SPIE Proceedings [SPIE Integrated Optoelectronic Devices 2006 - San Jose, CA (Saturday 21 January 2006)] Optical Components and Materials III - Tunable optical true time delay generator

Tunable Optical True Time Delay Generator For Phased Array Antenna

Olukayode Okusaga*+, Weimin Zhou* , and Gary Carter+

* US Army Research Laboratory

Sensor and Electron Devices Directorate AMSRD-ARL-SE-EM

2800 Powder Mill Rd., Adelphi, MD 20783

+ University of Maryland, Baltimore County 1000 Hilltop Circle, Baltimore, MD 21250

ABSTACT

We present an application of fiber Bragg gratings as tunable optical delays in

transmission for use as true-time-delay line in a RF-Photonic phased array antenna. Most delay line applications using fiber gratings require that they be used in reflection mode and they can provide only discrete variation of time delay. It also requires the use of bulky and expensive optical circulators. We have designed an optical true time delay array generator using fiber gratings in cascading transmission mode for such applications which significantly simplified the system and lowered the cost. A wavelength tunable laser is used as the light source. The laser light is modulated by an RF-microwave input signal, then enters into the optical true time delay array generator to provide a sequence of time delays ∆t, 2∆t,…n∆t. The goal is to obtain large group delay ∆t with low loss and with the capability of tuning ∆t continuously by varying the wavelength of the laser. We combined an apodized grating profile, large index step and increased grating length to achieve our goal. We fabricated and tested the grating with about 100mm length which showed at least ∆t=60 ps tunable time delay range. We have demonstrated the applicability of the transmission-mode fiber Bragg gratings in an optical true-time-delay type of phased array antenna.

1. INTRODUCTION

Photonic technologies provide new opportunities for future ground-based, naval and airborne phased array radar and communication antennas. The array must meet stringent requirements for bandwidth, frequency agility, EMI immunity, size, weight and cost. These engineering challenges are difficult or impossible to meet using conventional RF/electronic methods. One of the challenges is the beam-forming using true-time-delays to control and steer the phased array antenna with high resolution, high speed, and high precision. There are hundreds of previously proposed optical true-time-delay generation schemes for a photonic antenna system. For a N-element array with M-bit steering resolution, most of these systems require either 1 laser-transmitter with 1 x N beam splitter, N optical switch matrix to switch 2M fixed optical time delay lines, or a multi-

Optical Components and Materials III, edited by Michel J.F. Digonnet, Shibin Jiang, Proc. of SPIE Vol. 6116, 611608, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.644802

Proc. of SPIE Vol. 6116 611608-1

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wavelength system with 2M laser-transmitters 2M x 1 combiner, a WDM-switch/channelizer, 2M optical time delays, and N-channels with a WDM switch/distributor. Therefore, for each antenna element, 2M time-delays can be independently provided. However, a system with N=1000 elements and M=10 bits requires millions devices which is cost prohibited for such a system.

A new type of simplified optical true-time-delay (TTD) array generator architecture concept for microwave beam-forming and steering has been introduced [1]. This architecture of the true-time-delay array generator eliminates the need for optical switches, 1xN splitters, multiple lasers or any Wavelength Division Multiplexing device. Therefore, the cost of such a system can be reduced significantly. We have previously demonstrated such a system using free-space optics by making a variable time delay ∆t with a small mechanical displacement between mirrors and duplicated that delay to 2∆t, 3∆t,…N∆t in optical domain.

In this work, we have replaced the free space TTD array generator with optical fiber

system using fiber gratings in cascading transmission mode as a wavelength tunable variable TTD line. The advantage is to eliminate the mechanical parts so that the tuning speed of the delay change is much faster and the system is more reliable. This paper is focus on the design and development of such fiber based variable TTD system.

2. DESIGN OF THE FIBER GRATING TIME DELAY LINE 2.1. Design goals for the fiber Bragg gratings

In our phased array antenna, we employ a fiber Bragg grating as a tunable delay device to steer the microwave beam. A fiber Bragg grating is a section of optical fiber with a periodic variation in its index of refraction along its length. This variation in refractive index can be accomplished by unevenly exposing a photo-sensitive optical fiber to ultra-violet (UV) radiation. Therefore, by varying the intensity of the UV radiation along the length of the fiber, we can create the spatially varying refractive index that leads to Bragg effects.

In most applications, fiber Bragg gratings are used in reflection mode. Previously, others have demonstrated a true time delay system using fiber Bragg gratings in reflection mode. That is, the optical beam is sent in through one end of the fiber, travels some distance along the fiber to the Bragg grating position, and then is reflected back out the same end from which it entered. Unfortunately, the use of Bragg gratings in reflection mode only provides a discrete fixed time delay. In addition, it requires expensive and bulky optical circulators. This poses a problem for size, cost and complexity of the phased array antenna system. We attempt to avoid these problem by employing fiber Bragg gratings in transmission mode instead. The fiber grating can be considered as a one dimensional photonic band gap (PBG) structure. If the wavelength of the propagating light is close to the band edge of the band gap, a dispersion of the propagating light may occur, causing a time delay of the light propagation. To analyze the delay of effects of the fiber Bragg grating, we employ the coupled mode theory. This theory if useful in analyzing the behavior of electromagnetic (EM) waves in a weakly



coupled waveguide medium [2]. A Bragg grating can be said to be weakly coupled if the spatial variation in refractive index is small relative to the mean effective refractive index of the medium. This condition is met by all Bragg gratings used in our phased array antenna and so use of the coupled mode theory is appropriate.

Through the coupled mode theory, we understand the fiber Bragg grating induces

an additional time delay in an EM wave traveling through it by coupling forward and backward scattered waves induced by reflections caused by changes in the refractive index of the medium. The strength of this coupling effect is dependent on the detuning between the wavelength of the EM wave and the wavelength of the spatially varying periodic perturbations of the refractive index. This is, therefore, a necessarily wavelength dependent effect. We then vary the wavelength of the optical carrier to alter the time delay through the grating. Therefore we can use the fiber Bragg grating as the variable delay unit in our simplified phased array antenna architecture.[1]

Designing such gratings is challenging because of the strict Kramers-Kronig

relationship and Fresnel-like reflections lead to rapid oscillations in group delay versus wavelength. Thus ordinary fiber grating will have the problems of small or uneven delay, large intensity loss, etc. The goal is to design Bragg gratings that provide large and smooth variations in time delay over a wide bandwidth without large optical loss in the transmission. 2.2. Coupled Mode Theory As stated above, in designing our fiber Bragg gratings, we relied on the coupled mode theory. Detailed treatments of coupled mode theory can be found in many texts ([3], [4], [5]). What follows is a brief overview that explains the numerical methods used in designing our gratings. Following the work of Skaar [3], we assume the fiber is lossless, single mode in the wavelength range of interest and that the difference between the indices of refraction of the core and cladding is small. We are thus able to deal simply with the scalar wave equation governing the transverse components of the electric field [4]. We treat the electric field as an x-polarized wave with frequency ω and propagating in the z direction with wave number β. We right the total field as a superposition of forward and backward traveling waves. ),()(),()(),,( yxzbyxzbzyxEx Ψ+Ψ= −+ (1)

Here ±b (z) represent the z dependence of both waves and ),( yxΨ represents the transverse profile of the mode and satisfies the scalar wave equation:

0),( 2222 =Ψ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+∇ βyxnkt (2)

where ),(2 yxn is the unperturbed refractive index of the fiber and k = ω/c is the wave number of the mode in vacuum. The total field must satisfy the following equation for the perturbed fiber:



0),( 2

2222 =⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

∂∂++∇ xt E

zyxnk (3)

Substituting (1) into (3) and using (2) yields:

( ) ( )[ ]( ) 022222

2

=Ψ+−++Ψ+ −+−+ bbnnkbbdz

d β (4)

Multiplying by Ψ* and integrating over x and y gives:

( )( ) 0)(2 112

2

2

2

2

=++++ −+−+ bbzDkn

dz

bd

dz

bdcoβ (5)

where D11 is given by:

( )

∫

∫Ψ

Ψ−=

dA

dAnnn

k

zD co

2

222

11

2)( (6)

Here nco is the core index of refraction. Equation (5) can be decomposed into the following pair of first order linear differential equations:

( )

( ) +−−

−++

−=++

=+−

biDbDidz

db

biDbDidz

db

1111

1111

β

β (7)

For our purposes, D11 can be represented as a quasi-sinusoidal function of the form:

)(2

exp)(2

exp)()( *11 zzizzizzD σπκπκ +⎟

⎠⎞

⎜⎝⎛

Λ−+⎟

⎠⎞

⎜⎝⎛

Λ= (8)

where κ(z) is a complex slowly varying function of z representing the envelope of the sinusoidal index modulation of wavelength Λ and σ(z) is a real slowly varying function of z representing the dc perturbation of the refractive index. For the sake of simplicity, we define two new field amplitudes u and v as

⎟⎟⎠

⎞⎜⎜⎝

⎛′′−⎟

⎠⎞

⎜⎝⎛

Λ−=

⎟⎟⎠

⎞⎜⎜⎝

⎛′′+⎟

⎠⎞

⎜⎝⎛

Λ+=

∫

∫

−

+

z

z

zdzizizvzb

zdzizizuzb

0

0

)(expexp)()(

)(expexp)()(

σπ

σπ

(9)

By substituting (8) and (9) into (7) and ignoring rapidly oscillating terms that do not affect the field amplitudes we obtain the coupled mode equations:

uzqvidz

dv

vzquidz

du

)(

)(

*+−=

++=

δ

δ (10)

where Λ−= πβδ is the wave number detuning and the coupling coefficient q(z) is

given by:



⎟⎟⎠

⎞⎜⎜⎝

⎛′′−= ∫

z

zdzizizq0

)(2exp)()( σκ (11)

We can see from (10) that if the coupling coefficient is zero, the forward and backward traveling modes are not coupled. This represents the case of the unperturbed fiber.

In order to solve (10) for arbitrary index perturbations, we employ the transfer matrix method [3]. This method involves breaking the grating into several short sections. We then treat each subsection as uniform, evaluating u and v assuming constant q. From this calculation we extract an effective transfer matrix for each sub section. This matrix is given by:

⎥⎦

⎤⎢⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∆−∆∆

∆∆+∆=⎥

⎦

⎤⎢⎣

⎡∆+∆+

)(

)(

)sinh()cosh()sinh(

)sinh()sinh()cosh(

)(

)(* zv

zu

iq

qi

zv

zu

γγδγγ

γ

γγ

γγδγ

where ∆ is the length of the given subsection of fiber. By multiplying the transfer matrices for each subsection, we obtain a total transfer matrix that maps the modes at the output of the fiber grating to the modes at the input.

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡)0(

)0(

)(

)(

v

uT

Lv

Lu

Here L is the length of the fiber grating. Our simulations involve determining T for a given index perturbation profile and then calculating the resultant envelopes for the forward and backward propagating modes. 2.3. Simulation Results In running our simulations, our goal was to determine the effect of varying design parameters on the performance of our grating. First we modeled a uniform Bragg grating. As shown in Fig. 1 and Fig 2 below, the grating exhibits rapid fluctuations in both the delay and transmitted power at the edges of the stop band. These fluctuations are due to Fresnel like reflections in the grating. This is unacceptable when the grating are to be used in transmission mode as this is precisely the region that gives us the most delay with least power loss.



Group Delay v. Wavelength for a Uniform Bragg Grating

0

2000

4000

6000

8000

10000

12000

14000

1552 1552.5 1553 1553.5 1554 1554.5

wavelength (nm)

gro

up d

elay

(ps

)

Fig 1: Group delay v. wavelength for a uniform Bragg grating. The inset shows the same data for a narrower wavelength range so as to emphasize the fluctuations.

Transmission Coefficient v. Wavelength for a Uniform Bragg Gratinig

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1552 1552.5 1553 1553.5 1554 1554.5

wavelength (nm)

Tra

nsm

issi

on

Co

effi

cien

t

Fig. 2: Transmission coefficient v. wavelength for a uniform Bragg grating. The inset shows the same data for a narrower wavelength range so as to emphasize the fluctuations.

Zoom ed in Vie w of De lay

0

2000

4000

6000

8000

10000

12000

14000

1553.42 1553.44 1553.46 1553.48 1553.5

w ave le ngth (nm )

gro

up

del

ay (

ps)

Zoom ed in V iew

0

0.2

0.4

0.6

0.8

1

1553.4 1553.45 1553.5 1553.55 1553.6 1553.65 1553.7

w avele ngth (nm )

Tra

nsm

issi

on

Co

effi

cien

t



Apodization: To eliminate these fluctuations, we employ a method known as apodization. By gradually reducing the index strength at the edges of the grating, we can reduce fluctuations in both the time delay and transmission coefficient. However, apodization has the detrimental effect of reducing overall grating strength. We found the balance between delay smoothness and grating strength, as shown in Fig. 3, by applying a Gaussian index profile with a standard deviation equal to 30% of the fiber length.

Fig. 3: Time delay and transmission coefficient for Gaussian apodized grating. Overlaying both graphs highlights the region of interest where delay is slop is non-zero but transmission is high. Grating Length: We then investigated the effect of grating length on group delay. The results can be seen in Fig. 4. As expected, increased length led to greater delays We found that increased length led to both an increase in the relative delay and an

Fig. 4: Relative group delay for Gaussian apodized gratings of varying length.

Relative Group Delay for Gaussian Apodized Bragg Gratings

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1552 1552.5 1553 1553.5 1554

wavelength (nm)

rela

tive

group

del

ay (p

s)

L = 250 mmL = 125 mmL = 62.5 mm

Time Delay and Transmission Coefficient for Gaussian Apodized Bragg Grating

0

100

200

300

400

500

600

700

800

900

1552 1552.5 1553 1553.5 1554 1554.5

wavelength (nm)

del

ay (ps)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time delaytransmission coefficient



increase in the bandwidth over which the delay occurred. Perturbation Strength: Finally, we have determined the effect of varying the index perturbation ∆n. Plotted below are relative group delays for varying values of ∆n. The results are shown in Fig. 5.

Relative Group Delay for Gaussian Aphodized Bragg Grating

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

1551.5 1552 1552.5 1553 1553.5 1554 1554.5

wavelength (nm)

rela

tive

gro

up

del

ay (

ps)

delta n = 0.067%delta n = 0.033%delta n = 0.013%

Fig. 5: Relative group delay for Gaussian apodized gratings with different index steps. From our simulation results, it is clear that the ideal grating would have as great an index step as possible. It would also be as long as possible. Practically, these will be limited by the fabrication technique.

3. EXPERIMENTAL RESULTS 3.1. Fabrication and test of the gratings The fiber gratings were fabricated using conversional manufacturing technique. The manufacture of the gratings involved standard phase mask processes and an ultraviolet (UV) laser. Light from the UV laser was passed through the phase mask and incident upon the fiber to generate the index perturbations. The extent of the index change was related to the intensity of the UV light incidents on the specific section of fiber. The apordization profile is realized by spatially varying the UV light intensity. Due to the availability of the phase mask and UV laser source, we can only obtain 125 mm long gratings with a maximum delta n of about 0.033%. In our case, it is not the absolute delay of a CW beam through the fiber that wee need, but instead, the relative delay



induced in a 10 GHz RF signal superimposed unto the CW beams of different optical wavelengths.

To determine this induced relative delay, we modulated a CW beam with our 10 Ghz RF signal via a lithium niobate modulator. We then passed the modulated beam through a fiber Bragg grating before finally sending it to a photodetector. The electrical output from the photodetector was then passed into a network analyzer. We recorded the change in phase as the wavelength of the optical carrier was varied. Because the frequency of the RF carrier was much smaller than that of the optical carrier (~190 THz) and the characteristic frequency of the grating, we could approximate the group delay by the measured phase delay. Fig. 6 shows measured phase delay as a function of carrier wavelength.

Phase v. Wavelength for Bragg Gratings

-150

-100

-50

0

50

100

150

1551.5 1552 1552.5 1553 1553.5 1554 1554.5

wavelength (nm)

Ph

ase

(deg

rees

)

Fig. 6: Measured phase delay v. wavelength for a sample Bragg grating.

The chart suggests a maximum possible time delay of ~64 picoseconds. The useable time delay will of course be less than this as the signal experiences increasing loss in transmission mode as one approaches the central wavelength of the Bragg grating (~1553.0 nm). 3.2. Preliminary test of the phased array antenna

Finally, we implemented the phased array antenna by utilizing 14 near-identical fiber Bragg gratings as time delay elements in the TTD array architecture described in [1]. The center wavelength of all the gratings is approximately 1553.0 nm. We begin by modulating a continuous wave (CW) beam from a tunable laser via a lithium niobate



Phased Array Antenna Beam for 1661.3 nm carrier

ISO

4 degree angle

90

0

120

dB

30

N

Phased Array Antenna Beam for 1662.66 nm carrier

lB degree angle

90

dB

U

modulator. The modulated beam is then amplified by an erbium doped fiber amplifier (EDFA). Finally, the wave is transmitted to each node via a series of 1-by-2 splitters. At each node, the wave experiences a cumulative timed delay due to each Bragg grating. Our radio frequency beam is then transmitted by the antenna array as a superposition of 10 GHz waves from each node. To measure the shape and direction of the beam, we placed the phased array antenna at one end of an anechoic chamber. At the other, end we place a radar detector. By rotating the phased array antenna and measuring the received power at the detector, we can determine the beam profile and direction relative to the plane of the antenna. We performed such measurements for a several wavelengths around the central wavelength of our fiber Bragg gratings. Figs. 7 and 8 below show the results for the two extremes of the beam azimuthal angle, which gave a steering angle of 12 degrees.

Fig. 7: Measured Beam Profile from Antenna with an optical carrier wavelength far from grating stop band.

Fig. 8: Measured Beam Profile from antenna with an optical carrier wavelength close to grating stop band.

Proc. of SPIE Vol. 6116 611608-10


Our results, though modest, clearly demonstrate the feasibility of using fiber Bragg gratings in transmission as time delay elements in a phased array antenna. The Bragg gratings used were far from optimal. We were limited to index perturbations of 0.05% as well as to gratings of only 125 mm. As a result, we were forced to use wavelengths in the very high dispersion slop region to achieve sufficient time delays. Unfortunately, even small differences in the central wavelength and bandwidth of each grating led to very different time delays as we approached the high-delay/high-dispersion region of the gratings. These large variations in the time delays of each grating led to decoherence of the nodes and ultimately a very poorly formed beam. Further work will involve remedying this situation by developing longer gratings with greater index steps. Also, combinations of chirping and more complex apodization profiles should lead to gratings with broader bandwidths and shallower slopes while still providing adequate time delays to achieve greater steering.

CONCLUSION

In conclusion, we have designed and demonstrated a tunable optical true time delay array generator based on fiber Bragg gratings that were used in transmission mode. We have also made a proof of the principle demonstration of steering of a small scale phased array antenna beam with the optical true time delay array generator. This type of fiber based RF-photonic true time delay array generator greatly reduces the cost and complexity of the phased array antenna system. In the future, we will continue to develop this type of RF-photonic passed array antenna by improving the performance of the tunable optical true-time delay generator for tuning range, delay uniformity, loss reduction, etc.

ACKNOWLEDGEMENT

We would like to thank Dr. Steven Weiss, Dr. Robert Dahlstron, and Michael Stead for their help for patch antenna design, and antenna pattern measurements. We would like also to thank Prof. Jacob Khurgin at John Hopkins Univ. for helpful discussion for Bragg grating modeling. The fiber gratings were custom manufactured by AVENSYS.

REFERENCES

1. W. Zhou, S. Weiss, “A Low cost Optical Controlled Phased Array Antenna with Optical True Time Delay Generation,” Proc. SPIE, vol. 4998, pp. 133-138, Jan. 2003. 2. J. Zhao, “An Object-Oriented Simulation Program for Fiber Bragg Gratings,” doctoral thesis Rand Afrikaans University, Johannesburg South Africa, Oct. 2001 3. J. Skaar, “Synthesis and Characterization of Fiber Bragg Gratings,” Diploma Thesis, the Norwegian University of Science and Technology, Dec. 1997. 4. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983). 5. L. Poladian, “Resonance Mode Expansions and Exact Solutions for Nonuniform Gratings,” Phys. Rev. E 54, 2963—2975 (1996).

Proc. of SPIE Vol. 6116 611608-11


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SPIE Proceedings [SPIE Integrated Optoelectronic Devices 2006 - San Jose, CA (Saturday 21 January 2006)] Optical Components and Materials III - Tunable optical true time delay generator