Results of experiments designed to demonstrate spectrally selective absorption in dielectric waveguides on semiconductor substrates are reported. These experiments were conducted with three waveguides formed by sputtering films of PSK2 glass onto silicon-oxide layers grown on silicon substrates. The three waveguide samples were studied at 633 and 532 nm. The samples differed only in the thickness of the silicon-oxide layer, specifically 256 nm, 506 nm, and 740 nm. Agreement between theoretical predictions and measurements of propagation constants (mode angles) of the six or seven modes supported by these samples was excellent. However, the loss measurements were inconclusive because of high scattering losses in the structures fabricated (in excess of 10 dB/cm). Theoretical calculations indicated that the power distribution among all the modes supported by these structures will reach its steady state value after a propagation length of only 1 mm. Accordingly, the measured loss rates were found to be almost independent of which mode was initially excited. The excellent agreement between theory and experiment leads to the conclusion that low loss waveguides confirm the predicted loss rates

Burke, J. J.

Stegeman, G. I.

English

NASA Technical Reports Server

Guided-Wave Approaches to
Spectrally Selective Energy Absorption
A Final Report
prepared for
NASA Lewis Research Center
21000 Brookpark Road
Cleveland, Ohio 44135
(KASA^CE-182532) GUIDED-»A¥E fiEffiOACHIS 10 N88-178S2
SfECIfiALLY SELECTIVE EKEfiGX iBSpBPIIOH Final
Beport, 25 Jan. 1«B3i- 2 Mar. 1967 (Arizona
y .14 p CsCi 20N onclas
-63/32 ,0126017
G. I. Stegeman and J. J. Burke
Principal Investigators
Optical Sciences Center
University of Arizona
Tucson, Arizona 85721
Grant Number: NAG 3-392
Periods Covered: January 25, 1983 - January 24, 1985
(Optics of Surface Plasmon Polaritons)
January 23, 1985 - March 24, 1986
March 5, 1986 - March 2, 1987
https://ntrs.nasa.gov/search.jsp?R=19880008508 2020-03-20T08:13:39+00:00Z
Abstract
Results of experiments designed to demonstrate spectrally selective absorption in
dielectric waveguides on semiconductor substrates are reported. These experiments
were conducted with three waveguides, formed by sputtering films of PSK2 glass
onto silicon-oxide layers grown on silicon substrates. The three waveguide samples
were studied at 633 nm and 532 nm. The samples differed only in the thickness of
the silicon-oxide layer, specifically 256 nm, 506 nm, and 740 nm. Agreement
between theoretical predictions and measurements of propagation constants (mode
angles) of the six or seven modes supported by these samples was excellent.
However, the loss measurements were inconclusive because of high scattering losses in
the structures fabricated (in excess of 10 dB/cm). Theoretic calculations indicated
that the power distribution among all the modes supported by these structures will
reach its steady-state value after a propagation length of only 1 mm. Accordingly,
the measured loss rates were found to be almost independent of which mode was
initially excited. The excellent agreement between theory and experiment with
respect to the propagation constant leads to the conclusion that experiments with low-
loss waveguides would confirm the theoretically predicted loss rates of the different
modes, and thus the anticipated spectral selectivity of such structures.
Introduction
This report concludes a four-year study of the possible applications of guided-
wave structures to solar energy converters. The study began by examining the
application of surface plasmons, particularly the long-range surface plasmons that
propagate on thin metal films, and on pairs of such films separated by thin dielectric
layers. The results of our theoretical studies of such structures were published early
in the program.1"4 As explained in prior letter reports, our experimental attempts to
launch plasmons on thin metal layers by endfire coupling were not conclusive. They
were abandoned in 1985 in favor of studying more promising structures, namely
dielectric waveguides bounded by semiconducting substrates. The body of this report
describes these latter studies.
We begin with a brief description of the theoretical framework, which we have
incorporated into a computer program that can compute the real and imaginary parts
of the propagation constants of all modes (bound or leaky) that are supported by any
collection of homogeneous, isotropic films grown on arbitrary substrates. The real
part of the propagation constant yields the mode angle in the guide; the imaginary
part defines the loss rate. These were computed for the structures used in the
experiments.
We then describe the experiments, in which grating couplers were used to
selectively launch individual modes of our multi-mode guides. The mode angles were
measured by noting the angle between the normal to the structure and the direction
of the collimated input beam to the grating. The loss rates were measured for initial
excitation of each and. every mode. Because of scattering, the rates are not
characteristic of the modes initially excited, but reflect, rather, the collective loss rates
of all the modes due to both absorption and scattering.
The numerical and graphic predictions of theory and the results of
experimentation, with respect to both mode angles and losses, are summarized in three
tables and two graphs at the end of the report. The agreement with respect to mode
2
angle is excellent. The loss rates are inconclusive, because of scattering. We
conclude, because of the excellent agreement for the mode angles, that we are capable
of designing spectrally selective waveguide structures for solar energy applications,
but incapable of sputtering, with our present facilities, the low-loss waveguides
necessary to verify our designs.
Theory
The theory used to calculate the waveguide properties was detailed in a paper
by Chilwell and Hodgkinson.5 We will present a brief summary here.
Consider a stack of dielectric films lying parallel to the yz plane, thus:
y cover 1 j-l substrate
c 1 2 j-l s
This structure will support guided waves if at least one film is surrounded by films
of lower refractive index. For true confinement, the cover and substrate indices
must both be lower than at least one of the film indices. We write the x and y
dependence of the plane-wave fields as exp[ik(ax + /3y) - icot], where propagation of
the guided modes is in the y direction, there is no variation in z, and the films lie
parallel the yz plane. The total field distribution is a superposition of these plane-
wave fields. For a plane wave in the cover layer, incident on the stack at an angle
0 from the normal to the stack, we have
aj = nj cos0j = (nj2 - /S2)1/* ,
(3 = nj sinflj .
If the optical field is known at a single x value, it can be found everywhere with
the use of 2x2 matrices. For a single layer we write.
VJ->
where Mj is the field-transfer matrix. For TE modes, Uj and Vj are the complex
amplitudes (at the boundary of the jth and 0 + l)th layers) of the electric-field vector
and the magnetic-field vector (transverse to the direction of propagation), respectively.
These techniques are familiar from thin-film analysis.6 The field-transfer matrix is
given by
M: =
where $,- = kaj(Xj - Xj_ t ) is called the phase thickness of layer j, and f- = nj
with ZQ = (/JoAo)1/2- The field-transfer matrix for a stack of layers is equal to the
product of the individual layers' matrices,
JM - 77
 Mj.j-1
Thus by finding the field-transfer matrix for the entire stack of dielectrics, one can
calculate the field distribution throughout the stack for a given a and /J.
We can now apply this formalism to determining the guided modes. These
modes are evanescent in the cover and substrate, and oscillatory in at least one of the
dielectric films. In other words, nc, ns < /Jr, where 0r is the real part of 0. We
require the fields in the cover and substrate to decay exponentially in x; i.e., the
evanescent fields. Setting up the relations between the fields in the cover and the
substrate and applying the boundary conditions from Maxwell's equations leads to
[ > ] Uc = M [ 1 1 Us .\ -v I I y I s
I 7cJ lTsJ
Solving this equation leads to the modal dispersion equation
XM(£) = 7CMU + 7c7sMi2 + M21 + 7SM22 = 0 .
This equation holds only for discrete values of j8, which are the guided modes. By
allowing complex dielectric constants, and thus complex /3, one can calculate the loss
coefficients (due to absorption losses in the films) from j3, since the field propagates
as exp[-k/S;y], where /3; is the imaginary part of /3.
In modeling the experiment described below, a slight change in the formalism is
necessary. The substrate layer was silicon, which has a much higher index of
refraction than any of the film layers (nr a 4). Thus we must relax the requirement
of evanescent fields in the substrate (0r < ns).
A program was written to handle an arbitrary number of films with complex
indices of refraction. The program finds the roots of the above modal dispersion
equation in the complex /3 plane. From these, the effective mode index /Sr and the
losses in the guide /?j are calculated for each guided mode.
Experiment
To test the idea of wavelength-dependent coupling, samples were fabricated in
which a silicon substrate provided the absorbing dielectric layer. Since the index of
silicon is high (nr n 4), a low-index buffer layer is needed between the guiding layer
and the silicon. To achieve this, the wafers were baked in an oxygen atmosphere.
This resulted in a layer of silicon dioxide on top of the silicon. The SiO2 acted as
the buffer layer between the waveguide and the silicon substrate. Buffer layers
were fabricated with thicknesses of 0.74, 0.506, and 0.256 fim.
A relatively low-index glass, PSK2, was sputtered onto these processed silicon
substrates to form the actual guiding layer. The deposition of this glass was a major
stumbling block. The sputtering system in use was poorly designed and was host to
a large number of materials. The system spent a large portion of the time under
repair or in transition between different sputtering materials. Although many
waveguides of the PSK2 glass were fabricated, linear scattering losses on glass
substrates were never less than approximately 10 to 15 dB/cm. On the silicon
wafers, the losses were worse. As will be seen later, this became a severe hindrance
to the testing of the principles of wavelength-dependent coupling.
One of the requirements of these waveguiding structures is that either the
buffer layer or the waveguide have a taper, so that the longer wavelengths can be
coupled out at a different physical location than the shorter wavelengths. To
demonstrate that tapered films can be fabricated, tapered layers of PSK2 were
deposited on the silicon substrates. This was accomplished by de-centering the
substrate holder above the sputtering target. The substrates were held off-center, and
thus the end of the substrate closer to the center of the target had thicker layers
deposited than the portion of the substrate farther away from the target. This
procedure produced nicely uniform tapers. The taper was visible to the eye as a
series of interference fringes across the film. Also, by measuring the guided-mode
indices of the film, and fitting the observed /3 values to the ft values calculated by
the computer program, the thickness and index of the guiding layer can be estimated.
The thicknesses at either end of the film were indeed found to be different, with
tapers of about 1/2 fim over a length of 40 mm being typical.
To characterize the waveguides, a method to couple into the guides was
required. Since it was felt that the pressure of prism coupling into the guides would
crack them, grating couplers were used. A photoresist grating was written on the
surface of the waveguide using holographic techniques. By measuring the grating
line spacing and the angles at which light coupled into the waveguide, the j8 values
for the guide could be calculated. The computer program was then used to deduce
the index and thickness of the guides.
The next task in the characterization of the waveguides was the measurement of
the losses of the guide. To this end, a method developed by Himel and Gibson7 was
employed. When a guided mode propagates in a waveguide with scattering losses,
light is scattered out of the plane of the waveguide, forming a visible streak. A
coherent fiber bundle was placed in contact with the waveguide streak. A 20 p. slit
was scanned across the end of the fiber bundle, and the output fed into a
phbtomultiplier tube. The intensity seen by the photomultiplier was detected by a
6
lock-in amplifier, collected by a microcomputer, and plotted by a data-reduction
routine. The logarithms of the intensity values were taken and displayed by the
computer. If the intensity decay is an exponential function of length, then the
logarithm is a linear function of length, with the slope equal to the loss coefficient.
A linear regression best-fit routine was used to fit the line to determine this
coefficient. The loss values were read from the linear fit.
Results
The results of the experiments are tabulated in Tables 1 through 3, and also in
the accompanying graphs. The measured and the calculated values of the effective
index (equal to 0r) and the losses (proportional to /3() are shown. When no
experimental value is entered in the table, the measurement could not be made, for
reasons explained below. As can be seen, the agreement between theory and
experiment for /3r is quite good, while for /3{ it is not as good. This has several
explanations.
The root of the problem is the extremely poor quality of the waveguides. The
loss-measurement technique requires a visible streak extending over several
millimeters. As the streak gets shorter, the accuracy of the technique is reduced.
Also, experimentally, as the losses increase, the intensity of the streak weakens, and
the signal-to-noise ratio of the experiment worsens. For many of the lossier higher-
order modes, the streak was only a few millimeters long. The error involved in
fitting a best-fit line to such a short streak is quite large, as much as ±50%. Thus,
for losses above 30 to 40 dB/cm, very accurate measurements cannot be expected.
However, this does not explain why the losses in the measurable modes were
found to be almost constant. A possible explanation is that in the presence of high
scattering losses, as Marcuse has shown,8 the power in a waveguide distributes itself
among all the modes of the guide. So, in our samples, optical power is probably
being scattered from the mode of interest into lower-order modes. These modes all
have approximately the same losses. A rough calculation from Marcuse shows that
for a 30 dB/cm waveguide, the steady-state power distribution should be reached
after about 0.2 to 2 mm, depending on the correlation length of the refractive index
inhomogenieties that generate the scattering. The distance from the grating coupler to
the edge of the fiber bundle was typically on the order of 1 mm, so the experiment
was always performed in the steady-state power distribution region. In Marcuse's
words, " . . . once the steady state is reached, the average power carried by each
mode decreases at the same rate . . . ."9 Thus the losses appear to be almost the
same as in the lower-order modes. For the very high-order modes, where theory
predicts losses in excess of 100 dB/cm, the optical power is absorbed by the silicon
before it has a chance to scatter into the lower-order modes. Thus there is
essentially no streak, and no way to make a measurement of the losses. So the
higher-order modes do have extremely high losses, as expected.
It appears that we have verified Marcuse's coupled-power theory more
thoroughly than we have demonstrated wavelength-dependent coupling. However, we
did see that the higher-order modes have extremely high losses, as predicted by the
theory. Also, since such good agreement for the real part of the propagation constant
was seen, it follows that the imaginary part (which deals with losses) should agree
with experiment as well. Both derive from the same complex solution of Maxwell's
equations, which are quite sound. We are confident that with adequate waveguides,
the theory would be shown to be accurate.
Table 1. Effective indices and losses for Sample One.
layer thickness is 0.256 /z.
SiO, buffer
THEORY
Mode
Number Neff
loss
(dB/cm)
EXPERIMENT
loss
Neff (dB/cm)
1.5619
1.5524
1.5366
1.5142
1.4850
9.202
38.69
94.53
188
340
Wavelength = 0.6328 p.
0
1
2
3
4
Wavelength - 0.532 \i
0
1
2
3
4
5
6
1.5657
1.5589
1.5476
1.5316
1.5108
1.4852
1.4546
3.86
16.26
39.9
79.9
145
253
428
1.5620
1.5523
1.5361
1.5152
1.4851
1.5657
1.5600
1.5483
1.5334
1.5131
34.12
36.08
34.5
35.2
36.5
37.7
37.1
Table 2. Effective indices and losses for Sample Two. SiO2 buffer
layer thickness is 0.506 ft.
THEORY
Mode
Number Neff
loss
(dB/cm)
EXPERIMENT
loss
Neff (dB/cm)
Wavelength = 0.6328 ft
0
1
2
3
4
5
6
1.5628
.5563
.5454
.5301
.5103
.4860
1.4573
0.34
1.53
4.23
10.1
23.1
54.4
135
Wavelength - 0.532
0
1
2
3
4
5
6
7 1
.5664
.5617
.5539
.5429
.5287
.5112
.4906
.4668
0.083
0.373
1.01
2.37
5.30
12.1
29.3
77.5
1.5629
.5554
.5461
.5297
.5110
.4852
.4558
24.8
25.9
26.5
27.7
28.3
27.9
1.5679
1.5637
1.5548
1.5433
1.5273
1.5084
1.4878
1.4606
28.6
30.1
30.5
33.5
35.8
38.0
42.5
10
Table 3. Effective indices and losses for Sample Three. SiO2 buffer
layer thickness is 0.74 fi.
Mode
Number
Wavelength
0
1
2
3
4
5
Wavelength
0
1
2
3
4
5
6
THEORY
Neff
- 0.6328 p
1.5615
1.5542
1.5418
1.5245
1.5022
1.4751
- 0.532 p.
1.5652
.5599
.5510
.5385
.5224
.5027
.4796
loss
(dB/cm)
i
0.031
0.154
0.515
1.64
5.73
24.3
0.005
0.023
0.075
0.224
0.711
2.63
12.48
EXPERIMENT
• 10SS
Neff (dB/cm)
.5613
.5537
.5419
.5250
.5030
.4768
1.5660
1.5605
1.5528
1.5409
1.5242
1.5062
1.4841
27.7
21.7
23.2
30.9
33.1
39.4
23.9
27.0
26.9
29.1
31.0
32.5
RECEDING PAGE BUNK NOT FILMED
12
160r
120
If
O
CD
-a so
en
en
_O
40
theory
Sample 2. 0.506 microns oi silicon dioxide
wavelength = 0.6328 microns
experiment
3 4 5
mode number
80
 r
60
IT
O
aa
TJ 40
en
en
o
• Sample 2, 0.506 microns oi silicon dioxide
1 wavelength = 0.532 microns
20 -
theory
3 4 5
mode number
13
References
1. G. I. Stegeman, J. J. Burke, and D. G. Hall. "Surface-polariton-like waves
guided by thin, lossy metal films," Opt. Lett. 8, 383 (1983).
2. G. I. Stegeman and J. J. Burke, "Long-range surface plasmons in electrode
structures," Appl. Phys. Lett. 43, 221 (1983).
3. G. I. Stegeman and J. J. Burke, "Effects of gaps on long-range surface plasmon
polaritons," J. Appl. Phys. 54, 4481 (1983).
4. J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface polariton-like waves guided
by thin, lossy metal films," Phys. Rev. B 33, 5186 (1986).
5. J. Chilwell and I. Hodgkinson, "Thin films field-transfer matrix theory of planar
multilayer waveguides and reflection from prism loaded guides," J. Opt. Soc.
Am. A, 1, 742 (1984).
6. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1980). pp.
51-70.
7. M. D. Himel and U. J. Gibson, "Measurement of planar waveguide losses using
a coherent fiber bundle," Appl. Opt. 25, 4413 (1986).
8. D. Marcuse, Theory of Dielectric Waveguides (Academic Press, New York,
Academic Press, 1974), pp. 181-193.
9. Ibid, p. 184.
14


Guided-wave approaches to spectrally selective energy absorption

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server