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Low Loss Flexible Dielectric Waveguide

foMillimeter-Wave Transmiss ionand its App.lication to Device

Annual Technical Report SRO-005-2

on

Cotract N00014-79-C-0839

Project Number SRO-005

* William B. Bridges - Principal Investigator

Dleporting Period: 1 November 1L980 -28 February 1982 -

Prepared for office of Naval Research, Code 427

Arlington VA 22217 ~C

"i fo 1Approved for Public RMlease

tion in whole or in part, in permitted for any purposeof the U.S. Government

8 2.- -.------ --.-. 04 9-

4ECUAITY CLASSIFICATION OF THIS PAGE (Ifgm Data Enete*__________________

REPORT DOCUMENTATION PAGE m fAroa COPTinG FORM

REOR UMBE. GOVT ACCESSION NO . RECIPIENT'! CATALOG HMNSER11

SYD-005-2 W. ________________

4. TITLE (amd Subtile) S. TYPE OP REPORT 6 PERIOD COVeReDL -Loss Flexible Dielectric Waveguide for Annual Technical.Nillimster-Wave Transmission and its Application 11/1/80 - 2/28/82to Devices 6. PERFORMING ONG. REPORT WMNUER1

_____________________________C_ R82-- VV. AUTWOnfa) . N TAC ON NTNUE a10)

William 3. Bridges N00014-79-C-OS 39

SPERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMeNT PROJE[CT. TASICAREA A WOK UNIT NUM01ERS11

California Institute of Technology, 128-95 613Pasadena, California 911L25 611-02 0

$I. CONTROLLING OFFICE NAME AND ADDRESS 1I. REPORT DATE

Office of Naval Research August 1962Code 427 19. NUMUER111OF PAGES

Ann VA 2271.MONITOSNG A09G N PA-a AOORESSD ditmat kmn Cinellad OW..) I . SECURITY CLASS. (of thle NepUw

IS..g~~UICATONDOWMARACING

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* Approved for public relesases distribution unlimited.

I?. DISTRIGUTION STATEMENT (of Me akWm. inweinI Shook 20. Of dlfbwm hem RehPa

CM Scientific Officer: Tel. (202) 696-4218

it. Key WORDSI (CaUentha. vM . .1*19o uwmd m it 0068h0W Awl #~or 6

millimeter-waves XR8-5 phase shifterdielectric wvaeuides IMS-6 electra-opticsdielectric loss finite differenemto Lim4bOdielectric constant finite element method

*loss tangent nonlinear effectsTRACT (Cowhwem an wo old* I# nee~em aw iwustfr br WeekS amw.)

A finite-differnce method has been developed for computing the propaga-tion constant. and field distributions for dielectric waveguides of arbitrarycaoss section and dielectric constant. The result. of the method are com-pared with the exact solution for a round waveguide. adtional cluainare made for rca ulrwaveguides anid thes results conpared ith Narcatili' aaeV idiaste solutions.

UsSUlts are given for a dielectric waveguide phase shifter using a

Do I ~A*m, 147 OstInom op i wev so1 is UEY oseaeunc~usa3SS/W012-L41-661 EGUN"CLASSIFICATOSP ?"I$ PAGGFI eam Dt

2 Wi~~u~dn.App~u~tgy mes zeSan of Sbase whift at 9=a~ wasw 11,w Pa ui thwyvltpa~e to tx~. On

the LtaO~ewg01l4.. ImUtue sodbiation of 70% was observed in a micro-uvO bliw. &ifg Ina, z i go apw.Msnt with thecry., Other Uses, of amS-

Um/- a -aikpLo mterials In fte milUuiterwav xmv aamer discused,iao1-ing ileoticaliy-scumed mntensim and aetramislly-tumed filters.

*V1

*lo

.U,

MLIOmZ& fl3TN Olf TBIOZCgY

Pasadena, Califoria,

L Lose Piezibleo ielctr lbvogidesfor Nillmuter-Weve 1'rminis@uia

vAn its picta to Devices

uAlM ITabnice1 Report M-005-2

-~ Cmtrct =0016-79-C-0939

vZoilect Eiiber 3a-O5

wiLLSm a. fuidges, - Principal !vuiao

Dewpotlaq Periods 1. Novmber IPSO - 28 Vebvmmy 1902

Prepard foe Office of UmyaL moseurmbx Code 427

Arlington VA 22217

Anypei for Public Dte...

Demonoti. momIn vbole cc in parte Is pezzitted for amy purposeof the LU. oosrmet

7-=77M-M§. -7_77..-1:7

This report covers research perfoxned unider contract 300014-79-C-0839

at the Caifornia Xnstitute of Technology, Pasadena, California 91125 and,

under subcontract, at the Eughas Rsearch Laoat ae, NaLibs, California

90265 for the sed year of this three year program, 1 November 1980 through

28 Vebzuazy 1962.

Personnel contributing to this Work were:

Wia B. Bridges, Professor of B1.ctricsal Regineering and Applied Physics ,

Caitaohl Principal Investigator (213) 356-4609.

Marvin a. Klein, member of the Technical Staff, Nwffhes Research LAbs-,

C-principal Investigator (213) 456-6411, k247.

zdnzd Sohusig, graduate Student, * Caltech (213) 356-4654.

The authors of esoh section. of the report aL-e idmntified at the begin-

ning of the section.

*Pesent addroes Av. Bolivia, 971, DriM, Lim, Peru.

!A1

*.~~~~~~~ .. w zo n a wan. . . . . . . . . . . .. .

IX. agawuM. =

III. flURN-OP!ZC DMCBS XN DMZUCTRXC IVNOUZ . . Iz-I

z. zasoCnOE AND ra vM .M . ridges)

A. sNpg and Ass .ts

During the second yerm of this contract to study dielectric wave-

, uides, two major tasks were pursued. Firt, a method of cOmputin the pro-

pagation constants and the field distributions for the modes of dielectric

uveguide of arbitrazy cross section and arbitrary dielec1tic: constant was

developed, based on the method of finite differences. This technique was

applied to a ro I dielectric vaveguide so that a comparison could be made

with a can f o which & rigorous exact solution in known. The technique was

.4 ~also applied to rcaglrand squAze uvmegaides and compared with the.

promats so Lons o nmza.tiU and othere. A brief escription of the

method and som of the results ae given in Section ZZ of this report. MO

details anea elsMisre (m Sectin C beow).

he seond ma:or task nertkeathis yr was the exiLnation of the

feasibility of usig nonlinar or elec=o-oti materials in dlctric

waveg ide form to realse useful fUnctiMs. As a spePOfic eIM3le of such a

capoMnmt, an eego- i phase shiter am con s ot using a lithiu

niobate (LMO3 ) vV . Low freqnucy voltae applLed to electrodes

foxming & portion of the waveguide strucue induced Phase shifts In the

* 94 s signal pzoating along the V&Veguide. Approximately one

radian of phase shift could be obtained with applied electric fields well

below the beeakmm va for the LiMbO 3 dielectric. Other coaponents, such

as electr~on~cly sommed antennas and electronically taned filters were can-

sidereds, and sco insights were developed for the future of materials require-

*. ments for such applications.

a. Future Plans

The devslogment of the fnite difference method is nov felt to be

sufficiently complete for our use. Zn the future we may calculate cases of

4 % % % % , . . . . , . . . . . . ., • . . . . ,,, , ,,% . . .. -,- . . . ., . . . . . . . . . . . , . . ..

1-2

special interest to us, but we plan no further development of the theory

itself at this tim.

Work will continue an the application of nonlinear materials to milli-

1 mter wave dielectric devices an outlined in Section XXl of this report.

Tis work will benefit by cordnat with other, separately funded progras

at the Hughes Research Laboratories, through the end of the ubentract period,

31 August 1982.

We plan to return to the question of surface wave propa i along

loss dielectrics as a possible explnation of the low attenuations actually

observed in S-S fibersJ, losses woch lower than that predicted for the

MCI. mode with the measured loss tangent at 94 =s. (Th~ese puzzling results

were described in mre detail in our previous annual repo.) Wile the

waveguide attenuation actually measured for US-S was of the order of 20

*bImter, too large to be practical for -Is aplcations, we feel it is

important scientifically to resolve this enigma.

A min approach to the problem of realizing a flexible dielectric wave-

guide was considered newar the and of the period covered by this report, and

we are ae actively pursuing it. Low loss, high dielectric constant materials

are available for the mLllmter wave range, but they are all rigid materials

(for em.le, Alanina, GaAs, Silicon). We are now considering the use of

these materials in finely powdered ftac, contained in a thin, flexible poly-

mar Jacket (e.g., Tflon). Preliminary lmasurmnts of such powders are now

being carried cut at 10 = to determine the relation of dielectric constant

and loss tangent of the powder fam to the bulk form.' If thes prove to be

suacessful, then flexible waveguides will be fabricated for test. (We mst

kna the dielectric constant of the packed pawder before we can design a

r'easnable guide.) Whese messurments will then be extended to 94 Gas a soon

as possible. Wile the primary intent of this work is to provide a flexible

r-3

dielectric waveguide sedium, if successful, it could also impact the ease of

fabrication of rigid dielectric components as well. One can imagine a

complicated configuration of directional couplers, filters, etc., fabri-

cated by filling the voids in a thin vacuum-formed plastic sheet (similar to

"bubble-pack). Such an assembly could stand aloneas true dielectric wave-

guide, or be capped with a metal plate to form image guide. We intend to

pursue these ideas as well, if the basic measuaements on povders prove suc-

cessful.

2 C. Publications and Presentations

The following papers wee given at the Sixth International Con-

ference of infrared and Millimeter Waves in Mimi, Docember 1981:

1. "Measurement of the Dielectric Constant and Loss Tangent of

Thallium Mixed Halide Crystals MR8-S and 135-6 at 95 Gz", W. 3.

Bridges, N. B. Klein, and Z. Schweig..'

2. "Computer Analysis of etangur Dielectric Waveguide for

Millimeter Waves, Z. Schwaei and W. B. Bridges.

3. "Electro-Optic Devices in Dielectric Waveguide", No 3. Klein.

The following papers have appeared or have been submitted for publcation:

-,1. W. B. Bridges, N. 3. Klein, and R. Schweig, "t of the

I Dielectric Constant and Loss Tangent of Thallium Mixed Halide Crystals

. US-S and 338-6 at 95 BOX", = Trans. on Microwave Theory and Tech-

- niqmes, Vol. L M-30, pp. 286-292, Ma h 1982.

2. . Sahwefg, 'Dielectric Vaveguides for Millimeter Waves," Ph.D.

Thesis, California Institute of Technology, June 1982.

3. 3. Schmig and W. 3. Bridges, "Computer Analysis of Dielectric

Vavevuidese A Finite-Difference Method", submitted to ISEE Trans. an

Microvave Theory and Techniques.

er n, at

4 1 -,4

tui

:4'.;

4Ix. OOWUU AURUIS or -r-r-- -- R DZIUCNRIC WAVEGUIDS (Z. Schweig)

A. Itouto

Image guides made of rectangular high ppraittivity dielectric

material have been suggested as a practical Waveguiding structure for use

in mkillimeter-walve integrated Circuits (Mc~l) [Refgs. 11-1, 11-2]. The use

of a high-resistivity semiconductor material is particularly interesting

since the possibility that active devices my be fabricated directly into

the transmission line can be considered.

Recanglardieectic waveguides for integrated optical circuits have

been investigated analytically by NArctili (Ref. 11-3]. Several other

workers-Mmou and Toulios [Ref. 11-1], Solbach (Ref. 11-4] and Yeh [Ref.

11-53 among others- have developed techniques for analyzingretnua

dielectric guides. Some of these methods are Limited to weakly-guiding

optical waveguides (small index ratio), or impose geometric conditions that

areinsffiienlygeudiial for our purpMoss We also have investigated the

analysis of such dielectric waveguides and found that the approxmations intro-

duced by Narctili (3sf. 11-33 awe not valid when the permittivity of the

guide is high caped. to the outer mediu (a id/cI~ PV 10) . we propose

instead a nuerical method bead on finite-differences for cmputing accurate

propatin caraterstis ed fIA disftibUtios.

B. escriptio of the Problem.

A retM ua dielectric weveguide of relative permittivity 1tj, sur-

rounded by an infinite sedium of relative permittivity 10 is the besic elnt

.4 that we condider for our theoretical investigations (Fig. ZZ-la). In practioe,

the guide is often supported by a dielectric of uch lover permittivity 12

(Fig. 22-1b) or by a metal plane (rig. fl-Ic) . In first -aproximation, we am

neglect the influence of the dielectric support if the modes are well guided

Within the retnu acre.* The effect of the metal plane is to allow

11-2

cc Ko

i a)

K0

-b) K

b,,

4 K0

mett

I Figure Il-1. a. Rectngular dielectric waveguide aonsidered in our numerical

analysis; the outer medium is supposed to be of infinite extent.

b. zn practice, the waveguide is often supported by a low-dielectric

material which has, to first approximation, little influence on

the modes.

c. 'The image guide has only some of the modes of the rectangular

guidet the metal plane allows only the propagation of the modes

that have a vanishing tangential electric field, on the plane

surface.

*. .~ .. . ., -+ T ' r p ' ' '

L . ' '

11-3

po agaon of only those modes of the free-standing guide that have the

appropriate symmetry with respect to the metal boundary.

Our objective in to ddiign an efficient numerical tool for computing the

propagtion characteristics of rectangular dielectric waveguides and obtain

accurate representations of the electromagnetic fielas.

NC. Nrcatili a Analysis

arcatili [Ref. 11-3] obtained an appzoxmate analytical solution

to the recagular dielectric waveguide (Fig. 11-2) by making the following

'.4. assumptions:

1. The change of index across the interface is sall, i.e.,V---.-- 1 << l (11-1)

2. The powr propagating in the corner areas (cross hatched an rig.

11-2) can be neglected. (This corespond to asstion that

the mode is far f cutoff.)

3. Te boundary' conditions (continuity of the tangential componnts

of the 3- and 3-fields) need be satisfied only for the dominant

. Comoents.

A small index step between the guide and the cuter madium will lead to a

guided moe that is internally reflected at nearly grazing incidence.

These assumqptions result in solutions falling in two families of quasi-

plane wave modes, 3 and .z The lover four modes of each family arepq pq

sketched on Fig. 11-3. The Field variation is sinusoaidal inside the core

and exponentially decaying outside of it. The characteristic equations are

simple transendental relations that, far away from cutoff, can be solved in

CO) The 4upeuea4_47 deneU6 the d Aetion od po~adz~i~ o4Ce etectae4 ~ ~ ~ dU and tkt 6abWp ot/t pond to the mbA oJ xezcu etiLJvCeIn tkt x- ad y-dUeetioa.

.. .. . .. . " '... '"... .- " . .. .. -."...... -. ,.,.--.'...- . . .. 4 .. 4'.'4. - a-'--".

XX-4

4*94

.1*4

j8 ~ Ii

9...

NCV^ U- i-vii

co krz CONSTANT &~I Ey on He W

EvO Ig ONSTANT 0V

I - ~ -'Cos kvj

-41

(a)

cos Iiga COSAT 74 ya

OWN I,, ... do..

Co 4- y

Es

P o "

ILACTRIC FIELD -~MAGNETIC FIELD

Figure 11-3.* Doiawat queui-trazserse sodes: Ry sad 3 . The sprriptpq pqCatern to the direction of polarizations while the saboaripto

Indiatethe umber of eziaa in each direction.

IKO

11-6JY.7

closed fom. They correspond to the characteristic equations of two inmd-

edent slab problem.

Sam authors [ef. 11-6, 11-7, II..], however, apply these solutions to

hLgh-permittivity waveguides, for which one or more of Nercatili's assp-

tics are invalid:

1. The change of permittivity across the interface is large.

2. The power popagating in the corne areas is not negligible.

3. The boundary conditions cannot he satisfied with quasi-plane

wave modes.

This is, in essence, similar to the difference between the approximate

lIinearly-polarized* modes of a weakly-guiding round fiber [Ref. 11-10] and

the hybrid nodes [Ref. 11-10] that consttute exact solutions for the round

D. Ote Vt

I. ma and Toaias [aef. 12-1] ha e proposed coupling the two iade-

pendent slab pcobU= that constitute the equivalent of Nareatili's solution.

They define an Oeffective dielectric mstant':

a kk) (XX-2)- Xj- (Yo

isi the pazmttivity of region 1 (rig. 11-4), k 7 is the separation con-

stant obtained by solving the slab parallel to the z-zxis, and k is the free-

space waveber. To solve the second slab, parallel to the Y-azis, the

effective dielectric constant, te' is used instead of XcL. This modification

is not based upon ay t o argument and does not resolve the problems

ecoustered with Narcatili's method.

2. Solb e Easf. ZZ-4] loys a made-a"tching technique that pro-

oeeds to solve the problem defined in rig. Z1-S as follows

&.e~ j...'-'sa- ~ - - ~~~-A. . -. -. -. - .

11-7

'4

1

I

-S

I yy

I-, I

I

-of

N X -e X9%

I'a

(a) (b).7*

1"~~

94

Figire 11-4. I the %ffective dielectric cametat" method, two ulab problem.

(a) and (b), are coupled.~44 ~

I

9~

4,

I

'44

~4%~~*-V

- - -.---w- -. ~- ' - '-~---t~x'.ts:'.t-.X-A-.~ - - - --. - S *%*%. -..

-. r.4r.r....%.%~% ~ -- -- - z*s ~ ~ - -

* electric or'y mog~netic wall elcrcw l

m I

b x

W/2

rvJmut Zl-S. m e rnsiAfutbg aproaah Conaists in eupeniMa the fields ineach S~bwgion ina cmlete Get of waveguikoe s and theninstohia them at the interface.

k I.

v-I-

&0 discrete sigenvalue, probl.em is obtained by placing an elec-

tric wall at a finite distance from the dielectric guide.

b. In each region (I-IV, the fields are expanded in a Complete

net of waveguide modes that satisfy the boundary conditions (electric or

magnetic walls) in that region.

c. The coefficients of the expansion (up to a certain order) are

obtained by matching the fields at the interfaces.

This method does not appear flexible enough for our purposes and also my

present Certain c.onvergence problems because of the lack of Continuity at the

corners.

3. * eh [St. XI-SJ has proposed a numerical approach based on the

finite-elements method that is applicable to a wide rang of dielectric wve

guide probems. The foalation is very similar to the finite-differenc

method that we propose, but we believe it is less efficient in the case of

relatively simple geCastries such as a rcaglrwaveguide.

-~ 3. * inite Differences

Winite-differences (ID) can be applied to a wave ppatinprob-

len either by starting frE the wave equation or a variationed principle.

We investigated both approaches and found that only the latter isnamial

stable and accurate.

1. Wave 3qnstion Approach

.jlb usual= application of 1ID is to disoretixe the differential

equations, in this case the wave equations. We define our problem in terms

of the longitudinal ed, % and 3 * The wave equations for these compo-

nests are:

+ kn*-

fora 1, 2 (13

+ knT

11-10

wh"ai 2 2 2I - , -a-n, d. e p ,d-j).,a k -I k -B (11-4)

At the interface between the two regions, the continuity of the tangential

fields nst be satisfied. These fields are derived fro, the longitudinal

I ee m s. In tern of a3s and 33 , the boundary conditions become

94 2 + !,* F * +l 117 Sy 3x Ty J

:.:.,,(11-5)

34- + 3#2 3# 1 -!~3y ax II 3y 3x

we then proceed to define a finite problem by en oeng the waveguide in

a box with electric wlls (perfect conduectors) large enough so that it per-

turbe only inially the modes of interest. Becaus of syetry, we need

consider only one quadrant, and we cover that quadrant with a discrete mesh

as shown in Figure X-6. At each mesh point, the wave equations are re-

placed by their finite-difference equivalents.

These equations are valid for all points in region 1 or 2 except at

the interfaces. The mes was chosen so that a row of points lies exactly

on each interface. rr these points we introduce "m"age teal in the

finite-difference equations that are then eliminated by using the boundary

codtos(continuity of %and 13H) exprzessed in fnt-ff racwes. We

then obtain a linear eigenvalue problem of the foe-

AX a 2 X1 -7k2

where X is a vector of the values of 8 and Z33 at the mesh points and A is

a sperse, real mtrix. This problem is solved (an a computer) using standard

eigemvalue techniques. oever, the mtrix A does not have any particular

,, ,. .. . d .l '+l,"~m~-lllli im~l WTl l,.,, .. , .. . -+P . . ..llm - ~ ,,, m.,- '

i11-3

Jy

Ax

V4

4

enclosed ina "box. * ly symeetry, onl.y one quadrant need t

be consid4tee. The saesh point.s lying on the intrfaces require

a t r t

b °. '~w ; 1 % ; " ,'i' . , o- .' : , - ' '; . " '" . - ' 2 '- . - '. ;"- . -. ' '- - .' .. - . . - - .. . . - ,. " . " . . " .- ". . . . .- ' -" -y.

X1-12

structa'l symetry that would peeit a reduction of the numrical 3abo .

2. Test Case

We tested the method as outlined above by applying it to a one-

dimensiona probldm, the m@i-infinite slab. tis problem is easily solved

analytically [ef. 1-10] and pesmits us to test the effects of the "box

and our treatment of an interface. Fig. zX-7 represents the one-dimensional

mobh used and Fig. U-G elm, the god agreement. for the field distribution,

between the iLit~e-affoxemose solu.cam n the anal.yticaJ. one.

3. GUMtSgla ad

Uman we applied this method to the a guide, we checked

the finiteifre c solutions by cmpating them to either Nrcatili' s or

a round fiber* in the high-freqpency Ulit. In this limit the guide is many

wavelengths across and all slutns should conver" to the - curve. we

then attempted to apply the method to the problem of the rec alar wave-

guide. we found it to be Inaccurate far the limited uobar of mesh points

S used (N - 9 in each linea dimnlsow. Since the size of matrix A increases

as U2, computer storate, liaitatioms prevented en increase In N.

4. Variational Approach

An other approach is to start from a variational quantity and di -

cretise it by applying finite-diffeees. It is well knom ffr. XX-S,

1-1] that for prpgating electramgetic modes,'the following variational

principle holds

dr -0

where

() Th aesud dbua Ua c~en 4o that tUa 0A4-6eDon A the 6am £me46 th eMw poMULu 6wke gaud tht 4 am ou mde .

XX-13

.141

Mw3 d/

qad/

oIo

,0 1 oll o l' o l .4 1 1 11 ' 11 ......

FL9= XX7. m-dmm~ Ngaao .SJ ets o MF ota iIlbpcbs

w-d

,, -i

II

411

4 19

2~~ 6 IAr*rF *Lr' .Z

IZ-15

'T 2 2

ymff rO1p 1,c r -i~*' +T- t + ~j2.]JJ:l , t,± - LIZ sy ,x.

j

+ [2 + [T]2 2]}-711)

with Z5 and* ("to/0) 3z*

If we consider a tangular elment, S3. as depicted on Fig. n-9a such

that the Ain CesaBtnt inside the element, We Can cMpute the

WID: t.- n of to 3 by using finite-differences:

,i "I 1 4 XZ9

.4,:

*4,3

ah12LL2hl & 2J T h j

jSIP S 4j. h2 h2 bii (16

For the problemn of the rta ul guide we can then define a mash that

covens the area of interest with rectn ua elements (Fig. 11-la) . JT is

Obtained by adding the conrIbtn of each element. We note that no special

trestent is req~uired for the interf aces, an J contains the continuity con-

ditons. By setting to sero the partial derivatives of j with respect to

the field values % and Zs at each mesh pointsr we obtain a linear eigen-

value probLea of tetw

AX a2 4U (11-9)

,- - r, -y,' ' -"" "- '- ",-.

.' ' - ':-" . ",'''' -'' ': ' " ' . .' .. -" " ,'.' ..: .

77=j- ~

* 11-16

2 p 42

a.~ UI.2il l m orfefaedfe mIopttm

Z12-17

lY hi

ht 15 1 I T [ 23 29 3, 5

3 4 144

S o

foZM the matrix A. No special treatmint is required at theinterfaoes.

o "-l

I% where X in a vector of ordered field values, A in a symmetric band matrix:

and 3 in a positive definite diagonal matrix. By a simple similarity trans-

formation,

32~ Al -A' (Zr-l0)

we reduce the problem to

k2

where A' in now a symmetric bend matrix. This structure allow us to store

the mtrIx A more, efficiently and thus permits us to use a very fine mesh.

S. - Ninmrical Results

We have analyzed the modes-of a square dielectric guide because

it allows us to compare the dispersion cheracteristics with the theory po

posed by Narcatili and with the dispersion curve of a round fiber chosen to

have the sam diameter as the square guide.

Figure Zr-U presents the dispersion curv. as computed by these three

methods, for the dominant nod. of a dielectric guide made of Teflon 0 - 2.1).

At high frequency, as we espected, the dispersion curves are not distinguish-

able. They deviate at lower fraece because Narcatili' s theory predicts

a shamp cutoffe while the dominant mode of a round fiber has no cutoff fre-

quncy. *Te finite difference cllaingives an iatezoadiate result.

lb are limited, at low frequency, by the, six* of the mash that we can treats

the cuter box ust be further removed in order to-limit its influence on the

modes. The *m clcltin for a high-dielectric constant guide (made of

coaes, K - 13.1), show that Nrcatili's theory and the round fiber approzima-

tion give nearly the sam curve that differs noticeably from the YD results

(Pig. 12-12), only in the ntreite frequency range, between the "close

to cutoffu and "far from cutoff* regions.

. ... L

0Y

wxN

tC >cr go

o b w21

w *

to Z

-waft q)

C * Zf

a. III 4

CI) . D

0 ii8L w81VVV S~

LW ZX-20

046

0 IIa::Lz~(L

c. 2 Aw w~

0 LLLV

~ 41z i'i

F Q~

(94

'4[8 :8A JSVHd

ZX-21

i * ftre work

We am working an a package of nmria1 zoutlnes that wirll allow

ns to extract the daminaants eigengwalues and Pinrresponding .ie a~tmr I from

a symmetric bend strix that is stored In *a coact array. This will permLt

us a large increase in the grid size. We win ake a detailed analysis of

the fields of a r dlectric maveuide and compare thm to Marcatili's

solutions.

4-'S. o.

. . . . .. . . . . . . . . . . . . . . . .

11-22

m~slpOi 83CTIOE IZ

21-1. R. M. ]cG and P. P. TouULoe, "Integrated Circuits for the Nilliuster

" rough Optical 1requency lag," Proc. of the Uup. S.u:iLulmter

Waves, aw !c&, March 1970.

ZZ-2. Ib tuichi fiMo a Takao tami, OLoT,-Loss r Dielectlic

In.ge Line fm Minin aer-Wave Zntegrated Circuits," I= Trans.

Micramw Th. Tech., vol. NTT-26, Oct. 1978, pp. 747-751.

ZZ-3. 3. A. J. NMarcatli, "Dielectric lectangular Noveguide and Directional

Couler for integrated optics," se Syst. Tech. J., Sept. 1969,

pp. 2071-2102.

" -.4. ]laus Solach, "'he Zlectromagnetic Fields and the Phase Constants

of 'Dielectric Zuge L"," Trans. micromvem 'Th. Tea., vol.

"T-26, a . 1978, pp. 266-274.

11-s. C. Teh, K. Ma, . . Doug and W. P. 3gmn "Sigle-mode Optical

•ppo aptm., vol. 18, May 1979, pp. 1490-1504.

U--6. Harold Jacobs M tro 3. Chrepta, NZectnics Phase Mifter

Hi L.LImter-wIvm icandiactor Dielectric Inte:rated Circuits 1

'rams Microwave flu 2T c., vol. 2%1T-22 c. 1974, pp 411-417.

11-7. mameth L,. M.AM, ftbert S. Earn, Earold Jacobe and Zlae Prelbera,

0"2liltm uwagaide Frequency scanng Linear Array Antemne," I=

Trans. uLcxrm Th. Tech., vol. PTT-26, Oct. 1978, pp. 764-773.

I1-4. Chi a. Ise, S. Uak and A. P. Del'ons, "Optical Control of Millimeter-

Nave Propagatio in Dielectric WaVeguide,' MMW J. Quant. 0lect.,

vol. g-S, larch 1960, pp. 277-288.

ZZ-9. J. S. mocusby and A. Gopinath, luerical Analysis of a Dielectric-

Zoaded wNagulde with a Microscopic Line--Firite-Difference Methods,"

I= Trans. Microweve Th. Tsch., vol. i'i"-17, Sept. 1969, pp. 664-690.

C, ' .-...... .. .-- , -.. . . .. . . . . . .. . . ., .. .. . . . ....-. . . .-. . .. .. .. , .', ... .. .. ...

11-23

ZZ-3. s.. OWnge, Olama Optical lnweguides and Fabres Clarendon Press,

,forG, 1977.

U1-11. Douglas G. Co and 7. Briam Davies, "Compute: Analysis of the Fumd-

-mtal and Ngher Oder Nodes in ingle and Coupled Nicrostrip, =

"va Tn Micimw N ave Th. and Tech., vol. IfL!20, Out. 1972, pp.

"69-679.

:a, ,

a .t

'a[..i

i,*0

, ' .;,-i ,. -, -..,, -- -,, ... -.-.- ... . ... . ..- . . ... . . . . . ... . .- . .. . . .... . . . . . . .. . . . . . . ........... ...-...........-.-- '..'-. ...... .... .

Zil. M"M MM inOTZ CSV~ma D3L UC VV= (K. S. Klein*)

A. Introduction

Za recent years, integrated circuit techniques have become mareos-

ingLy Iiortant in implementing cominonents and subeystems at millimeter wave-

lengths. A nmnwe of passive and active devices have been demonstrated in

dielectric waveguide including directional couplers, filters, phase shifters,

scanning antennas, detectors and sources. *in most cases, the active devices

studied required careful mounting of a discrete electrical device in close

proximity to the vaveguide structure In a vey which optimizes coupling to

the waveguide. in this discussion we describe active devices in dielectric

waveguide which can be realised by direct electrical control of the bul

dielectria properties of the transmission medium. These devices have intrin-

sic high speed, and are directly compatible with com dielectric waveguide

Two general classes of materials have bulk dielectric propeties which

ca be electrically controlled: semiconductors and electroaoptic crystals.

Zn Inioto the genrto of carriers leads to changes in both the

real and imaginary parts of the co~lex permittivity. These effects have

.4 been used to construct phase shifters C3sfs. 111-I, 111-2, 111-3] and

switches [111-4] in dielectric waveguide using materials such as galliumn

arsenide and silicon. Large moultin litiles hav, been observed, but

the switching speed in mostwass in Limited by the carrierreo inio

time to values in the rag 0.1-1 usec. I n electra-optic materials (or

nonlinear dielectrics) an applied voltage produces a direct change in the

real (and imaginary) pert of the dielectric constant, due to distortions of

the crystal lattice. * aterials of interest in this category include

AkwMeba o4 thea Teeu,.ca Staid H4 ugh" R"CUeht Labo apU MIUba, CA.

~~ .. . -r---* . . . . .

111-2

ferroelectric crystals which are conly used for modulation in th, visible

such as LLM~03 and LiTaO 3 In theme materials the sodiumn response time is

instantaneous at frequencies up to 300 Gfe, and the modulation speed is

limited, only by circuait conditions. Because of their intrinsic high speed

response, nonlinear materials are also promising for frequency mixing appli-

cations at frequencies throughout the millimeter band.

The usefulness of nonlinear materials for frequency mixing in the milli-

meter band was first demonstrated by Boyd, et &I. [Refs. 111-5, 111-6] in

experiments conducted at 56 G~u. Around the same time electro-optic modula-

tion was demonstrated in Limbo at 126 G~z[ef.11- and in LiTao at3 3Rf 117

690 GWm [at. 111.4].

More recently we have measured the electro-optic coefficients for several

orietatonsin Li~bOj and LiTao 3 at 94 GM [nsf . I11-9]. Zn each of the

above experiments the samle was either smuted'in free space or in conven-

tional metal waveguide. Free space moanting requires large samples to

minimise diffraction loss, while mounting in conventional waveguide intro-

duces severe dimensional tolerances mid requires a fdhough for modulating

voltages. If instead the electro-optic material is prepared in the fore of

dielectric waveguide, then the ruiem t for large samples or critical,

dimensional tolerances is removad, and compatibility with other integrated

circuit components in facilitated.

Mhe discussion in this section presents the results of our analysis and

exprimnts on electro-optic devices in dielectric waveguide. Zn Part a we

describe the electro-optic properties of ferroelectric materials, and in Part

C candidate waveguide structures for phase shifting are considered. Part D

describes experiments on a LiMbO B-guide phase shifter at 94 M~, and in

Part 2 our analysis of other control devices is presented. Part V discusses

- .the prospects for improved materials, and our conclusions and future plans

ar e sussed in part G.

111-3

D. * ..CZiL Propertis of Ferroelectric Materials

Phase Shif ters using the electro-optic effect in bilk crystals are

-,comonly useid In the visible, and have speeds Limited only by circuit can-

utica. *In this waxk we describe our studies of electro-optic phase shifting

at 94 Oft. We have used a 6aenamnological model to calculate electro-optic

* coefficients for a erof materials,* and have measured electra-optic

coSf ces.for a ander of orientations in Li~bO3 and Li~aO 3

The phase shift tog a transverse modulator is given by

T.~ Far(1-)

*ere L is the crystal lengrth, V is the applied voltage, D is the electrode

spacing, n is the micrmave refractive index and r is the electro-optic

ocffjoient. fte specific dependence of both n and r on theoretio

of the microwMa nd low frequency electric fields is ignored here (for

brevity) bit is properly acoamted. for In cuir later ccuais.In order

to c Wrctus a gives electraopi mteril3L for phase shifting applications,

we will make ase of a figure of unrit R, defined by

a3

fte Isortet reom for utiliing the electra-optic effect is that the

eleIotr-pticeeffitents for oertain mterials in the microwave region are

ON& 18rer thm those in the visible ['ftf 111-6]. This enhancemient is an

iqpofa reqairmat since the expected phase shift varies inversely with

wavOegt and would otherwise be mall in the far infrared and near milli.-

meter region. It bas been shown that crystals-with the largest microwave

electra-opti (and nonlinearw) coefficients are those with the largest values

of Ltne sme tiblt [sefs- 111-5, zxx-6]. In the microwave region the

linear scetibility amn be a=& larger than in thvse, due to the

cotribution fro, lattice vibrations * More specifically, the electra-optic

Z11-4

coefficient for a given crystal in the microwave region can be written as

r a 41£ • (:ZZX-3)

*:: lwhere xi 4s the ionic (or lattice) c tu ton the linear e 4blity,

and 8 is an qipirical, factor which is nearly constant for a wide range of

materials and orientations. in low loss materials, the reiement for

large values of Xi is equivalent to requiring large values of er, the low

ftr."ncy relative dielectric constant. The importance of high t r materials

-'--' s € 5/2.is empasied when we note (using U ) that the figure of merit R "e

in ferrolectrics, values of zr in the range 20-100 are q LLte cowman.

fto materials of particular interest for device appications are

LRIbO3 and LTaO3 . Lrge samples of these materials are available, and

the microwave losses are low. Measured linear parameters and values of the

figure of marit R for several orilentans in L MO 3 and L""aO 3 [tf. 111-9]d*,=. ],

are given in Table 111-1

C. -Meuide Structures for ,hse ahifting

* lW no wish to consider possible dielectric wa vguide structures

for the particular case of electro-optic phase shifting. a candidate

structure should be judged against 3 major requiremens,

(a) The structure must comprise two (or more) metallic conductors

for aplican of mo.ulating voltagess

. (i fte mcrommve and modulating fields mst be confined in the

dieecticfor optimamitrato

(c) Te electric field lines should be straight and parallel to a

single principal crystal direction to avoid phase interference

effects.

In Table 111-2 we have listed four caoon structures and the particular

qrements satisfied by each. It is clear that H-guide is the preferred

Table lUII Measured Values of the Linear Parameters an rigur of Meit

fcc Li.bO3 adLLa03 .

11473-PI-

REQUIREMENTSSTRUCTURE CONFIGURATION SATISFIED

IMAGE GUIDE . C

SLOT LINE A. (B)

Iq mo A

TMEr treeA. ().C

U: lI

r..o*r

L,.-., -4.. 4;, .. .,,. ,.,......... .• ." ".... ..... .'... ... . . - .-

111-6

Tabi. XX1-2. * Vm Kilimster D.l6Cftic WV~guJde Stzuctuzea.-

11473-7

MICROWAVE PBOWRTOMATERIAL POLARIZATION REFRACTIVE ASRTO

INDEXCOEFFI9IENT

UlNbO 3 ORDINARY 6.7 -0.2

EXTRAORDINARY 5.2 -0.2

UTO03 ORDINARY 6.5 -0OAEXTRAORDINARY 6.5 -0.*

Is)

FIGURE OF MERITMATERIAL ORIENTATION n3 r

(10-7 aniNOLT)

UNbo3 32350112 4.6222 5.7

UT80 3 231.113 5.2

111-7

choice (parallel -plate transmission line partially loaded-with dielectric).

It in important to distinguish between the hybrid modes and the modes in

H-guide (see Pig. 1X1-1). The hybrid modes E 3ef. 11-10] have compnents of

electric field in the longitudinal direction and in both transverse direc-

tions, although the dominant transvere component is parallel to the metallic

conducting plates. The multiple components of electric field are a disadvan-

tage in that interferences in the electro-optic phase shift can be produced

(violation of requiement C above). One advantage of the hybrid modes is

that the electric field is small at the metallic walls, and thus wall losses

age low. Sover, at the present stage of development, material losses are

dominant and the low wall losses of the hybrid modes cannot be exploited.

The modes [Ref. 111-10, 111-11] have a single component of electric field

directed normal to the metallic planes. Wall losses are larger than for the

hybrid modes, but still lass than material losses. amO important advantage

of the TZ modes is that the lowest order mode (designated TE ) has no10

cutoff, so that energy can be coupled in or out of the dielectric medium.

This is especially oeful for radiative devices such an scanning antennas.

We have calculated the mode cutoff properties [Ref. 111-11] of an

E-guide filled with LiMbO3 (Y-axis normal to metallic plates, and the results

Iare plotted in Fig. 111-2. The lowest order hybrid mode is cutoff for

bA o S 0.1, while the TI modes Oropagate for all -alues of b. We also show

the cutoff width for the TZ mode, which is the first higher order TI mode30

which is likely to be excited in or experiments. The sample dimensions

we have chosen (ms below) could allow the lowest order hybrid mode to pro-

pagate, but the input radiation is orthogonally polarized to the dominant

A polarisation of the hybrid mode, so the coupling coefficient to this mode

should be very small.

We havs fabricated LimbO3 samples with two different cross sections:

1 1473-9

tEb

(b)

Pigum I-I. Slectzic field cmientation for (a) hibrid mode and (b) Ts

mode in the 3--guide atruatuze.

03.11473- IO I

0.35 2

4-. TE300.2 HYBRID MODE CTF

CUTOFF

bo0.1

EXPER MENTAL0.06 SA MPLE

0 0.06 0.1 0.15 0.2 0.25 *0.3

2a=0

V.,,

UawlelIs 2a -O.55 m, b - .30 Me

Semle 2s 2a - 0.55 -, b - 0.40 mm.

A umber of TN10 mods proportion were calculated for the two samle cros

sectios 2

(1) lateral. decay distance of fields into free space -0.*06m nor-

malized guide wavelength

(2) Impedance: s amle I1: 60 CMI

Samle 23 60 CS

(3) Power absorption coefficient noumaimd to that of plane wave in

0.m~97 (ain,0. m-1

(4) inced phame shift nralised to that of plane wae in TA~ 3

rr 0.96 (r lU 2.5s/cm for 20 kv/cm field).

Mhe above properties indicate that the radiation In the MLI 0 sof

is well confined With"n the LIMO 3 , and has nearly identical propeties to

those of an nbounded plane wave In the material.

D. LiO, U-Gude Uhare Maifters at 94 =a

We have designed ad constructed two LJ*03 3-guide phase shifters,

differing only In their means; ot coupling from ila-lO hollow metal waveguide

tieto LiMbO3 X-guide. 2Ma first device utilizses end couplinge and is shown in

Figure IUZ3a. Mhe LI~O swWLe Is mounted an a flat metal ground plane,

whichb Is also dho bottom portion of the hollow metal, waveguide. Mhe samle

11473-13

NoLLOW METAL V-CUT LINbO3, 0.3 -m x0.5mm x 17cm

11473- 14

.1 { xO.Umx3.Own

TEFLON INSULATED WIRE1006IN. DIAM CENTERICONUCTA

HOLLOW METALWAVgW= .W..

lb)

Vlgn IZZI-3. offg~a~csc tr difiezt umos phase shiftm e oyn

Ca) dlzsct mv oomy~tag to 151-10 vavegutde and

(b) ooVUW UWMUSUg ^OGbw.

S- - i.16.

extends int the metal waveguide I the latter tapers down to the same height

em the Limbo3 P and to twice the width. The upper plate of the H-guide is

Isolated from the surmin metal structure and in held in place by spring

loading. This device is simple to construct and align, and has a wide band-

wit W m to the lack of tuning elements. One disadvantage is that the

disomt4M4_ty In the upper plate increases the VWR and reduces the coupling

efficiency.

The modulatioprorac and insertion loss of the above device were

measured by insertion of the device Into the active ac of a vaveguide phase

bLIde The beldve was first balanced by adjusting the variable attenuator

in -the reference acm for maxium fringe contrast. An adjustable phase shtifter

in the referemam -E WOs then set at the midpoint of the fringe pattern, i.e.,

the linear region. ic this bias condition an ac voltage applied to the

crystal causes an solitafe modlation on the detector output at the applied

frequency (I ks). * Th fractional mdltoan tjien he related directly to

the peak induced phase shift.

Or device - U Wea Made using the smaller crs-section samle.

Y'.~ Ti~s insertion less was 1.2 43, of which only 30d is due to sample absorption.

this suggests that further 41vmrvna in transition and coupling design could

lead to a aensiderable reduction In insertion loss. For a peak applied vol-

tap of I=0 Ve. the amlitde modulation mws 67%# and the induced phase shift

~ i.was 56 peak-tope! in good agreement with theory, based on the electro-

optic coefficisnts given in [mf. - X-9].

The second phase shifter which we designed and tested follows the design

of a device described and demnstrated at 200 Ml~ by Cohn and Mienberg

Ct. ZIZ-12]. The key element of this device in that probe coupling is used

InSGead of end coupling to Wa-l0 arvguldes. *a cross section of our device Is

s In fig. 221-3b. A short section of teflon Insulated wire with insulation

...................................................... . . . . . .

ZXX-13

rawrd at each end provides the coneection between the hell. metal Waveguide

and the .o3,-guide. One end of the wire probes the field in the hollow

metal waveguLde. The center (insulated) section Js a coaxial vaveguide con-

_,s,-tn, ... and the qpos£ts a axtand, along the end ot the LO a3 mple

and contracts the upe 3-guide Plate. The hollow metal wavevuide sections

r straight trough the device and are terminated by adjustable shorts for

tuning. fte bandwidth is restricted by the tuning elements, but the devicei as y to construct and align.

am device mesrto were aain made using the phase bridge technique

described earlier. the insertipnloss was 8 d, of which 3 do results from

nterial absorption. •ft have ot ,'eimented with varilian of the probe

penetratio depth.int te metal wavogus)e (the penetration now is .030);

ptw 1pepstration could x di ee e insertion loss below 8 dS. For a peak

lied voltage of 1000 V, the ,Wlt34 .mdulation ws 70%, and the Induced

Phase shut wes 589e ,A n agreement With callations.

3. Ode PUevi es

. teils which ame useful fam bulk p ase hifting can also be used

'fm mnzImi freCq awmdim . U, m mersi effiienc in this

ocas cm be titea as

~L. =ZZ-4)

wmm dis am ELIGN l m fl1.0imt0, L Is the Interaction length,

amda I~s ase.,.-- -G n an& Zl, wi.ting S. Z.T.4,we hawsumsds

2. 1 d e o m t Ith the

3 . - -p-ee .

I" '" " e,' . - " . ' :--4* .. -," . , ;.. , . .• •... %.4" ,...".- . .. * . . . . . . %

If we sgme that the lsmfth I* Is Limited to a1 where a is the aheozytion

oofioat m theb onaversion efficimo Is a0 at 100 GR is

-(9 x 10) (11-5)

Far an area of 0.5 x 0.5 =2m and an input power of 10 kV (well below the

dielectric breakdown threshold in LUO 3 ), the calculated efficiency is

3.61%. this will be reduced slightly when Absorption is mclvded in the

calculaion. Me. Above ooamriom efficiency is already of practical interest,

but still larger Vmae" am calcoulated frsomteilasDaTi0 3 end 10O3 .

2. Uleotgonioally-sft .. eaywave antna

It is well imm that periodically perturbed waveguides will

zadiate latemally at one or mars fixed angles, thus l edin to applications

as scanning mmatmbs. In uft, dielectric waveguidem have beemnousd for been

scanning via frequency sweeing L'sf. =2-13]. -Twvo isdaaeof this

technique are that fixed fbpquemy operaticn is not possible, and beau spread

In the 2-plane is large since the Waveguide, height is mll. -in mem recent

$ . maw eT, imh at a. Cuef. 111-14] ellainated te 3[-plan spreading by using an

3-guide struatue with flaring of the metal plates to produce a one-dimensional

barn. -Mem nnming was still obtained by freqnucy sweeping.

In bofth ~ri described above, the dielectric guiding sofdine n

silicon. If we substitute LbOfor thes silcon, then te e~lar-piUb3

1poperties of the U*O 3 can be used to provide scanning at a fixed frequency.

Mugre =1-4 phcues a shetch of te Li003 sale (with periodicidnttos

and final 3-guide antenna ansubLy. Mwe lobe agle in the 3-plane of the afth

space haoic is give. by [Nsf. 112-13]iu

$10 .0 +a 6

U=O SAPL

ANTENNAASSEMBL

~~5d

-- S.Z - . t ~ i p-le U a~ at O x O

5*9st

• lr z1z-16

Uhere X is the free space wavelength, X is the guide wavelength end d is

the spacing between perturbations. In all cases of practical interest (with

Xg A ) only negative values of a are possible. if we choose 8: d 1 then

only the a - -1 harmonic will radiate so that

ny applying a modulatng voltage between the two plates of the H-guide struc-

twr (Fig. 112-4)X anm be varied, thus varying the angle 0_1. If we asm

that Xg ./n, where n is the microwave refractive index, it is esay to

show that the angular motion Per uni of applied electric field (using

An - n3r a3) is

All1 3 W (111-6)

whzere z is the too-ortic coefficiat. -2us, the scann antenna

described here is crstiedby the swfigure of swit as the bulk phase

modulator described earlier (see Nq. -21' For a 20 kV/cm field in a

Z&1O 3 device, A08 - + 0.60. owver, meach larger scanmng angles (an the

czder of 1 radian) are predicted for aTi.O3 umder the an conditions.

3. 2lectronicaUy tunable filter

Fiad-frequency bandpass or bandstop filters have been demnonstrated

by coupling a pillbox or ring resonator to a wave travelling in dielectric

W-.av-eguide. The center frequency in this type of device is detemined by the

di..sions and refractive index of the resonator structure. If the refrac-

tive index cam be varied theoall, m the center frequency can be

adjusted, resulting in a tmable filter. A sketch of such a device along

with the output frequency spectrum is show in Fig. ZXX-S. M Te straight

wNvguide sections am be fabicated fro, a cnveanment low-loss material

Sunk a CM .ft , e close-coupled ring resonator could be fabricated from

~~ ~ ~~~~~~~~~~~~..... ...................-............ ,.... .......-.....-.-. '.'.'.'.,--..,-............. :.:,,.,....., .......................................-.......... ,.......-'..,.

11473-21

LiNbO3 OR GaAsRING RESONATOR

Vigur. 222-S . Sahmma mrumtt of a tunabU ing reaanator fUlterbaaedOf Imag £inq. ori atf-guide. 30th bwAu-pa and band-ze~eat dateziinUesn m be zea"Usd.

III-Is

LiMbO3 (ith a large elotro-optic coefficient and noderate loss) or GaAs

(with a small.r olectro-optic coefficient and low loss).

Toi analyse this tunab.lity of the device, we ass that the resonator

Q (cc linewidth) is detezined. by dielectric loss. Thie line.idth ln this

case is

AV tan-.. (Vt-an)

The center frequency v can be written as

2nlrD

where a is the order of itrenc.c is the speed of light, n is the

refractive index and D is the ring diameter. The change in v induced by

a change in n in

n

Thus,, the xequired Index change to tune by cue inwidth v Av) is

obtained from combining Upa. 1114. and IIJ-U4.

An - ntnd (111-12)

Since An - n 3 Z , the field required to tune by one Ulnevidth is

n aG tana (111-13)(n3r) nr

This field is equal to 20 ky/cs for LiMbO3 , and So kV/a for GaAs. We see

that the tmbilJty is Uaited, based on presently available materials. It

is hoped that further reductions in dielectric loss at millimeter WvalengthS

will lead to imroved filter Fo ae

7. Prospects foro atrioved

It is ct fro the previou discussion that then is a strn need

fw materials with larg elect.o-otcalar coefficients and low loes.

N'.4--*..... .....- .-. --.... ..

111-19

fte Phase shifting perforxmnce of several] candidate materials in their

* present state of development in plotted as a function of length in Fig. 111-Er.

We have assmed anm operating frequency of 94 GH~Z, and an applied field of

20 k/cn. We note that certain materials with large electro-optic coeffi-

cients have low losses (e.g., GaAs), and perform nearly as well over a length

L & /0. The mat promising material at present appears to be Ba~i03

although cinmrcially. available samlas of this material are very expensive

and of poor quality. any materials iroWemaus leading to lover absorption

losses should lead to significantly improved device performance.

a. Cocusions and Future Plans

We have described the impleetto of a number'of electro-optic

control devices In dielectric waveguide. ft'e devices we describe still

require the assmLy and alignment of a numer of carefully machined dis-

crete caomnts. an eventual goal would be the complete monolithic integra-

* tic. of all comoents auto a single chip.

At the present state of developmnt, the most promising materials for

device aplctosare Li~O., and perhaps GaMs one important advantage

of these materials is that they are readily available in large lengths

(2-6 inches).

In the remaining year of this SMo Program, we plan to redesign the

transitions in both R-guide phae shifter described in section D, in order to

reduce the inertion loss.* We also plan to construct and test a Li~sf.,

frequency doubler or scanning antenna, using H-guide.

=Z-20

11473-22

1000 '

z looSON// (333)

10 um%4fLr.s(3= M. ~

'4~

(rl (231)

~10-1

.11-

10-2 10-1 1 10 100 1000LENGTH, cm

riguie iz1-6. =&i OGPhan. shift 'vs. length fcc sevezal electro-optic

v s Im ds to the amidition L = 1/6, wbeze a is the abuwptionaeffliit for the given Matezil en ointti

111-21

RZPZD aN=8 FOR SECTIONIIIr

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L ice,.4- -1 '.

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