber transmission [2] and is

    commonly quantified by the group velocity dispersion (GVD), where the group velocity,

    vg, of the transmitted signal is defined as the velocity at which the information is

    conveyed along the optical wave and is usually referred to as the signal velocity[6]. GVD

    is a result of the dependency of the group velocity on the frequency components present

    in the transmitted signal, where different frequency components travel through the optical

    fiber at different speeds. GVD for a uniform medium can be calculated as:

    =

    2

    2

    d

    nd

    cGVD [1.2]

    where is the wavelength of the transmitted signal, c is the speed of light, and n is the

    refractive index of the uniform medium.

    In our analysis, we treat the signal as an analog signal, where we only consider

    the shape of the signal and hence all types of dispersion mentioned above will have the

    same affect on our correlation measurement.

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    1.2.4 NoiseNoise in optical communication links is introduced in either active optical

    elements in the optical link or at the receiver end. Noise produced along the DWDM

    optical link is primarily due to Amplified Spontaneous Emission (ASE) [2,4], which is

    light produced by spontaneous emission and amplified in an optical gain medium. ASE

    is generated in optical active elements such as optical amplifier and light sources. ASE is

    directly proportional to the signal power and inversely proportional to the amplifiers

    gain and the links bandwidth. Optical amplification nodes such as in Erbium Doped

    Fiber Amplifier (EDFA), are intended to amplify the amplitude of the optical signal only,

    however, background noise and transmission link noise get amplified as well in addition

    to the generated ASE. The spectrum of the background noise is often wide; however,

    some of that noise can land near or on the signals wavelength spectrum and cause the

    signal to get impaired due to interference between the signal and the noise. This noise

    affects the receivers ability to properly decode the optical signal and hence introduces

    errors.

    The noise is quantified in term of the Optical Signal to Noise Ratio (OSNR),

    which is mathematically defined as:

    dBP

    POSNR

    NOISE

    SIGNAL10log10= [1.3]

    where PSIGNAL is the optical signal power and PNOISE is the optical noise power. The

    higher the OSNR the better the signal quality is. This measure is very frequently defined

    as a design factor when determining the QoS requirements of an optical link.

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    The noise added to the signal is often approximated as Gaussian noise that affects

    the entire data stream traversing a specific link with the same probability [12,15,17]. We

    use this approximation in our simulation presented in chapter 3.

    1.2.5 JitterIn optical telecommunications, jitter is defined as variation in the signal

    characteristic between consecutive pulses such as a variation in the pulse width and/or the

    phase of the pulse [23]. In our analysis, we only consider temporal variation such as

    variation in the pulse interval or signal frequency variations. Our assumption is based on

    the way we treat and analyze the output signal, where the signal is considered to be

    incoherent. Jitter is often quantified based on the type of variation measured, which in

    our case would be a displacement in the pulse peak value.

    1.3 Link Quality Measurement

    In the telecommunication industry there already exist several standard methods

    for measuring the quality of an optical link and the overall BER of the transmission link.

    One standard technique is to directly measure the BER using a BER tester. A Bit

    Error occurs when a transmitted signal gets corrupted by an internal or external event that

    causes for example the reception of a 0 when a 1 is transmitted. The BER is a

    statistical measure of how often these errors occur. For BER measurements to be

    statistically significant, at least 100 errors need to be collected at the receiver end. This

    requires a lot of time, several seconds or several minutes. In optical data communication

    links the BER is expected to be below 10-9 for a good connection. The test time required

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    for 95% confidence interval would depend on the transmission bit rate [23]. In table [1.1]

    we show the test time required for standard bit rates used in optical data networks [24].

    Bit rate Industry standard name Test time

    40 Gbps OC-768 1 sec

    10 Gbps OC-192 3 sec

    2.5 Gbps OC-48 12 sec

    155 Mbps OC-3 3.2 min

    Table 1.1: Test time required to establish a reliable BER measurement for various

    bit rate standards[24]

    Eye diagram measurement is another common measurement technique. Eye

    diagram measurements are much faster than BER tester and are considered to be the

    current industry standard for measuring and analyzing the performance of optical links

    [12]. An eye diagram is constructed by superimposing every possible bit sequence from

    simple 101s and 010s, to isolated ones after long runs of consecutive zeros and other

    problem sequences that often show up weaknesses in an optical link. The eye is

    generated on real-time oscilloscopes by accumulating millions of bit sequences, a process

    which takes up to tens of seconds using the fastest real-time scopes in the industry. Once

    generated, data measurements are observed over a time window equal to three data

    periods wide, which, at ultra-high speeds, can be done in milliseconds. Figure [1.4]

    illustrates a typical eye diagram screen shot on a real-time scope [13]. Features of the eye,

    such as the eye opening, the eye overshoot/undershoot (i.e. amplitude distortion at the top

    and the bottom of the eye), and the eye width are commonly used to determine the

    Confidence interval is a statistical measure used in BER calculations, where an intervalwith a given probability is generated multiple times from a random set of samples.

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    different types of impairments we discussed earlier and more. The effects of noise and

    dispersion cause the eye opening to get smaller, while amplitude distortion is often

    recorded using the eye overshoot/undershoot thresholds. Jitter and timing

    synchronization impairments are recorded using the width of the eye. The figure shows a

    perfect eye diagram where no impairments added to the signal. The masks labeled mask

    1 through mask 5 are used as a pass/fail test to measure the type and amount of

    impairments present. Mask 1 is used to measure the eye opening, while masks 2 and 3

    keep track of the eye overshoot and undershoot. Finally masks 4 and 5 are used to

    measure the width of the eye.

    Figure 1.4: Reproduced from [13], screen shot of an eye diagram taken using a real-

    time scope

    The results obtained from the eye diagram are related to the BER of the

    transmitted signal through the Quality factor or Q-factor of the signal, which is defined

    as:

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    01

    01

    =factorQ [1.4]

    where x and x are the mean value and the standard deviation of the impairment

    measured and the subscript x denotes the bit value of 0 or 1. Once the Q-factor is

    quantified the BER is calculated using the formula described in equation [1.5]:

    =

    22

    1 QerfcBER [1.5]

    Both BER testers and eye diagram measurements are slow as they require the

    accumulation of a very large number of samples in order to obtain a valid statistical

    measurement. In addition, the signal has to be converted to the electronic domain, in

    which the signal is analyzed. The need to accumulate a large number of samples,

    typically millions, to achieve a reliable measurement stands as a bottleneck as it limits

    how fast an action can be taken when an error occurs. As we discussed earlier in this

    chapter, next-generation optical networks require real-time response to signal failure or

    signal degradation, which existing techniques cannot offer. To solve this problem new

    link monitoring methods are being developed such as the OPM we describe in this

    dissertation.

    1.4 OPM: Existing Methods

    Optical performance monitoring (OPM) has been recently introduced in the

    literature. One approach based on asynchronous amplitude histograms has been proposed

    and shows to be promising [15,16]. In this method a small amount of power is tapped from

    the optical link and used to measure the quality of the link. This eliminates the need for

    Optical-Electronic-Optical (O-E-O) conversion of the main data signal and maintains the

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    signal in the optical domain. The method is based on a statistical approach, where the

    tapped optical signal is first collected on a high-bandwidth photodiode. Next, the

    generated electrical signal is asynchronously sampled at a lower rate than the rate of the

    signal. The samples are then collected and an amplitude histogram is generated

    representing the frequency of occurrence of digital 0s and 1s and anything in between.

    Figure [1.5a] and [1.5b] show two amplitude histograms generated using asynchronous

    sampling (a) and to validate the results it is compared to the histogram generated using

    synchronous sampling (b). Using information obtained from the shape and amplitudes of

    the generated histograms the Q-factor is calculated and then related to the BER of the

    signal.

    Figure 1.5: Reproduced from [15], Amplitude histogram generated using

    asynchronous (a) and synchronous (b) sampling

    The asynchronous amplitude histogram technique requires gathering a large

    number of samples (at least one million samples are usually needed) before a meaningful

    result is obtained [25]. This requires a sampling time of multiple milliseconds, which is

    not acceptable if the device is to be used in real-time protection or provisioning of all-

    optical links. This technique, however, meets the transparency requirement imposed by

    next generation networks as the monitoring technique is independent of the bit rate or

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    modulation format. Amplitude histogram measurements also do not take all kinds of

    impairments into consideration, such as dispersion. The system always assumes the use

    of dispersion-compensated fiber.

    Amplitude Power Spectrum (APS) analysis techniques have been recently

    deployed for monitoring and analyzing the behavior of any types of signals transmitted

    over an optical dispersive/noisy channel. In such analysis, signals are treated as analog

    waveforms and are often independent of the data format or bit rate, which is very

    desirable in monitoring all-optical networks in order to achieve the desired goal of

    complete transparency.

    Figure [1.6] shows the general block diagram of an APS monitor, where a single

    DWDM channel is shown. A low-frequency subcarrier (SC) is added to the data stream

    (baseband signal). The baseband signal is combined with the SC either electronically or

    optically and the combined signal is then used to modulate the laser transmitter. A

    unique SC frequency gets transmitted on each DWDM channel [18,26,31] (or a separate

    channel on a different wavelength () can be dedicated for monitoring [13]). The optical

    fiber channel is then tapped at any point in the transmission line and the SC is filtered out

    and monitored. The SC tone can be detected by either using an electrical band pass filter

    (BPF) after photo detection (as shown in fig [1.6]) or by optical pre-filtering prior to

    photo detection. The idea behind APS technique is to superimpose a narrow-band

    spectral signal or an RF tone (referred to as subcarrier tone or pilot tone) on the optical

    baseband data signal. The SC signal travels the complete same path with the baseband

    signal (original data). The subcarrier is extracted at intermediate nodes throughout the

    optical channel and monitored without disrupting the original signal. The average power

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    and shape of the subcarrier can be directly related to those of the baseband signal, hence

    providing information about the OSNR and dispersion that the original data encountered.

    Cross talk, which is a non-linear impairment, can be measured by measuring the crosstalk

    encountered by SC tones in adjacent DWDM channels.

    Figure 1.6: Reproduced from[18,26]

    Block diagram of a APS monitor

    There are several constraints on the SC signal that need to be taken into

    consideration when using APS techniques. Since the SC tone is transmitted over the

    baseband data signal, we have to make sure that no interference occurs between the two

    transmitted signals. For this requirement to hold, the SC tone frequency has to be higher

    than the spectral tail of the data signal such that no crosstalk can occur between the two

    signals [31]. Figure [1.7] shows the frequency spectrum of baseband signal along with a

    subcarrier signal for a certain WDM channel.

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    18

    Figure 1.7: Reproduced from[31]

    Illustration of the frequency spectrum of both the

    data signal and the SC signal

    Furthermore, the depth of modulation (power or strength of modulation of the SC)

    has to be sufficiently smaller than that of the baseband signal. Precautions also need to

    be taken when monitoring the WDM channels power levels, since power fluctuation

    (gain or loss) may occur at the transmitter. Therefore, it is important to fix the SCs

    power level relative to the channels power [26]. Further constraints are required on the O-

    E module (e.g. photodetector) of the monitor circuit. Since the signal is not monitored at

    the receiver and is usually tapped somewhere along the channel, it is important to set the

    sensitivity of the O-E interface to be much higher than the downstream receivers

    sensitivity. This ensures accurate measurements and encounters for any additional signal

    degradation that may occur between the tap and the downstream receiver.

    Although APS monitoring techniques may seem to be a good solution for a lot of

    OPM applications, they still suffer from several weaknesses. They require modification

    of the transmitter to add the SC generation circuitry, which could be a major problem due

    to physical limitations in long-haul networks. The monitoring speed of such techniques

    is limited by how fast electronics (the O-E module) can go. This could be a bottleneck in

    applications that require high-speed fault detection and restoration. In addition, there are

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    several SC-specific obstacles that need to be overcome before any of these techniques

    could be standardized [2, 12, 13].

    Other all-optical monitoring systems have been proposed [42,45,51], however, most

    of them deal only with a specific type of signal impairment such as dispersion, or jitter

    and often use assumptions in the network layout that severely limit the existing

    configuration of the core optical network. In the next section we describe our proposal

    for OPM in all-optical networks and show how it compares to other existing methods.

    1.5 OPM: Our Proposal

    Let us first summarize the motivation behind OPM in a next generation all-optical

    networks. When a link is found to be unhealthy (e.g. a link failure due to cable cut or

    signal degradation due to impairments in the link), an immediate action needs to be taken

    to either set up an alternative path for the data (link restoration), or switch to a backup

    path that has been already established (link provisioning). At high bit rates (>10Gbps)

    and with DWDM channels with very high BW, a large amount of data can be lost within

    a very small period of time (e.g. a link disruption of 1s at bit rate of 40Gbps a total of 40

    million bits would be lost, which is equivalent to 10,000,000 traditional phone lines).

    Therefore, using previously discussed techniques to keep track of the links health is not

    adequate nor scalable as the network wont be capable of acting fast enough to link

    failures.

    We can outline the essential features required in any OPM technique that will

    satisfy the next generation Internets network requirements (i.e. transparency, reliability,

    protection, and real-time link provisioning). The monitoring system should be:

    - Independent of the transmitted signal format

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    - Fully implemented in the optical domain- Capable of near-instantaneous error detection (picoseconds)

    In this dissertation we introduce a novel approach for solving the problem of

    optical link health monitoring. We propose a new monitoring technique based on the use

    of optical correlation, where a known bit stream or a test signal (e.g. 0 1 0) is

    continuously transmitted or transmitted as a burst at a known frequency. It is very

    important to keep in mind that the data transmitted over the bit stream is irrelevant to our

    technique as we treat the signal as a pure analog signal and analyze the amplitude and the

    shape of the signal. The test signal is sent over a dedicated channel (i.e. a different

    wavelength) and gets multiplexed with the data stream in a DWDM system. The signal

    gets affected by all the impairments that the data channel encounters in as it undergoes

    the same path as the data. The signal is either picked up at intermediate nodes along the

    link or at the receivers end by tapping a small portion of the signals power. The signal

    is then optically correlated with a clean version of the transmitted bit stream. Information

    from the correlation output (amplitude, side lobes, rise/fall time, frequency components,

    and others) is then extracted and used to set a threshold that indicates whether the

    transmission link meets the quality of service (QoS) and performance requirements

    specified by the carrier or not. The thresholding is either implemented in the optical

    domain using an optical saturable absorber or electronically using a fast comparator.

    1.6 Physical Implementation

    Our approach is based on a time-integrating or temporal optical correlator (TOC).

    The correlator is physically implemented using an N-Tap Delay Line (TDL), Nweight

    elements with one at each tap, and anN-input summer. In general terms, the TOC is used

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    to measure how differenta deteriorated bit sequence is (received at its input) from a clean

    replica of the transmitted bit sequence (i.e. not affected by any impairments). At the

    input of the TOC, the received signal r(t) is split into N copies, where each copy is

    delayed by a discrete time increment . Each copy is then optically multiplied by a

    weight function sk(t), where sk represents the weight function at the kth tap in the TDL.

    Each weight function is chosen to represent the pulse shape for a [0 1 0] or other specific

    sequence and is determined by the transmitted bit sequence and the number of taps

    implemented. Finally the amplitudes of the delayed copies are summed incoherently (no

    phase components) resulting in an output C(t) that represents the cross-correlation

    function between the delayed copies and the weight functions. Coherent summing could

    also be used.

    Additionally, we propose a new design for an optical correlator based on the

    White cell that can produce hundreds or even thousands of delays with a tolerable amount

    of loss. The White cell [7] technology has been adapted by the optics research group at

    The Ohio State University and used in several applications such as: Optical true time

    delay, optical switching, and others. We will discuss the detailed design of the White-

    cell-based TOC in Chapter 2.

    1.7 Routing Protocol based on OPM

    Information obtained from OPMs need to be included when calculating new

    routes for data signals or backup routes when signal failures occur in next-generation

    Internet networks. The routing decision needs to be based on how healthy the overall

    path is between the transmitter and the receiver or between intermediate nodes. Current

    routing protocols primarily base routing decisions on the shortest available path to the

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    22

    receiver, where the shortest path is measured in terms of the number of hops (or spans),

    the propagation delay, the blocking probability of intermediate nodes, or a combination

    of those factors and others [1,35]. OPM data will need to be added as an additional factor

    in the routing decision formula in order to sustain reliability requirements of future

    networks.

    Recently, this topic has been actively addressed in the research field. Most of the

    proposed ideas are based on pre-knowledge of the network topology and its physical

    parameters such as links lengths, type of fiber used in each link, number of active

    elements, etc.

    [1,3]

    . Pre-knowledge of network topology and parameters requires a lot

    of processing and storage power, and furthermore conflicts with the network transparency

    requirement. Other ideas suggest establishing routes based on worst-case scenarios [3],

    meaning that switches will have to choose their paths based on the behavior of the worst

    link along the path. This approach results in low bandwidth utilization and literature

    shows that results are rarely reliable in making routing decisions due to the changing

    network dynamics [35].

    The final goal of routing in the optical domain is to increase the revenue of the

    network and keep the level of QoS promised to customers. Choice of a good route-

    computation algorithm is essential to the performance of these networks. The physical

    capacity available in optical data networks has increased (theoretically) to several Tbps

    with optical switching. How much of this available physical capacity that can be utilized

    reliably, depends on the route-computation algorithm used. With each fiber link capable

    of carrying 40Gbps or more worth of data, the impact of even a few percent improvement

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    in the usable network capacity is significant, which can be of the order of hundreds of

    Gbps, if not Tbps.

    In a joint work with the Computer Information Science Department at The Ohio

    State University [49] a new route-computation algorithm, called Domain Optical Routing

    Protocol (DORP) was proposed. The protocol combines intelligent routing with the

    immediate availability of information about quality of signal provided by the optical

    correlator-based OPM. The route-computation algorithm defines the weight of a link

    using its available capacity and its quality as well. The proposed distributed protocol

    requires the nodes inside a domain to exchange availability and quality information,

    where a domain is defined as a sub-section of nodes geographically spaced within a pre-

    specified distance. Inside the domain all nodes will exchange link state information,

    which includes availability and quality. Between domains, border nodes will advertise

    the aggregate cost to pass through corresponding domains. In this way the domain cost

    will be more updated and more meaningful for the purpose of routing.

    The division of the network into domains is done to avoid problems associated

    with network scalability. For example, if the network size is extended then the

    distribution of the link state information will take more time, making the information

    itself old and misleading for the purpose of routing. Also it is known that the Internet is

    composed of autonomous networks and that for administrative reasons its impossible to

    distribute the detailed link state information among all such networks. To overcome

    these two problems the proposed protocol is based on domains.

    Some preliminary simulations of the effectiveness of DORP are presented in [49].

    Figure [1.8] shows a comparison between the availability-based protocols (such as OSPF,

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    RSVP) with DORP using NSF network with 16 nodes, 25 links and 4 wavelengths per

    link. Results indicate that DORP outperforms the availability-based routing protocols in

    generating more revenue. In this simulation the revenue is given by the number of

    accepted calls. The QoS factor is simulated by dropping the quality of only one link

    randomly for short periods of time (few seconds) below an acceptable threshold. In

    availability-based routing, calls that use links with quality below the threshold do not

    generate revenue where as in DORP using the information provided by the optical

    correlator avoids these links and hence all accepted calls are generated. For more than

    one link with quality below the threshold the advantage of DORP against the availability-

    based protocol increases.

    Figure 1.8: Reproduced from [49], Performance analysis of DORP against

    availability-based routing protocol

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    1.8 Document Organization

    The dissertation is organized as follow: In Chapter 2 we will explain the

    theoretical principles behind optical correlation and discuss the different types of optical

    correlators available. We then discuss how optical correlation can be used in OPM.

    Later in the chapter we will introduce a new design for a temporal optical correlator

    (TOC) based on the White cell and discuss the details of the design.

    Chapter 3 will describe some of the simulations obtained to support our design.

    We present simulation results describing how the different types of impairments affect

    the correlation output. We finally relate our obtained results to industry-standard

    monitoring technique and explain how we can relate our measurements to the BER of the

    transmitted signal.

    In Chapter 4, we describe in detail the OPM proof-of-concept experimental

    apparatus implemented. We divide the setup into five sections, namely: Input system,

    MEMS, impairment generation circuitry, TOC, and output system and explain the design

    details of each.

    Chapter 5 will discuss the experimental results obtained using the proof-of-

    concept setup and compare the obtained results to their expected theoretical values. We

    first describe the alignment procedure used to align the optics used in the White cell-

    based TOC. We then show correlation output results obtained and how the correlation

    function respond to each of the impairment types we discussed in chapter 1. We finally

    show a detailed power loss analysis of the system and discuss its feasibility.

    Finally in chapter 6 we conclude the dissertation with suggestions for future work

    that could be implemented to enhance the current design.

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    CHAPTER 2THEORY

    2.1 Introduction

    In this chapter we explain the theory behind optical correlation and how we use

    correlation techniques in optical performance monitoring (OPM). We also describe in

    detail the design of a new optical correlator based on the linear White cell. In section 2.2

    we briefly discuss the concept of correlation and its significance in signal processing

    applications. We then, in section 2.3, explain how we utilize the correlation function in

    OPM applications. Following in sections 2.4, 2.5 and 2.6, we describe in detail the

    design of a new White cell-based optical correlator and discuss its advantages.

    2.2 Principal of Correlation

    The concept of correlation was introduced in 1890 by the English statistician,

    Galton [8]. He defined the relationship between any pair of statistical events or processes

    through the concept of statistical regression. His definition was considerably extended

    throughout the twentieth century and a new time-dependent measure was introduced,

    which is termed now as the correlation function.

    The correlation function is defined depending on the field of study that is being

    considered and not all definitions are identical. Although most definitions quantify the

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    co-relation between two random variables at a specific time or between different time

    instants of the same variable, the mathematical representation can vary.

    Statistically, the correlation functionX,Ybetween two random variablesXand Ywith

    expected values (i.e. mean values) E(X) and E(Y) and standard deviations X and Y, is

    defined as:

    )()()()(

    )()()(),cov(

    2222,

    YEYEXEXE

    YEXEXYEYX

    YX

    YX

    ==

    [2.1]

    where the numerator represents the covariance between the two variables and the

    denominator represents the product of their finite non-zero standard deviations. The

    absolute value ofX,Y cannot exceed 1. The value 0 indicates no correlation, or that the

    variables are independent. For any value ofX,Y that is less than 1, the function is

    termed as a cross-correlation function. Correlation function values that are close to 1

    indicate a high degree of similarity between the two variables. A value of 1 indicates a

    complete match between the two variables and is termed as auto-correlation. The values

    between 0 and 1 define the strength of the correlation function and are usually referred to

    as the correlation coefficients. The correlation function can be constructed from those

    coefficients by a direct averaging of the time-dependent function. The averaging process

    can be thought of as an extension of the mean square value.

    In signal processing, the function is defined somewhat differently. The definition

    is represented without normalization, that is, without subtracting the mean and dividing

    by the standard deviation. In this definition we will consider the example of a data signal

    transmitted over an optical transmission medium (e.g. fiber optic link), which is our

    interest in this dissertation. The two variables of interest are the transmitted signal s(t)

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    over the fiber optic link and the received signal r(t-), where r(t) is delayed by a time

    variable,, due to transmission and tis the reference time. The correlation function,(t),

    is defined by the integral:

    +

    = dttrtst )()()( [2.2]

    The infinite limits indicate that the correlation function is continuous over an infinite data

    stream. In the discrete domain, we can re-write (t) for a finite number of samples of

    the received signal by the following summation:

    )()()( 10 k

    Nk k

    ktrtst ==

    [2.3]

    whereNis the number of samples of interest. We will be using the definition in equation

    2.3 for our analysis and simulations throughout the rest of this document.

    2.3 Optical Correlation for OPM

    In optics, correlation functions are commonly used in interferometry to quantify

    the degree of coherence between electromagnetic waves [10]. Correlation functions are

    also well-known in the literature for signal processing applications, primarily as encoders

    and decoders for optical code division multiple access (OCDMA) [22].

    Optical correlators come in two basic styles: spatial and temporal. In temporal

    correlation, a time-varying signal (e.g., intensity or phase) is compared to a reference

    time-varying signal, using, for example, an acousto-optic device[46,47,48]

    or an optical

    tapped delay line[35,36,37,38,39,40]. The result of the comparison is then summed or

    integrated to produce the correlation output. Temporal correlators based on tapped delay

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    lines encounter low power attenuation and can produce a large number of delays ranging

    from picoseconds to tens of nanoseconds.

    Spatial correlators, on the other hand, are widely used in image detection and

    processing applications. They usually take advantage of holograms, for example, to

    compare a two-dimensional image with some reference image [20]. Spatial integrating

    correlators are much faster than time integrating ones, processing approximately 1010

    samples/sec, which is about three orders of magnitude higher than time-based integrators

    [xx]. Their disadvantage is the range of spatial shifts (equivalent to delays) possible since

    delays are usually produced in a crystal by a spatial shift, which is in the range of

    femtoseconds or tens of fs. The losses could be much higher too.

    Our approach is based on a temporal optical correlator (TOC), using an optical

    tapped delay line. Although any optical tapped delay line can be used in a temporal-type

    optical correlator, we introduce a novel one in this dissertation that is based on the White

    cell. We show that our WC-based correlator outperforms existing temporal correlators in

    the number and the range of delays produced by a factor of 100 or more with power

    losses below 7dB.

    2.4 Time-Integrating Optical Correlator (TOC)

    The TOC is implemented using a tapped delay line (TDL), a set of weighting

    elements or reference elements, and an optical summer. The correlation takes place

    between the received signal, r(t), after going through the optical link and a reference

    signal representing a copy of the original transmitted signal. The reference signal present

    at the TOC is represented by the weighting elements, s(t). The weights could be

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    amplitude weights or phase weights. Amplitude weights are either 1s or 0s, whereas

    phase weights are implemented by phase shifts of either 0 or .

    In figure [2.1] we show the structure of a TOC, where the correlator is physically

    implemented using anN-tap TDL. The input to the correlator is a distorted square pulse

    with a frequency of 1/T. The signal gets delayed and multiplied byN-weighting elements

    representing the original square pulse. The outputs are then all summed producing a

    correlation output with a period of 2T.

    Figure 2.1 : N-tap time-integrating optical correlator. Figure shows the correlationoutput between a degraded input and the weighting elements at each tap

    The correlation output is generated as follows: The received time varying signal

    r(t) enters the TDL, where a small amount of the power is siphoned off at each tap. Each

    tap is delayed relative to the next tap by a fixed time increment of . Each time-shifted

    replica of rk is multiplied by a weight sk present at each tap, and the resulting

    multiplication products are summed. The result is the correlation function of Equation

    2.3, between the deteriorated test signal rk and the TDL weights sk. As described

    previously, if the two signals are identical, Eq. (2.3) becomes an autocorrelation, and (t)

    will have a high peak in the center of the time slot, and low side lobes. If the signals are

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    less well-matched, Eq. (2.3) becomes a cross correlation function, and the peak decreases

    whereas the information in the sides of the pulse increases. Information from the

    correlation output such as peak amplitude, side lobes, rise/fall time, frequency

    components and others is extracted and processed (optically or electronically). The

    processed data is then compared to a reference threshold or a reference function to

    indicate whether the tested transmission link meets the signals quality requirements

    specified by the carrier or not.

    The key element of the TOC is the tapped delay line, and the more taps the higher

    resolution of the correlation output. One way to implement taps is using fiber splitters.

    Figure [2.2] shows two common styles: the tree in (a) consists of a 1xNsplitter followed

    by N lengths of fiber. Each fiber is longer than the previous one by a distance of one

    span [53,54,55,56]; the other type in (b) uses 2x2 couplers/splitters in various types of lattices

    [57,58,59,60]. The number of splitters is equal to the number of taps, and for each tap there is

    a separate, precisely cut length of optical fiber. Such designs are not scalable as the

    amount of power loss increases dramatically with each splitter added. Additionally, the

    lengths of the fibers have to be cut very precisely in order to ensure correct delays.

    Another recent approach uses fiber Bragg gratings[61], where the gratings are

    imprinted at various distances along the fiber. As the light beam enters the fiber, portions

    of the beam get reflected at each grating resulting in multiple reflected beams with

    different delays. Such technologies become impractical to implement if a very large

    number of taps are needed. The largest number of taps reported is 63[61] using fiber

    Bragg gratings (FBGs). This means a maximum resolution of only 64 samples, which

    may not be enough for a high-resolution correlation output. In addition, the length of

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    each grating in the FBG needs to be long in order to get high reflectivity. This introduces

    ambiguity in the time delay.

    Figure 2.2: Two types of tapped delay lines. (a) 1xN splitter followed by N fibers

    with different lengths each providing a different delay. (b) 2x2 couplers/splitters

    with each splitter amounts for a single tapIn our design, the implementation of the correlator is based on a free space

    approach rather than fibers. The correlator utilizes the concept of the White cell, which is

    described in the next section.

    2.5 White cell principle

    The White cell [6] was introduced by J. White in 1942 for the purpose of

    spectroscopy, specifically for measuring low-pressure vapor spectra. Since then, the

    White cell has been adapted and utilized in many other applications such as optical true

    time delay [62,63], optical computing [7], and in optical reflectometers [7].

    The White cell is a free-space optical device consisting of three spherical mirrors

    with equal radii of curvature, R, figure [2.3]. The three mirrors are organized such that

    one mirror, mirror M, is facing the other two, mirrors A and B. Mirror M is referred to as

    the field mirrorand mirrors A and B as the object mirrors. The distance between the

    mirrors is equal to their radius of curvature,R= 2f, wherefis the focal length. The center

    of curvature of mirror M, CC(M) is located between mirrors A and B, where the centers

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    of curvature of both A and B, CC(A)&CC(B), are located on mirror M. CC(A) is

    located a small distance above the center of mirror M, while CC(B) is located the same

    distance below the center.

    Figure 2.3: The original White cell with three spherical mirrors

    Figure [2.4] shows how light propagates through the White cell. The light first

    enters the White cell using an input turning mirror (ITM). The input light beam is

    focused onto the ITM, which is tilted such that the light beam gets directed towards

    mirror A as shown in figure [2.4a]. Mirror A sees the input spot on the input turning

    mirror as an object and images it to a new spot (bounce 1) on mirror M. As we see in

    figure [2.4b], the location of the new spot is formed at an equal and opposite distance, y1,

    from the center of curvature of A, CC(A). Meanwhile, mirror M sees the light on mirror

    A as an object and re-images it onto mirror B at an equal and opposite distance,y2, from

    CC(M). The process repeats and the second bounce is formed similarly on mirror M at

    an equal and opposite distance from CC(B).

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    Figure 2.4a,b,c: Beam propagation in the original White cell

    2.5.1 Beam Propagation in the White CellThe re-imaging process between the field mirror and the object mirrors generates

    a spot pattern on mirror M. The number of spots generated is controlled by the distance

    and/or the diameter of mirror M. The location of these spots is controlled by location of

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    the input spot(s) and the locations of the centers of curvature of mirrors A and B with

    respect to the optical axis of mirror M. Figure [2.5] illustrates a specific spot pattern as

    viewed on the front of mirror M. As we see in the figure there are eight generated spots

    that toggle back and forth around the center of mirror M until the final spot eventually

    walks off the edge of mirror M. The final spot is picked up using an output turning

    mirror (OTM) that usually directs the beam outside the White cell, where the beam is

    analyzed or further processed.

    Figure 2.5: Single input bounce pattern on mirror M in the White cell

    It is also possible for multiple beams to circulate in the White cell with each beam

    tracing a unique spot pattern. Figure [2.6] shows the spot pattern formed for each of

    three input beams indicated by three different spot colors.

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    Figure 2.6: Multiple inputs bounce pattern on mirror M

    Note in figure [2.6] that each input spot follows an independent path without

    interfering with other beams before leaving mirror M. Now, if the each spot is made to

    land on a pixilated reflective surface whose angle we can control, each beam can then be

    manipulated independently at any given bounce. This property will be exploited in our

    design of our White cell-based TOC.

    2.5.2 White cell Imaging ConditionsIn order for a White cell to function as described in section 2.4, there are two

    imaging conditions that have to be maintained at all times. Namely, Mirror M has to

    image onto itself through either of the object mirrors A or B with a total magnification of

    -1. Secondly, each of the object mirrors A and B has to image onto each other through

    mirror M.

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    2.6 White cell-based TDL

    In our design we adapt the White cell to be used as the tapped-delay line in the

    temporal correlator. To do so, we perform several modifications to the original White

    cell as illustrated in figure [2.7]. The modifications are highlighted in red. First, we

    replace White cell mirror M with a Micro Electro Mechanical System (MEMS) and a

    field lens along each arm. The MEMS consists of a two-dimensional array ofmirrors,

    each can be controlled to be tipped to a certain angle, either +or - or stay flat with

    respect to the pixels normal. In addition, we build an additional White cell arm which

    will eventually be used to produce delays, arm C, as shown in the figure.

    Figure 2.7 : Modification made to original White cell (shown in red)

    The White cell arms are placed such that one arm, arm B, is located along the

    MEMS normal, while the other two arms A and C, are positioned along angles equal to

    twice the tip angle of the MEMS pixels (i.e. 2). In figure [2.8] we show three pixels,

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    where one is flat and the other two are tipped at angles . Consider a beam coming

    from object mirror B and striking a pixel at an angle normal to the MEMS surface plane,

    the deflection angle of the beam will depend on the tip angle of the mirror. If the pixel

    is tipped to an angle equal to +, the beam will get deflected at an angle equal to twice

    the tip angle, +2, which sends the beam to arm A. Similarly, if the pixel is tipped to -,

    the beam will get deflected at -2or to arm C.

    Figure 2.8: Pixels tip angle and deflected beam angle

    Note that the mirrors alone provide a reflective surface; however, since they are

    flat (as opposed to spherical like the original Mirror M), the imaging conditions discussed

    in section 2.5.2 will no longer hold. To fix this problem we add a field lens placed at a

    calculated distance from the MEMS plane along each of the arms. Ideally, a spherical

    mirror with a radius of curvature R f_lens is equivalent to a flat mirror right next to a lens

    with a focal length ff_lens =2

    _ lensfR. The focal length of the field lenses we used were

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    slightly different, chosen to compensate for the separation between the field lens and the

    MEMS while maintaining imaging the White cell.

    2.6.1 White cell delay arm

    In the original White cell, a beam bounces a fixed number of times and hence

    encounters a fixed time delay. The total delay is proportional to the separation between

    the object mirrors and the field mirrors or in other words, the distance light has to travel

    in the White cell before exiting. In the modified White cell shown in figure [2.7] above,

    this same delay is produced in the White cell containing arms A and B along with the

    MEMS. The delay increment of our White cell-based tapped delay line, , discussed in

    section 2.3, will be produced in arm C. We modify arm C shown in figure [2.8] to

    produce a longer time delay by increasing the separation between the MEMS and mirror

    C. We will refer to arm C in our discussion as the delay arm.

    Beams circulating in the White cell TDL can either bounce back and forth

    between mirrors A and B or get sent to the delay arm. The delay produced in the White

    cell A-B-MEMS will be considered as a null delay or zero delay and we will refer to this

    White cell as the null cell. Beams that visit the delay arm get delayed by for each round

    trip in arm C compared to the time it takes to make a round trip to B. Hence by

    controlling the number of times a beam is sent to the delay arm, we can control the total

    delay a beam accumulates before it exits the White cell.

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    2.6.2 Design ConstraintsDelay arm design

    In order to maintain the imaging conditions in the delay arm, an even number of

    lenses or a lens train is added between the field lens and mirror C. Other methods of

    producing time delays in the White cell, such as using glass or silicon blocks [62] have

    been demonstrated.

    The lens train contains a group of lenses placed such that the first lens, lens1, is

    located at a conjugate plane (CP) of mirrors A and B, and that is at the same distance

    from the MEMS. The second lens is identical to lens1 and is placed at a distance equal to

    twice their focal length (2fdelay). Figure [2.9] describes the optics layout of the delay arm

    along with the locations of the produced images in the arm.

    Figure 2.9: Delay arm showing the image locations produced by each lens

    First the field lens sees the MEMS as an object and forms a virtual image of the

    MEMS at a plane located behind the MEMS (1

    st

    image in the figure). Lens1 then sees

    this image as an object and produces a real image of the MEMS between lens1 and lens2

    of the delay arm (2nd image in the figure). The second lens in the lens train, in turn treats

    this image as an object and produces an image of the MEMS (3 rd image in the figure)

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    with a magnification of -1 back at the same location as the 2nd image through mirror C.

    The lenses are chosen such that the second image is located at a distance equal to the

    radius of curvature of mirror C away from mirror C. The rays forming the image then

    follow the same path backwards to the MEMS with a total magnification of -1, hence,

    conforming to the White cell imaging conditions.

    Note that the total delay produced is due to the extra distance that the beam

    travels, which is highlighted in blue in the figure. The delay produced is always going to

    be a multiple of. The delay increment, , can be calculated as shown in equation (2.4):

    ++=

    2

    2

    1

    12nc

    thnc

    thc

    D [2.4]

    where c is the speed of light in air,D is the round trip distance = 8 * fdelay, th1 and th2 are

    the thicknesses of the lenses 1 and 2 in the delay arm and n1, n2 are their refractive

    indices respectively.

    Field lens design

    There are two constraints that are considered when determining the separation

    between the MEMS and the field lens. We first have to make sure that the optical mounts

    housing both pieces can fit side by side. Second, we have to make sure that all the beams

    leaving the MEMS and diverging towards any of the White cell mirrors will be captured

    by the field lenss clear aperture. As a rule of thumb, we always try to keep the

    separation between the MEMS and the field lens as small as possible in order to reduce

    the overall size of the entire system.

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    Input beam considerations

    As beams circulate in the White cell, they get focused onto on a column of spots

    on the MEMS pixels at each bounce. The size of the focused spot is critical in the

    design of the White cell components. The spot size has to be small enough to fit on the

    MEMS pixel to avoid any power loss but not so small that it diverges too fast and gets

    apertured at the optics used.

    Both constraints were considered when designing the input optics. The input

    system is designed to produce an input spot size such that the MEMS pixel captures >

    99.99% of the beams energy. Additionally the pitch between adjacent beams is set to

    match the pixels pitch. In our calculations we approximate the input beam with a perfect

    Gaussian beam with a beam waist ofo. This approximation holds with little error since

    the beam enters the input system from a single mode fiber array.

    We calculate the ratio between the spot size and the pixel size by finding the ratio

    between the power landing on the MEMS pixel and the total power of the same Gaussian

    beam. We assume square pixels with dimension, a, to simplify the calculations. The

    electric field of a Gaussian beam is represented by the following equation:

    o

    yx

    eAyxE

    22

    ),(

    +

    = [2.5]

    where A is a constant and x and y are the beams position variables. We will drop A in

    the remaining calculations as it wont affect the final result. To calculate the power ratio,

    we integrate the intensity of the Gaussian beam over the pixels area and divide by the

    total power [11].

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    =

    dyedxe

    dyedxe

    P

    P

    oo

    oo

    yx

    a

    a