Filipovic Double-Slot Antennas on Extended Hemispherical

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    1738 IEEE TRANSACTIONS ON MICROWAVETHEORY AN D TECHNIQUES, VOL. 41, NO. 10,OCCOBER 1993

    Double-Slot Antennas on Extended Hemisphericaland Elliptical Silicon Dielectric LensesDaniel F. Filipovic, Student Member, ZEEE, Steven S. Gearhart,Student Member, IEEE, and Gabriel M . Rebeiz, Senior Member, IEEE.

    Abstract-In this paper, the far-field patterns and Gaussian-beam coupling efficiencies are investigated for a double-slotantenna placed on hemispherical lenses with varying extensionlengths. The radiation patterns of a double-slot antenna on asilicon dielectric lens are computed using ray-tracing inside thedielectric lens and electric and magnetic field integration onthe spherical dielectric surface. The measured radiation patternsat 246 GHz and Gaussian-beam coupling efficiencies show goodagreement with theory. The theoretical results are presented inextension length/radius and radius/X and therefore result inuniversal design curves for silicon lenses of different diametersand at different frequencies. The theoretical and experimentalresults indicate that for single units, there exists a wide range ofextension lengths (ext. length/radius = 0.32 to 0.35) which resultin high Gaussian-coupling efficiencies (50-60%) to moderatelyhigh f#s. These Gaussian-couplingefficienciescanbe increased to80-90% with the use of a X,/4 matching-cap layer. For imagingarray applications with high packing densities, an extensionlength/radius = 0.38 to 0.39 (depending on frequency) willresult in peak directivity and a corresponding Gaussian-couplingefficiency 15-20% lower than for single units.

    I. INTRODUC~IONNTEGRATED ANTENNAS on thick dielectric substratesI uffer from power loss into substrate modes [l], 2]. Oneway to avoid this problem is to integrate the antennas on a verythin substrate, typically less than .02Xd for dipoles and .04Xdfor slot antennas. However, the substrates become very thinand fragile at millimeter and submillimeter-wavelengths. One

    way to synthesize a thin substrate is to place the antenna ona very thin dielectric membran e [3]-[5], which is typicallybetween 1-3 pm thick. The membranes are integrated onsilicon or GaAs wafers and the antennas radiate as if sus-pended in free-space. Therefore appropriate design methodsmust be used to render the patterns unidirectional. Anotherattractive method to eliminate substrate modes is to place theantenna on a dielectric lens. The dielectric lens has the samedielectric constant as the planar antenna wafer. The structureof the dielectric lens does not support surface-waves. A ntennasplaced on dielectric lenses tend to radiate most of their powerinto the dielectric side making the pattern unidirectional onhigh dielectric constant lenses. The ratio of powers betweenthe dielectric and air is for an elementary slot antennaand E , for an elementary dipole antenna [l],where E , is the

    Manuscript received October 7, 1992; revised April 13, 1993,The authors are with the NASNCenter for Space Terahertz Technology,Electrical Engineering and Computer S cience Department, University ofMichigan, Ann Arbor,MI 48109-2122 .IEEE Log Number 9211919 .

    relative dielectric constant of the lens. The dielectric lens isa very attractive solution since it also provides mechanicalrigidity and thermal stability.Dielectric lenses can be hemispherical, hyperhemispherical,or ellipsoidal, and many researchers have placed variousantennas on these lenses for receiver applications. The hy-perhemispherical lens is a hemispherical lens with an attachedextension length of R In, where n is the index of refraction ofthe lens, and R is the radius of the lens. The hyperhemispher-ical lens was borrowed into the millimeter-wave field fromoptics [l], [6] and it was found that radiation patterns fromthese lenses were broad and even multi-lobed in some cases.The hyperhemispherical lens satisfies the sine condition, w hichguarantees the absence of circular coma, and is aplanatic,implying the absence of spherical abberations [7]. The latercondition imp lies that if an optical system is designed such thatall the rays are being focused to a point, the hyperhemispher-ical lens can be added to the system and all the rays will stillfocus to a point. In antenna terms, the hyperhemisphericallyshaped dielectric lens bends the rays radiated by the integratedantenna towards the broadside direction, thereby sharpeningthe pattern and effectively increasing the gain of the integratedantenna by n2. The hyperhemispherical lens is capable ofcoupling well to a Gaussian-beam system, but couples wellto a converging beam and not to a planar equiphase front.On the other hand, any antenna placed at the focus of theelliptical lens will result in a far-field pattern with a main-beam that is diffraction limited by the aperture of the ellipticallens. In a ray analysis, an elliptical lens with a source at itsmore distant focus refracts the emitted rays so that they emergefrom the lens parallel to each other [8]. The diffraction-limitedpatterns have been verified for the log-periodic and spiralantennas [9], and also for a simple dipole antenna [lo], adouble-dipole antenna [ll], and a double-slot antenna [12].The difference between these antennas is in the sidelobe andcross-polarization levels. The elliptical lens is compatible w itha large f-number imaging system due to the potential ofachieving very narrow beam patterns. As will be seen later, theelliptical lens couples well to a Gaussian-beam at its minimumwaist (where there is a planar equiphase front).The log-periodic [131, spiral [14], double-slot, and double-dipole antennas have been successfully used on quartz andsilicon dielectric lenses from 30 GHz to 600 GHz [15]-[18].The antennas were placed on hyperhemispherical or ellipticaldielectric lenses and were characterized by the measured far-field pattern. Recently, Buttgenbach experimentally placed a

    0018-9480/93$03.00 0 1993 IEEE

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    FILIPOVIC et al.: DOUBLE-SLOTANTENNAS 1739

    spiral antenna at a specific position behind the hyperhemi-spherical point (but before the elliptical focus) and achievedgood patterns and a high-aperture efficiency (coupling to aplane wave) [19]. Buttgenbach based his analysis on thequality of the measured far-field power patterns and thereforedid not present a full characterization of the Gaussian-couplingefficiency of an extended hemispherical lens.The need for a full characterization of the extended hemi-sphere (Fig. 1) prompted us to develop a ray-optics/field-integration formulation to solve for the radiation patterns andGaussian-coupling efficiencies of a double-slot antenna onhemispherical lenses with a varying extension length. Theextended hem ispherical system is very practical, since it resultsin an antenna/lens system which couples to a wide range ofquasi-optical systems simply by varying the extension lengthbehind the hemispherical position. It is important to note thatthe hyperhemispherical lens is a special case of the extendedhemispherical lens. Section I1 shows that there also existsa specific extension length that effectively synthesizes anelliptical lens. Section I11 presents the theoretical analysis ofextended hemispherical lenses and shows the directivity andmaximum Gaussicity as a function of the extension length.The term Gaussicity is defined as the coupling efficiencyof a far-field pattern of an antenna to the far-field pattern of aGaussian-beam. T he Gaussian-coupling efficiency is defined asthe total coupling efficiency which is the Gaussicity m ultipliedby any system losses (reflection loss, backside loss, impedancemismatch loss, etc.). Section IV show s the reflection losswith and without a matching-cap layer. Section V describesthe directivities and Gaussicities versus extension length asa function of frequency. Three particular values of extensionlength, 1700 pm, 2200 pm, and 2700 pm were chosen forexperimental verification. Section VI describes the measuredradiation patterns at 246 GHz and compares them with theory.Section VI1 presents the experimental setup at 246 GHz usedfor measuring the Gaussian-coupling efficiency of an extendedhemispherical lens. The theoretical and experimental resultsindicate that with a well designed quasi-optical system, thereexists a wide range of extension lengths which yield a highGaussian-coupling efficiency.

    11. SYNTHESIS OF AN ELLIPTICALENSIn this section, an elliptical lens is synthesized from anextended hemispherical lens by carefully choosing a particular

    extension length. The analysis is done in two dimensions sincethe geometry is rotationally symmetric. The defining equationfor an ellipse is: (;>a+ ( ) 2 = 1where the foci are at &c and c = d m . t is alsoknown from optics that for a given index of refraction n,the eccentricity of the ellipse such that the geometric focusbecomes the optical focus is [8]:

    d F 5 2 1 (2 )eccentricity= - -b n

    ExtensionLength\ + SiliconIntegrationPlane s)

    .na

    iFig. 1. The extended hemispherical ens and the ray-tracing/field-integrationtechnique.

    From this one can derive that:(3 )

    bnc = - (4 )

    A hemisphere of unit radius is defined by x 2 + y 2 = 1,choosing only positive y-values. T he distance from the circulartip of an extended hemisphere to the end of its extension isequal to 1+ L , where L is the extension length. The distancefrom the tip of an ellipse to its more distant focus is equal tob + c. These distances must be equal in order to superimposethe two lenses, which yields L = b + c - 1. The ellipse mustbe shifted down by a value yo = L - c so that the focusof the ellipse has the same coordinates as the focus of theextended hemisphere. Thus given the index of refraction, theparameter b is varied until the extended hemisphere appearsto have the closest geometrical match to an ellipse (b willlie within a narrow range no matter how this is defined).This has been done for a dielectric constant of E , = 2. 3(polyethylene), 4.0 (quartz), and 11.7(silicon), and is show n inFig. 2. It is obvious that the higher dielectric constant yields amore exact geometrical approximation. For a silicon lens, thefitted ellipse values are a = 1.03 and b = 1.07691, and thisyields an extension length of L = 2670 pm for a 13.7 mmdiameter lens. There are many ways to synthesize an ellipse[19] and it will be shown later that the synthesized siliconellipse presented above is a very good approximation to a trueelliptical lens.

    111. THEORETICALNALYSISA double-slot antenna is chosen as the feed antenna for theextended hemispherical lenses. This antenna has been used

    previously by Kerr et al . in a 100 GHz receiver [20] an drecently Zmudzinas built a 492 GH z SIS receiver using adouble-slot antenna on a quartz hyperhemispherical lens [171.The double-slot antenna patterns are calculated assuming asinusoidal magnetic current distribution on the slot and using

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    1740 IEEE TRANSACTIONS ON MICROWAVE THEORY AN D TECHNIQUES, VOL. 41, NO . 10, OCTOBER 1993

    E,= 11.7QSynthesized EllipseTrue Ellipse-.-.- Hyperhemispherical Plane-----

    Fig. 2. The synthesis of an elliptical lens from a hyperhemispherical lensand planar wafers. The extended hemisphere is a very good geometricalapproximation to an elliptical lens at high dielectric constants.

    an array factor in the E-plane direction [21]. The double slotslie in the r - z plane, and the slots point in the direction of thez-axis. The w avelength of the sinusoidal current distribution inthe slot is the mean wavelength [22] given by A = A,/&and t = (1+ ~ ? ) / 2 . he current in the slot is given by:I = I,,,, sin[k,,(l - Izl)]. - 1 5 z 5.1

    21 = 0.28A,,, (5where k,,, = 27r/A,,, . The corresponding normalized H-planefield pattern is:

    (6)sir18[cos( ,l CO S 8) - O S ( / ) Ik:,l - , ~ c o s ~ Hwhere k , = k,i2,1 = 27r/Xd,,, for the dielectric side, k , =27r/Xalr for the air side, and 6 is the angle with respect to thez-axis. The element pattern is a constant in the E-plane. TheE-plane array factor is given by:

    (7)where 4 is the angle from the .r-axis in the I-!] plane , k , isdefined as above, and d is the spacing between the two slots.Fig. 3shows the calculated radiation patterns at 246 GHzof a double-slot antenna with length 21 = 0.28A,,, an dspacing d = O.lGA,, , into a dielectric with a relative dielectricconstant of t, = 11.7 . The double-slot antenna results insymmetrical patterns in the infinite dielectric half space with a-10 dB beamwidth of around 48" and a cross-polarizationlevel lower than -30 dB in the 45O-plane. The phase isconstant across the main-beam, and the power radiated inthe main-beam illuminates the whole spherical surface of theextended hemispherical lenses considered in this paper. Thepatterns radiated to the air-side are broader with a -10 dBbeamwidth of 70" in the H-plane and a nearly uniform E-plane,and contain 9.0% of the radiated power.The radiation patterns from the extended hemisphericallenses are computed using a ray-tracing technique [23]. Thedouble-slot antenna patterns into the dielectric are used tocalculate the distribution of the electric and magnetic fieldsacross the spherical surface of the extended hemisphericallenses (Fig. 1). It is important to note that this analysis isnot limited to double-slot antennas and is applicable to anyplanar antenna designed to yield similar patterns in the dielec-tric; for example, the double-dipole and spiral/log-periodic

    CapacitorIr3

    TlCS

    (a)

    -90 -6 0 -30 0 30 60 90Angle (degrees)

    (b)Fig. 3 . The double-slot antenna (a ) and its radiation patterns into a silicon

    ( f I - = 11.7) dielectric (b).

    antennas. For a given ray, the fields are decomposed intoparallel/perpendicular components at the lens/air interface,and the appropriate transmission formulas are used for eachmode [24]:(8)(9)

    (10)l =7TI = i + r l (11)

    n J1 - 2 sin2Oi - os B i'11 = n J 1 - n 2 sin2Bi + cos 8;711 = (1 + rll) 1 - 2CO S 0,

    n cos 6'; - JI - n,2 sin28in COS 8, + J1 - n 2 sin20,

    where n is the dielectric constant, 8, is the angle of incidencefrom the normal to the spherical lens (Fig. l), and r an d 7are the reflection and transmission coefficients for the parallel( 1 1 ) and perpendicular (I) olarizations. Once the electricand magnetic fields have been found, equivalent electric andmagnetic current densities [24] are calculated just outside thespherical surface using:

    J s = li x H (12)

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    FILIPOVIC er a[ . : DOUBLE-SLOT ANTENNAS 1741

    0' 80zil

    7 0

    where n is the normal to the interface, and ii = & when theorigin of the coordinate system is defined to be the center ofthe spherical surface. In the far-field, the transverse electricfield is equal to:

    e.- 25 2.G-

    h- 2 0 &

    v, , - b C0 ExperimentalDirectivity- ,,*-' - 15

    where N and L are defined by:

    L = JLMseJ Cr' + ds' (17)where S I is the closed surface just outside the lens, r' isthe distance from the origin of the coordinate system to theequivalent electric and magnetic currents, r is the distancefrom the origin to the far-field point, and 4 is the anglebetween r and r' . A matching layer at the lens/air interfaceis not yet considered in this analysis.The computed E and H-plane power patterns and the phasesof the electric field in the E-plane of a 13.7 mm d iameterlens fed by a double-slot antenna at 246 GHz are shown forextension lengths of 1 600 pm, 18 00 pm, 2000 p m, 2200 p m,2400 pm, 2600 pm, 800 pm, and 3000 pm (Fig. 4). It isseen that the patterns become progressively narrower resultingin higher directivity up to 2600 pm and then the mainlobewidens an d the sidelobe levels begin to increase. It is importantto note that the phase of the field is not constant in themainlobe except around the synthesized elliptical position(determined to be L = 2670 pm). This is seen on the 2600 pmplot where the phase is nearly constant in the mainlobe andthen shifts 180" in the first sidelobe. The corresponding peakdirectivity and the Gaussicity (pattern coupling efficiency) asa function of the extension length are shown in Fig. 5.TheGaussicity is computed using an overlap integral between thefar-field patterns and the far-field Gaussian-beam expression(see Appendix). The directivity has a broad peak of 30.2 dBcentered at L,k = 2550 pm and remains within 1.0 dB ofthe peak between 2400 pm and 2800 pm . The correspondingaperture efficiency (coupling to a plane wave) peaks at 84%and is above 68% between 2400 p m and 2800 p m. This peakposition agrees well with Buttgenbach's formulation on thediffraction-limit of a lens (see [19 ] for more detail). In the far-field, the decrease in G aussicity at the larger extension lengthscan be interpreted as the result of the formation of out-of-phasesidelobes whose level progressively increases as the extensionlength is increased. It is seen that the Gaussicity is very highup to 2200 pm (above 95%) and drops to 8 8 4 6 % at the peakdirectivity and synthesized elliptical positions.The near-field waist and radius of curvature are found froman inverse Fourier transform of the far-field Gaussian-beam[23] (Fig. 6). These are referenced to the aperture plane at thetip of the lens (Fig. 1). As expected, the radius of curvature isinfinity at the synthesized elliptical position ( L = 2670 pm )

    Dw==Fig. 4. E and H-Plane pow er patterns and phase in the E-pla ne at24 6 GHz for extension lengths of 1600 p m , 1800 p m , 2000 p m , 2200 p m ,2400 p m , 2600 pm , 80 0 p m , and 3000 p m (dielectric constant = 11 .7) .Th e (- . - -) line corresponds to the phase.

    t rEyperhemispherical Position j.L1000 1400 1800 2200 2600 3000

    B O r ' ' ' I " " I ' ' I " 10Extension Length (pm)

    Fig. 5. Directivity and maxim um Gau ssicity (pattem couplin g efficiency) asa function of extension length at 246 GHz (see text).

    and changes sign immediately afterwards. This means thatthe synthesized elliptical lens is a good approximation to a

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    1742 IEEE TRANSACTIONSONMICROWAVE THEORY AND TECHNIQUES, VOL. 41, NO. 10, OCTOBER 1993

    L /R0.15 0.22 0.29 0.36 0.44

    I , , I I I , , I , c 1006.0 ' I t I \,

    t Exper. Waist0 Exper. Rad. Curv.

    2.01000 1400 1800 2200 2600 3000

    -5 0

    -100

    Extension Length (pm)Fig. 6 . Waist and radius of curvature as a function of the extension length at246 GH z. The dots and crosses indicate values obtained from the experimentalset-up (see text).

    true elliptical lens and couples best to a Gaussian-beam atits minimum waist. The Gaussian-beam radius of curvatureapproaches the lens radius (6.858 mm) when the extensionlength is small, as expected. The beam w aist is nearly constantat 5 .6 f0.3mm for extension lengths between 1000 p m a nd2700 pm and 5.8 f O . l mm between 1800 pm and 2300 pm .It is mainly the radius of curvature that is changing from-13 mm to -cc between 1000 pm and 2700 pm. Therefore,the converging Gaussian-beam must be very well characterizedon the lens aperture for optimal Gaussian-coupling efficiency.In order to gain a more intuitive understanding of theoptimal radius of curvature, the phase of the electric field onthe aperture plane is presented in Fig. 7 for the lens system at246 GHz. The phase is calculated using a ray-optics approachall the way to the aperture-plane. This method has proven toresult in a caustic with the extended lens system and is not usedfor far-field pattern and Gaussian-beam calculations (a causticis a region where an infinite number of rays converge andtherefore results in a singularity). However, the method doesyield a physical understanding of the problem. The phase of theelectric fields on the planar aperture is seen to follow a nearquadratic behavior with varying curvature depending on theextension length. For larger extension lengths (L 2200 pmand above) the phase is plotted up to the caustic region. Forlow extension lengths, the aperture fields extend significantlybeyond the diameter of the lens due to the weak refraction ofthe wide an gle rays, and this contributes to the h igh Gaussicity.This is not shown in Figure 7 since the phase is only plottedto 180".At L = 2700 p m (just near the synthesized ellipticalposition) the phase is nearly constant, and then begins toincrease positively for increasing extension length.A similar analysis of a 13.7 mm diameter lens wasperformed at 100 GHz and 500 GHz, assuming the sameradiation patterns of the feed antenna. Fig. 8 shows thepatterns and phases for extension lengths of 1600 pm ,

    Radial Distance (mm)0.0 1.0 2.0 3.0 4.0 5.0 6.030 i I I I t I I , , ! I I I

    k0

    -90*

    -120v)

    f -150

    3000

    i1-1801 ' ' ' ' I0.0 0.2 0.4 0.6 0.8 1.0Radial Distance (normalized)Fig. 7. Phase of the aperture electric field at 246 GH z for extended hemi-spherical lenses with different extension lengths with the double-slot antennaas the feed.

    1800 pm, 2000 pm , 2200 pm , 2400 pm , 2600 pm , 2800 p m ,and 3000 p m a t 500 GHz. The directivity and Gaussicitycalculations at 100 GHz, 246 GHz and 500 GHz are shownin Fig. 9. The corresponding waists and radii of curvature areshown in Fig. 10.At 100 GHz, the peak in the directivitycurve occurs at 2480 pm and is very broad. T he correspondingGaussicity is very smooth with a drop of 10% at thesynthesized elliptical position. O n the other hand, at 500 GHz,the directivity curve shows a distinct peak of 36.3 dB centeredat 2600 pm (with a corresponding aperture efficiency of72%) and drops by 0.5 dB at the synthesized ellipticalposition. Again, this position agrees well with Buttgenbach'sdiffraction method (see [19] for more detail). Note thatat higher frequencies, the peak directivity is closer to thesynthesized elliptical position, which is the result of thegeometrical optics approximation becoming more accurate.The Gaussicity peaks at 500 GHz at the hyperhemisphericalposition of 2000 pm with a value of 97% and then dropsto 82% at the 2600 pm-2700 pm position. Again, as thefrequency increases, the ray-optics approximation becomesmore valid, and this explains the peak in Gaussicity at thehyperhemispherical position.

    The directivity and Gaussicity are calculated for a trueelliptical lens using the same approach for the extendedhemispherical lens at 246 GHz. The true elliptical lens isdefined such that the minor axis (perpendicular to boresight)is equal to the radius of the extended hemispherical lens,so that the physical area on the aperture plane is the samefor both lenses. The E and H-plane mainlobes are slightlynarrower than those of the synthesized elliptical lens and have0.5 dB higher sidelobes. The directivity is 30.6 dB which is0.6 dB higher than the synthesized ellipse. The elliptical lensGaussicity is 88% and is the same to within f l% or thesynthesized elliptical lens. The corresponding minimum waistat the aperture plane is 5.6 mm .

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    FILIPOVIC et al.: DOUBLE-SLOT ANTENNAS 1743

    OeeRaFig. 8. E and H-Plane power patterns and phase in the E-plane at500 GHz for extension lengths of 1600 pm, 1800 p m , 2000 p m , 2200 pm,2400 pm, 2600 p m , 2800 pn, nd 3000 p n (dielectric constant = 11 .7) .The ( - .- -) line corresp onds to the phase.

    L /R0.15 0.22 0.29 0.36 0.44

    7 0t

    pypsrhemispherlcd Position

    1000 1400 1800 2200 2800 300060 ' ' ' ' ' ' ' I ' ' I ' I " ' " ' 10Extension Length (pm)

    Fig. 9. Directivity and maximum Gaussicity (pattem coupling efficiency) asa function of extension length at 10 0 GHz, 246 GHz, and 500 GH z (see text).

    IV. REFLECTION oss CALCULATIONSThe ray-tracing technique presented earlier (Fig. 1) alsoresults in a full cha racteriz ation of the reflection loss at

    L/ R0.15 0.22 0.29 0.36 0.44

    6.0

    ' .0Rad. Curv. 1100GHzI'aad. Curv. 248GHz- - Rad. Cum. 500GHz

    100

    -50 E3w

    \2. 0 1 ' ' ' I " I ' ' ' I ' ah I ' ' ' ' 1 -1001000 1400 1800 2200 2800 3000

    Extension Length (pm)10 0 GHz, 246 GHz, and 500 GHz (see text).Fig. 10. Waist and radius of curvature as a function of extension length at

    the lens-air interface as a function of the extension length(Fig. 11). The reflection loss is calculated by using equations8 and 1 0 and integrating the reflected power ov er the entiresurface of the lens. At low extension lengths, the calculatedloss is 1.52 dB which is close to the 1.55 dB predicted fromsimple transmission-line theory (between silicon and air). Thereflection loss increases to 2.1 dB at the synthesized ellipticalposition ( L= 2670 pm ) due to the power loss from thetotal internal reflection of wide angle rays (above 65') . Th eGaussian-coup ling efficiency of the extended hem isphericalsystem must include the reflection loss to result in a co mpletecharacterization of the system . This results in an additionaldecrease of 13% in the Gaussian-coup ling efficiency at thesynthesized elliptical positions compared to the Gaussian-coupling efficiency at the hyp erhemispherical position. Thecalculated reflection loss at the synthesized elliptical posi-tion is 1.8 dB for an an tenna with a symm etrical patternand a 10 dB-beamwidth of 46" (corresponding to a direc-tivity of 12 dB) and a nearly c onstant 1.52 dB for an tennaswith a 10 dB-beamwidth of 40" and 31" (corresponding toa directivity of 13 dB and 15 dB). This mean s that it isadvantageou s to use a high gain an tenna for a feed intothe extended hemispherical lens. This is important at highfrequencies (above 300 GHz) where it may be difficult tomanufacture an accurate matching layer for the silicon lens.While it is not known accurately, it is expected that thespiral antenna [19] and log-periodic antenna [13] have apattern directivity into the lens of around 12 dB. As ex -pected, the calculated reflection loss of an elliptical lens isnearly equal to the reflection loss at the synthesized ellipti-cal position.

    Figure 11 also includes the reflection loss using a X4matching cap layer with dielectric constant equal to &&.The reflection loss for the d ouble-slot antenna (directivity =11.1 dB ) is nearly z ero up to the hyperhem ispherical position,and then increases to 0.6 dB at the synthesized elliptical

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    1744 IEEE TRANSACTIONS ON MICROWAVE THEORY AN D TECHNIQUES, VOL. 41, NO. 10, OCTOBER 1993

    L /R0.15 0.22 0.29 0 .36 0 .443 .0 I I I I 1 I I I I 1 I I I I I I I I I I I 3. 0

    2.5 -hmam 2.0

    -m -1.5s.d3Q) 1.06:p:

    -0.5 -c

    lOdB Direct.D .Slot (1 l . ldB)12dB Direct.13dB Direct.__...5dB Direct._ _ __ _ - - - -

    With Matching Layer

    2.5

    2. 0

    1.5

    1 .o

    0.5

    0.01000 1400 1800 2200 2600 3000Extension Length (Gm)

    Aperture Radius (R /Aa i , )2 6 11 15 19 234 5

    90h6\"v

    BO 15100 30 0 500 700 900Frequency (GHz)

    haWv__ True Ellipse_ _ _ _ Synth. Ellipse0 Directivity at LpkA Gauss ic i ty a t Lp k

    Fig. 11. Reflection loss at the lens/air interface as a function of theextension length for different feed antenna directivities with and without amatching layer.Fig. 12. Directivity and maximum Gaussicity (pattern coupling efficiency)as a function of frequency (or lens radius) for a true elliptical lens, a synthe-sized elliptical lens, and an extended hemispherical lens at peak directivityposition (I&).

    position. The radiation patterns and the directivities remainessentially the sam e with the matching cap layer. As expected,with a loss of 0.3 dB, 0.1 dB, and zero for the 1 2 dB, 1 3 dB,and 15 dB pattern directivities at the synthesized ellipticaloptimum matching layer (Le. non-uniform) for the higherextension lengths.

    R/hairthe reflection loss for the h igher directivity anten nas are lower 0.40 0.40

    _ _ _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _position. No attempt is made in this paper to design an 0.38

    0.30 0.36p:V. GAUSSICITY S. FREQUENCY

    A comparison of the directivity and Gaussicity betweenthe true elliptical lens, the synthesized elliptical lens, and anextended hemispherical lens at peak directivity position for100 GHz-1 THz is shown in Fig. 1 2. The true elliptical lenshas a constant Gaussicity of 88% and a quadratic increase inthe directivity, as expected from ray-optics calculations. Thedirectivity of the synthesized elliptical lens shows a 1.2 d Bdrop compared to the elliptical lens at 1 THz due to theresidual phase error on the planar aperture. The Gaussicitydrops from about 90% at 10 0 GHz to 78% at 1 THz dueto the same effect. As was seen in Fig. 9 at 246 GHz and500 GHz, there exists a distinct peak in the directivity ata specific extension length ( L p k ) . Fig. 13 shows that L p kasymptotically approaches the synthesized elliptical positionwith increasing radius/wavelength (or increasing frequencyfor a constant radius). The peak directivity is slightly higherthan the synthesized elliptical directivity and is nearly thesame above 500 GHz. The Gaussicities for peak directivitypositions are the same as those of the synthesized ellipticalposi tion to within f l % above 200 GHz. At 100 GHz, thepeak directivity position is close to the hyperhemisphericalposition, and therefore results in a slightly larger Gaussicity.The Gaussicity and directivity for extension lengths of2000 pm, 2350 pm , and 2700 pm are shown in Fig. 14. Thehyperhemispherical lens results in a constant directivity of

    2 1.3 4 1 .3 40 .32,3 2 1 - - - - Synthesized Ellipt ical Posit ion- kt i0.301 ' ' ' ' ' ' ' 0 .30100 30 0 500 700 900

    Frequency ( G H z )Fig. 13. Extension length for peak directivity versus frequency (or RIA).

    22 dB and a constant G aussicity of 97%. Notice that thedirectivity is constant with frequency due to the constant n2magnification of the hyperhemispherical lens. The Gaussicityat 2350 pm is slightly lower than the hyperhemisphericallens and the directivity increases to around 30 dB at highfrequencies. The Gaussicity at 2700 pm (close to the synthe-sized elliptical position) is the lowest of all three positions,but results in the largest directivity. The Gaussicity at thesynthesized elliptical position (and at L , k ) drops to 78% at1 THz while the Gaussicity for the 2350 pm position drops to88% at the same frequency. Although the hyperhemisphericalposition shows the highest theoretical Gaussicity, it is hardto experimentally achieve this efficiency due to the difficultyin aligning to the strongly converging beams needed at the

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    90hRv

    70

    f l 0

    . - - 2000pm (Hyperhemisphere)- - 2350pm__ 270Opm (Synth. Ellipse)60100 30 0 50 0 70 0 900

    Frequency ( G H z )Fig. 14. Directivity and Gaussicity (pattern coupling efficiency) as a func-tion of frequency (or lens radius) for an extended hemispherical lens atL = 2000 pm, 2350 pm, nd 2700 pm.

    aperture of the lens (see section VII). Thus the region between2200 pm and 2400 p m results in the best compromise betweenalignment, directivity and Gaussian-coupling efficiency.Since all the calculations w ere done in terms of wavelength,Figs. 12 and 1 4 present universal design cu rves to predictthe performance of extended hemispherical silicon lensesfor different diameters when using the same antenna feedpatterns. These graphs shows that for high gain systems, a13.7 mm diameter silicon lens can be used in an extendedhemispherical configuration up to 1 THz without a significantdrop in the Gaussicity. For a matched load, the Gaussian-coupling efficiency is found by multiplying the Gaussicitypresented above by the reflection loss at the lens-air interface(shown in Fig. 11) and by 91.0% to take into account thepower radiated by the double-slot antenna to the back-side (air-side). It is important to note that the reflection loss for higherextension lengths (near L,k and the synthesized ellipticalposition) will have an additional loss of about 0.5 d B (10%)over the hyperhemispherical position (2000 pm).

    VI. EXPERIMENTALESUL TS: ATTERNSThe double-slot antenna was fabricated for 246 GHz mea-surements using standard photolithographic techniques. Allthe conducting layers are 2000 A gold deposited on a high-resistivity (40 00 R - cm) silicon wafer. A bismuth bolometeris placed in series at the center of the do uble-slot antenna usinga coplanar-waveguide transmission line (Fig. 3). The series

    feeding is necessary in order to result in the sum mode of thedouble-slot antenna. The bolometer is 20 pm x 1 5 pm andis integrated on a 1.2 p m thick polyimide patch for thermalinsulation from the substrate. The m easured d c resistance ofthe bolometer is 60 R. The left and right ends of the coplanarline are terminated by a polyimide/gold capacitor which acts

    as an RF short. The center strip of the coplanar waveguideline runs out from the right end to a large pad for dc biasingand low frequency detection. The coplanar waveguide spacingis 15 pm and the width 10 pm. This yields a quasi-TEMtransmission line impedance of 50R [25]. The measured RFimpedance at the bolometer position is 60 + j 5 0 R o n a4 GHz microwave model, and results in a good match to thebolometer.

    Experimen tal measurements at 246 GH z were performedon a 13.7 mm diameter silicon lens (cy = 11.7) without anytype of matching layer and the double-slot antenna as a feed.Three particular values of extension length were chosen forthe purpose of experimental verification: 170 0 pm , 2200 p m,and 2700 pm. The extension lengths were achieved by addinghigh-resistivity silicon wafers. These positions were chosenbased on their different properties: a phase curvature acrosstheir aperture planes of high, low, and virtually none, respec-tively; and a radiation pattern that is broad, narrow w ith nearlyno sidelobes, and narrow with low sidelobes, respectively. Th eposition of 2700 pm represents the extension length wherethe extended hemispherical lens has effectively synthesized anelliptical lens. The hyperhemispherical position is at 2000 pmand no measurements were done at this position. However,the 170 0 pm extension has the same features as the 2000 p mposition in terms of Gaussian-coupling efficiency and the smallradius of curvature needed to couple well to a Gaussian-beam.No pattern measurements were done on a true elliptical lens.

    The patterns were measured at 246 G Hz using an 8 2 GHzGunn source, and a wideband (220-270 GHz) tripler. TheGunn source was modulated at 104 0 Hz, and the output fromthe bolometer was fed to a lock-in am plifier. Measured patternsat the extension length of 2700 p m (Fig. 15) demonstrate adirectivity of 29.4 dB f .3 dB with relatively low sidelobes(-16 dB). The corresponding aperture efficiency (coupling toa plane wave) is 70% 4 5 % . Notice that the theoretical analysispredicts a directivity of 29.9 dB (78% aperture efficiency)at the synthesized elliptical position. Good agreement existsbetween the theoretical and experimental patterns (Fig. 16).Measured patterns at 2700 pm for f10% of the 246 GH zdesign frequency result in nearly the same directivity, andtherefore the double-slot antenna has good pattern bandwidth.The measured power at broadside is nearly the same from22 2 GHz-270 GHz, also indicating good impedance band-width for the double-slot design. The measured patterns atan extension length of 2200 p m are slightly broader than thesynthesized elliptical lens with a directivity of 26.7 d B f0.3 dB. Again, there is close agreement between theory andexperiment (Fig. 17). At an extension length of 1 700 pm, thepatterns become wide with a peak gain of 19.1 d B f .3 dB,and it is considerably more difficult to laterally align the feedantenna to the focus, resulting in non-symmetric patterns withripples (Fig. 18). As was seen earlier, this wide pattern has nodetrimental effect on the coupling efficiency to a convergingbeam. Th e ratio of the 246 GHz measured p eak received powerbetween the extension lengths of 2700 pm and 17 00 pm is10 d B f .5 dB and this is the same as the difference inthe measured directivities (including the effect of the differentreflection losses at the lens surface).

    I -

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    1746 IEEE TRANSACTIONS ON MICROWAVE THEORY AN D TECHNIQUES, VOL. 41, NO. 10, OCTOBER 1993

    ~ E-plane_ _ _ - H-plane -Gains29.4dB0 I I I I , 1 1 1 1

    H-Exper.H-Theory-5 -

    hmc -10av -.r(d0Q)

    .?; -15 -

    av - l o t I \

    :104 1-2 0-30-4 0 I iI I-30 -2 0 -10 0 10 20 30Angle (degrees)0 20 4060 -40 -20Angle (degrees)Fig. 15 . Measured pattems for the synthesized elliptical lens (2700 pm ) at24 6 GHz. The pattems are diffraction-limited by the size of the aperture. TheSI N ratio is better than 40 dB . Fig. 17. Comparison of the calculated pattem s versus experiment at 24 6 GH zfor the double-slot antenna on an extended hemispherical lens with 2200 p mextension length.0

    -5hmav

    -10.r(

    W

    -2 0

    -25 ' I ' I ' I ' I ' I '-30 -2 0 -10 0 10 20 30Angle (degrees)Fig. 18. Comparison of the calculated pattems versus experiment at 24 6 GH zfor the double-slot antenna on an extended hemispherical lens with 1700pmextension length.

    -35 ' I '__-30 -20 -10 0 10 20 30Angle (degrees)Fig. 16 . Comparison of the calculated pattems versus experiment at 24 6 GH zfor the double-slot antenna on a synthesized elliptical lens (extension length2700 pm).

    1700 W yVII. EXPERIMENTALESULTS:GAUSSIAN-BEAMOUPLINGA Gaussian-beam experiment was performed at 246 GH zwith the purpose of coupling all the power radiated by acorrugated horn into the double-slot antenna/lens system. Atwo-lens quasi-optical system was designed which achievesa wide variety of waist sizes and radii of curvature (Fig. 19).The 10-cm Rexolite lenses used were numerically machinedusing parametric equations and result in no spherical aberra-tions [26]. The source was a WR-03 corrugated horn having

    symmetric E, H, and 45' patterns with a computed waistsize of w o = 2. 1 mm. The waist can be traced throughthe lens system using the q-parameters [27]. In Fig. 19, dl,d2, and d3 are the lens separation distances, and f i and f 2are the respective f / # ' s (f/# f / D , where f is the focallength and D s the diameter of the lens). Care must be takenthat the edge illumination of the lens is below the -30 d Blevel so that the Gaussian-beam does not deform from itsideal shape. The experimental procedure went as follows:

    / .~5 t perturePlane/':-dl- -2* 4 -d,-Fig. 19. The setup for the Gaussian-beam coupling experiment. The w aist atthe aperture is 5.2-5.9 mm for all three lenses, and only the radii of curvatureare different.

    the distances dl , d2, and d3 and the f / # ' s f i and f 2 werefirst calculated for maximum coupling between the corrugatedhorn and the extended hemispherical lens system. Then, thedistances dl , d2, and d3 were tuned experimentally to resultin peak measured power in the bolometer.

    An equi-phase wavefront is needed for the synthesized ellipse and2700 pm extension length (syn thesized ellipse):

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    FILIPOVIC et al. DOUBLE-SLOTANTENNAS 1747

    is obtained at the minimum waist. A quasi-optical system L/ Rwith final values of dl = 96 mm , d2 = 68 mm, d3 =312 mm, f1/2.0, an d f2/1.4 resulted in a peak receivedpower with a calculated minimum beam-waist of 5.1 mm at theplanar lens aperture. The beam waist for optimum Gaussicitycalculated from the present theory is 5.2 mm. T he final valuesof dl, d2, an d d3 are within fl mm of the initially calcu-lated values.

    A quasi-optical system withfinal values of dl = 95 mm , da = 122 mm, d3 = 224 mm ,f1/2.0, and f2/1.4 resulted in peak received power. Thecalculated beam waist and radius of curvature were 5.78 mman d -65 mm, respectively. The corresponding minimum waistis 2.8X and is located -35 mm (away from the horn) from theaperture plane. The final values of dl, d2, and d3 are withink5 mm of the initially calculated values.

    A quasi-optical system withdl = 106 mm, d2 = 120 mm, d3 = 86 mm, fllO.9, an df2/2.0 esulted in peak received power. The calculated beamwaist and radius of curvature were 6.07 mm and -27.7 mm ,respectively. The corresponding minimum waist is 1.1X (aresult of the small radius of curvature necessary at the apertureof the lens). The final values of dl, d2, an d d3 differ by asmuch as 6 25 mm to the initially calculated values. We believethat for this extension length, the radius of cu rvature across theaperture is so strong that the desired aperture field distributionwill distort rapidly with misalignments of the feed antenna tothe lens. This is commonly seen in optics where it is difficultto align to a lens system with small f / D ratios.The raw measured powers were 1.03, 1.18 and 1.00 for the1700 pm , 2200 pm, and 2700 p m positions, respectively. Inthe experimental setup, the 2200 pm and 2700 pm systemsused the same set of objective lenses (f1/2.0 an d f2/1.4)and therefore have approximately the same reflection anddielectric losses in those lenses. The 1700 pm experimentrequired f l l0 .9 an d f2/2.0 lenses and has approximately anadditional 6-10% loss due to the added thickness of theflO.9 lens. The measured power at the 1700 p m position istherefore multiplied by 1.08 to take into account the excessdielectric loss for the 1700 p m quasi-optical system, resultingin a corrected power of 1.11 (shown as a cross in Fig. 20).The theoretical Gaussicities are multiplied by the differentreflection losses at the silicon-air interface (see F ig. 11) for thethree lens systems, and by the back-side power loss (91%) oyield the actual Gaussian-coupling efficiency. The theoreticalGaussian-coupling efficiencies are presented in Figure 20, to-gether with the measured powers which have been normalizedto the 2700 um position. This position was chosen for thenormalization because the experimental waist and radius ofcurvature at 2700 pm agree very well with the theoreticalvalues. The normalization is necessary since no absolutepower measurements were done at 246 GHz. It is seen thatwithin experimental error, the measured values agree well withthe theoretical predictions at extension lengths of 2200 p man d 2700 pm. Notice that the 2700 p m position results inthe lowest measured Gaussian-coupling efficiency. Also, themeasured Gaussian-coupling efficiency at 2200 p m is 7% an d18% higher than the measured Gaussian-coupling efficiencies

    2200 pm extension length:

    1700 pm extension length:

    0.15 0.22 0.29 0.36 0.447 0hMv

    ~ G.C.E. (GaussicityW/ Reel. LOSS &Back-Side Loss)

    7 0

    60

    50

    40

    30

    20Experimental G .C . E .(normalized)

    0 Raw Datat Corrected Data10

    01000 1400 1800 2200 2600 3000Extension Length (pm)

    Fig. 20. Measured and calculated Gaussia n-coupling efficiency as a functionof extension length. This takes into acco unt reflection at the lens/air interfaceand power lost to the air side (91%).

    for the 1700 pm and 2700 p m positions, respectively. Thisagrees well with our calculations in Section V which state thatthe 2200 pm-2400 pm positions ( L / R= 0.32 to 0.35) resultin the best compromise between directivity and Gaussian-coupling efficiency.

    VIII. DISCUSSIONND CONCLUSIONIn this paper, a ray-optics/field-integration approach hasbeen used to fully characterize an extended hemispherical

    lens system with a double-slot antenna feed. We have alsopresented a formulation for synthesizing an ellipse from an ex-tended hemispherical lens. The results show that the directivityis strongly dependent on the extension length (especially athigh frequencies). The calculated Gaussicity (pattern couplingefficiency) is very high up to approximately 2200 pm and thendrops gradually by about 10- 15%at the synthesized ellipticalposition (depending on frequency). The corresponding beamwaist on the aperture-plane is nearly constant (5.6 40. 3 mm)and the radius of curvature ranges from -13 mm to -ea. hu sthe incident Gaussian-beam must be very well characterized onthe planar aperture for optimum cou pling efficiency. In fact, wehave built a lens system with a 10 dB difference in directivityand still succeeded in achieving nearly the same Gaussian-coupling efficiency for the low and high directivity systems.Our calculations also show that a 13.7 mm diameter siliconlens can be used up to about 1 THz without a significant dropin the Gaussian-coupling efficiency (maximum 20%) and hasan associated directivity greater than 40 dB. The Gaussian-coupling efficiency for a double-slot antenna at a positionbetween 2200 pm to 2400 p m ( L / R = 0.32 to 0.35) isapproximately 60-50%, which includes the reflection loss andthe back-side power loss. This is expected to increase to about90-80% when a matching cap layer is used.The question arises of where to place the antenna on alens for the best possible performance. The answer, according

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    1748 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 41, NO . 10, OCTOBER 1993

    to our calculations, depends on the specific application (forexample, a sing le unit or a unit in an imaging array). For singleunits, the hyperhemispherical position is not the best placesince it results in a low directivity, and requires small f/#systems that are difficult to align. This was well demonstratedby our quasi-optical set-up and we found that it was verydifficult to choose the position of the len ses for best G aussian-coupling efficiency at the 1700 pm extension length. In ouropinion, one should use an extension length that results inan acceptably high directivity and therefore a large f/# orthe objective lens. This also yields an easy-to-align quasi-optical system. However, the high directivity is achieved atthe expense of a reduction in the Gaussian-coupling efficiency.For a 13.7 mm diameter silicon lens, we believe that agood compromise between the increase in directivity andthe decrease in Gaussian-coupling efficiency is achieved at2200 pm-2400 pm extension length ( L / R = 0.32 to 0.35).The corresponding Gaussicity is very high being always above90% for frequencies below 1 THz. his was well demonstratedin our experimental setup at 246 GHz where the 2200 p mpositions resulted in a 7% and 18%higher cou pling efficiencythan either the 1700 p m o r 2700 pm positions, respectively.For imaging arrays, the extension length resulting in peakdirectivity should be chosen so as to result in the best possiblepacking density in the focal plane. For a 13.7 mm diameterlens, the aperture efficiency at L p k is 84% at 246 GHz and72% at 500 GHz. The corresponding Gaussicity is high at246 GHz with a value of 88% and drops to 78% at 1 THz. AtL p k , the reflection loss at the lens-air interface contributes anadditional 0.5 d B (11%) reduction in the Gaussian-couplingefficiency (with or without a Am/4 matching-cap layer) com-pared to the 2200 pm position. It is possible to reduce thereflection loss with a higher directivity feed antenna. TheL p k position is advantageous because it results in a high-packing density with only a 15-20% drop in Gaussian-coupling efficiency when com pared to the 2200 pm-2400 p mpositions. It is also interesting to compare qualitatively theperformance at this position to a corrugated horn. At peakdirectivity position, the extended hemispherical lens at L p kwill result in about 20-25% higher packing densities (i.e.aperture efficiencies) and about 25-40% lower Gaussian-coupling efficiencies (including back-side power loss and aAm /4 matching-cap layer) than a corrugated horn designedfor the same f/# ystem. This is not a high penalty to pay forhigh-packing densities in imaging arrays.Finally, all our calculations are presented in RIA andL/ X and therefore present universal design curves for siliconlenses of different diameters at different frequencies. Similarcalculations on quartz lenses are available from the NASA-CSTTRJniversity of Michigan and will be published in theOctober 1993 International Journal of Infrared and Milli-meter Waves.

    APPENDIXThe electric field of a Gaussian-beam is of the form:

    where 8 is the direction in the far-field from boresight (assum -ing circular symmetry), and e,, is a unit vector representingthe polarization of the beam. In the near-field:EG au s s (r ) = ~ , , ~ - ~ ~ ~ 2 ~ ~19)

    where r is the radius in a planar field representation (assumingcircular symmetry), w(z) is the waist of the Gaussian-beam,R( z ) is the radius of curvature, and E, , is a unit vectorrepresenting the polarization of the beam. The value 80 (orw(z)) controls the amplitude term and 81 (or R(z ) ) ontrolsthe phasing term. The coupling efficiency of an antenna toa Gaussian-beam (Gaussicity) is calculated using the formula9 = l ( ~ a n t e n n a l ~ G a u s s ) 1 2 , hich written out in the far fieldis [28]:

    9Gaussicity =

    where F ( 8 , 4 ) s the electric field in the far-field pattern of theantenna, and F ( r , d ) s the electric field in the planar repre-sentation. The amplitude and phasing terms are varied to op-timize the coupling efficiency (Gaussicity). For high couplingefficiency (>80%), the near-field Gaussian parameters canbe found from a Fourier transform of the far-field Gaussianparameters [23].ACKNOWLEDGMENT

    This work was supported by the NASA/Center for SpaceTerahertz Technology at the University of Michigan. We arevery grateful to Thomas Buttgenbach, Prof. Jonas Zmuidzinasand Prof. David Rutledge, all at the California Institute ofTechnology, for their immense contributions to this project.We are also grateful to Dr. Andy Harris, Max-Planck Institutefor Extra-Terrestrial Physics, Garching bei Munchen, and Dr.Tony Kerr, NRAO, for their detailed review of the m anuscript.

    REFERENCESD. B. Rutledge, D. P. Neikirk and D. P. Kasilin gam, Integrated circuitantennas, Infrared and Millimeter-Waves, vol. 10, K. J. Button, Ed.,Ne w York Academic Press, pp. 1-90, 1983.G. M. Rebeiz , M illimeter-w ave and terahertz integrated circuit an-tenna, Proc. IEEE, vol. 80, no . 11, pp. 1748-1770, Nov. 1992.W . Y . Ali-Ahmad, W.L. Bishop, T.W. Crowe, and G .M . Rebeiz,A n 86- 106 GHz quasi-integrated low-noise Schottky receiver, IEEETrans. Microwave Theory Tech., vol. 41, no. 4, pp. 558-564, April1993.S. S. Gearhart, C.G. Ling, and G. M. Rebeiz, Integrated millimeter-wave comer-cube antennas, IEEE Trans. Antennas Propagat., vol. 39,no. 7, pp. 1000-1006, 1987.D. F. Filipovic, W. Y . Ali-Ahmad, and G. M. Rebeiz, Millimeter-wavedouble-dipole antennas for high-gain integrated reflector illumination,IEEE Trans. on Microwave Theory Tech., vol. 40, no. 5 , pp. 962-967, 1992.

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    D. B. Rutledge and M. M uha, Im aging antenna arrays, IEEE Trans.Antennas Propagat., vol. AF-30, pp. 535-540, 1982.M. Born and E. Wolf. Princ ides of Optics. New York: Permaeon Press,_ 1 Ipp. 252-252, 1959.E. Hecht, Optics, 2nd Edition. Reading, MA: Addison-Wesley,pp. 129-131, 1987.H. van de Stadt, Th. de Graauw, A. Skalare, R.A. Panhuyzen, R.Zwiggelaar, Millimeter and submillimeter studies of planar anten-nas, First Int. Symp. on Space Terahertz Technology, Ann Arbor, MI,pp. 235-255, Mar. 1990.C. J. Adler, C.R. Brewitt-Taylor, M. Dixon, R. D. Hodges, L. D. Irving,

    and H. D. Rees, Microwave and millimeter-wave receivers with integralantennas, IEEE Proc.-H, vol. 138, pp. 253-257, 1991.A. Skalare, Th. e Graauw, and H. van de Stadt, A planar dipole arrayantenna with an elliptical lens, Microwave and Optical Tech. Lett.,vol. 4, no. 1, pp. 9-12, 1991.D. F. Filipovic, S. S. Gearhart, and G. M. R ebeiz, Double-slot andlog-periodic antennas on extended hemispherical dielectric lenses,in Proc. 3rd Int. Con8 Space Terahertz Technology, An n Arbor, MI,pp. 382-393, Mar. 1992.R. H. Duham el and D. E. Isbell, Bro adband logarithmically periodicantenna structure, IRE National Co nvention Records, Part I, pp. 119-128, 1957.J. D. Dyson, The unidirectional equiangular spiral antenna, Trans. IRE,AP-7, pp. 329-34, 1959.T. H. Biittgenbach, A fixed tuned broadband matching structure forsubmillimeter SIS receivers, IEEE Trans. Appl. Supercond., vol. 2,pp. 165-175, Sept. 1992.Q. Hu, Z.A. Mears, P. L. Richards, and S. L. Loyd, Millimeter-wave quasioptical SIS mixers, IEEE Trans. Mugn., vol. 25, pp. 1380-1383, 1989.J. Zmuidzinas, Quasi-optical slot antenna SIS mixers, IEEE Trans.Microwave Theory Tech., vol. 40, no. 9, pp. 1797-1 804, 1991.A. Skalare, H. van de Stadt, Th. de Graauw, R.A. Panhuyzen, andM. M. T. M. Dierichs, Double-dipole antenna SIS receivers at 1 00 and400 GHz, in Proc. 3rd Int. Conj Space Terahertz Technology, An nArbor, MI, pp. 222-233, Mar. 1992.T. H. Biittgenbach, An improved solution for integrated array opticsin quasi-optical mm and submm receivers: the hybrid antenna, IEEETrans. on Microwave Theory Tech., this issue.A.R. Kerr, P.H. Siegel, and R.J. Mattauch, A simple quasi-opticalmixer for 100-120 GHz, IEEE-M77 Int. Microwave Symp. Dig.,pp. 96-98, 1977.R. S. Elliott, Antenna Theory and Design. New Jersey: Prentice-Hall,Chap. 4, 1981.

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    M. Kominami, D.M . Pozar, and D.H. Schaubert, Dipole and slotelements and arrays on semi-infinite substrates, IEEE Trans. Antennasfropagat. , vol. AP-33, pp. 600-607, June 1985.R. E. Collin , Antennas and Radiowave Propagation. Ne w York:McGraw-Hill, ch. 4, 1985.C.A. Balanis, Antenna Theor y: Analysis and Design. New York: Wiley,ch. 11, 1982.K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Lines and Slotlines.Dedham, MASS: Artech House, ch. 7, 1979.R. Johnson and H. Jasik, Antenna Engineering Handbook, 2nd Ed. NewYork: McGraw-Hill, ch. 16, 1984.A. Yariv and P. Yeh, Optical Waves in Crystals. New York: Wiley,ch. 2, 1984.S. E. Schwarz, Efficiency of quasi-optical couplers, Int . J. InfraredMillimeter Waves, vol. 5, pp. 1517-1525, 1984.

    Daniel F. Filipovic (S88) was born in DetroitMI on October 26, 1968. He received the B.S.E.and M.S. degrees in electrical engineering from theUniversity of Michigan, Ann A rbor, in 199 0 and1991, respectively. He is currently a graduate stu-dent at the University of Michigan working towardthe Ph.D. in electrical engineering.His research interests include millimeter-wave an-tennas, quasi-optic systems, and planar multipliers.

    Steven S. Ge ar har t (S91) was born July, 1965 in Roanoke, VA. He receivedthe B.S.E.E. degree from Virginia Tech, Blacksburg, VA in 1988 and the M.S.degree in Electrical Engineering from the University of Michigan, An n Arborin 1990.He is currently working towards a Ph.D. in Electrical Engineering atthe University of Michigan. His research interests include millimeter-waveantennas and imaging arrays, integrated receivers and multipliers, and solid-state fabrication.

    Gabriel M. Rebeiz (S86-M88-SM 92), for a photograph and biography,see this issue, p. 1719.