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Second International Symposium on Space Terahertz Technology Page 63

ANTENNAS FORSUB-MILLIMETRE WAVE

RECEIVERS

Joakim F. Johansson and Nicholas D. Whyborn

Department of Radio & Space Sciencewith Onsala Space Observatory

Pranay Raj Acharya, Hans Ekstriim, Stellan W. Jacobsson,and Erik L. Koliberg

Department of Applied Electron Physics

The Millimeter Wave Laboratory

Chalmers University of TechnologyS-412 96 Gothenburg

Sweden

ABSTRACT

This paper reports on investigations of two antenna types whichare suitable for implementation at sub-millimetre wavelengths:the diagonal horn and the sandwiched tapered slot antenna.

The diagonal horn is studied theoretically by expanding theaperture electric field into Gauss-Hermite modes. A few of thesemodes are then used to model the radiation pattern. The resultsindicate that the fraction of the power radiated into the funda-mental Gaussian mode is about 84 %. About 10 % of the power isradiated in the cross-polarised component. Radiation patterns fora 4 x 4 diagonal horn array, measured at 100 GHz, show goodagreement with the theoretical predictions.

The sandwiched tapered slot antenna consists of a slotlin.e an-tenna which is sandwiched between thick quartz super- and sub-strates. An elliptical lens is used to collimate the beam. Model ex-periments have been performed at 30 and 350 GHz. The radiationpatterns are worse at the higher frequency, probably due toalignment problems.

Second International Symposium on Space Terahertz Technology

1. INTRODUCTION

Commonly used millimetre wave feed antennas, e.g. corrugated horns, be-come very difficult to realize at sub-millimetre wavelengths. The corrugatedhorns radiate an almost perfect Gaussian beam [1], but the tolerances needed areat the limit of what can be achieved using normal fabrication methods. Somefeed types are easier to make, but, as always, there is no such thing as a freelunch. Pyramidal and conical horns exhibit a lack of symmetry in the cardinalplanes of the radiation pattern which makes them unsuitable for launchingGaussian beams. The pyramidal horn has the added inconvenience of astigma-tism, i.e. the phase centres for the E- and H-planes do not generally coincide (cf.[2]). The need for an alternative to these horns at sub-millimetre wavelengths isevident.

We have investigated the so-called diagonal horn (cf. [2,31), and it seems to bean interesting candidate for sub-millimetre feeds. The diagonal horn antenna isshown in the following sections to be quite an efficient Gaussian beam launcher.One marked advantage with this horn type is the ease with which it can be ma-chined. When using waveguide technology at millimetre and sub-millimetrewavelengths it is quite common that the mixer is made in the so-called split-block technique. The component is machined in two halves, and when joinedtogether the extra losses are relatively small. The diagonal horn lends itself tothis technique (see Figure 0).

Figure 0. A diagonal horn made in the split-block technique.

The tapered slot antenna is an open structure antenna which radiates a beamIn the endfire direction (along the substrate). Classical tapered slot antennas re-quire thin substrates (of the order of <= 10 gm at 350 GHz).

One way to solve the substrate problem is to sandwich the antenna between athick substrate and superstrate, and then use an elliptical lens to decrease thebeamwidth. Results from model experiments at 30 and 350 GHz are presentedIn the third section of this paper. The results show that it is difficult to achievegood agreement between these two experiments, which is probably due to thestringent tolerance requirements at the sub-millimetre frequency.


2. THE DIAGONAL HORN

The diagonal horn has the following electrical field distribution in the aper-ture [2, 31 (see Fig. 1 for reference):

Ea? = Eo['%c cos---nY +9 cos ]ejka2a 2a lx1<a

k8 2.71[2a2 X2 Y2-

A 2L

yka

This means that the field consists of two orthogonal TE i 0 modes, the powerevenly distributed between them. This set of modes must be excited somehow.Love [31 used a circular transition from TE i 0 , but the transition seems ratheruncritical, and a direct transition from the rectangular waveguide is good enoughfor most purposes. The aperture equi-phase surface can be assumed to be asphere centred at the horn apex, and is here approximated by a paraboloid.These assumptions are probably not too wrong, at least not for long horns.

Figure 1. The geometry of the diagonal horn.

The aperture field is seen to have the desired symmetry properties by intro-ducing the following auxiliary coordinate system:

z x—y=

X

,a+ y

f2-

ir4EE, cos cos

gri elk°

2i7a 211aZ4

E = 4 .Eap = E0 sinsin2in

gri efkO

212-a

E° [cosaa_ 2a

Eo[- = cos-- a 2a

(3)

41W•• • • •••••4••••••.,•• • • ••••••• 4•••••••••••••••••••

1 + -8- 0,90528472

8Per

1

ir2P

CO + PLY

PCO P

CO + PCT

0,0947153

(5)

Page 66 Second International Symposium on Space Terahertz Technology

Combining Eqns. 1 and 2 yields the following:

The co-polarised aperture field (77-directed) is thus symmetric with respect tothe -4T7 coordinate system. The cross-polarised aperture field component (-di-rected) is ant-symmetric, and the feed thus has no boresight cross-polarisation(note that we here use the so-called. Ludwig's 1

st definition [4] for the polarisa-

tion). The aperture field components are shown in Fig. 2.

Figure 2. The magnitude of the co- (left) and cross-polarised(right) electric field at the aperture of the horn.

The fraction of the power in the respective components can be found bysolving the integrals

a a a

= 1 f tEni2 drdY 1E4 12 cady (4)

-a -a -a -a

where the electric field components are given by Eqn. 3. The numerical resultsare given by

(8)


It is seen that the cross-polarised part is quite large (= 10 %), and this might beexcessive for some applications. However, in many cases, this cross-polarisedcomponents could be dumped in a termination through the use of a polarisinggrid. The loss one would encounter by dropping the cross-polarised part is then= 0,43 dB.

2.1. GAUSSIAN MODE EXPANSION

A powerful technique to study the radiation pattern of an aperture antenna isto expand the aperture field into Gauss-Hermite or Gauss-Laguerre functions (cf.[1, 5, 61).

The electric field for a well-collimated beam can be written as

w(z)ei[o(z)-0,4] e

-ik[x 2+ 2YE(x,y,z) e-f' --zA] 2R(z)

(6)

• Kinm efim+n)[(13(z)-0A] aX

_w(Z)j=

—aop1 = —ao

where a modified Hermite function, defined by

I.— x 2/Hns(x) = lim(x)

Y 217' m!

Is used to get a compact notation.The beam parameters in Eqn. 6 are given by (cf. [61)

w(z) = / 1 + [z/,]2

R(z) = z[l +[zclz12]

(P(z) = arctan 1--Zc

itw3zc

where w denotes the beam waist radius, R the phase radius of curvature, zc theconfocal distance, and 0 the so-called phase slip. Returning to Eqn. 6, one ob-serves that w and R are common to all modes, whereas the phase slip Co getsprogressively multiplied for higher order modes.

If one now has an aperture field EA where most of the phase variation can becontained in a spherical phase factor, viz.

EA(x,y) = E(x,y,zA) = ex,y) e-i k[x2+YT2RA (9)

then Eqn. 6 collapses into a very convenient form.

3. 2coszL e-{alwAr dt f -[atlwAr dt"Co =

P tot X wi

2

(13)

8 Second International Symposium- on Space Terahertz Technology

Using the orthogonality properties of Hermite polynomials [7], and some alge-braic manipulations, the coefficients 1C„„ are given by

00

Kmn = ex,y) 4112.X]j7 nrY1 dxdy

2 WA WAirw A

If now the ex,y) function is real-valued, one avoids all numerical problems due torapid phase variations in the integrand.

The diagonal horn has no phase variation over the aperture except for thespherical part. It thus lends itself to this Gauss-Hermite analysis. The g(x,y)functions for the co- and cross-pol parts are given by Eqn. 3.

The mode power content is given by

A2

I Kinni2 2

lex,Y)12 dxdY

and the results for the diagonal horn are the following expressions

2

coslrlL col- #17„,{-avyA kalvA vidudv Even rn, n (12a)pco z A 2

mn =P tot X w

(10)

P mnP tot

Eck, JAL=

"tot 1r wi

0 0

0 0

s1n2Lsin 174 124- ] dudv

2

Odd m, n (12b)

The expressions in Eqns. 12a and 12b can be simplified for a few simple casesby breaking down the double integrals into single integrals. The result for thefundamental Gaussian is

wA - a pt

0,863191

0,843025Opt


The choice of the ratio willa is in principle arbitrary, but Occarn's Razor* tellsus that the most natural choice is to maximise the fundamental mode coupling[81, i.e.

a [-fil oalt di .

The coupling has a maximum at wAla 0.86. An optimisation program gave thefollowing results (correct to six decimal places):

(14)a

(15)

The diagonal horn thus has quite a high fundamental Gaussian mode content.The mode content for the higher order co-polar and cross-polar components isshown in Table I.

In=0 ' n=2

tn=4 n=6

m=0 0,8430.

3,655.10-1° 0,005405 0,0009189 5,110.10-6m = 2 tt 0,01620 0,003339 6,859.10-6 0,0003185

m = 4 * * 1,562.10 0,001012 0,0009922

rn = 6 * * * 0,001356 0,0005954

m=8 * * * * -57,364•10

n= 1 n=3 n = 5 n=7 n=9

m = 1 0,04848 0,007725 0,0004141 1,117.10- 4,800.10-

m = 3 tir 6,037.10- 0,001545 0,001380 0,0006026

m = 5 "4r * 0,002060 0,0008870 0,0001456

m = 7 * * * 0,0001112 2,909.10-

m = 9 tr * * * 0,0002786

Table I The power fraction for the mnth co- (top) and cross-poimodes (bottom). The stars denote redundant informa-tion.

*Entia non sunt multiplicanda prmter necessitatem" — A philosophical principledevised by William of Occam (c. 1290 - 1349)

2rwozc (16)


Now when we know the optimum waist radius, it is easy to find the equivalentGaussian beam parameters. If one assumes the following (see Figure 3 for refer-ence)

wA Alzj2 = Ka

RA ZA [1 + [zciz,j2] =

(PA = arctan-a = arctan xK2a2zc AL

then some algebraic manipulations will yield the results

wo

ZA =

Ka

it K.2 a2]

AL

2a2..

Ka

1/1 + tan20A

+ cot2oA

(17)

The phase slip (PA is again seen to be an important parameter in this analysis.

Figure 3. The geometry of the equivalent Gaussian beam

(19)


Table I showed that there are just a few terms that contain a significant partof the power, namely the 00, 11, and 22 terms. It is hence possible to devise a,simple model for the radiation pattern of the diagonal horn. The far-fleld radia-tion pattern is given by (except for an unimportant constant):

F 0(9,(p) = .e-2P2 k°° +- K22 e-j"A [4p2COS2 9 — 1] [4p 2Si -2

Fcr(e,c9) = e -2P2 1 K11 4p sin cos 912 (18)

= ° tant9

The coefficients for the optimum waist size (Eqn. 15) are found by numericallyevaluating the integral in Eqn. 10, and the coefficients for the model in Eqn. 18are

K22 - 0,138628Koo

0,239816Koo

Combining Eqns. 18 and 19 one can draw the conclusion that the far-field radia-tion pattern is quite rotationally symmetric. The cross-pol level is approximately

61-2 1 2K1112

Igcoor- -15,1 dB (20)

If the phase slip factor is zero, the radiation pattern will exhibit deep nulls,whereas a non-zero value will yield a more 'smeared' pattern.

It will be shown in the following section that this simplified model is quiteaccurate.

2.2. MEASUREMENTS

In order to test the theoretical predictions, an array of diagonal horns wasmanufactured and the radiation patterns were measured. The array is shown inFigure 4. The respective horns are fed by standard waveguide (IEC R-900) andthe back side hole patterns match "standard" flanges. A waveguide detector isbolted to the back side. The patterns were measured in an anechoic chamberusing a computerised antenna measurement system.

D

E


Figure 4 The diagonal horn array.

The horns in the array had the following dimensions:

C3 2a = 14,0 mm= 55,0 ram

The horns were measured at 99 GHz (A, - 3,03 mm) and the Gaussian parame-ters are thus given by (see Eqns. 15, 16. and 17)

wo 4,98 mmzA 17,7 mm

fa Ka 6,04 mmCa OA 34,54°

The E-, H-, and D-plane co-poi patterns, as well as the D-plane cross-polpatterns were measured for four of the sixteen horns In the array (see Fig. 5 forreference)

Figure 5. The enumeration of the array elements and the planedefinitions. The measured horns are shaded.

.....I ..

•„„8 ,..•. .4s......••::".•• i*b.

.......:••i

•

......

.8•8

.. .. :. ..

..•■

::

1 ...A, . ..ilif•111;,...e , , .. 4.4.1.',

I

0

-30

-10

-20


Figure 6 shows that the measured radiation pattern is rotationally symmetricdown to about -17 dB. The D-plane pattern has a 'shoulder', but except for thatthe pattern looks nice. The E- and H-plane sidelobes are probably hidden bynoise below the -30 dB region. The D-plane cross-pol component is shown inFigure 7. The pattern is a little bit asymmetrical, end shows on-axi,s cross-polari-sation. The reasons for these non-idealities are probably found in the difficulty toaccurately set up the antennas at 100 GHz. A small error in feed angle will 'leak'co-pol power into the cross-pol measurement. Any lack of polarisation purity ofthe transmitting horn might influence the accuracy as well.

The horns do not seem to be especially influenced by being embedded in anarray. Figure 8 shows a comparison between four H-plane element patterns. Theuniformity is excellent, and one can thus safely use the horns in such an array,without deteriorating the radiation patterns.

-60 -30 30 60

Figure 6. Measured radiation patterns for the H (solid), E-(dashed), and D-planes (dotted) of a diagonal horn inthe array (#33 in Fig. 5).


-10

CD

0 -20

-30-60 -30 0 30

Figure 7. Measured radiation patterns for the D-plane co-pot(solid) and cross pot (dotted) components of a diagonalhorn in the array (#33 in Fig. 5).

Figure 8. Comparison between measured H-plane radiation pat-terns for four different diagonal horn array elements(#11, #33, #43, and #44 in Fig. 5).

till1111

--,----.11111-30-60 30-30 60

0

,.., A., ?...... .

.:-.-30-60 60-30 30


It is quite interesting to compare the measured patterns with the ones pre-dicted by the theoretical model, introduced in Eqn. 18. Figures 9 through 11show this comparison. The H-plane pattern shows excellent agreement, whereasthe theoretical model fails to show the characteristic shoulders in the D-plane(Fig. 10). The cross-pol level (Fig. 11) is predicted to within 1 dB, and the pat-tern form is qualitatively correct. The simplistic model can hence yield quite agood agreement with measurements.

Figure 9. Comparison between measured (dotted) and theoreti-cal (solid) H-plane radiation patterns.

Figure 1 0. Comparison between measured (dotted) and theoreti-cal (solid) co-pol D-plane radiation patterns.

-30-60

A

30 60-30

Second International Symposium on Space Terahertz TechnologyPage 76

Figure 11. Comparison between measured (dotted) and theoreti-cal (solid) cross-poi ID-plane radiation patterns.

3. SANDWICHED TAPERED SLOT ANTENNASVarious forms of slotline components are attractive, topologically and electri-

cally, for integration with e.g. sub-millimetre wave SIS mixers. The thickness ofthe slotline substrate should be small, so that no surface waves are excited. For aslotline antenna the requirement is even more stringent, and the thicknessshould, as a rule of thumb, be less than - 0.03 X/hre-r-1) (cf. [9]). Hence, therequired thickness of a quartz substrate at 350 Gliz is of the order of < 20 gm..Such thin substrates are difficult to handle as well as to fabricate. In order toavoid these problems, we developed a sandwiched slotline antenna, Le. a slotlineantenna sandwiched between two thick dielectric sub-isuperstrates. The sur-rounding of the antenna will then have the same dielectric constant, which isequivalent to a tree antenna without any supporting substrate, see Figure 12. Itshould be noted that sandwich type antennas have also been developed else-where (see e.g. [10, 11]).

Elliptical lens(LDPE)

***

45 mm MetallizedKapton foil

Dielectric, Er = 4(Quartz or Stycastrm)

52 I=

Figure 13. Dimensions of the 30 GHz scale model. Lens notshown.


Mount

Contact

Slot-line Antenna

Figure 12. "Artist's view" of the sandwiched slotline antenna,including a bearnshaping lens. (side view)

Several 30 GHz scale models were built to evaluate the sandwich concept, seeFigure 13. The best antenna found was a slotline antenna of the BLTSA (BrokenLinearly Tapered Slotline Antenna) type [12), with an elliptical lens made of lowdensity polyethylene (er = 2,3), mounted in front of the sandwich. The sidelobelevel is typically below -20 dB, and the cross-polarisation in the D-plane is lessthan -10 dB. Representative E-, H-, and D-plane patterns of this scale modelantenna are shown in Figure 14. This scale model antenna was chosen to empir-ically find suitable dimensions for the sandwiched BLTSA antennas for integra-tion with SIS mixers at 350 GHz.

60-60 -30 0 30Angle [0]

90

„

11111111111111r-40-90

-40

-40

Second International Symposium on Space Terahertz TechnologyPage 78

411111111111111A 111111111111311111

11111111111111-90 -60 -30 0 30 60 90

Angle [0]

111111111111111111111TAMEil

.1211101.111111R11111-90 -60 -30 0 30 60 90

Angle [0]

Antenna diagrams measured at 30 GHz (scale model).The panels show the radiation patterns in the E- (top).H- (middle), and D-plane (bottom), respectively. The D-plane plot shows both co- (solid line) and cross-poi(dashed line) data.

Figure 14.

BLTSA antenna Contact pad;

-10

0

11.riAllraullonme1111111111111111111111111

-40


In order to test the antenna properties at 350 GHz, a slotline antenna and abismuth bolometer detector (see Figure 15) were integrated on a 0,5 nun thickcrystalline quartz substrate and sandwiched between two -2 mm thick pieces ofcrystalline quartz.

Bi bolometer

Figure 15. Schematic of a slottine antenna for 350 GHz with anintegrated bismuth bolometer. The resistance of thebolometer should match the impedance of the slot-line, - 50 D.

The fabrication of the antenna and the bolometer is straightforward: The an-tenna, (Cr/Au) and the bismuth bolometer are both manufactured by lift-off. Thelift-off process gives a smooth gold edge, which is essential for good electricalcontact between the bolometer and the antenna. To obtain a uniform bismuthlayer the substrate is cooled to approximately -60 °C during the evaporation. Theresistance of the bolometer is continuously monitored during evaporation. Theevaporation of bismuth is stopped when the bolometer has reached the desiredresistance to match the impedance of the antenna.

The measured E- and H- plane antenna patterns for the sandwich slotline an-tenna at 350 GHz are shown in Figure 16.

-90 -60 -30 0 30 60 90Angle [0]

Figure 16a. Measured E- plane antenna pattern for a sandwiched1:21r TO A ivrt#asrivikes es. .2r.11 CILIrdir

0

-10

V 1 ! ! i

. I I I . II . .

•I .

-40


-90 -60 -30 0 30 60 90Angle [0]

Figure 16b. Measured H- plane antenna pattern for a sandwichedBLTSA antenna at 350 GHz.

At 350 GHz, the sidelobe level in the E-plane is almost 10 dB higher com-pared to the 30 Gliz scale model measurements. In the H-plane the patternshows more asymmetries, in addition to a 5 dB increase in sidelobe level.

The deteriorated quality of the antenna patterns recorded at 350 GHz, par-ticularly in the H-plane, is most probably due to alignment problems. For in-stance, the lens has to be accurately aligned (within 50 pm), and it is essentialto avoid any air gaps between the quartz pieces.

4. CONCLUSIONSThe diagonal horn antenna has been theoretically investigated. The model

using the Gauss-Hermite expansion yields an agreement with measured datawhich ranges from good to excellent. The horn has a high fundamental Gaussianmode content (a 84 %). The design lends itself to conventional millimetre andsub-millimetre construction methods, such as the split-block technique. Thesmall interactions that were seen in the array measurements indicate that thediagonal horn antenna is a strong candidate for focal plane imaging arrays.

The sandwiched tapered slot antenna is a planar feed which can be easily in-tegrated with e.g. SIS mixers. The model experiments made at 30 GHz showdiscrepancies with 350 GHz measurements. The stringent tolerance require-ments at sub-millimetre frequencies could at least partly explain these discrep-ancies.


REFERENCES

I 1) R. Wylde, "Optics and Corrugated Feedhorns", IEE Proc.,Vol. 131, Pt. H,No. 4, pp. 258-262, Aug. 1984.

[21 E.I. Muehldorf, "The Phase Center of Horn Antennas", IEEE Trans.Antennas Propagat., Vol. AP-18, No. 6, pp. 753-760, Nov. 1970.

[31 A.W. Love, "The Diagonal Horn Antenna", Microwave J., Vol. V. pp. 117-122, Mar. 1962.

141 A.C. Ludwig, "The Definition of Cross Polarization", IEEE Trans. AntennasPropagat., Vol. AP-21, No. 1, pp. 116-119, Jan. 1973.

[51 J.A. Murphy and R Padman, "Phase Centers of Horn Antennas UsingGaussian Beam Mode Analysis", IEEE Trans. Antennas Propagat., Vol. AP-38, No. 8, pp. 1306-1310, Aug. 1990.

[61 P.F. Goldsmith, "Quasi-Optical Techniques at Millimeter and SubmillimeterWavelengths", Ch. 5 in Infrared and Millimeter Waves, Vol. 6, K. Button,Ed., pp. 277-343, Academic Press, 1982.

[7] M. Abramowitz and LA. Stegun, Handbook of Mathematical Functions, 9thprinting, ISBN 0-486-61272-4, Dover Publications, New York.

[81 D.H. Martin, et aL, Millimetre-Wave Optics (Compendium), Queen MazyCollege, London, UK, 1988.

[91 K.S. Yngvesson, D.H. Schaubert, T.L. Korzeniowski, E.L. Kollberg, T.Thungren, and J.F. Johansson, IEEE Trans. Antennas Propagat., Vol. AP- 3,No. 12, pp. 1392-1400, Dec. 1985.

[10] T. L. Hwang, D. B. Rutledge, and S. E. Schwarz, "Planar SandwichedAntennas for Submillimeter Applications", Appl. Phys. Lett. 34(1), 1January 1979.

[111 A. Eckart, A.I. Harris and R Wohlleben, 'Scaled Model Measurements ofthe Sandwiched V-Antenna", hit. J. IR and MM Waves 2, 6 (1988).

[12] P.R. Acharya, J.F. Johansson, and E.L. Kollberg, "Slotline Antennas forMillimeter and Submillimeter Waves*, Proc. 20th European MicrowaveConf., Budapest, Hungary, Sept. 10-13, 1990, Vol. 1, pp. 353-358.

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