An investigation of the coupling efficiencies to a gaussian-beam of a double-slot antenna on a hyperhemispherical lens is presented. It is shown that both lenses couple equally well to an appropriate gaussian beam (about 80 percent). The radiation patterns of both lenses with a double-slot antenna are computed using the ray-tracing method. The experimental radiation patterns are presented and show close agreement to the theoretically computed patterns

Filipovic, Daniel F.

Gearhart, Steve J.

Kormanyos, Brian K.

Rebeiz, Gabriel M.

English

NASA Technical Reports Server

Page 382 Third International Symposium on Space Terahertz Technology
The material presented below is intended as a review only. A full length paper has been
submitted for publication in IEEE/MTT (May 1992).
DOUBLE-SLOT ANTENNAS ON EXTENDED HEMISPHERICAL
DIELECTRIC LENSES
\V\
Daniel F. Filipovic, Steve J. Gearhart, Brian K. Kormanyos and Gabriel M. Rebeiz
**^~ NASA/Center for Space Terahertz Technology
Electrical Engineering and Computer Science Department
University of Michigan
Ann Arbor, MI 48109-2122
ABSTRACT
An investigation of the coupling efficiencies to a gaussian-beam of a double-slot antenna on
a hyperhemispherical lens is presented. It is shown that both lenses couple equally well to
an appropriate gaussian beam (about 80%). The radiation patterns of both lenses with a
double-slot antenna are computed using the ray-tracing method. The experimental radiation
patterns are presented and show close agreement to the theoretically computed patterns.
https://ntrs.nasa.gov/search.jsp?R=19930018570 2020-03-17T05:44:18+00:00Z
Third International Symposium on Space Terahertz Technology Page 383
I. INTRODUCTION
The use of a hemispherical lens with an attached extension length can greatly improve
coupling to a gaussian-beam system. In optical theory, an extension length of r/n is used,
and this extended lens is termed a hyperhemispherical lens. This extension length was chosen
since it satisfies the sine condition, which is where first-order aberrations are removed [1].
The hyperhemispherical lens was borrowed into the millimeter-wave field [2,3,4], but it was
found that radiation patterns from these lenses were very broad and even multi-lobed in
some cases. The hyperhemispherical lens is capable of coupling well to a gaussian-beam
system. However, it couples most efficiently to a converging beam and not to a plane
wave. Recently, several researchers showed that a narrow, diffraction-limited beam could
be achieved by putting the antennas on an elliptical lens [5,6]. The same effect was also
found by taking a hyperhemispherical lens and adding a planar extension to it [7]. Figure 1
shows that the focus of this longer extension length lens superimposes exactly on the second
focus of an elliptical lens. It is known from optical theory that a plane wave converges to
the second focus of an ellipse, and therefore a lens with this extension length is simply a
close geometrical approximation to an elliptical lens. The validity of this approximation
depends on the maximum allowed phase tolerance. For high dielectric constants (see Fig.
1) and relatively low frequencies, the phase difference becomes small and the approximation
is valid. Generally, for lens diameter of 12.5mm, t larger than 4, and frequencies less than
300GHz, the approximation is very good.
Page 384 Third International Symposium on Space Terahertz Technology
II. THEORETICAL AND EXPERIMENTAL PATTERNS
The theoretical radiation patterns are computed using a ray-tracing technique [9]. First,
the feed antenna pattern into the dielectric is calculated using standard far-field methods.
Figure 2 shows the calculated radiation patterns for a double-slot antenna with L = 0.28Aat>
and d = 0.16Aat>. These parameters were chosen to result in a symmetric pattern inside the
dielectric and a low cross-polarization in the 45°-plane. Ray-tracing is then used to calcu^
late the electric field distribution across the aperture plane (Fig. 3). In this method, the
fields are decomposed into TE/TM components at the lens/air interface, and the appropri-
ate transmission formulas are used for each mode. The power reflected into the substrate
is neglected in this analysis. A diffraction integral over the aperture then yields the far-
field pattern from the lens. Experimental measurements were performed at 246GHz on a
13.7 mm diameter silicon lens (e=11.7) with the double-slot antenna as a feed. Different
values of extension length were achieved by adding high-resistivity silicon wafers, resulting
in 3 extension lengths: hyperhemispherical, intermediate, and elliptical (Fig. 3). Measured
patterns at the elliptical focus (Fig. 4) demonstrate a gain of 28.6dB±0.3dB with relatively
low sidelobes (-16dB). From the measured patterns, the resulting aperture efficiency (cou-
pling to a plane wave) is 73%. The theoretical patterns calculated for this position are a bit
wider than the measured patterns (Fig. 5). This discrepancy arises from the fact that rays
at a certain angle end up hitting the critical angle at the lens/air interface, resulting in no
transmission of rays after this point. This limits the aperture size and results in a wider theo-
retical pattern. Note that this discrepancy is only significant at the elliptical focus for lenses
with high dielectric constants. Measured patterns at the elliptical focus for ±10% of the
Third International Symposium on Space Terahertz Technology Page 385
246GHz design frequency (Fig. 6) result in nearly the same gain, and therefore the double-
slot antenna has good pattern bandwidth. The measured power at broadside is nearly the
same from 222GHz-270GHz, also indicating good impedance bandwidth for the double-slot
design. The measured patterns at the intermediate focus (Fig. 7) are similar to the elliptical
focus, but with a gain of 24dB±0.3dB. In this case, the critical angle is not a problem, and
there is close agreement between theory and experiment (Fig. 8). At the hyperhemispherical
focus (Fig. 9), the pattern becomes very wide with a gain of 18.1dB±0.3dB and shows a
multi-peak behaviour, as indicated by theory (Fig. 10). As will be seen later, this has no
detrimental effect on the coupling efficiency to a converging beam. The ratio of the 246GHz
measured received power at broadside for an elliptical lens and a hyperhemispherical lens
was lOdB which is the same as the difference in the measured directivities. This indicates
that no power is coupled to substrate modes that may arise in the flat wafers.
III. GAUSSIAN-BEAM COUPLING
In order to match the double-slot/extended hemisphere system to a gaussian beam, one
could compute the electric field across the aperture and match this to a gaussian beam.
Since we had already predicted the far-field amplitude and phase distributions, we chose to
compute the coupling efficiency to a gaussian beam in the far-field (see Appendix). In this
calculation, the power radiated by the slot antennas to the air-side (which is 11.5% of the
total power) is taken into account, and no lens-air interface loss is considered. The power
loss radiated to the air side could be reflected using an appropriately designed cavity at
the expense of impedance bandwidth. Figure 11 gives the gaussian-beam parameters which
Page 386 Third International Symposium on Space Terahertz Technology
yield the highest coupling efficiency, and shows that all three focus positions are capable
of coupling equally well to a gaussian beam. However, the non-elliptical foci require a
converging wavefront, whereas the elliptical focus couples directly to a Gaussian beam with
an equal phase wavefront. Note that equivalent gaussian-beam parameters in the near field
may be found through a simple inverse Fourier transform. A gaussian beam experiment was
performed at 246GHz, in which it was attempted to couple all the power coming out of a lens
into the double-slot antenna. For the elliptical focus, the lens was placed at the minimum
waist position, where the radius of curvature is infinite, indicating an equal phase wavefront.
For the hyperhemispherical position, the lens was placed closer to the lens, at a position
where there is a negative radius of curvature. The proper negative radius of curvature
and position were computed knowing the gaussian-beam parameters from Figure 11. It was
found that the ratio of powers with either focus is the same within experimental error (±4%),
indicating that both the hyperhemispherical focus and the elliptical focus will match equally
well to an appropriately designed gaussian-beam system. Similar measurements were done
on a log-periodic antenna from 90-250GHz. The results are similar to those presented in this
paper and have been submitted for publication in IRMMW (May 92).
IV. ACKNOWLEDGEMENTS
This work was supported by the NASA/Center for Space Terahertz Technology at the Uni-
versity of Michigan.
Third International Symposium on Space Terahertz Technology Page 387
APPENDIX
The field representation of a Gaussian beam is of the form:
The coupling efficiency between an antenna pattern and a gaussian beam is calculated using
the formula [12,13]:
| //[gco • F(0, <f>Y] exp-W*") exp^W*) sin Od6d<j>\
£) |2 sin 0d0d<£ //exp-2( W sin
where F(0, <£) is the far-field pattern of the antenna, and eco is the co-pol unit vector. The
value 0o controls the amplitude term and 0i controls the phasing term. These values are
varied to optimize the coupling efficiency.
REFERENCES
[1] Born and Wolf, Principles of Optics , Permagon Press, New York, 1959, pp. 252-252.
[2] D.B. Rutledge, D.P. Neikirk and D.P. Kasilingam, "Integrated Circuit Antennas," Infrared
and Millimeter-Waves, Vol. 10, K.J. Button, Ed., Academic Press, New York, 1983, pp. 1-
90.
[3] D.B. Rutledge and M. Muha, "Imaging antenna arrays," IEEE Trans. Antennas Propa-
gat, Vol. AP-30, 1982, pp.535-540.
[4] J. Zmuidzinas, "Quasi-optical slot antenna SIS mixers," IEEE Trans, on Microwave
Theory Tech., accepted for publication Jan. 1992. Also presented at the 2nd Int. Symp. on
Space Terahertz Technology, CA, March 1991.
[5] A. Skalare, Th. de Graauw, and H. van de Stadt,"A Planar Dipole Array Antenna with
an Elliptical Lens," Microwave and Optical Tech. Lett., Vol. 4, No. 1, 1991, pp. 9-12. Also,
"Millimeter and Submillimeter Studies of Planar Antennas," First Int. Symp. on Space
Terahertz Technology, Ann Arbor, MI, March 1990, pp. 235-255.
[6] C.J. Adler, C.R. Brewitt-Taylor, R.J. Davis, M. Dixon, R.D. Hodges, L.D. Irving, H.D.
Rees, J. Warner, and A.R. Webb, "Microwave and Millimeter-Wave Staring Array Technol-
ogy," IEEE MTT-S Int. Microw. Symp. Digest, June 1991, pp. 1249-1252.
[7] T.H. Buttgenbach, "A Fixed Tuned Broadband Matching Structure for Submillimeter
SIS Receivers," presented at the Third Int. Symp. on Space Terahertz Technology, Ann
Arbor, MI, March 1992.
[8] A.E. Siegman, Lasers, University Science Books, New York, 1986.
[9] R.E. Collin, Antennas and Radiowave Propagation, McGraw-Hill, New York, 1985, pp.
190-199.
Page 388 Third International Symposium on Space Terahertz Technology
er=4.0 e r=2.3
Figure 1: The synthesis of an elliptical lens from a hyperhemispherical lens and planar
wafers. The extended hemisphere is a very good approximation to an elliptical lens at high
dielectric constants.
c -10
CO
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Angle (degrees)
Figure 2: The double-clot antenna (left) and its radiation patterns into a silicon (e=11.7)
dielectric (right).
Third International Symposium on Space Terahertz Technology Page 389
Aperture
Plane
Critical
Angle SiliconWafers
Silicon
Wafer
Feed Antenna
Hyperhemispherical Elliptical
Intermediate
Figure 3: The ray-tracing method. Note the three focus positions that are achieved by
adding high-resistivity silicon wafers.
-5
03
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O
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— — 45 — p l a n e _
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Angle (degrees)
Figure 4: Measured patterns at the elliptical focus at 246GHz. The patterns are diffraction-
limited by the size of the aperture
Page 390 Third International Symposium on Space Terahertz Technology
-5
ca
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Figure 5: Comparison of theory vs. experiment for the elliptical focus. The critical angle
limits the size of the aperture, resulting in wider theoretical patterns.
- Gain=28.9dB
m
T3
o
—
~
-5
-10
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Angle (degrees)
Figure 6: Measured patterns at the elliptical focus at 222GHz (left) and 270GHz (right).
Third International Symposium on Space Terahertz Technology Page 391
H-plane
— — 45—plane
-25
-30 -20 -10 0 10 20 30
Angle (degrees)
Figure 7: Measured patterns at the intermediate focus position at 246GHz.
-5
03
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Angle (degrees)
Figure 8: Comparison of theory vs. experiment for the intermediate focus.
Page 392 Third International Symposium on Space Terahertz Technology
C
'3
o
t- ' ' ' '/J- Gain = 18.1dB /
i 'C
-5 r "
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 J
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Angle (degrees)
Figure 9: Measured patterns at the hyperhemispherical focus position at 246GHz.
j n -Exper . -
E-Theorv -
-25
-30 -20 -10 0 10 20
Angle (degrees)
- -lO'r
-20 r
-^7— H-Exper. -
-r\- H-Theory -!
-30 -20 -10 0 10
Angle (degrees)
20 30
Figure 10: Comparison of theory vs. experiment for the hyperhemispherical focus. Notice
the predicted multi-peak behaviour.
Third International Symposium on Space Terahertz Technology
Coupling to Gaussian Beams
Page 393
Focus Position
(extension)
Elliptical
(.39 radius)
Intermediate
(.32 radius)
Hyper-
hemispherical
(.25 radius)
Gain
28.6dB
25.7dB
IS.ldB
Gaussian Beam Parameters
0 (amplitude)
5.0°
8.2°
13.3°
O^phase)
-
11.3°
13.5°
Matching
Efficiency
~ 79%
~ 83%
~ 81%
Gaussian Beam Electric Field: exp[-(0/0o) ] exp[j*7T*( 0/0t) ]
Max. Power Elliptical_
Max. Power Hyperhemispherical
Figure 11: Table of Gaussian beam parameters.


Double-slot antennas on extended hemispherical dielectric lenses

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