WE2E-7
METAL MESH
COUPLERS USING
OPTICAL TUNNELING EFFECT
AT
MILLIMETER
AND
SUBMILLIMETER
WAVELENGTHS
Jongsuck
Bae',
Jung-Chih Chiao*, Koji
Mizuno',
and
David
B.
Rutledge'
'Research
Institute
of Electrical Communication, Tohoku
University,
Katahira
2-1-1,
Sendai
980,
Japan
'Department of
Electrical
Engineering, California
Institute
of
Technology
Pasadena, California
91
125,
USA
ABSTRACT
A
new
metal
mesh
coupler
that makes use
of
a tunneling
effect
of
evanescent
waves
between
a metal mesh
and a dielec-
tric plate, has been proposed
as a
quasi-optical
component for
millimeter
and submillimeter wavelengths.
Theoretical calcula-
tion
and experimental
measurement performed
from
40
GHz
to
60
GHz
show that
the
transmittance of
the coupler
can
be
changed
more
than
50
%
for
the variation
of
a spacing less
thafl
0.18
mm
between
a capacitive
mesh
and
a silicon plate
at around
57
GHz.
INTRODUCTION
At
millimeter
and
submillimeter wavelength
regions, there
has
been
substantial interest on
the
development
and
applica-
tions of
quasi-optical devices,
such
as
coherent
power-combin-
ing
[
11
[2].
Fabry-Perot
(FP)
interferometers
have
been
widely
used
as
tunable
optical
couplers
or
filters
as quasi-optical
com-
ponents.
The FP-type optical couplers consist
of
two reflectors
and make use
of
interference
between propagation waves
in
the
couplers to change
their
coupling coefficient. Consequently,
the
large
and rapid
change
of
the
coupling coefficient
with frequen-
cies results
in the narrow bandwidth
of the FP-couplers.
An
opti-
cal
tunneling
type
metal
mesh
(OTM)
coupler
has
been proposed
by
us
as
a new
quasi-optical
component
to overcome
the trade-
off between bandwidth and
coupling coefficient
of the FP-
cou-
plers.
The OTM-coupler consists
of
an
inductive
or
a capacitive
metal
mesh
and
a flat
dielectric
plate placed
close to
the surface
of the mesh (Fig.
l),
and
makes use
of
an
optical tunneling
of
evanescent
waves
to change reflectance and
transmittance.
The
evanescent
waves
are
induced
by
an
incident
wave
on
the
mesh,
and decay
quickly
away
from
the mesh, normally
less
than
U20
from the
surface
[3].
Therefore,
in
contrast to a FP-interferom-
eter,
the
coupling coefficient
of
the
OTM-coupler can
be
signifi-
cantly changed
by
small
adjustments
of
spacing
between the
mesh
and the
dielectric
plate.
In
principle, the
OTM-coupler
can
also
be
wide band because the
transmission properties
of
the
couplers depend
primarily
on
the
mesh
parameters
(g,
2a,
and
r
illustrated
in Fig.
1).
In
this paper, theoretical
simulations
and
experimental
results
are
reported to
show
the
feasibility
of the
OTM-couplers.
THEORETICAL
ANALYSES
The OTM-coupler consists
of
a silicon
plate and
a capaci-
tive
metal mesh
on a quartz
plate.
The quartz
plate
has
a refrac-
tive
index
of
2.12
and
a thickness of
2
mm.
The
silicon plate
has
a refractive
index of
3.42
and a
thickness
of
1
mm.
The reflec-
tance
(IS1112)
and
transmittance
(IS2112)
of
the
OTM-couplers
with
different
mesh parameters have
been
estimated
by
using the
Hewlett-Packard
High Frequency
Structure Simulator
(HFSS)
and
the
Method
of
Moments (MOM) in the frequency
range
be-
tween
40
GHz
and
60
GHz.
In the
fist
simulation, one-dimensional
capacitive
metal
pattern
(a
strip
grating)
has
been
assumed because of
its
ease
of
calculation.
The
strips
are
assumed
to be
perfect
conductors and
have
zero
thickness.
The
rf loss of
quartz
and
silicon
plates are
also
assumed
to be
zero
to simplify
the calculations.
A
uniform
plane
wave is assumed
to be
normally
incident
on
the grid, with
the
electric field polarized perpendicular to
the strips.
The sur-
Dielectric plate.
A
Reflected waves
Incident
and
Dielectr
t
Metal mesh
sic
plate
Fig.
1
Configuration
of
the OTM-coupler.
787
CH3389-4/94/0000-0787$01
.OO
0
1994
IEEE
1994
IEEE
MTT-S
Digest
face current
distribution
is determined using the method
of
mo-
ments
[4].
Once
the
current distribution has
been
determined, the
induced
EMF
technique was
used
to calculate
the impedance
of
the
capacitive
grid.
This
technique
is very similar
to the
one
used
by
Eisenhart and
Khan
[5]
and
is further detailed
by
Weikle
[6].
Finally,
the
impedance
is used
to find the
reflected and transmit-
ted
wave
through the structure using a simple transmission
line
circuit.
Fig.
2 shows
the
results calculated
by
both
methods
for
reflectance
and
transmittance as a function
of the
spacing
L
be-
tween
the capacitive
strip
grating and
the
silicon plate at
60
GHz.
The simulations
have been
done for
the
capacitive strip grating
with
a pitch
(g)
of
1.465
mm
and a gap
(24
of
0.585
mm.
The
simulation results
show
that the optical tunneling
effect
clearly
appears around
L=O,
and that the coupling coefficient
can
be var-
ied more than
a
50
%
range
by
changingL
only
0.18 mm,
i.e.,
h/
28.
Fig.
3
shows
the
calculated imnsmittance
of the OTM-cou-
pler
with
a strip grating
of
g=1.70
mm
and
2~4.69
mm
as a
0.0
0.5
1.0 1.5
2.0
2.5
Spacing
between
the quartz
and
silicon
plates
(mm)
Fig.
2
Theoretical
results
for reflectance and trans-
mittance at
60
GHz
1
.o
I....
g=
1.70
mm
L=
140
pm
0.0
50
55
60
Frequency
(GHz)
Fig.
3
Theoretical transmittance
of
the
OTM-coupler
with a
mesh
plate
of
pitch
size
g
of
1.70
mm
as
a
function
of frequency
for different spacing
L
be-
tween
the
mesh
and silicon
plate.
function
of
frequency
for
different spacing
of
L.
From
the
simu-
lation results,
it is
Seen
that the
OTMcoupler
has a relatively
flat
band
transmission property
in the
frequency range
between
50
GHz
and
57
GHz.
The
coupling coefficient
can
be
changed
by
more
than
40
96
over a
10
%
frecluency
range
by
varying
L
within
0.14
mm.
The
maximum
change
of
83
%
on
the
coupling coeffi-
cient
can
be achieved at 57
GHz.
In
Fig.
3,
the transmittance
of
the
coupler for
L=
0
is zero
at
57
GHz
and increases abruptly
when
frequency
is increased. This variation
has been
caused
by
a
resonance effect in
the
strip
grating
[7].
EXPERIMENTAL SETUP
Experimental measurements have
been
done
to
confm
the theoretical predictions.
The
measurement
setup
includes
an
HP85
106C
millimeter-wave
network
analyzer, transmitting and
receiving homs and
an
OTM-coupler
as
shown
in
Fig.
4.
The
frequency range
is from
40
GHz
to
60
GHz.
The
spacing be-
tween
the
mesh
and silicon plate
is variable
in the range form
0
to
10
mm
with an
accuracy
of f10
p.
The
parallelism
between
them
is adjusted
by
using
a He-Ne laser. The transmittances
of
the couplers were measured after calibration.
Three
capacitive
metal
meshes
with
dimensions
(g,
2~)=(1.48,0.59),
(1.58,0.65) and (1.70.0.69) in millimeter have
been
used
in
this
experiment. Those meshes
are
fabricated
on
a
z-cut
quartz
plate
by
using
photolithographic techniques
with
an
accuracy
of
f5
pm.
The
thickness
of
the
metal
meshes
is about 1
pm.
The
quartz
plates are
40
mm
in diameter and 2
mm
in thick-
ness, and
the
silicon plates are
63.5
mm
in
diameter and 1
mm
in
thickness.
The
refractive indices
of the
quartz
and
silicon plates have
been
determined
by
measuring transmission properties
using
the
same experimental setup as described above.
From
the measured
results,
the
refractive index
of
the quartz plate
is estimated
to
be
2.12
M.05
and the
field
attenuation constant
is about
0.5
Nep/
cm.
The refractive
index
of the
silicon plate
is
3.42
M.05.
A
noticeable transmission
loss
of
the silicon plate
has
not
been
ob-
served
in this frequency
‘mge.
EXPERIMENTAL RESULTS
Fig.
5
shows
the theoretical and measured transmittances
of
the
OTM-couplers
with
capacitive
meshes
with
(a)
g=1.48
mm
and (b) 1.70
mm
as a function
of
L
at frequencies
of 40 GHz,
analyzer
Fig.
4
Experimental
setup.
788
50
GHz,
and
58
GHz.
The shapes
of
the
curves
are
similar,
how-
ever
the
theory
is about
15%
higher
than the
measurement
at the
peak
values. From Fig.
5@),
it can
be
seen
that
the
measured
curves shift
to
right
by
the
order
of
10
pn
of
L
in
comparison
with
the
theory.
It might
be
caused
by
uncertainty
of defining the
origin
position
of
L
in the
experiment.
The
results
show
that
the
tunneling effect occurs
only
for
the spacing less
than
0.18
mm.
For larger spacing,
the
couplers
behave
like Fabry-Perot inter-
ferometers.
It is difficult
to estimate
an
effective distance
of
tunneling
precisely
from
Fig.
5
since
the
tunneling
effect
appears together
with
the Fabry-Perot etalon
effect
due
to a finite thickness
of
the
dielectric
plate.
Fig.
6
shows
the
measured
transmittances
with
and
without
the
tunneling effect
for
the
OTMcoupler
as
a func-
tion
of
L
at
58
GHz
with
the
mesh
size
of g=1.70
mm.
The circles
indicate the
same
data
shown
in Fig.
5
(b)
and
solid
line
indicates
measured
transmittance
for the
same
coupler,
which
was
mea-
sured
with
an
extra
W
of
L,
shifted
by
-hn
and superimposed
on
the
circles
in
the
same range
of
L.
In
Fig.
6,
the difference
be-
tween two
curves
is caused
by
the tunneling
effect
alone.
Com-
paring
these
two
curves,
it is found
that
the
optical
tunneling
ef-
fect
decays
exponentially
with
a decay
constant
of about
60
Nep/
-
0.0C'
.
'
*
'
.
.
.
*
'
. .
*
.
'
0.0
0.5
1
.o
1.5
(b)
Spacing between
the
quartz
and
silicon
plates
(mm)
Fig.
5
Comparison
of
the
theoretical
and measured
transmittances
of
the OTM-couplers with mesh
plates
of
(a)
g=
1.48
mm
and
(b)
g=
1.70
mm
at
40
GHz,
50
GHz,
and
58
GHz.
mm.
The
distance
where
the strength
of
the
tunneling effect
falls
to
l/e2
of
the maximum
value
is
about
70
pm.
i.e.,
W4,
includ-
ing
the
shift
of
the
origin position
by
40
pm.
For
the
other
two
OW-couplers,
similar
values
of
the decay constant
have
been
obtained
at around
58
GHz.
From
Fourier optics
theay
[8]
in the
capacitive
mesh,
an
evanescent
wave
of
the
first
order
has
a de-
cay
constant
of
about
7 Nep/mm.
Thus,
the
estimated decay con-
stant
is
mm
than
8
times
larger
than
that
of
the
evanescent
wave
induced
on
the
metal mesh.
This
fact
shows
that the
observed
changes
of transmittance
in the coupler
do
not result
from
simple
coupling
between
the
evanescent field
and
the
silicon plate.
Fig.7
compares
the
measured
transmission
propemes
of
three
OW-couplers
with
L=
0
as
a function
of
frequency
from
40
GHz
to
60
GHz.
In
the
experiment, differences
between
the
measured
curves
show
that
the
changes
of
transmission property
depend
on
the
mesh
parameters,
mainly
on
the
mesh
pitch. The
small fluctuations
in Fig.
7
are
caused
by
small
amount
of
scat-
tered wave
from
a mirror
mount
of
the
OTM-coupler.
A
strong
dip
and
a peak
of
transmittance
are
observed from the experi-
mental
results. These drastic
variation
of transmittance indicates
that
the resonance
exists,
as
predicted
by
the theory,
at around
58
GHz
for
a mesh
plate
with
g=
1.70
mm.
In
order
to confm
the
theory, the transmittance
of
the
OTM-coupler with
a capacitive
mesh
of
g=1.70
mm
as
a function
of
frequency
from
50
GHz
to
60
GHz
for
various values
of
L
has
been
measured and
shown in
Fig.
8.
The predicted
and measured
transmittances
are
similar
up
to about
57
GHz
except
a shift
of
about
50
p
of
L.
The
experi-
mental
results
show
that the
coupling coefficient
can
be
changed
by
more
than
30%
over
a
10%
frequency
range
by
small varia-
tions
of
L.
The
change
of coupling coefficient
is smaller
than the
theoretical
prediction
by
10%.
In
the
experiment
as
shown
in Fig.
8,
strong
dips
and peaks
have
been
observed
at around
58
GHz
for
L
between
0
and
90
pm.
It is clear that there
are
tworesonant
frequencies.
The
strong
peaks
at higher
resonant
frequency
(f,,)
around
59
GHz
are
from
Wood's
anomaly
[91,
where
the
wavelength is
equal
to
the
pe-
riod
of
the mesh
multiplied
the
effective refractive
index
of
the
silicon plate.
Since diffraction
happens
abovefh,
an
operation
of
the
OTM-coupler
is limited
to the
frequency
of about
59
GHz.
It
f=
58 GHz
o
With
0.0
0.0
0.5
1
.o
Spacing
between
the
quartz
and
silicon
plates
(mm)
Fig.
6
Transmittance measured
with
and without
a
tunneling effect for the
OTM-coupler
with
a
mesh
plate
of
g=
1.70
mm
789
should be noted that
this resonant
frequency
is higher than
the
frequency expected
by
the
previous mesh theory
(51.6
GHz)
[lo].
From
our
experimental
results,
it is found
that the
effective
refractive index
of
the
silicon
plate
decreases
as
L
increases,
ap-
proaching
3
as
L
goes
to
0.
This value
is smaller
than
the actual
refractive index
of
silicon,
3.42.
This
effective refractive
index
has
been
also predicted
by
our
theoretical
simulation
results.
In
Fig.
3, the two
resonant
frequencies predicted
by
the theory
for
L=O
are
57 GHz
and
60.7
GHz while the
experimental
values
are
57.6
GHz
and
59
GHz, respectively. When
L
is larger
than
10
pm, the resonant frequencies obtained
from
the
theory and
the
experiment
are
very
different. In
the
experiment,
the
resonant
effect
in the OTM-coupler
is very
sensitive
to
the
distance
and
parallelism between the
mesh and
the
silicon
plate.
To
explain
the difference, more
experiments
at around
resonant
frequency
will
be required.
.
L=
140
wn
CONCLUSION
The optical tunneling
type metal mesh
(OTM)
coupler
has
been
proposed as
a new
quasi-optical component
at millimeter
and submillimeter
wavelength
regions.
In
the
experimental
re-
sults
performed
f”
40
GHz
to
60
GHz, the
coupling coeffi-
cient
of
the
OTM-coupler
can
be
changed
by
more
than
30
%
over
a 10
8
frequency range
by
adjusting
a spacing
of
less
than
h/28
between the mesh
and
the silicon plate
as
predicted
by
the
theory.
The
theoretical
and
experimental results
have shown that
the OTM-
coupler
is a potential
component to be
used
at milli-
meter
and
submillimeter wavelengths.
ACKNOWLEDGMENTS
We would like
to
express
our
gratitude to Messrs.
Y.
Aburakawa,
T.
Fuji,
and
M.
Miyajima
at Tohoku
University for
fabricating
the metal
mesh and
the
other experimental apparatus.
We
also
thank Michael DeLisio
at
Caletch
for assistance
with
the theoretical
simulations.
0.0
40
45
50
55
60
Frequency
(GHz)
Fig.
7
Comparison
of
measured transmittances of the
OTM-couplers with three different mesh
sizes
of
g=
1.48,
158,
and
1.70
mm
as
a function
of
frequency when
L=
0.
REFERENCES
J.
Bae,
Y.
Aburakawa,
H.
Kondo,
T.
Tanaka, and
K.
Mizuno.
“Millimeter and Submillimeter
Wave
Quasi-Opti-
cal Oscillator
with Gunn
Dicdes,
“
IEEE
Trans. Microwave
Theory
Tech.,
vol. MTT-41,
pp.
1851-1855.
1993.
M.
Kim,
E.
A.
Sovero,
J.
B.
Hacker,
M.P.
DeLisio.
J.
C.
Chiao,
S.
J.
Li,
D.
R.
Gagnon,
J.
J.
Rosenberg,
and
D.
B.
Rutledge,
“A
100-Element HBT Grid
Amplifier,”
IEEE
Trans. Microwave
Theory
Tech., vol. MTT-41,
pp.
1762-
1771,1993.
Z.
S.
Agronovich,
V.
A,
Marchenko, and
V.
P. Shestopalov,
“The Diffraction
of
Electromagnetic Waves from Plane
Metallic Lattices,” Sov.
Phys.
Tech. Phys., vol.
7, pp.
277-
286,1962.
R.
F.
Harrington,
“Field Computation
by
Moment Meth-
ods,”
Robert
E.
Krieger Publishing Company, Malabar,
Florida, original ed.
1968, reprinted 1982.
R.
L. Eisenhart,
P.
J.
Khan, “Theoretical and
Experimental
Analysis of
a Waveguide Mounting
Structure,”
IEEE
Trans.
Microwave
Theory
Tech.,
Ml’T-19.
pp. 706-719,
197
1.
R.
M.
Weikle
11,
“Quasi-Optical Planar
Grids
for
Micro-
wave and
Millimeter-Wave
Power Combining,”
Ph.D.
Dis-
sertation,
California
Institute
of
Technology,
1992.
M.
S.
Durschlag and
T.
A.
DeTemple, “Far-IR Optical
Properties
of Freestanding
and
Dielectrically
Backed Metal
meshes,”
Appl.
Opt., vol. 20,
pp.
1245-1253, 1981.
V.
Yak.,
“Properties
of
a
Fabry-Perot Interferometer
with
Mirrors
in
the
Form
of
a Backed Metal Grid,”
So.
Phys.
M. C.
Hutley,
Difiaction
Gratings,
London: Academic
Doklady,
vol. 10,
pp.
788-790,
1966.
Press.
1982.
DD.
175-210.
[lo]
R.
C.’Compb;l,
L.
B.
Witbourn, and
R.
C.
McPhedran,
“
Strip grating
at
a dielectric interface and application
of
Babinet’s
principle,”
Appl.
Opt., vol.
23,
pp.
3236-3242,
1984.
0.5
v)
s
I-
nn
”.”
50
55
60
Frequency
(GHz)
Fig.
8
Measured transmittance
of
the OTM-coupler
with
a mesh
size
of
g=
1.70
mm
as
a function of
frequency for different spacing
L
between the
mesh
and
silicon
plate.
790