Computer aided design and simulation of an intergrated photonic delay line system for phased array antenna and other microve signal processing applications

Rochester Institute of Technology

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Theses

Thesis/Dissertation Collections

8-1-1993

Computer aided design and simulation of an

intergrated photonic delay line system for phased

array antenna and other microve signal processing

applications

Kevin Baldwin

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Approved by:

Computer Aided Design and Simulation of

an Integrated Photonic Delay Line System

for Phased Array Antenna and Other

Microwave Signal Processing Applications

by

Kevin Baldwin

A Thesis Submitted

in

Partial Fulfillment

of the

Requirements for the Degree of

MASTER OF SCI ENCE

in

Electrical Engineering

Prof.

David ASumberg

(Thesis Advisor)

Prof.

1. Lorenzo

Prof.

Fry

Tseng

Prof.

_

(Department Head)

DEPARTMENT OF ELECTRICAL ENGINEERING

COLLEGE OF ENGINEERING

ROCHESTER INSTITUTE OF TECHNOLOGY

ROCHESTER, NEW YORK

ABSTRACT

Overthe past few _years, phased_array antennas and variable RF/Microwave

delay

lines havebeen the subject of much research. This thesis presentsaphotonic solution to

the generation of multiple, compact

delay

lines. Variable time delays are generated

by

optically

tapping

points on an acousto-optic cell

by

theuse of adeformablemirrordevice.

Isolation of a particular time

delay

is accomplished

by

the conversion of a time

delay

point intoa_{corresponding}spatial

frequency by

the use of appropriate optics. The desired time

delay

is recovered

by heterodyning

a local oscillator with the desired spatial

frequency,

selected

by

a tiltable mirror device. Multiple

delay

lines are produced

by

the

use of a

binary

optic device. The design and simulation ofthe integrated optical system

was carried out _using a real _ray

tracing

program written

by

the author. Theoretical signal

ACKNOWLEDGMENTS

I would like to thank Dr.

Tseng

and Dr. DeLorenzo for _sitting on _{my advising}

committee and _{especially Dr.}

Sumberg,

without whose patience and guidance this endeavor could not

have

come to realization. I would also like to thank Captain Ed Toughlian oftheRome

Laboratory

Photonics Center for_extendingto methe _opportunity to work on this

truly

novel project in times when original ideas are _scarce, Dr.

Henry

Zmuda for his _advice, RIT's Department ofElectrical

Engineering

for the marvelous educational _opportunitygiven _{to me,} Dr. A. Matthew for_allowing meto work inone of thebestareas onthe_{RIT campus,}

Mom, Pop,

andtheGrandparents.

Iwould also liketo thank some special people I have come to know overthe past

few years. To

fully

express the roles

they

have _played, I must draw an _analogy to a sonnet:

"The housewasold,withtangledwings

outthrownof which no one could evenhalf

keep

track. Andinasmall_room,somewhat neartheback,was an odd window

sealed with ancient stone.

There, inadreamplagued_childhood,quitealoneIusedto go,

when nightreignedvague and_black,

partingthecobwebswitha curiouslackoffear andwithawondereachtimegrown.

One later

day

Ibroughtthemasonsthere

tofindwhat view_mydimforbears hadshunned,

butas_theypiercedthestone

arush of airburst fromthealien voidthatyawnedbeyond.

They

fled,

butIpeeredthrough

andfoundunrolled allthewild worlds of which_{my dreams had}told." - HowardPhillips Lovecraft

I would like to thank Khaleda Najeem for _revealing to me corridors yet to be

explored, Evelyn

Monsay

for

helping

remove the rubble from windows re-sealed

by

others,Lee Minich who stood

by

myside atthewindowand offeredhis_{council, and,} most

importantly,

Mr. Eric Rogala who has also forsaken the masons and dared to stride

Table

of

Contents

ABSTRACT ii

ACKNOWLEDGMENTS iii

Table ofContents iv

ListofTables ix

ListofFigures x

List ofAcronyms xv

Table ofSymbols xvi

I. Introduction 1

n. Phase

Array

Antenna Fundamentals 3

Phased

Array

Antenna Operation 3

DerivationofRequired Time

Delay

for

Achieving

Steering

Angle 5

Phase

Shifting

versusTrue Time

Delay

Beam

Steering

8

IE. Special Components Used intheIntegrated System Design 1 1

OperationoftheAcousto-OpticCell in

Bragg

Mode 1 1

DerivationoftheExpectedAcoutso-Optic Cell Output: Amplitude

Modulation 12

Significanceofthe

Bragg

Angle 18

DerivationoftheExpected Acoutso-Optic Cell Output:

Frequency

Modulation 18

DependenceofOutput Angle onAcoustic

Frequency

21

Operationofthe

Binary

Optic Device 22

IV. SinglePhotonic

Delay

Line Concept 24

Generationof aTrue Time

Delay (TTD)

24

General OpticalSystem for

Tapping

thePhotonic

Delay

Line 26

V. DesignoftheIntegrated Photonic

Delay

Line System 29

The Significanceof

Ray

Fansand

Delay

Lines for System Design 29

Underlying

Values Used for

Designing

30

SimTI: ComputerSimulation andDesign Tool 31

Integrated System Overview 31

General DesignoftheIntegrated System 33

A Closer LookattheIntegrated System Front End Design 36

ACloser LookattheLocal Oscillator PortionoftheSystem Front

End 43

ACloser LookattheMultiple

Delay

Line Generation 54

A CloserLookattheThird PortionoftheSystem: Collimationof

theIndividual

Delay

Lines 57

ACloser LookattheFourth Sectionofthe System: Extractionof

theProper TTDandConfigurationforDetectionofthe Heterodyne

Signal 63

Specificationof

Coupling

Lens for Detection

Assembly

71

VI. Real

Ray

Tracing

withTechniques for Computer Realization 80

General

Ray Tracing

Technique 80

Background 81

Basic

Philosophy

behind "UserFriendly"

Optical System Design 81

Optical Componentstobe Considered 81

Useof aGlobal Coordinate System 82

General

Terminology

82

RepresentationofOptical Surfaces 83

Describing

Planar Surfaces 84

Describing

Spherical Surfaces 84

ApplicationofSnell'sLaw 85

Atan

Arbitrary

Planar Surface 85

Atan

Arbitrary

SphericalSurface 86

AlignmentofOpticalComponents AbouttheOptical Axis 87

A Common Mathematical Operation 87

DecompositionofOptical Componentsinto Respective Surfaces 88

SpacerDecomposition 88

Wedge Decomposition 89

Lens Decomposition 91

Ray

Tracing

Throughthe

Bragg

Cell 94

Ray Tracing

Throughthe

Binary

Optic Device 96

VU. SimH: An Overview 97

Introduction 97

Specifying

Components (Unitsof

Measurement)

97

ParametersofOpticalComponentsUsed

By

Simll 97

Block Parameters 98

Wedge Parameters 98

Lens Parameters 98

Acousto-OpticCell 100

GeneralProgramUsage 101

Entry

andManipulationofData 101

Back-Tracking

To Abort UndesiredOperations 102

Examining

anOptical System 102

General

Terminology

104

Optical System

Entry

andManipulation:The File Pulldown 105

DescriptionsofthePulldown Functions 106

Ray Tracing

ThroughtheSystem: The

Tracing

Pulldown 109

DescriptionsofthePulldown Functions 110

Viewing

Generated Data: The Output Pulldown 115

DescriptionsofthePulldown Functions 115

Viewing

theOptical System: The Graphics Pulldown 118

Descriptionsofthe Pulldown Functions 118

AnImportant Note About

Using

theGraphics Screenfor Analysis 123

EvaluationoftheIntegrated System: The Simulation Pulldown 125

Descriptions ofthePulldown Functions 126

MethodofOptimization 130

VIII. CalculationofSignaltoNoise Ratio 132

The Form ofOptics Related SignaltoNoise Ratios 132

Signal Power 132

The Classical Noise Sources 133

AdditionalConsiderations in SNR: EffectsofNon-Ideal Detector Size 138

DeterminationoftheSignal andLocal Oscillator Electric Fields 139

Determination of

Intensity

PatternatDetector Plane 142

Quantification oftheEffectofDetectorSizeonSNR 149

Bibliography

154

Works Cited 154

Additional References 155

Appendix A 156

Simll Source Code 156

AppendixB 157

Analysisofthe

Binary

Optic 157

AppendixC 161

DerivationofTrigonometric

Identity

161

Appendix D 162

List

of

Tables

Table 1. SpecificationofFrontEnd

Components

53

Table2. Specificationof

Delay

_{Line CollimationComponents} 56

Table 3.SpecificationofIndividual

Delay

LineCollimation Components 62

Table 4. Various Lengths ofGlassUsedin

Specifying

DMD Distance 67

Table 5. Input_{Gaussian Beam Characteristics} 73

List

of

Figures

Figure 1. BlockDiagramofaPhased

Array

AntennaSystem 3

Figure 2.GenerationofPlanar Wavefront fromMultiple Point Sources 4

Figure 3. Phased

Array

Antenna Output Field 5

Figure 4. DerivationofRequired ProgressivePhase

Delay

for Beam

Steering

6

Figure 5. AntennaOutput for

Steering

Angleof 15o 7

Figure6.Antenna Outputfor

Steering

Angleof45o 8

Figure 7. Squint

Pointing

Error in Antenna Output 9

Figure 8. An Acoutic Wave

Propagating

intheTransducerof anAO Cell 11 Figure 9. ReflectionsofaBeamofLightoffof aStructure

Possessing

aPeriodic

IndexofRefraction 13

Figure 10. AngleDefmationsUsed in Fresnel Coeffecient Calculations 14

Figure 11. Typical Heterodyne Detection Scheme 21

Figure 12.

Intensity

DistrubutionoftheOutputofthe

Binary

Optic foraPlane

Wave Input: Mesh Plot 22

Figure 13.

Intensity

DistrubutionoftheOutputofthe

Binary

Optic foraPlane

Wave Input: Contour Plot 23

Figure 14.

Tapping

aSpecific Time

Delay

onthe

Bragg

Cell 24

Figure 15. Architureof aSingle Photonic

Delay,

asProposed

by

Zmudaand

Toughlian 26

Figure 16.

Geometry

fortheDerivationofRequired Mirror Tilt Angle in Terms of

theDesired TTD 27

Figure 17. The Integrated System:

Ray

Fan Analysis 33

Figure 19. SystemFrontEnd

Terminology

37

Figure 20.

Focusing

LasertoActive Areaof

Bragg

Cell 38

Figure 21.

Maintaining

Proper

Bragg

Angle Incidence 39

Figure22.

Maintaining

Proper

Bragg

AngleIncidence:Required Wedge Angle 39

Figure23.Collimationof

Ray

Fans

Exiting

SystemFront End 42

Figure 24. The LocalOscillator PortionoftheSystem Front End 44

Figure 25. ASimple Telescope Configuration 45

Figure 26. TheDesignofSpacerl fortheSystem Fron End 47

Figure27. Possible LocalOscillatorBranch Configurations 48

Figure 28. Final Spacerl Dimensions 49

Figure29. DesignofSpacer2oftheSystem Front End 49

Figure 30. System for GenerationofMultiple

Delay

Lines 54

Figure 31. Collimationof anIndividual

Delay

Line 57

Figure 31. Collimation ofanIndividual

Delay

Line 58

Figure32. DeterminationofDMD Location for

Ray

FanConvergence 64

Figure 33. SeparationofSignalandLocal Oscillator Beams 69

Figure 34. Iterative

Ray

Tracing

Process 80

Figure 35.Global Coordinate System 82

Figure 36. DefinitionofComponent Descriptors 83

Figure 37. RealizationofSnell's Law in Coordinate System 85

Figure 38. DecompositionofaSpacerinto Surfaces 88

Figure 39. DecompositionofaWedgeinto Surfaces 90

Figure 40.Decompositionof aPlanoconvex lens intoSurfaces 1 91

Figure 41.Decompositionof aPlanoconvexlens into Surfaces II 92

Figure43.Decompositionof aPlanoconvex lens into Surfaces II 94

Figure45.

Specifying

Lens OrientationtoSimll 100

Figure46.SimHFront End 101

Figure 47. A TypicalSelection Boxin SimH 101

Figure 48. A TypicalPrompt BoxinSimH 102

Figure 49. ASample System DescriptionWindow 103

Figure 50. TheSample System

Description,

as seen_usingtheGraphicsOption 104

Figure51. Introductionto

Terminology

usedin

Describing

theIntegratedSystem 105

Figure 52. The File Pulldown 105

Figure 53. Macro Alter Window 106

Figure 54. Add Component Window 106

Figure 55. Enter Parameters Box for

Adding

aComponent 107

Figure56. Processof

Inserting

aComponentintoan

Existing

Optical System 108

Figure 57.

Altering

theParametersof an

Existing

Optical Component 109

Figure58.

Ray Tracing

Pulldown 1 10

Figure 59.

Ray Tracing

Parameters 1 10

Figure 60. Sign Convention Used in Simll for

Describing

Input

Ray

Trajectories Ill

Figure 61. Sign Convention Used

by

Simllin

Describing Binary

Optic Diffracted

Orders Ill

Figure62. Resultof

Using

the

Ray

Trace Option 112

Figure 63. Beam Trace Window 1 12

Figure 64. Result of

Using

theBeam Trace Option 113

Figure 65. Multi-Beam Trace Prompt Box 113

Figure 66.

Ray Tracing

OptionsundertheMulti-Beam TraceOption 114

Figure 68. SimHDefaultWindow 114

Figure 69. Output Pulldown 1 15

Figure70. Sample

Ray

Trace Information Window 1 16

Figure 71. A Detailed

Description

Windowof aSystem Component 117

Figure 72. Windows

Showing Refracting

Surface Parameters 117

Figure 73. The OutputOptions Box 1 18

Figure 74. GraphicsPulldown 118

Figure 75. A Sample OpticalSystemasSeen FromtheTextScreen 119

Figure 76. A Sample Optical Systemas SeenFromtheGraphics Screen 1 19

Figure 77. TheGraphicsOptionsWindow 120

Figure 78. An Exampleof

Showing

theIntercept NumbersontheGraphics Screen 120

Figure 79. An Exampleof

Showing

Surface PointsontheGraphics Screen 121

Figure 80. An Exampleof

Plotting

Data

Using

Simll 123

Figure 81. An Optical System Under Normal View 124

Figure 82. An Optical System Under Increased Magnification 124

Figure 83. An Optical System Under Further Magnification 125

Figure84. An Optical System Under Still Further Magnification 125

Figure85. The Simulation Pulldown 126

Figure 86. Information Generated

By

AO Collimation Check Under Simulation

Pulldown 126

Figure 87. The Physical

Meaning

oftheLens Displacement Optionunderthe

Simulation Pulldown 127

Figure 88. Lens

Steering

Parameter Window 128

Figure 89. Optimize Thickness Window Available intheSimulation Pulldown 130

Figure 91. Originofthe

Cylinderical Signal

_{Beam 140}

Figure 92.ACondensed

Ray

Diagram

oftheIntegrated System 149

List

of

Acronyms

DMD DeformableMirror Device

TTD TrueTime

Delay

AO Acousto-Optic

Table

of

Symbols

Squarerootof- 1

Section II.

0

X

As

k

4>(0)

C0(

v

d

td

'o

Beam_steeringangle

Wavelengthofantenna

driving

signal

Difference inperpendiculardistances

Wavenumber of antenna

driving

signal

Progressivephase

delay

Angular

frequency

ofantenna

driving

signal

Speedat which emittedsignalpropagatesinair

Antennaelement_spacing

Time

delay

Section UI.

q

corf, ^

So

vs

n

An0

O

e

Acousticwave number

Acousticsignal angular

frequency

Amplitudeof acoustic wave

Speedof sound intransducer

Averageindexof refraction oftransducer

Maximumdeviationoftransducerindex fromaverage_value, n

Phase shift ofacousticwave

Angulardifference between incidentoptical_ray andacoustic

Ar Incrementalchangeinreflectance

Ax Incrementalchangeinposition onthe transducer

dr/dx Change inreflectanceperchangeinposition

k Wavenumberofoptical wave

dn/dx Change in indexofrefractionper changeinposition

dr/dn Changeinreflectanceperchangein indexof refraction

0₁ Angle between incident_rayandsurface normal

02

Angle betweentransmitted_rayand surface normal

3

Anglebetweenreflected_rayand surface normal

n\ Indexof refraction seen

by

incident ray

n2 Index of refraction seen

by

transmitted_ray

L Optical beamwidth projectedontransducer

A Wavelengthofacousticwave

0B

Brag

angle

^signal

Frequency

oftheacousticsignal

nBragg

Indexof refraction of

Bragg

cell

r Reflectance

c0'

^optical

Angular

frequency

of optical wave

t Time

Ejn

Electricfieldamplitudeincidentonthe transducer

Eout

Electricfieldamplitude reflected

by

acoustic wavefronts

4*5

(t)

Signalwaveusedin

heterodyning

^LOW

Local oscillatorwave usedin

heterodyning

As

Amplitude ofsignal wave

toet

*s

A0

^signal

Intensity

seen

by

thedetector

Phaseshift of signalbeamwithrespectto thereferencebeam

Change in

Bragg

angle

Differencein RFsignalinthe

Bragg

cellfromcentral

driving

frequency

Section IV.

xo

t

em

F

q

Distancefromx=0_point

alongthecenter ofthe transducer

Truetime

delay

Tiltangle of mirror

Focallength

Anglebetween desired spatial

frequency

and optical axis

SectionV.

d

Fl

F2

F3

Beamdiameter

Focal lengthofLI

Focal lengthofL2

Focal lengthofL3

nglass>nBK7 Indexof refraction oftheglass usedinthe systemconstruction

Indexof refraction of air

Eedgeangle ofWedge 1 andWedge2

Minimumfocal lengthneededfor CL1

Focal lengthofCL1

Radiusof curvature

Thickness of

Gap

1 noi_air

0_w

1min

fCLl

ROC

A0 One halftheangular spread ofa_{ray fan}

fLl

FocallengthofL1

Dm

Diameterofbeam enteringtelescope

^out

Diameterofbeam

leaving

telescope

Fl,F2 Focal lengthoflenses usedintelescope

d Lengthof glassbetweenCL2andLI

0OA

Angle betweenoptical axisbeforeand afterthesystemfrontend

0}Vf

Angle between reflectingsurfaceofSpacerl andinputoptical axis

hx

A dimensionofSpacer2

dgst

Estimated lengthofglassbetween CL2andL 1

dact

Actual length of glassbetween CL2andLI A% Percentdifference

bfl Back focal length

yjast Heightof a_{p ray}asitexitstheopticalsystem

6'last

Angle exiting p raymakes withtheopticalaxis

tBL

1est Estimated lengthofBL 1

ROCspiest

Estimatedradiusof curvature ofSP1

(L3)

fSPlest

Estimated focal lengthofSP1

*BL

1 Actual lengthofBL 1

Cside

Lengthof a sideofa pentaprism

mx Slopeof aline

bx

y interceptofaline

xo>_Yo Apoint on aline

tBL2

Lengthof glassbetween SP1 andBS3

A, B, C,

D

Zo

w,

z

0,

o

o

Elements

oftheparaxial_raymatrix

Rayleighrange of aGaussianbeam

Waistradius ofGaussian beam

Distance from beamwaisttocurrent position onbeamaxis Beam divergence angle

SectionVI.

xo>yo

R

'm

Or

0,

3V

m

0q

9i

A

X

Centerof curvature

Radius of curvature

Angle between_refractingplaner surface and xaxis

Angle between incident_ray and x axis

Angle between incident ray and surface normal

Angle between exiting rayand x axis

Angle betweensurface normal and_{exiting ray}

Angle betweensurface normal and x axis

Diffractiveordernumber

Angle betweenmthdiffractiveorder and optical axis

Angle between incident rayand opticalaxis

Periodofdiffraction grating

Angulardifference betweenadjacentdiffractiveorders

Section VII.

R Radius of curvature

n Indexof refraction

Section VIII.

/

Mean-squared

value of a randomvariable

erf

Varianceof random variable

tfshot

Noisepowerassociatedwith shot noise

ai2<tor*

Noisepowerassociatedwithdarkcurrent

a]

johmon Noisepower associatedwiththermalnoise

<isig> Averagevalueof signalcurrent

9-t

Responsivity

ofadetector

q Fundamentalcharge of anelectron

/zco

Energy

storedinaphoton

<PS> Averageopticalpowerinsignalbeam

<Pl> Average optical powerinreferencebeam

B Bandwidthofthedetectionsystem

R,

Rl

Totalresistancein detectioncircuit

k Boltzman'sconstant

T Ambienttemperature(in

Kelvin)

ir\

Darkcurrent

Ts

fractionoftotalinputpower placedinsignalbeam

T^o

Transmission efficiencyof

Bragg

cell

Tp

Transmission efficiencyofPolarizer

Tcube

Transmission efficiencyofbeamsplitter

Gpjn

Gainofphotodetector

Gamp

Gainofdetectioncircuit

BO

Splitting

ratioof

Binary

Optic

As

Amplitude of signalbeam

fo

Opticalcarrier

frequency

fs

RFsignal

frequency

X

Opticalwavelength

x, y,z Cartesiancoordinates

0 Mirrortiltangle

V

Velocity

of soundinthetransducer

T Desiredtruetime

delay

F Effectivefocal lengthofthesystem

fx

Spatial

frequency

O,

f

, ())"

Relativephaseshifts

Es

Electricfieldof signalbeam

ELO

Electric fieldofLocal Oscillator beam

Tl Intrinsic impedanceof air

I

Intensity

pattern

PLO Power

density

oflocal oscillatorbeam

Ps Power

density

of signalbeam

PDC

DCcomponentoftime_varying

intensity

pattern

pSIG

ACcomponentoftime_varying

intensity

pattern

L Introduction

Phasedarrayshave beenthesubjectofintensiveresearchforseveral

decades,

with

the_primary focus oftheseefforts centeredonmicrowave components and system. More

recently,

however,

_{optically based}systems have beenproposed as possible alternatives to

some ofthemoreconventionalelements.

Many

true time

delay (TTD)

_{beam steering} systems have beenproposed, such as

the schemes presented

by

Toughlian & Zmuda1'2 _and

Sumberg

& Toughlian3>4- The

system addressed

by

this thesis combines an acousto-optic deflector with a segmented

mirrordevicetoobtaintime

delay by

the

following

process.

AnopticalbeamofdiameterDpasses throughan acousto-optic deflectortowhich

an RF

frequency

is applied. The laserbeam that passes through the acousto-optic cell

carries afinite time slice ofthe RF signal.

By

means of a shift inthe optical

frequency,

that time slice is impressed upon across section ofthe laser beam. The signal _carrying

optical beam is then transmitted through an integrated (all glass) optical system to a

photodetector, where it combines with a second beam at the unshifted laser frequency.

The two beams produce a heterodyne signal.

Using

a mirror to steer one of the laser

beams,

it ispossibleto select various

delay

points oftheoriginaltime slice and reproduce

the instantaneous RFsignal _occurring atthat point. _{Time delays up} to

D/vs

are _possible,

where_vs isthe_velocityof sound_{propagating in}theacousto-optic cell.

1_{H.ZumdaandE.Toughlian,"Variable PhotonicDelayLinefor Phased}

ArrayAntennasand

RF/Microwave SignalProcessing",Final TechnicalReport,(Rome_Laboratory,Griffiss Air ForceBase,

NewYork,June ₁₉₉₁₎

2_{H.ZmudaandE.Toughlian,"Adaptive Microwave Signal Processing: A Photonic}Solution,"

Microwave

Journal,Vol. 35,No.2Feb 1992,pp 58-68

3_{D.Sumberg,"An Integrated PhotonicDelay}LineforPhased

Array

AntennaApplications",Final TechnicalReport,(RomeLaboratory,Griffiss Air ForceBase,NewYork,

May

1993)

4_{D.Sumberg,"An Electro-optic Based Variable}Photonic

Delay

Linefor Phased_ArrayAntenna

The potential advantages of the segmented mirror photonic

delay

line over

existing architectures _{lie in it's ability} to provide _extremely rapid reconfiguration ofthe

antenna pattern and an

infinitely

variable time delay. An important advantage lies in

steering the beam using a TTD technique as opposed to _employing a phase _shifting

technique. In some _existing antenna systems, optical

heterodyning

schemes have been

employed to provide an RF phase shift that

is,

unfortunately, independent of the RF

frequency. Such a system suffers from a phenomena know as squint, which results in

different

frequency

components of the RF carrier _{pointing in different} directions.

By

utilizing aTTD beam_{steering technique,}theeffects ofsquint areeliminated5

.

This thesis addresses the concept and design of a integrated photonic

delay

line

system, concentrating on the role of a personal computer in

determining

system

specifications andperformanceevaluation. The integratedsystemis capable of_providing

25 separate

delay

_{lines (although only 20 lines} will utilized in the actual _system) with a

high packing density.

The availability oftrue time

delay

lines for RF signals _mayalso be utilized inthe

realization of microwave signal _processing architectures.

By

_using the variable photonic

delay

lines in conjunction with a photonic amplitude _weighting

device,

a microwave

transversal filtercan be realized. Such an amplitude _weighting effect can be included in

theoptical system

by

theuse ofliquidcrystal lightvalues.

5_{H.ZumdaandE.Toughlian,}"VariablePhotonicDelayLine for PhasedArray Antennasand

RF/MicrowaveSignalProcessing",Final Technical Report,(RomeLaboratory,Griffiss AirForceBase,

II. Phase

Array Antenna

Fundamentals

Phased

Array

Antenna Operation

A phased-array antennais an antenna system which steers the outputbeamofthe

antenna

by

_adaptivily

controlling

the time ittakes fora common signal emitted from the

source to reach a particular radiative element. A simplified block diagram of a

one-dimensionalantenna_arrayisshownbelow:

Phase Fronts

Delay: 8

(

_nj ,0)

Delay:

8(

_1*2,8)

Common

Source

/113

Delay: 6

(

n3

,0)

Delay: 6

(

_n4,0)

Delay:

6(

_n5,8)

Figure 1. Ablock diagramof a phasedarrayantenna system. Theoutputdirectionofthebeam,specified

by

theangle6with respectto the_arraynormal,iscontrolled_byvaryingthe timerequiredfora signal emittedfroma common sourcetoreach a particularelementintheantenna. Thus,theamount oftime_delay

neededat a particular elementisafunctionofboththespatiallocationof a particular element andthe desired steeringangle.

Theamountoftime

delay

depends onthe desiredsignal

direction,

specified

by

the

angle 0 in Figure

1,

and the spatial location of the radiative element, designated

by

n[.

Thus,

in order to achieve a desired steering

direction,

the signal must be delayed an

The mechanism

by

whichthe beam is steered canbe seen

by

first_considering the

output_{field resulting fromthe emissionsof an}

arrayofsynchronized pointsources. Each point source represents anidealized

radiating

elementintheantennaarray.

Phase Front

Phase Front

Planar

Wavefiront

Directionof Propagation

Individual

Radiating

Element

Figure 2. The resultingoutputfield froman_arrayof synchronized point sources. Sphericalwavefronts of equal phase are shown_emergingfromeach point sourceinthearray. Itisevidentthat thesuperposition of thesphericalwavefrontsfromeach source contributeto thegeneration of a planar wavefront_propagating

normalto thearray.

By

considering the linear array of_radiating antenna elements as an _array of point

sources, the output field of the antenna _{array may be} explored. As in Figure

2,

the

resulting output field from the antenna generated

by

a linear array of synchronized oscillators will appeartobea planerwaveinthe farfield.

This statement has been supported _using aMathCad simulation to determine the

[image:27.557.136.425.154.429.2]

by

summing

thesphericalfields generated

by

1 1 point sources, symmetrically distributed

aboutthe 0 point ofthe x axis and with a separation distance between adjacent elements

of one half a wavelength. The figure below represents a contour plot of the _resulting

outputfield.

300-+00

300

200-

100-M

Figure3. Contourplot ofthefield_resultingfromthesuperposition of1 1pointsources,locatedalongthe loweraxisoftheplotand centered aboutthe"zero"point. Theseparationusedbetweenadjacent elements

was one-halfthewavelength ofthecarrier wave. Notethat the_resultingfieldappearstobequiteplanar, propagatingnormal_arrayorientation.

From MathCad result shown in Figure

3,

it is apparent that the _resulting output

field distribution displays planer wavefronts characteristics in the "forward looking"

region,

directly

in frontofthearray.

Derivation

of

Required Time

Delay

for

Achieving Steering

Angle

As has been already stated, inordertosteerthe _{resulting beam}atime

delay

inthe

signal between adjacent elements must be introduced.

Since,

in _{this example, the} signal

berealized as a phase delay. Sincetotalphase

delay

is

being

considereditcan be

directly

usedinthequantificationof a_{time delay.}

Theexpressionfortherequiredtotalphase

delay

interms ofthesteer anglecan be

derived

by

_{considering Figure}4:

DirectionofPropagation

PlanarWavefiront

Wave Fronts contributing toPlanar Wavefiront

Figure 4. The geometryofthesituation

leading

to thederivationoftheamount of required phase

delay

betweenadjacent antennaelementsinordertoachieve_{desired steering}angle oftheantenna outputbeam.

Inthefigure,Asrepresentsthedifferenceinperpendiculardistances fromthewavefronttoadjacent point

sources and0is_steeringangle ofthebeamwith respectto the_arraynormal.

By

taking

a

"snapshot"

in time of the wavefronts that contribute to a planar

wavefront, an expression canbe derived for the progressive phase

delay

in terms ofthe

steeringangle. FromFigure 4:

sin0=

As As

Element

Spacing

X

2

As=

A,sin0

(1)

Theprogressive phase

delay, O(0),

willbegivenas:

,/nN , . 2%

XsinQ

. .

(Q)

=_kAs=- ₌

7usin0

X

2

(3)

wherekisthewave_number, -y-.

Fromthis derivation it canbe seenthat inorderto steerthe beamat angle 0 with

respect to the _array normal, the signal radiated

by

a particular element shouldpossess a

phase

delay

of _+/-O(0) comparedto the elements adjacent to it. The +/- _{factorreflects}

the not

knowing

if the adjacent element is on the "right" or "left" of the element in

question. Inordertoillustrate_{the point,}several_{MathCad beam steering} simulationshave

been carried out forvarious steer angles. In all_{cases, the} antennais alinear array of 1 1

elementsarranged _alongthexaxis, centeredabouttheorigin.

PhaseFronts ofOutput Field

500-

400-

300-

200-

100-n 1 1 r

100 200 300 400 500

M x

Figure 5. Acontour plot oftheoutputfield distribution fora steer angle of15with respecttothenormal

Phase FrontsofOutput Field

mkp 3y-'X'

^

40CT

300"

Pi

P

20CT

P)P

1 '

100-&'!' 0-]

()

1 100

1 200

1 300

1

400 50

M x

Figure 6. Acontour plot oftheoutputfield distributionforasteer angle of45with respecttothenormal

to thelinearantenna array.

Noting

thattime andphaseare

linearly

relatedata signal

frequency,

therequired

time

delay,

tj,maybe expressedintermsofthephasedelay:

_

<E>(0)

_

7tA,osin0

_

X,osin0

(4)

coo

27T.V 2v

Thus,

the proper directional orientation of the output beam of a phased _array

antenna maybe achieved

by

_generating the proper time delays for each _element, based

uponthe_{desired steering}angle.

Phase

Shifting

versus

True Time

Delay

Beam

Steering

As stated in the

Introduction,

some phased _array antenna schemes make use of a

fixed phase

delay

system to control the direction of the output beam.

However,

for

broadband signals such adirectional controller will result in the _pointingerror knownas

squint. Squint results from different

frequency

components of the transmitted signal

generalizing

the derivation of the _{beam steering} angle,

0,

presented earlier to multiple

wavelengths.

Recalling

fromequation 1 that:

A?

sin0=

(5)

Element

Spacing

Forthe transmission ofabroadbandsignal, it is no longerpossible to _specify the

spacingofthe _radiatingelementsinterms ofthetransmissionwavelength, as was done in

theearlierderivation.

Therefore,

letthe_spacingbetweenadjacentelementsbe fixedata

value ofd. Thephase

delay

requiredtosteera

frequency

component oftheoutputbeam

willbegivenby:

<p= dsind

(6)

X

For a fixed phase _system, O will remain a constant value for all frequencies

(wavelengths). Since all valuesareconstrained in equation exceptforthe _{beam pointing}

angle, the _{beam pointing} angle will become a function of wavelength, _{resulting in} the

specification of adifferent beam direction for each

frequency

in the

driving

signal. This

phenomenais known as squint. Thissituationisshownin Figure 7.

[image:32.557.187.367.446.623.2]

"high

Figure 7. Theeffectofusinga phase_shiftingschemetogeneratetheoutputfieldof a phased_arrayantenna. Different_frequencycomponentswill result_{in different beam steering}angles. _{This pointing}erroristermed

On theother

hand,

itcan be seenthat

by

_using aTTD scheme to steerthe output

beam

direction,

that theeffects of squint canbeeliminated. Thiscan beseen

by deriving

therequiredtime

delay

fora given_steeringanglefromequation6:

$ 2ic . . _A rf . n

td

= = _-dsm0= _sm0

(7)

co A v

where dis the separation distance between elements inthe _array and vis the _velocity of

theoutputbeamradiation. Fromthis_{relationship it is} clearthatthe _steeringangle isnow

independent of the signal frequency. Thus the effects of squint are removed from the

III. Special

Components

Used in

the

Integrated System

Design

Operation

of

the

Acousto-Optic

Cell in

Bragg

Mode

The

Bragg,

or

Acousto-Optic,

cell is the heart of the integrated optical system,

providing abridge between electrical and optical signals.

By

_utilizing an Acousto-Optic

cell,inthe

Bragg

mode,itispossibletodeflect

(steer)

anincidentbeam proportionally to

theacoustic

frequency

_propagatingthroughthecell as wellasplacetheRFfrequencies on

anoptical carrier.

Themechanism

by

which the

Bragg

cell accomplishes these taskscanbe derived

by

adopting a geometrical optics point ofview ofthe cell's operation. In this simplistic

method of analysis, the acousto-optic cell _{may be looked} at as a piece of _{material, the}

transducer, into which an acoustic wave is introduced

by

the use of a piezo-electric

material, as showninthefigure below:

+xaxis

V

v

Piezo-Electric

1 Material

\

TapperedEnd

tofoil back-reflections

Figure8. Anacoustic wave_{propagating in}the transduceroftheacoutso-optic cell.

Directionof

Acoustic

Wave

[image:34.557.208.351.428.624.2]

Derivation

of

the

Expected Acoutso-Optic Cell

Output:

Amplitude

Modulation

Theacoustic wave

traveling

inthe transducerisgiven

by

theexpression6:

s(x,t)=

S0cos(qx-L~lt)

(8)

2tc where Q.=

2nf

_{isthe angular}

frequency

ofthe signal and_q= is _thewavenumber. In A

this case, the acoustic wave _{is propagating down} (+x

direction)

the cell. The acoustic

wave

traveling

inthe transducerestablisheslocalizedchangesintheindexof refraction of the transducer proportional to amplitude of the acoustic wave. Under these conditions,

the index of refraction in the transducer _{may be} written as a function of spatial

coordinatesinthetransducerandtime7:

n(x,t)=

n-An0cos(qx-L~lt)

(9)

In order to _simplify the determination of the interaction of light with the

time-varyingsinusoidal indexgrating,it is observedthat the optical

frequency

is much greater

than the acoustic frequency. Under this condition, the periodic index structure will

appeartobealmost _stationary with respect tothe light

during

the interaction8.

Thus,

the

indexof refraction ofthe transducer_{may be}describedas:

n(x,t)=

n-An0cos(qx-0)

(10)

where O is the phase shift in the sinusoidal structure caused

by

taking

a

"snap

shot"

ofthestructure at a particularpointintime.

Next,

consider

illuminating

the transducerwith a plane wave that makes an angle

of0with respectto theacousticwavefronts,as shownin Figure 9.

6B. SalehandM.CTeich,FundamentalsofPhotonics. (John

Wiley

&Sons, Inc.,New York ₁₉₉₁₎ Chap. 20

7B.SalehandM.CTeich,FundamentalsofPhotonics.(John

Wiley

&Sons,Inc.,New York ₁₉₉₁₎ Chap. 20

+xaxis

-172

Lsinfl Lsinfl

Figure 9. Reflectionsof abeamoflightoff of a structure_possessinga periodicindexof refraction.

From a prior

knowledge,

the beam reflected off of the periodic structure is the

beam desired for analysis. It is assumed thatthe incidentwave is _partially reflected

by

each periodin the _{transducer, due} to the _changing refractive index inthe _transducer, and

that thereflectancedoes not_{significantly}reducetheamplitude ofthe transmittedlight9.

If Ar=

dr/

_{a* is the incremental reflectance at apoint x onthe}

transducer,then

the total reflectance overadistance L isgiven

by integrating

the infinitesimal reflectance

overtheilluminatedportion ofthetransducer:

ci/2 ., a dr

r=\ ej2kxsme^-dx

(11)

J"^2

OX

where a phase

factor,

exp[y2fcsin0], has been introduced in order to account for the

difference in phase across the beam with respect to the x = _{0 point. An expression for}

dy,

may be found

by

considering

dy.

=

dry dry

The expression for

dry

_{may be} obtained

by

_examining the expressions for the

reflectanceinthe transducerwhenthelight incident iseitherintheTEorTMmode.

TM Case

In _general, the expression for the Fresnel reflection _coefficient,

describing

the

portion oftheincidentelectricfieldreflected off a

boundary

interface,

isgivenby:

_

,^2cos01-n1cos02

HjCOsOj+^COSOj

wherethedefinitionsofthequantitiesareshowninthefigure below:

(12)

Incident

Ray

SurfaceNormal Reflected

Ray

Boundry

Refracted

Ray

Figure 10. Theangulardefinitionsrequiredintheanalysis oftheFresnelcoefficientsfortheTEandTM

cases.

When applying the formula to determine the reflectance from a period index

structure, the

following

values mustbe adopted: ni = _{n +}

An,

n2 = _n,

Q\

= _7T./2

0,

_and

Snell's Law is requiredforthe determinationof02- Theorigin ofthese valuesis obvious

by

reviewing the situation. Upon substituting into the TM Fresnel reflection coefficient

n-sin(9)-(n+-An)- _|l

(th-_An)

(n+ An)sin(9)-hn- \l

-(n-t-An)2

J

(13)

Anexpressionfortheincrementalchangeinrintermsof asmall changeinn_may

be found

by

_writingtheFresnelcoefficient as aTaylorseries _expansion,about

0,

interms

ofAnand_extractingtermsontheorderofAn.

Thus,

anapproximationfor Arisgivenby;

Ar= dr dAn An

(14)

An=0 Uponsubstituting:

Ar =

L

(sinOJ-A/l-cosO)2)

1

-cos(9)2|

/

-cos(e)2-Vi-

-cos(9)2-sin(9)+

\sin(e)-t-Vl-cos(9)2)

n-sin(9)-t-n"\/l-_cos(9)

(15)

An

Simplifying

theexpression_utilizingtrigonometricidentities:

Ar:-1 /m2

/m (sin(0)-sin(9))

/

. ... 1 ...2 -cos(9) - sin(6)-

--sm(9)n cos(0)

sin(0) (sin(9)-i-sin(0)) sin(9)

(n-sin(9)-fn-sin(9))

An

(16)

Furthersimplification:

.._ sin(9)

Ar. An

2-n-sin(9)

(17)

Resulting

inafinalexpressionfortheinfinitesimalreflectionintheTM case:

(18)

Ar= _An

2sinz0 TECase

_

1cos01-n2cos02

(19)

HjCOsO^/^COSOj

Upon substituting in thevalues mentioned_{previously in}the evaluation ofthe TM

case:

rx =

(n-i-An)sin(9)-n- _\l

-(n-i-An)

(n-i-An)-sin(9)-t-n- 1-

-(20)

(n-h_An)

Extracting

terms of the first order ofAn from the Taylor series expansion of_rx

abouttheorigin:

dr Ar=

dAn

An

(21)

An=0

This leads to theexpression:

sin(9)

Ar:=

1 ...2 \sin(0)-Vl-cos(9)

'

, , . ...

cos(9) -- '~

sin(9) +

l-cos(9) sin(9)-i-A/l-cos(9) l-cos(9)

cos(9)

/

n-sin(9)+_n-^/l -cos₍₉₎

(22)

An

Theexpressionsimplifiesto:

Ar._l

>os(9)2-sin(9)2)

Ar 2

(-n-sin(0)2)

(23)

Theexpression yields afinalresultfortheinfinitesimalreflectionintheTEcase:

(24)

-cos20 .

Ar= _An

2sin20

By

utilizing the small angle approximation, cos20=

l,

it _can be _{seen that the}

resulting approximation formulas fromthe TE andTMreflection cases possess the same

Ar=

An

2wsin 0

(25)

Returning

to theexpression required forthe

integration,

the expressionfor

dry

7

must _{be determined.}

By

_using the expression for the infinitesimal reflectance as a

functionofinfinitesimal index_changes,an expressionfor

dry

_{may be derived:}

dr dr dn -1 d

dx dn dx 2nsin20c&c

dr -1

(n

-An0

cos(qx

-O))

dx 2msin2 0

By

applying the

identity

that _sin(;c)=

reflectancefromthe

Bragg

cellbecomes:

(26)

,

qAn0sm(qx-<&)

(27)

the integral for the total eJX-e~JX

V

1 , v* fi/2

=jreJ

?J J-L/2

j(2ksin6-q)x

dx 1 , -/>

(LU

jr e J <

0J J-L/2

J{7ksia&+q)x

dx

Solving

forthefirst integral:

(28)

2" i, T J eJ(2ksin6-q)x dx= 2

j(2k%ixi-q)

2 2

(29)

1 ;<j> r= jreJ a 2J j(2ksmB-q)^ -j(2ksind-q)^

e 2 -e 2

ra =yr'e*

-sinc[(2Jfcsine

-q)]

(32)

2 2k

where_sinc(x)=

sin()/

. v '

/tut

Therefore,

evaluationoftheentire reflectanceintegral leadsto:

r =yrV<I,-smc[(2A:sin0-gr)]-jre'^

-smc[(2ksmQ+q)

]

(33)

2 2k 2 2k

Significance

of

the

Bragg

Angle

Since the maximum of the sine function occurs when the argument ofthe sine

function is zero, the _resulting expression for the total reflectance will be at a maximum

when either 2sin0=

q or

2sin0

=_{-q. Underthecondition when 2sin0}=

q, thefirst

term ofthe expression dominates. This represents the

"up

shifted"

case and corresponds

to the _operating mode ofthe

Bragg

cell usedin the optical systemoperation. Anexplicit

statementofthe

Bragg

conditionis givenbelow:

sin0s=^

_2A

(34)

sin0B =

^

=

Xfsisnal

(35)

Derivation of

the

Expected Acoutso-Optic Cell Output:

Frequency

Modulation

Another important resultthat can be seen from the reflectance term occurs when

the temporal dependenceofthereflectanceisreintroduced

by letting

O >L~lt:

r= Lsinc[(q-_2k

sinQ)]ejni

(36)

2 2k

Consider aplane wave incident on the

Bragg

cell at the

Bragg

angle. The output

E0Ul=rEin

(37)

Suppressing

the spatial

dependence

ofthe inputelectric

field,

the output electric

field displaysajcottime dependence:

EoutocreJ(ap,"f

(38)

Substituting

inforthereflectance expression:

Eout

oc-jr'Lsmc[(q-2ksmQ)]eja,ejm^

(39)

2 2k

Again,

suppressingthenon-temporal relatedtermsfound intheexpression:

0,~ey("+<W'

(40)

Fromthis result, itis apparent thatthe output fieldwillbe

frequency

shifted from

theinputfield

by

the valueofthe acoustic

frequency

foundinthe transducerofthe

Bragg

cell.

Thus,

if a plane wave is introduced into the

Bragg

cell at the

Bragg

angle (for

maximum reflected output from the _cell,) the acoustic signal

traveling

in the transducer

willbeplaced upon an optical carrier. The resulting

frequency

ofthe outputfield is given

by:

(0TOr=Q+_(i)opllcal

(41)

RecoveryofAcousticSignal: Optical

Heterodyning

By

theprocess of optical heterodyne

detection,

anRF signal thathas been placed

on an optical carrier is recovered

by "beating

down" the optical carrier with a

non-frequency

shifted reference beam. The process of signal _recovery can be examined

by

consideringtheinterferenceofthetwobeamsat anopticalsquare-law detector.

The signal beam can be characterized as a plane wave of amplitude

As,

optical

frequency

co0, and an RF

frequency

(ORp.

Therefore,

the signal wave will possess the

form:

,(0

=

Os

represents a relative phase shift between the signal and the local oscillator

beam.

Thereference,orlocal_oscillator,wave will alsobea plane wave. Howeveritwill

onlyexhibitthe

frequency

oftheoptical carrier:

LO(t)

=

ALOexp[jG>0t]

(43)

Since bothbeams are _{coherent, the resulting}

intensity

at the detectorwill be the

square ofthemagnitudeofthesumofthewaveforms:

^(OH^O

+

^otOf

(44)

which_{may be}written as:

Id*

=

%%

+

*A

+

^'lo

+

%*u>

(45)

By

employingthewellknowntrigonometricidentity:

eje+e'fi

cos0=

(46)

2

theform ofthe

intensity

atthe detectorisfoundtobe:

IDel

=|^r+|Aor

+2A/|^|2|^o|2cos(((0o+(0^)/-{Do('+

<&s)

(47)

Upon simplifying, theresulting form isshown

below,

IDe,

(0

=

IS

+

ho

+

^hho

cos(co^r+

Os

)

(48)

which indicates that the

intensity

pattern incident on the detector will _{vary in} time at a

rate equal to the RF

frequency

placed onthe signal

beam,

with a phase

delay

equal to the

phase

delay

presentin thesignalbeam. Sincethe electrical signalwill beproportional to

the

intensity

incidentonthesquare-law

detector,

theRFsignal willberecovered.

Atypical optical _setupusedin theplacement and extraction of an RFsignal on an

Beamsplitter

Laser

Optical

Frequency

Shifter

Optical Phase

Shifter

Beamsplitter

/

M\

Mirror N / _Mirror

Figure11. Ablock diagramof atypicalscheme usedinheterodynedetection. Electrical

Signal

Various means _{may be} used to place the RF signal on an optical carrier.

However,

in the case ofthe optical system _only a

Bragg

will be considered.

Also,

the

presence of an optical phase _shifter, in the case of the integrated system, is rather

complex and willbe discussedlater.

TheConnectionBetweenHeterodyne SystemsandPhasedArravAntennas

From the classic heterodyne optical _system, one can see a possible application of

technique tophased _array antennas. Ifeach _radiating elementof the antenna were to be

attached to an separate

heterodyning

system, the RF signal to be broadcast could be

placed upon the signal beam

(utilizing

the optical

frequency

shifter) and then phase

shifted the amount neededin orderto steerthe beam in a particular direction. Some of

the problems that exist with such a configuration is the amount of space required for

configuration and the high price ofthe components required. The integrated system is a

novel _way of_realizing multiple

heterodyning

systems, possessing a_{high packing}

density

ofthe

delay

linesthatisnot presentinthemultiple system case.

Dependence

of Output Angle

on

Acoustic

Frequency

Upon varyingthe

frequency

of the acoustic wave in the cell, the deflection angle

approximationto the

Bragg

equation and

differentiating

the output angle,

0,

with respect

tothesignal

frequency,

fsjg.

^~Vsignal

A0=

-2nBraggVS

(49)

Operation

of

the

Binary

Optic

Device

Ingeneral, a

binary

opticis an optical component on which asurfacereliefpattern

has beenetched thatwill result in phase shifts ofthe incidentbeam

by

values of0 or-K.

The surface relief pattern is governed

by

the input and desired output field pair. The

binary

optic deviceused in the integratedsystem has been designed tobreak an incident

plane wave into 25 equal

intensity diverging

plane _waves, each beam will represent an

individual

delay

line. In order to confirm the operation ofthe

binary

optic, the phase

function ofthe surface was enteredinto aMATLAB program andthe magnitude squared

of the Fourier transform of the transmission function was found. The is analogous

examining the farfield

intensity

pattern thatresults when a plane wave is incidenton the

Binary

Optic. A mesh and contour plot of the _resulting

intensity

pattern are shown

below.

|2-D FFT|A2 of

binary

optictransmission function

200

100

|2-D FFT|A2 of

binary

optictransmission function

25 Equal

Intensity

Diffracted Orders

50 100 150 200 250

Figure 13. Acontour plot ofthe_resulting

intensity

pattern withthe_Binaryopticis illuminateswith a uniform plane wave. Notethe25 distinctorders.

Introduction

to the

Deformable

Mirror Device

(DMD)

The deformable mirror device is a two-dimensional _array of _{electronically}

controlled mirrors. Eachmirror _{may be addressed, controlling} the X and Y tilt angle of

the mirrored surface.

Using

state-of-the-art _technology, it is possible to generate device

possess over one million mirror segments in an area of one square _centimeter, with an

active

(reflecting)

area greaterthan70% ofthesurface10.

10_{L.Hornbeck,"Deformable-MirrorSpatial Light}Modulators,"

ProceedingsofSPIE,Vol. 1150-_1206.

IV.

Single

Photonic

Delay Line

Concept

Generation

ofa

True Time

Delay

(TTD)

The time delays required for the operation of the phased _array antenna are

obtained

by

_{actively selecting,} or

tapping,

points on a

Bragg

cell illuminated

by

a

collimatedbeam. The source ofthe time delays canbe seen withthe aid ofthe diagram

shownbelow:

+xaxis

Maximumpositive A

time

delay

point

Incident

Beam

*

"Zero"

time_delaypoint

Ray

As s o ciatedwith

MaximumDrive

Frequency

Ray

As s ociatedwith

MinimumDrive

Frequency

x= xr

Time

delay

with respecttox=₀

Maximum ne gitive

time

delay

point

Figure 14. The_Braggcell,

indicating

theregionfromwhichtimedelayscanbeselected and a_rayfan

associated with aparticulartimedelay. The illuminatedportion ofthe_Braggcelldefinestheregionfrom whichtimedelayscanbetapped.

In this case, the

Bragg

cell is illuminated

by

abeamofdiameter d andis driven

by

thedesired output signal oftheantenna. The availability of signaldelaysresults fromthe

finite time it takes the RF signal to propagate through the AO Cell across the beam

[image:47.557.103.456.242.492.2]

illuminated

by

the source divided

by

the _velocity of sound

traveling

in the transducer

mediumor:

D

.

co!ei=_D^

vs

_vscos0fl

Inordertomaintain some_{symmetry in}theopticalsystem, the"zero" time

delay

point waschosentobe thecenter oftheincidentillumination.

Therefore,

thepossible

time delays fall intherange of:

^

S,S+

(51)

2vscos0B

2vscos0B

Aparticulartime

delay

value ofthesignal _{may be}chosen

by

"tapping" the output

face of the

Bragg

cell.

Tapping

the cell _{may be interpreted} as _selecting out an

infinitesimally

smallarea(equivalentto adelta

function)

from theilluminatedportion of

the

Bragg

cell.

By

tapping

the cell at a particular_point,the_{resulting light}

leaving

thecell

fromthatpointwill serveas a_{carrier,carrying}thesignal

frequency

aswell astheselected

time delay. In Figure

14,

the

Bragg

cell is

being

tapped at a point adistance of_x0 from

the center(x=

0)

_oftheincident beam.

Thus,

_{thesignal placed on}

Bragg

_cell

tap

at_x=x0

willbeadvancedfromthesignal placed on abeamtappedat x=₀

by

a value of

td

=+-e-seconds

(52)

vs

As the signal _propagatingthrough the

Bragg

cell _varies, the outputbeam from the

AOcell will be deflectedaccordingly. The highestandlowestfrequencies serveto define

a_{ray fan} thatwill be associated with a particulartime

delay

forall RF signal frequencies

General Optical System for

Tapping

the

Photonic

Delay

Line

From the previous _section, it is known that each particular time

delay

for all

signals can be looked at as

tapping

particular points of the

Bragg

cell.

However,

the

problemof_selecting a particular_rayfan (time

delay)

forthepurposes of

beating

downto

recoverthe time delayedsignalmustbeexamined.

A novel optical architecturehas been proposed

by

ZmudaandToughlian in order

to select particular _ray fans (time

delays)

in order to recover the delayed signal11. A

simplified version (a driver for _only one element of _{the antenna)} of the

heterodyning

systemisshownbelow:

Splitter

Tiltable Mirror

Bragg

Cell

Positive Lens

Figure 15. Architectureofa single photonicdelay,as proposed_byZmudaandToughlian.

In theabovesystem, theray fans aretransformed into planer waves

by

the use of a

positive lens that is placed suchthat its focal length is located atthe center ofthe

Bragg

cell.

Thus,

the positive lens serves to collimate the fans. Once the fans are collimated,

each time

delay

is associated with aparticularplane wave ofa unique spatial frequency.

nH.ZmudaandE.Toughlian, "Adaptive Microwave SignalProcessing:APhotonic

Solution,"

Microwave

In orderto select aparticular plane wave (time

delay,)

atiltable mirroris introduced into

the system.

By

_controlling the tilt angle ofthe mirror differentpoints on the

Bragg

cell

maybe tappedas shown abovein Figure 15.

Thus,

by

_adjustingthe angle of_{the mirror,} a

particular location on the AO cell is selected, corresponding the to the selection of a

particular time

delay

forall signals. The selected plane wave isthen interfered with the

local oscillator of the

heterodyning

system. In this system, the time

delay

becomes a

functionofthe tiltangle ofthe mirror andthefocallengthofthepositive lens used. The

appropriate mirror tiltangle associated with _selecting a particulartime

delay

is given

by

the

formula12,

_assumingthat the tiltangleofthe

Bragg

cellisnegligible:

0m=|tan-l^

(53)

This formula is derived from the _geometry of the system and _considering the

reversibility oflight. Consider

tracing

a plane wave back through the _system,

traveling

normalto the face ofthe detector. Such a plane waveis associated withthe desiredtime

delay. Upon

tracing

theplane wavebackthrough the signal portionin the system, itwill

be brought to afocus at some point onthe

Bragg

cell, as shown in Figure 16. The point

selected onthe

Bragg

cell correspondstothedesiredtime

delay

extraction point.

-X

Tiltable Mirror

BraggCell

Positive Lens

Figure 16. _Geometryforthederivationof required mirrortiltangleintermsofthedesiredTTD.

12H.ZmudaandE.Toughlian,"Adaptive Microwave Signal Processing: APhotonicSolution,"

Microwave

In order to cause the signal beam to become parallel with the optical axis, the

mirror mustbe tilted at an angle of20. This is due to the law ofreflectivity,

0r

=

0'r-Fromthe

diagram,

it isobviousthat the

following

_relationshipexists:

tan0=^ F

(54)

Ifthe center ofthe cell is assumed to bethe zero

delay

reference point, then the

time

delay

associated with _{x0 is simply} the value of _x0 divided

by

the _velocity of the

signal_propagatinginthetransducer,or:

(55)

tan0=

^iL

F

where

tj

isthetrue time

delay

ofthesignal.

Recalling

thatthemirrortiltangle shouldbe

twice the value of

0,

or20 =

0m,

_yieldsthe result shown _{previously for} mirrortilt angle

requiredtoachieve a certaindelay:

0_m

2

fv

_VS t_ld

\

V. Design

of

the

Integrated

Photonic

Delay

Line System

The

Significance

of

Ray

Fans

and

Delay

Lines for System

Design

As stated in the previous section, _ray fans are generated in the system

by

considering afixedpoint on the

Bragg

cell and _varyingthe

driving frequency

ofthe cell

between thehighestandlowestRFvaluesinthe signal. The highest

frequency

will result

in thelargestpositive deflection ofthebeamfromthe

Bragg

angle, thus it willdefine the

upperlimitofthe_{ray fan}asitexitsthe

Bragg

cell. The lowest

frequency

will resultinthe

greatestnegativedeflection ofthebeam fromthe

Bragg

angle, thus

defining

the low limit

ofthe _{ray fan}as itexitsthe

Bragg

cell. Sincea_ray fanis associated withafixed point

onthe

Bragg

_cell,itisassociatedwitha specificTTD forallRF frequencies.

Aphotonic

delay

line,

or_simply

delay

linefor _short, is the superposition ofthe all

possible_{ray fans along}theilluminatedregion ofthe

Bragg

cell.

Therefore,

a

delay

line is

composedof all possible

delay

values. Aparticular

delay

value isselected

by

_probingthe

delay

linetoselectout a particular_{ray fan}associated with a particularTTD. Thepurpose

of the optics of the integrated system, and the simple system shown _previously, is to

create a situation in which the individualrays fansare causedtoconverge in a mannerin

which the

delay

_{line may be}manipulated to extract a particularTTD value. In both the

integrated and the simple photonic

delay

line system all _{ray fans} converge upon a

deformable mirror

device,

which can select a particular _{ray fan}

(TTD)

for heterodyne

detection (conversion ofthe optical signal to the desired delayed electrical _signal) from

Underlying

Values Used for

Designing

Before

describing

how the system is

designed,

it is importantto present some of

thefactors thatwillbeconsideredthroughoutthe design. The importanceofthesevalues

willbecomeapparentinthesystemdesign.

The laser source used in the systemis an IR _{source, operating} at

1319nm,

which

hasan outputbeam diameterof0.6mm.

Unless otherwise _stated, all glass components used in the system are fabricated

from BK7. At the particular wavelength of the laser to be used in the system, the

refractiveindexofBK7 is 1.50348. Therefractiveindexof airisconsideredtobe 1.0. The central RF operating

frequency

of the

Bragg

cell is 1.3*109 Hz. The

bandwidth ofthe system is 0.2* 10^

Hz,

resulting in the highest

driving frequency being

1.4*10^ _{Hzandthelowest}

driving frequency

1.2*10^_Hz.

The index of refraction of the

Bragg

cell is 3.34. The distance that the active

region ofthe cell occupies _along theoptical axis ofthe systemis 5 mm. The velocityof sound _{propagating in} the

Bragg

cell 5125 m/s. From these parameters, the

Bragg

angle

may be determined:

(l319*10-9m)(l.3*10V)

sin0B

=-^ ^; - =0.1672878

(57)

B

{2)5\25mls

0B

=9.63016=0.16808_rad

(58)

The angular spread of a _{ray fan may be} calculated from the bandwidth of the

system. The angular difference betweenthe an extreme RF

frequency

andthe central RF

frequency

isgivenby:

A0=

^

=

1^^(O.1*1OV)

(59)

"sound

5125%

A0=_O.O257366rad

Simll: Computer

Simulation

and

Design

Tool

In this _section, the name Simll will be mentioned several times in the

determination of componentspecifications. Simll is a_program, written

by

_{the author,} in

order to _carry out a real _ray

tracing

analysis of the integrated system, as well as other

optical systems.

By

_{usingSimll information concerningthe}relative displacement of rays

at particular planes in _{the surface,} i.e. a geometrical estimation ofbeam

diameters,

and

difference in optical _ray slopes after _surfaces, i.e. a measurement ofthe collimationofa

beam,

the performanceoftheoptical system

being

designedcanbeevaluated. Simll has

also has the _capability to optimize optical component _parameters, i.e. the thickness ofa

component, until the difference in slopes after a user designated surface falls within a

given tolerance. Suchanoptimizationisquiteuseful,removing fromtheuser theneedto

closely calculate component parameters to achieve well collimated beams. Since the

optimization is accomplished _using real _{ray tracing,} the error introduced from applying

paraxial methodsforthe calculationhas beenminimized.

Integrated System

Overview

The design ofthe integrated system is an extension ofthe single photonic

delay

line system shown earlier. The extension to the system is done in order to increase the

number of optical

delay

lines available and insure that each new individual optical

delay

line is a reproduction ofthe single

delay

line associated with the "simple" system. The

insertion of extra opticsbetweentheoutputofthefrontend ofthe systemandtheDMD is

requiredin orderto accomplish the replication ofthe

delay

line. Oncethe

delay

line has beenreplicated, additional optics are furtherrequiredtoshapetheindividual

delay

lines.

The integrated optical system_{may be looked} at as

being

composed offour major

end,"

is to place the RF signal onto an optical carrier via an acousto-optic _{cell, to} break

the input beam into reference and local oscillator

beams,

and to recombine the beams

after the RF signal has been place on the optical carrier for later heterodyne detection.

The output