of 11
Supplementary Materials for
Nonreciprocal infrared absorption via resonant magneto-optical coupling
to InAs
Komron J. Shayegan, Bo Zhao, Yonghwi Kim, Shanhui Fan, Harry A. Atwater*
*Corresponding author. Email: haa@caltech.edu
Published 6 May 2022,
Sci. Adv.
8
, eabm4308 (2022)
DOI: 10.1126/sciadv.abm4308
This PDF file includes:
Supplementary Text
Figs. S1 to S7
Supplementary
Text
Methods
Device Fabrication
The amorphous silicon was deposited
on the InAs wafer using
plasma
-enhanced chemical
vapor deposition
(PECVD
) with argon gas at 200 °C. We then spin coat
ed a 500 nm thick layer of
ZEP 520A onto the amorphous silicon
(spin for 1 minute a
t 2,000 revolutions per minute and bake
the sample on a hot plate for 5 minutes at 180 °C
). The grating pattern
was then written onto the
sample using an
electron beam pattern generation (
EBPG) system
with a beam current of 100 nA
and an aperture of 300 mm
(dose of 240 mC/cm
2
). The sample
was baked after exposure and etched
using a dielectric
inductively coupled
plasma reactive
-ion etcher with a SF
6
/O
2
cleaning cycle
before and after etching.
The resist
was removed in an
overnight
soak in a solvent stripper (Remover PG)
, and the
recipe
was adjusted after
scanning electron microscope (
SEM) and confocal images of the
produced grating
were taken to measure the periodicity and depth.
Measurements
Before the sample is measured, we
performed
transmission measurements of the InAs
wafer itself to confirm that the sample is optically thick. After the sample
was prepared, it
was
mounted on a glass slide covered with copper tape. The area surrounding the sample
was dressed
with Texwipe strip
s to scatter any light that d
oes not reflect off of the sample from going to the
detector and the 0 field measurements are taken.
For measurements with the magnetic field, we use
d a separate mount on the two
-theta stage
that accommodates the Halbach
magnet
array. The Halbach array was purchased from Dr. Arne
Laucht at the University of New South Wales and contains a set of 90
-degree-rotated permanent
neodymium magnets with supermen
dur pole pieces all housed in a copper assembly
(Figure S
7)
[
29
]. Th
e p
ole
p
ieces
are
t
hreaded
a
nd
c
an
b
e
t
uned
t
o
c
hange
t
he
st
rength
o
f
t
he
m
agnetic
f
ield
across the surface. To measure the uniformity of the field across the sample surface for each
air
gap length, we use
d a Hall sensor to map the field from the edge to the center of the sample. Once
again, we dress
ed the area around the sample with Texwipes to scatter away any light that is not
specular reflected by the sample.
In Figure 6 of the ma
in text, we equate the changing of the magnetic field and incidence
angle on through the Onsager
-Casimir relations. Because of a built
-in limit to the two
-theta stage
of our measurement system
, we are only able to swing the detector to a negative incidence
-85°
(and no angle narrower) as shown in Figure S
2A. This means that we rely on Onsager
-Casimir
relations to interchangeably use a negative magnetic field at a positive incidence angle with a
positive magnetic field at a negative incidence angle. Though t
his is simply confirming symmetry
assumptions, we show the effect of positive and negative magnetic fields at +/
-
85
°
incidence in
Figure S
2
C.
For each measurement, we collect
ed
four spectra with polarizers at the source and detector
allowing only either
p
or
s
-
polarized light through. For all measurements, we confirm
ed
that there
is no polarization conversion or nonreciprocal behavior of the
s
-
polarized light. Each measurement
scanned from
35
to 70° angles of incidence in 5° increments.
The
p
-
polarized abs
orptivity spectra are shown in Figure
s S
3
and S
4
. The shoulder resonance is
strongly visible in the simulated spectra for narrow incidence angles
but smooths out in the
measured spectra where it is visible as a plateau.
We attribute the overall smoothing t
o higher loss
in the InAs
.
For narrower angles where the magnetic field effect goes from divergent to convergent,
(45° to 35° incidence), we see that there is a strong magnetic field effect that causes an absorption
resonance at longer wavelengths for posi
tive field. As we go to narrower angles, the magnetic field
effect is weaker and the resonance at shorter wavelengths begins to dominate (
Figure S
3
). This is
also why for a stronger field, the linewidths narrow at narrow incidence angle compared to the
weaker field case (i.e. the longer wavelength resonance corresponding to a shift in the plasma edge
from a positive field dominates
, as seen in
Figure 3A).
At wider angles of incidence, though the absorptivity peaks occur at the same wavelength,
the magnit
ude of the peak is suppressed for negative field values when compared to positive field
values for both the simulation and the
experiment
(Fi
g
ure 5
, Figure S4
)
.
With the eventual application of using this structure to directly measure the emissivity, we
al
so measure
d
the temperature dependence of the dielectric function up to 450 °C (Figure S
5
). The
curves shown in the figure are obtained from Drude model fits of ellipsometry data. We see almost
a micron shift in the ENZ wavelength regime from room temperat
ure to 450 °C, which could mean
that a slightly larger period structure is needed to have a stronger resonance at 18.1 mm (450 °C)
as opposed to 17.3 mm (293 °C). While the general trend is that both the imaginary and real part
of the dielectric constant g
row with temperature, the imaginary part of the dielectric constant is
slightly larger at room temperature than at 350 °C according to our measurement and fit.
Data analysis
The experimental reflectivity data was collected with J.A. Woollam
IR VASE 32 sof
tware.
Data analysis was done in MATLAB.
To fit the experimental data, we used a locally weighted
linear regression with a quadratic polynomial
model and a span of
20
%. This corresponds to a
weighted fit
over a 0.6 mm range
(41 data points).
We then found the local maxima of the fitted trace
and marked the adjacent data points that
were with 5% of the local maximum (error bars in Fig. 5).
The fitting method was compared to a multi
-
gaussian fit, which produced the same maxim
a and
trends in linewidth.
Simulations
Simulations were done in COMSOL using the
electromagnetic waves, frequency domain
package. A parametric sweep of the frequency and incident angle were done for each run (Figure
S1 d
-
f). To look at the electric field
intensity within the structure at a given angle and frequency,
we take the norm of the electric field (Figure S
6
).
Figure S1:
Slab waveguide
angular
dispersion for varying
a
-
Si layer thicknesses
,
t
,
on top of
n
-
InAs
.
The dispersion relation of the
slab waveguide is found by solving equation E7 in the main
text. The dashed gray line (1.101 x 10
14
rad/s, or 17.2
μ
m)
is the same as the one used in the
comparison of the experimental and simulated traces in Fig
ure 5 as a reference for the reader.
The
dis
persion for
t
=
2.5
μ
m is closest to the dimensions used in our experiment
(and simulations)
.
There
is a considerable shift in theory for the solution to the dispersion for a small change in
a
-
Si
thicknes
s
, with the dispersion shifting to lower
frequencies (longer wavelengths) for a thicker slab
layer.
Figure S
2
: Schematic of reflection setup (A) and confirmation of the Onsager reciprocal
relations (B and C).
The sample and detector are mounted on a two
-
theta stage (with the FTIR
source fix
ed). To test the Onsager
-
Casimir
relations, which equate a negative magnetic field at
positive incidence to a positive field at negative incidence, we look at the magnetic field effect at
+/
-
85
°
incidence (A). Unfortunately we cannot rotate the detect
or beyond
-
85
°
incidence. We
then simulate 85
°
incidence for positive and negative fields (B) and compare the field effect at
positive and negative incidence angles (C). What we observe is that the interchanging of field and
incidence angle effects hold
.
Figure S3: Simulated (A
-
C) and experimental (D
-
F) data on the narrow
-
angle transition
from strong
-
to
-
weak nonreciprocal absorption.
To better visualize the heatmap shown in Figure
S3 C, we show linecuts of the simulated data with experimental data undernea
th. We mark with
red arrows the shoulder peak that is not effected by a positive field at shorter wavelengths (left
arrow in D
-
F) and the peak of the GMR that is strongly shifted by a positive magnetic field (right
arrow in D
-
F).
.
Figure S
4
:
Experimental (
A
C
) and simulated (
D
-
F
) spectra for the absorptivity at varying
incident angles and magnetic field strengths.
We observe a relatively large shift for positive
magnetic field when compared to a negative in
-
plane field for the
45°
incide
nce angle case. The
relative shifts become harder to discern as we go to more oblique angles in both our measurement
and in the simulations using the measured grating parameters
Figure S
5
:
Temperature dependence of the dielectric constant of InAs.
T
he solid lines are the
real part and the dashed lines are the imaginary part of the dielectric constant.
Figure S
6
:
Electric field intensity plots showing the plasmon mode confinement within the
GMR structure
. One unit cell of the periodic array is shown for four different wavelengths. The
mode intensity is stronger at longer wavelengths (
D
) than shorter wavelengths (
A
)
for the
dimensions of the fabricated grating.
The overall
unit cell width
is 6.9
μ
m.
Figure S
7
:
Image and schematic of the Halbach array with tunable supermendur pole pieces.
Both the image and the schematic are courtesy of Chris Adambukulam and Arne Laucht
(
1
)
. In
the image, the magnets are housed in a brass and copper enclosure. The schematic shows the
magnet rotated 90°.