Naval Research Laboratory IIKWashington, DC,20375 5000

NRL Memorandum Report 6741

0

N Fiber Optic Feed

DENZIL STILWELL, MARK PARENT AND LEw GOLDBERG*

Radar Analysis BranchRadar Division

*Optical Techniques BranchOptical Sciences Division

November 6, 1990

SD

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED1990 November 6 Memorandum 1985-1990

4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Fiber Optic Feed 53-0611-A0

6. AUTHOR(S)

P. D. Stilwell, M. G. Parent, L. Goldberg

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) B. PERFORMING ORGANIZATIONREPORT NUMBER

Naval Research Laboratory NRL MemorandumWashington, DC 20375-5000 Report 6741

9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/ MONITORING

AGENCY REPORT NUMBER

ONT, Department of the Navy800 N. Quincy StreetMr. Jim Hall (ONT-214)Arlington, VA 22203

11. SUPPLEMENTARY NOTES

*Optical Techniques Branch, Optical Sciences Division12a. DISTRIBUTION /AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution unlimited.

13. ABSTRACT (Maximum 200 words)

This report details a Fiber Optic Feeding (FOF) concept for beamforming in phased arrays.Experimental data is presented which validates the basic underlying assumptions. Elaborations on thisbasic concept are presented which illustrate the power of this new approach to beamforming. Allradar and communications functions have a realization in the architecture, including monopulse, mul-tiple beams (on same or different frequencies), beamspace adaptivity (open or closed loop), and wide-band beam and null forming. It presumes an active antenna aperture but uses TR modules containingno phase shifters. Identical TR modules are used at each of the antenna elements and which require aminimum of digitally controlled components. The architecture is appropriate for arrays on any plat-form and accommodates sparse and/or conformal designs without the necessity of introducing signifi-cant microwave modifications. The approach can use existing state-of-the-art components to afford-ably implement high performance arrays. Of particular importance is the capability of forming timedelay beams from an array without the use of phase shifters.

14. SUBJECT TERMS 15. NUMBER OF PAGES

48

Array antennas, Fiber optics 16. PRICE CODETime delay beamforling

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT

TTrT ACC'rrTt n UNCLASSIFIED UNCLASSIFIED SARNSN 7540-01-280-5500 Standard Form 298 (Rev 2-89)

P rtubed by Af%1S id 139-I2q 102

CONTENTS

I INTRODUCTION ........................................................................................... 1

II FOF SYSTEMS CONCEPT ............................................................................... 2

I1-1 Optical Corporate Feed ........................................................................... 211-2 Optical Beamsteering .............................................................................. 411-3 K-Space/Beamspace Diagrams .................................................................. 6

11I EXPERIMENTAL RESULTS ............................................................................. 7

IV MULTIPLE BEAM FORMATION ...................................................................... 10

IV-1 Dependent Beams (Pattern Synthesis) ......................................................... 10V-2 Independent Multiple Beams (Anti-Jam) ..................................................... 11

IV-3 Time Dependent Beams (Chirp) ............................................................... 13IV-4 True Time Delay Beams (Wideband) ......................................................... 14

V CONCLUSIONS AND FUTURE EFFORTS .......................................................... 16

VI APPENDICES ................................................................................................ 18

VI-I Optical Detection and Mixing ................................................................. 18VI-2 Faraday Cell ....................................................................................... 18VI-3 Bragg Cell ......................................................................................... 18VI-4 Corporate Fed Array ............................................................................. 19

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FIBER OPTIC FEED

INTRODUCTIONThis report concerns R&D performed under the Surface

Surveillance Block Program at NRL directed to the use of opticaland fiber optical technologies in the implementation of phasedarray systems, particularly radars. Arrays consist of a set ofdiscrete radiating elements wherein the signal driving eachelement, whether from the transmitter or from a reflection from atarget in the far field, is a time shifted version of the signalat any other element. Time delay arrays are difficult toimplement directly (save for a mechanically scanned, space fedarray) so present day emphasis has been on phased arrays, inwhich the signals are delayed at most by one cycle at theradiating frequency. This is normally accomplished with phaseshifters, of either a ferrite or a diode type, located at eachantenna element.

The Fiber Optic Feed (FOF) program represents analternative method of obtaining a discrete set of signals withthe proper phase shifts for electronic beamforming. This methodimpresses the microwave frequency on an optical carrier in oneleg of an interferometer. In the other it generates a scannedoptical beam. The superimposed optical fields are sampled with afiber array. The optical carrier from each fiber signal isstripped off by heterodyne detection after it has been routed tothe proper antenna element. The resulting set of signalsexhibits the proper phase shifts for directing beams anywhere inthe antenna half space. The technique exploits the similaritybetween optical beam scanning at a wavelength scale of the orderof a micron, and microwave beam formation at a scale of 1-100cm. This process configures an optically scaled version of thearray antenna. Very small time delays occurring from a slightdivergence angle between the reference and scanned beam createthe requisite phase shifts to steer microwave beams. Quitesurprisingly, a simple elaboration of the system makes tha phaseshift from element to element dependent on microwave frequency insuch a manner that time delay beamforming can be realized.Consequently, this architecture is capable of wide instantaneousbandwidth for electronically steered beams at large angles frombroadside with no broadening due to bandwidth.

The successful development of the FOF approach wouldhave a significant impact on the utility of array antennas inNaval systems. It would allow for a significant reduction inweight and size while increasing flexibility due to thereplacement of microwave transmission lines with fiber optics.It would simplify requisite transmit-receive (TR) modules drivingthe antenna elements by an elimination of the phase shiftersection and accompanying digital control circuitry. It woulddecrease vulnerability to RFI and EMP while being only marginallymore susceptible to ionizing radiation. These properties can be

Manuscript approved August 30, 1990

translated into reduced system cost and complexity, allowing awider range of Naval platforms to be equipped with highperformance array antennas/radars than heretofore appearedpracticable.

Recent efforts have solidified the conceptual basis andprovided experimental confirmation of fundamental ideas. SectionII introduces some of the important concepts upon which the FOFarchitecture is based. Section III presents experimental resultssupporting the basfc assumptions of the program. Section IVexplores some of the ramifications of the architecture in termsof the implementation of common radar functions. Section Vsummarizes the contents of the report and points to the nature offuture investigations. Section VI contains a set of appendicesrelating to particular device characteristics which might not befamiliar to the reader.

II FOF SYSTEMS CONCEPTThe basic concepts behind the FOF architecture involve

building blocks from two distinct disciplines, microwaves andoptics. This section will discuss some of the concepts leadingto a multidisciplinary design. Additional material in theappendices will elaborate on some particular building blocks.

II-1 Optical Corporate FeedThe method of implementing the equivalent of a

corporate feed structure is key to the overall FOF concept.Figure II-1 shows the essence of this concept, namely, thecoupling of optical beams to a two dimensional array of fiberswhich are in turn connected to a much larger array, the microwaveantenna, after detection. The fibers sample incident opticalfields and at the other end, after heterodyne detection,regenerate a microwave beam by the superposition of microwavesignals from the array. In order to generate the microwavesignal it is necessary to have two optical wavefronts incident onthe fiber optic pickup. One is the unshifted optical carrier andthe other is both frequency shifted and propagating at an anglefrom the first. The field at a given fiber optic cable inputaperture, i, located in the fiber optic (FO) pickup plane isgiven by

E(y i ) = A, expj(K1 .y1 +i 1t) eqn II-1+ A2 expj(K2ey, + n 2t)

where y, is a vector in the y plane (the vertical direction inthe figure) to the ith fiber, the A's are the amplitudes of thelight waves, the K 's are the propagation vectors of the wavesand the n's their angular frequencies. The fiber array samplesthese plane waves and connects to a larger but scaled version ofthe samples, the microwave array elements. The two lightwavecomponents traverse nearly identical paths after beingconstrained to a fiber. The relative phase varies with distancedown the fiber in proportion to the difference wavenumber between

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the components. Since all other fibers map samples of the twowavefronts in the same manner, fiber lengths need be identicalonly to an accuracy small relative to a reciprocal differencewavenumber, i.e. as l/(K,-, 2 ) = 1/AK . This is proportional tothe microwave wavelength (A). A detector at the antennabackplane square law detects E to regenerate a microwave field atthe ith antenna element proportional to

a cos(AK.yi + Ant) eqn 11-2= a cos(k.Yi + Wt)

where now the spatial term is written in the antenna elementvectors, Y,. Other terms at light and doubled light frequenciesdo not flow in the microwave circuit. The difference terms, ofwavenumber and frequency (k,w), denote the microwave wavenumberand frequency respectively. The amplitude, a, is a function ofthe individual A's and the detector properties (see appendix).From this equation it is seen that the wave propagation vectorcreated at the antenna is a scaled version of AK. The microwavefrequency w is the difference, An, between the optical beamfrequencies.

The antenna elements are considered to be canonicallyspaced at A/2. An equivalent spacing, A/2, of the optical fibersis not possible. In fact, if normal diameter fibers are used,say 125gm, they are spaced some 150A apart. For this reason avery small angle change between the incoming optical waves causesa large change in the sine of the angle of the microwave beam.From the condition that equal phase shifts occur between theoptical and the microwave sample points, one can write, fromfigure II-1,

(Ay/x)sine = (AY/A)sine eqn 11-3

where e is the angle of divergence between the optica± waves ande is the resulting launch angle from the antenna. For Ay = 150Aand AY = A/2 one notes that

sin8 = (1/300) sine

and a "magnification" of 300 exists in the fanning out of thecorporate feed. This implies that the total angular change indivergence optically is less than 4 milliradians. (Greaterdivergences actually yield real quantities but a more complicatedanalysis is necessary.) For example, a 0.19° divergence betweenthe two components will induce a r phase shift between adjacentfibers. This is the shift required between broadside andendfire. To a very good approximation the two optical beamspropagate along the same direction, diverging at most by 4milliradians. This has the advantage that nearly the same fiberoptic waveguide mode is excited by the two waves and they can beexpected to have a long correlation path in fiber. It will benoted that the two optic waves do not travel the same paths in

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the fiber. Each travels an undulating path corresponding to aguided mode. The two optical components are subject to similarpropagation conditions such that the relative input optical phaseshifts are preserved in the microwave signals generated.

Equation 11-2 indicates that the microwave arrayelements must be positioned in a like manner to that of thefibers although with a larger spacing. The fiber spacing wouldnormally be that obtained by close packing a large number offibers and polishing the ends. This leads to a hexagonalrelationship of a fiber with its nearest neighbors. For a filledarray small errors in the actual spacing of the fibers would notcause an appreciable error in the field at the microwave elementbecause of the strong mutual coupling of the elements which wouldin effect interpolate the proper field. For a sparsely filledarray however, the mutual coupling would not perform such acorrection and the microwave element might have to be slightlyrepositioned to be in the proper place. Due to the variabilityof fiber diameters the lattice of input samples would be locallyhexagonal but globally somewhat random. This feature could beexploited to achieve non-periodic arrays which would reduce theeffect of grating lobes from the microwave array. For sparselyfilled arrays where there is little mutual coupling betweenmicrowave elements, this technique is useful in suppressingvariation in sidelobe level, at the cost of increasing theaverage sidelobe level.

11-2 Optical BeamsteeringSynthesis of an optical beam control system now

devolves into a problem of creating the two variably divergentoptical waves. Figure 11-2 illustrates a method of creating twoindependently controllable plane waves. This is a Mach-Zehnderinterferometer in which a rotation of either of the mirrors willchange the relative divergence of the waves impinging the fiberoptic pickup plane. The solid lines in the diagram represent therays for a broadside beam. The dashed lines indicate a newmirror position and a new beam ray through the upper leg leadingto a spatial phase gradient across the fiber array. Mechanicalrotations limit beam switching speed but can be used insituations where very slow response is adequate.

Figure 11-3 illustrates the first beamformingimplementation concept which evolved in this study. It is of aMach-Zehnder type in which a low frequency acousto-optic beamdeflector (AOBD) in the upper leg scans a spot in the Fourierplane of the cell which in turn alters the arrival direction of aplane wave at the fiber optic pickup plane. The lower leg of thecircuit simply offsets the light incident by a microwavefrequency by use of an acousto-optic modulator (AOM). Theassembly is therefore an implementation of the FOF ideas. Thepreference for AO (acousto-optic) modulators over EO(electro-optic) ones is due primarily to relative maturity ofdevelopment. AO devices of the types required are far and awaythe most highly developed active, signal processing components

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available to the optical designer. There are, however, a numberof drawbacks to the indicated circuit. The microwave AOM cellexhibits low diffraction efficiency, exhibiting of order 10 dBthroughput loss. Also, any change in the microwave frequencywill dramatically shift the position of the bottom beam. Anotherproblem is that it does not provide beam steering in twodimensions. A major objection is that it shows no method ofreceiving, only of transmitting. If the AO cell frequency ischanged to provide the local oscillator frequency for the receivemode, beam deviation would be extreme and the system would notwork.

Receive beamforming is accomplished by pre-phaseshifting the set of LO (local oscillator) signals. Therelative phase shifts from the LO signals and the antenna elementdelays combine and transfer to the IF signal. When appropriatephase shifts are arranged on the LO to be conjugate to the timedelay shifts, simple summing amplifiers are all that is needed tocreate a coherent array signal output for a given arrivaldirection.

An improved circuit is illustrated in figure 11-4.Here the frequency shifting AOM is relegated to the back leg ofthe interferometer circuit coupling a master laser diode to aslave. As a result, the throughput reduction due to the AOM ismade insignificant except insofar as the slave diode can beinjection locked. Injection locking requires about 1% of theoutput power of a diode laser. To the right of the lasers, theforward legs, two AOBDs are used to deflect the beams and therebycontrol their divergence. One AOBD would suffice but two areused for symmetry and for easy extension to a 2D version. Theuse of two AOBDs has an advantage in a one dimensional system inthat if both are driven at the same frequency (e.g. 80 Mhz) andare both operated in an upshift mode, the beam steering frequencydoes not appear on the radiated microwave signal because thedifference frequency is used. Since the AOBDs are in excess of80% efficient, optical losses are minimal.

Figure 11-4 also shows a conceptualization of the TRmodule which could be used in the system. The light from theparticular fiber mapped to a given array element is detected byeither a PIN diode or an avalanche photodiode (APD). Since thesignal level is quite low (probably not greater than -40 dBmsince higher output powers would destroy an APD) a couple ofamplification stages are shown to raise the signal power up tomicrowave mixer LO levels. A diode switch controlled by a TRlogic line switches to the power amplifier for the transmit stateor to the mixer for the receive state. The output of the mixeris coupled to a common IF line by use of a Lange coupler.

Figure 11-4 also indicates that the AOM consists of AOcells. Figure 11-5 illustrates the circuit intended. In thiscircuit light from the laser diode on the left is doublydiffracted by Bragg cells. By choosing the feeding pointscorrectly it is possible to obtain a double upshift of thedriving frequency with little or no output angular deviation and

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no transverse beamshift with drive frequency. An alternatefeeding arrangement achieves double angular deflection with nofrequency change. These two designs form the basic buildingblocks for the FOF optical system. In the AOM form each microwaveBragg cell may have an octave bandwidth with reasonableefficiency, e.g. 1-2 GHz with 25-30 %. Thus well in excess ofthe requisite 1% energy can be coupled into the other diode overan octave of bandwidth. (The Faraday cell has been omitted forsimplicity, see the appendix VI-2.) Consequently, the circuitshould be able to perform frequency agile beamforming over anoctave bandwidth. In the beam deflector configuration lowfrequency (TeO2) cells can be used which will operate at > 80%efficiency. Operating frequency range is not important since theangular deviations required are quite small.

It is instructive to do a light budget calculation forthe above circuit in order to estimate the level of microwavesignal available after the detector. In the back leg anattenuaticn of approximately 20 dB results from the two AO cellsand reduces the available light to be injected to about the 1%required. In the forward legs each laser diode can emitapproximately 10 mw of signal power. Figuring the AOBD loss at 1dB and the beam splitter loss of 3 dB brings us to the fiberarray with +6 dBm from each leg. An estimate of the powerdivision loss when divided into a 10x10 array would be 20 dB, butonly about 10% of the total light intercepts the fiber cores, a10 dB loss. Estimating mismatch and propagation losses at 3 dByields a light power of -27 dBm from each leg at the detectorinput. Using the equation for the heterodyned mixed differencefrequency power from the appendix,

p = P1P2R2G2r/2 eqn 11-4

with G = 30, r = 50 ohms, and a responsivity, R, of 0.5 amp/wattyields a microwave signal of -46 dBm. The effective conversionloss, P/P , is 19 dB. Future arrays might need be 100x100 butimproved lasers should be available with about 100 mw yieldingagain, -46 dBm of microwave power. This is some 65 dB above thenoise in a 1 MHz band with 3 dB noise figure. Neodymium YAGlasers presently exist with these levels of power.

11-3 K-Space/Beamspace DiagramsFigure 11-6 shows a method of obtaining 2D beam

deflections using two AOBDs. By the simple act of rotating oneof the AOBDs by 900 it is possible to steer beams in anydirection. Both AOBDs may be contained in the same leg of theinterferometer. They are shown here in different legs forclarity. This can be seen if one considers the divergence of thetwo plane waves by the artifact of considering what would happenif a Fourier transform lens were inserted conceptually one focallength in front of the fiber array aperture. From basic opticsplane waves are then brought to a focus in the focal plane. Twospots of light will be generated, see figure 11-7, one

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corresponding to each of the incident plane waves. The vectorconnecting the two spots is proportional to the projection oftheir difference wavenumber in the plane of the fibers and thisdetermines the phase gradient at the microwave aperture whichcontrols the beam direction. It is therefore proportional to thequantity AK in equation 11-2 above. This construct can be usedwith any number of frequency components in the beamsteering cellsand is the definition of a K-space diagram.

The solid circle in Figure 11-7 on the x-axisindicates the point where light would focus for one of the wavesif a lens were inserted. The x-axis is the locus of all possiblepositions this spot could occupy. The distance from the y axisis proportional to the deviation from the central operatingfrequency, e.g. 80 Mhz. A similar situation exists for they-axis open circle. The vector connecting the two circles isrelated to the divergence angle or projection onto the fiberoptic pickup plane, i.e. AK. The angle between the x-axis andthe maximum gradient of phase with position is the azimuth angleand the length of the vector is proportional to that gradient.These two parameters are the natural coordinates of beamspace.In a polar plot where azimuth angle is measured from the x-axisand length of the vector is related to elevation angle, the K-space quantities can be reinterpreted in terms of the far fieldposition of the main beam. The diagram indicates the center ofthe far field pattern. Other factors such as the size of thearray, whether it is filled or not, etc. will dominate the actualbeamspace pattern shape by a convolution of their angularspectrum with the beam center "delta" function. The open/closedcircles denote the master laser light frequency and upshiftedlight frequency. From the K-space representation one cancalculate the actual radiated frequency as the difference encodedby the two types of circles, plus the difference between the xand y vernier frequencies.

III EXPERIMENTAL RESULTSThe first experimental arrangement studied is

diagrammed in figure III-1. This circuit has a potentialadvantage in that the frequency offset between the two legs ofthe modified Mach-Zehnder interferometer is obtained by sidebandinjection locking techniques and does not require a separateoptical component (e.g. an AO cell) to modulate the lightemanating from the master laser diode. Direct modulation of oneof the laser diodes provides FM sidebands to which the slavelaser is be locked. The figure shows the monitoring optics usedin the adjustment and tuning of the laser diodes. An 8 elementarray of fibers was fabricated to interface to an 8 elementmicrowave array to allow experimental verification of the properoperation of the circuitry.

Instead of actually connecting the output of the fiberarray to a linear array antenna, a parallel plane microwave lenswas used, figure 111-2. The entire perimeter of the "D" sectionis filled with coaxial probes. Probes not attached to a

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transmission line are terminated in a matched load. This lenslocates a series of input ports on a circular locus relative tothe central output port on the straight side of the "D".Radiation inside the parallel plane region is entirely absorbedeither by the terminations or by the output transmission line.When the RF phase front is altered, a new beam direction isgenerated. By using the central output probe, the scannedpattern from the array, the array factor, may be measured. Thispattern is not the same as would be measured for a linear arraybecause the field probe does not change angle, it only measuresthe phasor sum of the radiation from the probe array and as suchis not influenced by the element patterns nor the diminishedprojected area of the array at high angles from broadside. Phaseshifts from element to element can progress to large multiples ofr radians replicating the scanned pattern with period 2w. Thisis called the phase scanned pattern or the array factor.

This experimental arrangement did not work wellbecause of the effects of carrier feedthrough in the slave laserleg. Although the slave was locked to a sideband, the frequencyunshifted light component from the master laser occurred withinthe passband of the slave. So instead of having only onelightwave component in the output of the slave laser there weretwo, one at the master laser frequency, n, and one at n+w. Thesegenerate multiple beams from the probe array from intermodulationproducts. To alleviate this problem recourse must be made to acircuit generating only a single lightwave component in each leg.Although the experiment did not succeed in generating a 3.2 Ghzsignal with good spectral purity, the experiment did show thatfor frequencies above about 6 GHz this would be a viableprocedure. At this frequency offset there would be sufficientcarrier rejection to yield signal purity of the magnituderequired.

Figure 111-3 illustrates a modification which yieldshigh spectral purity. A single microwave Bragg cell is insertedbetween the master and slave diodes. In essence it operates in asingle sideband, suppressed carrier mode since the undeviatedmaster laser light will not focus into the semiconductor laserjunction and will not influence the output light from the slave.It was observed that a change of operating frequency of 1 MHzshifted the sideband out of the proper geometry to injectsignificant power into the laser junction and the system wouldthen not injection lock. The use of a doubly diffracted beamundergoing no angular deviation but twice the frequency shiftwould cure this problem and permit wideband frequency agility.The layout indicated in the figure is not optimum because thetotal light path from the front of the master laser and that fromthe back to the beam recombination point should be the same.This is because of the finite coherence length of light fromlasers. Even though the feedback beam passes through a slavelaser, coherence is maintained. For this experiment however,coherence did not present a problem and the arrangement indicatedworked satisfactorily. It should be noted that the two AOBDs

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indicated in the figure should be located as closely as possibleto the lenses (not shown) which relay the light beams to thefiber array. In this way walkoff due to the beam not propagatingin the direction of the optical axis may be minimized. Walko~fis unavoidable in this architecture and since it alters theoverlap of the two beams at the fiber optic pickup plane it mustbe accommodated in the optical design.

Figure 111-4 shows the results using a single fiber ofthe array. As the AOBD drive frequency ranges from 25 MHz to 105MH . the power level sensed at the output shows a fairly symmetricvariation. This range is well in excess of the transducerbandwidth and is therefore attenuated severely at band edges.The rolloff is due to the combined effects of beam walkoff andtransducer efficiency. This information was taken using anetwork analyzer so the actual phase of the output was alsoavailable. By repeating these plots for all the fibers it waspossible to adjust the magnitudes and phases to be nearlyidentical. Magnitudes were adjusted by varying the gap betweenthe end of the fiber and the sensitive area of the APD. Thephase was altered by trimming the length of fiber at a splice.

Figure 111-5 shows the total response when 7 fiberswere combined using the microwave lens. One of the amplifiershad failed limiting the array size to 7 for the experiment. Thefive largest peaks correspond to a situation where the output ofthe fiber-detector combination drive all elements in phase.There is then a 2v phase shift between major peaks. Theirmagnitudes are modified by the AOM-aperture frequency response,i.e. walkoff. The fine scale peaks are sidelobes and showrather severe phase errors caused by misalignment of the opticsduring this particular run.

Figure 111-6 shows the final array factor patternobtained. Both theory and experimental results are shown, thetheory being that of 7 phasors with a linear progression of phaseshift with equal weights. Although theory and experiment do notagree exactly, the agreement is quite good. It is only throughthis agreement that the abscissa scale can be accurately set.The natural scale is frequency into the AOBDs and a measure ofphases would require breaking the transmission line. But theagreement with theoretical shape allows an identification of thefrequency change for 2v phase shift thereby giving the conversionfactor between frequency change and phase gradient. Themagnitude disagreement at ±2v phase shift is caused by therolloff in the AOBD-aperture frequency response. The nullpositions do not seem to occur in exactly the correct place butthat is due to non-linearity in the sweep frequency source usedin the experiment. Of most significance in terms of the level towhich errors in magnitude and phase have been reduced is the nulldepths, 27 dB below the peak response. The depth of null isindicative of a 0.5 dB rms power imbalance or a 30 rms phasevariation at the 7 elements, or some intermediate combination ofsmaller rms errors.

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IV MULTIPLE BEAM FORMATIONThe extremely simple method in which the FOF is made

to form beams, namely, by the selection of drive frequencies intotwo AOBDs, inexorably leads to the question of pattern synthesis.By this we mean methods of perturbing the quiescent antennapattern to achieve some particular result, usually that ofplacing a null in some direction from which jamming is expectedor observed (open loop vs closed loop). By diminishing the lightbeam intensity at the edges of the fiber optic pickup byapodization, by inserting multiple frequencies into the AOBDs, orby creating additional beams in any way in the optical subsystem,the radiation pattern may be modified.

IV-1 Dependent Beams (Pattern Synthesis)Figure IV-1 sketches a modification to the optical

system which can add an additional, parasitic beam to the mainpattern. An additional beam is generated by splitting the lightin the upper leg and routing it through another AOBD, reflectingit from a mirror which can be rotated about two axes, and thenrecombining with the main beam. The fraction of light extractedmay not have to be considerable since this technique wouldprobably try to place a null in a far out sidelobe and hencerequires only a small fraction of the light that the mainbeamdoes. To get independent control of the far field pattern fromthis parasitic circuit, the phase, amplitude and beam direction(4 parameters) must be available. Figure IV-2 shows the K-spacediagram for this situation. It shows the two basic mainbeamfrequencies and the parasitic beam which can occur at any pointin the diagram because of the arbitrary e,* available from themirror tilts. The intermodulation term between the solid blackcircles will not occur in the RF passband and can be ignored.With the proper adjustment of the amplitude (drive power in theAOBD) and phase (phase of the drive signal) this component can bemade to create a null. Parasitic beams can be formed in a numberof ways in the optical subsystem in order to have a multiplicityof nulls controlled by the system. All must however be createdin the same leg of the interferometer.

Consideration of the circuit in Figure IV-1 and thenature of the K-space to beamspac, relationship will show thatthe angles e,* are "attached", aloeit somewhat loosely, to themain beam direction. As the main beam direction is altered theparasitic beam moves also to maintain nearly the same directionrelative to the main beam direction. Were it not for thenon-linearity in the mapping from 8 co cose a change in beamdirection would carry the parasitic beam along exactly. Due tothis and the fact that the farfield pattern is modified dependingon the look direction by both the element pattern and theaperture projection in that direction, the parasitic beam willnot maintain a correct set of parameters (e,*,A,W) to maintain aglobal null. Further since the parasitic beam is probablyattempting to create a null in the far-out or random sidelobepattern region the requisite phase and amplitude is not known a

I0

priori, nor is it constant-with look direction. It is thusnecessary to search for a null. This means closing the loop insome manner, either by correlating with another antenna beam(beamspace cancellation) or by operating on receive only andsearching 8,*,A,v until a null is obtained. This 4D search maynot be well behaved and a better strategy might be to keep e,*fixed as determined by open loop procedures and searching onlyA,p in the sidelobe region.

Another method of creating additional dependent beamsis to drive the AOBDs with multiple frequencies. This will leadto a monopulse beamformer. Consider the K-space diagram infigure IV-3. Each of the AOBDs is driven by two frequencies. Ofthe 6 intermodulation products possible two occur at IF and canbe ignored in the RF beam formation considerations. The 4remaining beams are organized as shown in the beamspace part ofthe diagram. It will be noted that such a cluster of beams canprovide beam sharpened behavior if the signal to noise is highenough and the beam responses can be separated. Figure IV-4shows the situation for a normal monopulse situation and the FOFequivalent circuit. Reference to IV-3 will convince that each ofthe beams though occurring at RF has a distinct IF frequencybecause of the vernier frequency required in the beamformingcircuitry. The use of a frequency channelized IF receiver willallow separation of the beams such that sums and differences canbe made in exact conformity with the classic monopulse processor.After channel separation all the channels must be translated to acommon center frequency.

It will be noted that uniform weighing of the signalsis a key factor in the synthesis of the monopulse cluster.Attempts to use non-uniform weights for a more general multibeampurpose generates unwanted parasitic beams. With non-uniformweights, say A A for the main beam and bX , b for a secondbeam (b

other sources. A cross-correlation with the main channel thenestablishes the approximate weight required to use in extractingor cancelling that jammer from the main signal channel. The setof waveforms, main plus set of auxiliaries, can be input to acanceler circuit (e.g. a Gram Schmidt) to maintain radarperformance in a multi-jammer environment.

Figure IV-5 shows a diagram of one hardwaremodification which implements beamspace anti-jam using an FOFarchitecture. The main modification is a replication of thecontrol subsystem and adding receiving units to the TR module. Amultiplicity of receivers accesses simultaneously andindependently a number of individual beams. The figure indicatesthe TR module required to do this. Corresponding receivers ateach antenna element TR module are driven by an optical controlsubsystem which generates a phase steered LO signal feeding themicrowave mixer. This then extracts different Fourier componentsfrom the phase projection onto the array, thereby accessingdifferent beams in space. Only one of the chains includes atransmitter ( another chain could be coupled in to permitspoofing ). Subsequent to the IF combiners the individualreceiver channels are routed to the signal processor where crosscorrelation properties are estimated and eliminated from thefinal weighted result. This does not generate additionaltransmit beams but does generate a multitude of receive beams.Each of these beams might require patterr ynthesis to further(beyond basic pattern rejection) reject c .,er jammers. In thisway, the near orthogonality of beams may be further improved.

An alternative exists to increasing the TR modulecomplexity. This alternative obtains multiple beam performanceby providing additional optical beams. K-space diagrams forcases using decoupled K and n (beam deflection without frequencyshift, frequency shift without beam deflection) involve novernier frequency shifts. One of the beams, usually thereference beam, is taken as the origin and can without loss ofgenerality be assumed to propagate along the optical axis of thesystem. The microwave frequency is given by the differencefrequency between the beams while the phase gradient is simplythe projection of the steered beam onto the plane of the fiberarray. Figure IV-6 illustrates a general case. This circuitexcites a large number of beams simultaneously. All of the slavelaser diodes are locked to the master laser and each beam pathpasses through a pure AOM and a pure AOBD. Combining throughhalf or partially silvered beam splitters allows all the beams tobe superimposed on the fiber array. The four fiber subarraysshown on the right are optically overlaid to synthesize an arraywith four times the number of samples with half the effectiveinterelement spacing in each dimension. The relay optics are notshown for simplicity. The microwave input for each of the beamsis to the AOMs and the independent beam steering frequencies isinput to the AOBDs. Shown in the lower right hand corner of thediagram is the K-space diagram for this case. Four independentbeams are shown, each with a different azimuth direction and a

12

different elevation direction. Each can also operate on adifferent RF. The range of microwave frequencies must be lessthan an octave to avoid difference frequencies from differentbeams generating in-band signals. To receive the transmittedsignal using the synthesized pattern, the mixer in the TR moduleis driven with the same controls but frequency shifted by theoffset required to downconvert (or upconvert) to the IF band.The proper phase gradients will exist to filter out the separatpsignals and relocate them to their desired IF.

One difficulty with this procedure is that the mixerin the receive leg of the TR modules sees a set of distinct localoscillators. The time waveform is the Fourier transform of thisspectrum and could, for certain possible sets of local oscillatortones, be a repetitive narrow pulse. This would cause no problemfor a linear system (filters work this way) but for a nonlinearmixer, driven very hard to achieve minimal conversion loss andmaximum dynamic range, the conversion loss could be expected tobe increased, sometimes very considerably.

IV-3 Time Dependent Beams (Chirp)Figure IV-7 shows a time dependent beamforming case.

This diagram is intended to beamform using chirped radarwaveforms. Because of the intrinsic dispersion of a phased arrayantenna, a change in the RF will squint the beam, see appendixVI-4. By synchronously changing the AOBD control frequencies, asindicated, a constant beam direction in space can be maintained.Although one of the vectors on the left in figure IV-8 is longer,the effect of increased RF causes it to shorten in proportion tothe change in operating frequency upon transfer to the beamspacediagram. (Note that the spot on the y-axis designating the lightfrequency is further encoded to indicate the change infrequency.) If the AOBD chirps are chosen correctly the beampointing direction does not change. This allows the entirebroadband waveform to be directed at a target and thereby avoid awaveform filtering arising from pattern squint. A similardiscrete beam switching is effective with frequency hoppedwaveforms.

One of the most accurate methods of reducing radarclutter with moving array antennas uses the displaced phasecenter array (DPCA) concept. Here one switches between subarraysto obtain two separate returns with all radiating and receivingelements in exactly the same position. A subtraction of the tworeturns then cancels all fixed returns while giving a "dipole"signature for moving targets. Such switching can be incorporatedin an optically fed array by the act of shifting the fiber pickuparray illumination appropriately. This can be accomplished in anumber of ways either mechanically (by mirror rotations) orelectrically (by AO cell drives). Under-illuminating the fiberpickup array allows optical beam displacements to shift themicrowave radiating aperture from one subarray to another. Suchbeam displacements can be effected by simply adding an additionalx deflection AOBD, say, in the y deflection arm of the beam

13

deflection circuit. Then the x subarray addressed is purely afunction of the difference in frequency of the x deflectioncells. In this manner the DPCA subarrays can be electronicallyaddressed and the DPCA algorithm implemented. Because ofunder-illumination the amplitude weighing would likely be of agaussian nature leading to a low sidelobe antenna pattern.

IV-4 True Time Delay Beams (Wideband)True time delay behavior of an array can be obtained

in a direct manner by treating the wide spectral band asindependent subbands as discussed in figure IV-6, see figureIV-9. Here the K-space diagram would show all the vectorspointed in the same azimuth direction but having slightlydifferent phase gradients (wavenumber projections) to match thatrequired to launch or receive signals from the desired direction.This is not a frugal method of using the available number oftotal beams however and may result in considerable conversionloss in the receive mixers (see last paragraph of section IV-2).

A far more elegant method would use the circuitryillustrated in figure IV-10. Two beam ports are required, 1 and2, which attach to the frequency translators of figure IV-9 inbeams 1 and 2. The desired pulse, scaled in frequency, would besplit and passed through discriminator circuits, one with apositive slope and one with a negative. This would create twowaves impinging the fiber optic pickup plane in addition to thereference. If a sinusoid at frequency 1 were applied to thecircuit, beam 2 would have weight zero and the gradient whichmust be established by the beam deflector is that to sendfrequency 1 in the desired direction. The converse argumentwould apply if only frequency 2 were applied. If a frequencyintermediate to the two band edges were applied both beams wouldbe excited but with a weighing determined by the discriminationcircuitry. Since both beams would be excited at the samefrequency with only the amplitude weighing being different, anintermediate effective plane wave would be generated. Because ofthe small angles on the optical side of the circuit theinterpolation is linear and the proper phase gradient isestablished to transmit each Fourier component in the directiondesired.

The discriminator circuit can be built using eithermicrowave or optical techniques. A particularly simple opticalmethod would use an AOBD for the input of the RF signal and aFourier transform lens to gain access to the spectrum of thesignal. If no operation is performed on the spectrum and all thelight from the AOBD is allowed to fall on a detector, the inputsignal, somewhat attenuated, is reconstructed. By putting a maskin the frequency plane of the circuit, generalized filtering canbe accomplished. In particular a mask which has a variabletransmittance can be used to create a discriminator whose outputamplitude is a linear function of microwave frequency. Byreversing the slope of the variable transmittance, the oppositediscriminator can be constructed. One could also use microwave

14

filters. The out of band response of a multipole filter can beused to synthesize the requisite discriminator behavior, the lowpass response for one of the circuits and the high pass responsefor the other. The main problem with the microwave solution isthat the delay through the circuit as a function of frequency isdifficult to keep constant.

The time delay properties of this circuit can be seenby considering the signal which results from superimposing twoplane waves of the same wavenumber magnitude but differentpropagation directions. Obviously one has to get interferencesince this is the basis of the classic Lloyd's mirror experimentin optics. In equation form one has

a1Cos(t+7,1 ) + a2Cos(( t+ 2) = N Cos(wt+v)

where the amplitudes on the left are related by the response ofthe discriminator circuits, i.e. a, = 1 - a2, and where thesubscripted phase terms are just KySin(a i). Applying elementarytrig transformations one can evaluate N and p as

N = 4 (((aCos(v1)+a 2Cos(V 2)) 2 + (aSin(v1 )+a 2Sin(V2 )) 2 )and= Arctan((a1 Cos(V 1)+a2Cos(V 2) )2/(aSin(,1)+a2Sin(V2) )2).

The amplitude terms, a,, are functions of operating frequencyonly whereas the phase terms are a function of the position inthe array and the two design frequencies involved in thediscriminators. The expression for N shows the requiredinterference effect. A numerical examination of the resultingphase term shows it to be a linear function of operatingfrequency and element position with only weak quadratic errors(and even weaker quartic and higher terms). Such errors can becompensated for in the optical circuit by introducing oppositespherical curvature of phase front by movement of one of thelenses.

The linear phase shift introduced on the frequencycomponents performs the necessary operation to allow broadbandbeamsteering. Define

So(t) = S( ) eqn IV-l

where the overbar is used to denote the Fourier transformoperator and the subscript denotes the fiber under consideration.To have time delay performance the signal at the ith fiber shouldthen be

si(t) = so(t-r i) = exp(jwTi) S(w) eqn IV-2

This expresses the fact that the Fourier transform of a timedelayed version of a signal is a linear phase shift of thespectrum. In an optical system the signal at the ith element isgiven as

15

So(t) exp(jyi ) = exp(jyikp) S(w) eqn IV-3

For time delay performance to result the terms in the exponentialmust be identical. The gradients can be computed by equating thephase shift between elements on the fiber side to that on theantenna side, namely

y Kp = Y kpeqn IV-4

y K sin(O) = Y k sin(e)

where subscript p denotes projection into antenna or fiber opticplane. This yields

if .= Y, sin()/c eqn IV-5

sin(8) = AY w sin(e)/Ay n eqn IV-6

where AY is the antenna element spacing and Ay is the fiberspacing. The discriminator circuit performs the correct operationfor creating apparent time delays without introducing delaylines. The apparent delay comes from the progressive phase shiftwith frequency introduced by the optical system. Bysuperposition a pulse whose spectrum is contained in thediscriminated frequency interval could be expected to be launchedin the proper direction.

The effects of the interference caused by the twoinclined optical plane waves of the same frequency (but ofgenerally different weights) modifies the pattern to be expectedfrom the antenna. The sinusoidal modulation across the apertureresults in two vestigial beams being superimposed on the desiredbeam. These are similar to range sidelobes encountered in pulsecompression. They appear in the directions representing thelimits of dispersion if only the center frequency of the pulsespectrum were directed correctly. They evidence the linear taperof the discriminator on the spectrum radiated in thosedirections. They can be expected to be of order -13 dB relativeto the main beam.

V CONCLUSIONS AND FUTURE EFFORTSThis report has presented in some detail concepts

related to the Fiber Optic Feed program. It has shown a numberof systemic properties which might be exploited to advantage infuture Naval radar systems. The architecture supports a fullrange of radar capabilities including pulse compression,monopulse, anti-jam, beamspace adaptivity, DPCA, frequencyagility, etc. and also allows wideband beamforming. Basicexperiments have verified the design principles in a transmitmode. The transition of this potential capability intooperational hardware could improve Naval systems in terms ofweight, complexity, flexibility, maintainability, and the like.

16

This is because of a simpler beam control circuit which operateswith global commands, the replacement of transmission lines withfiber optic cables and the elimination of phase shifters andassociated digital hardware at the element level.

The major emphasis in the future must be to translatethe concepts into a reasonably robust assembly whereby anexperimental evaluation of all the capabilities can be made. Themain questions to be resolved by this experimental venture are

1--are there sufficient controls to use components of normalreproducibility to obtain high quality beamforms,2--can each of the conceptual uses be translated intopractice, and3--what level of performance can be obtained at the moderatelevel of effort to be expended on the laboratory gradeimplementation?

Specific concerns relate to the relatively high gain required inthe TR module (> 50 dB) . In fact such gains have beendemonstrated using MMIC technology (Pacific Monolithic-privatecommunication with E.Wilson 23 Sept 87).

With a test bed assembly the potential of thearchitecture with conformal arrays could be experimentallyassessed. It seems obvious that geometric factors may beaccommodated by optical compensation, e.g. introducing sphericalaberrations conjugate to the phase effects resulting fromelements positioned on a spherical surface. Likewise, phase andamplitude errors due to an element being embedded in a finitearray may be ameliorated.

17

VI APPENDICES

VI-1 Optical Detection and MixingTnere is little distinction between the processes of

detection and mixing as used in the optics. At the end of eachfiber optic line there is a detector operating in a heterodynemode. The current flowing in the non-linear element is given by

I E = (A1exp(v,) + A2exp(q,2))2

2A1 _Acos((V- 2 )~ Sqrt(P1 P2 /2) cos(V 1- 2 )

for the case of two incident waves. The proportionality can beconverted into an equality by multiplying by the "responsivity",R, of the diode and by any gain, G, associated with the detectionmechanism (for an PIN diode G=1 whereas for an APD, G = 10 to100). Usually there is a matching resistor, r, loading thedetector to the microwave transmission line (50 n). Then thepower flow in the transmission line at the difference frequencyis just p = P P2R2G2r/2.

The conversion loss of the whole process is given by the ratiop/P. The noise performance observed after the first amplifieris essentially the noise figure of that amplifier with littleadded noise from the APD.

VI-2 Faraday CellA Faraday cell is used with laser diodes to isolate

the laser oscillator from external mismatches which can modifythe mode of oscillation. It uses the same phenomenology as aferrite isolator in microwave circuits. Laser injection lockingcan occur at about 1% of the laser output power. If the returnloss of the output of a laser is less than 20 dB, reflections candramatically influence the lasing. The reflection sets up anexternal cavity so the lasing spectrum must simultaneously be amode or eigenvalue of the two cavities, the 100 micron lasercavity and the cavity defined by the external reflection pointwhich may be of order millimeters. Consequently, the lasing islikely to be quite erratic if there are longitudinal vibrationsof a magnitude similar to an optical wavelength. Insertion of aFaraday cell isolates the lasing output from "properly alignedoptics" which tend to retroreflect energy.

VI-3 Bragg CellFigure VI-l sketches the acousto-optic interaction

known as the Bragg interaction. An electrical signal drives thepiezoelectric transducer and converts the electrical waveforminto an acoustic wave traveling in the cell material. When theincident light and acoustic wave have the geometry shown, thereis an efficient conversion of light from the incident light beam

18

into the diffracted light beam. These cells are of a 1D natureso the diffraction occurs in the plane which includes the celllength and the optical wavenumber vector. The diffracted lightbeam exhibits a shift in frequency by the acoustic frequency.Upshifted or down shifted signals can be obtained with equalease. At low frequencies, 30 to 100 MHz, up to 90% of theincident light can be diffracted. The efficiencies decreasesignificantly with frequency. At present of order 25-30%diffraction efficiency is available in the 1-2 GHz band.

In practice there is usually weak scattering intoother beams and these limit the bandwidth of the interaction.The undiffracted beam is normally spatially filtered by Fouriertransform optics and a half plane stop. Whether the cellconstitutes an AOM (modulator) or AOBD (beam deflector) isprimarily determined by the lateral extent over which theacousto-optic interaction is designed to work. This is usuallyexpressed in terms of the time-bandwidth (BT) product of thecell. This is the time aperture (in acoustic velocity terms)illuminated by the incident light and the 3 dB bandwidth of theinteraction (in terms of input electrical frequencies). For BTof order 10 the device is an AOM whereas for BT of order 1000 itis an AOBD.

VI-4 Corporate Fed Antenna ArrayThe FOF architecture involves corporate fed antennas

and as such there is an intrinsic dispersion connected with thebeamforming. Dispersion is used to denote a frequency dependencein the beam direction. Figure VI-2 shows an idealized sketch ofa one dimensional linear array fed by a corporate power dividerand phase steered by phase shifters in each element path. If alinear phase progression exists across the array, a beam will beformed in a direction

8 = Arcsin((AV/r) (A/Ao))

where 0 is the angle from broadside, A.2 is the spacing betweenradiating elements, A is the operating wavelength, and AV is thephase shift between adjacent elements of the array. As thefrequency of operation is increased the beam squints towardbroadside. If the phase shifter is reciprocal then both thetransmit and receive beams are handled properly by the corporatedivider/combiner. For the purposes of this report we also notethat usually, there is a significant loss in the power divisioncircuit so the signals are amplified before transmission by solidstate amplifiers. Further, the phase shifters are usuallydigitally controlled so a digital bus is routed to the phaseshifters. Since the beam pattern and sidelobes are very stronglyinfluenced by the accuracy with which the phase shifters are set(modulo 2r), sometimes a lookup table is stored with the phaseshifters to allow a more precise n bit approximation to accountfor individual variability of the phase shifters as a function offrequency of operation.

19

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