of 20
Experimental D
emonstration of
>
23
0
° Phase Modulation in Gate
-
T
unable
Graphene
-
Gold
Reconfigurable Mid
-
Infrared
Metasurfaces
Michelle C. Sherrott
1,2
ǂ
, Philip W.
C.
Hon
2,3
ǂ
, Katherine T. Fountaine
2,3
, Juan C. Garcia
3
,
Samuel M. Ponti
3
, Victor W. Brar
1,4
,
Luke A. Sweatlock
2,3
, Harry A. Atwater
1,2
*
1
.
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125, USA
2
. Resnick Sustainability Institute, California Institute of Technology, Pasadena, CA
91125, USA
3.
Northrop Grumman
Corporation,
NG Next
Nanophotonics & Plasmonics Laboratory
,
Redondo Beach, CA 90278
, USA
4. Department of Physics, University of Wisconsin
-
Madison, Madison, WI 53706, USA
ǂ
Equal contributors
*Corresponding author: Harry A. Atwater (
haa@caltech.edu
)
Abstract:
Metasurfaces offer significant potential to control far
-
field light propagation through the
engineering of amplitude
, polarization,
and phase at an interface.
We report
here
phase
modulatio
n of an
electronically
reconfigurable metasurface
and demonstrate its utility for
mid
-
infrared beam
steering
. Using
a
gate
-
tunable graphene
-
gold
resonator
geometry, we
demonstrate
highly
tunable reflected p
hase
at
multiple wavelengths
and show up to
237°
phase
modulation range
at an
operating
wavelength of 8.5
0
μm.
We observe
a smooth
monotonic
modulation of phase with applied voltage
from 0° to 206°
at a wavelength of
8.70 μm
.
Based on
these experimental data
,
we demonstrate with
antenna array
calculation
s
a
n average
beam
steering
efficiency
of 50% for
reflected light
for
angle
s
up
to 30°
,
relative to a
n
ideal metasurface,
confirming
the
suitab
ility of this geometry
for
reconfigurable
mid
-
infrared
beam
steering devices
.
Keywords: Metasurface, graphene,
phase modulation, field
-
effect modulation, beam
steering,
mid
-
infrared
Metasurfaces have been demonstrated in recent years to be powerful structures for
a number of applicati
ons including beam steering
1
, foc
using/len
sing
2, 3
,
and more
complex functionalities such as polarization conversion
, cloaking,
and three
-
dimensional
image reconstruction
4
-
8
, among others
9
-
14
.
These
functionalities
are accomplished through
careful engineering of phase fronts at the surface o
f a material, where geometric
parameters of resonant structures are d
esigned to scatter
light
with a desired phase
and
amplitude
.
Howe
ver, all of these structures have functions that are fixed
at the point of
fabrication, and cannot be
transformed
in any way
.
Therefore, s
ignificant effort has been
made in the community to develop metasurfaces
that can be actively modulated. There
exist numerous examples of metasurface designs which enable active control of reflected
or transmitted amplitude,
taking advantage of
different t
echnologies including
MEMS,
fie
ld
-
effect tunability, and phase change
materials
15
-
19
, discussed
further
in recent reviews
of the state
-
of
-
the
-
art in metasurfaces
13, 20, 21
.
For mid
-
infrared (mid
-
IR) light, graphene has been demonstrated as
an ideal
material for active nanophotonic structures
for a number of reasons, including its low
losses in the mid
-
IR and its intermediate carrier concentration (10
12
-
10
13
cm
-
2
), placing
its plasma frequency in the IR
THz regime
22
-
26
.
Additionally
, since
it is atomically thin
and
has
a linear density of
electronic
states, its charge carrier density can be easily
modulated via electrostatic gating in a parallel plate capacitor configuration
27
-
30
. Its
corresponding complex
permittivity
can therefore be modulated over a wide range,
potentially at
GHz
speeds
.
Recent
works have demonstrated that the incorporation of
graphene into resonant gold metasurfaces can also be used to significantly modulate
absorption profiles
, operating at MHz switching speeds
18
.
This has been
accomplished
by either the un
-
assisted modulation of the graphene dielectric constant, or by exploiting
the strong confinement of light by a graphene plasmon excited between metal
edges to
enhance the
sensitivity of the design to the graphene’s optical constants
.
17, 31
Additional
examples have used the tunable permittivity of graphene to modulate the transmission
characteristics of a variety of waveguide
geometries
32, 33
.
Despite the significant progress that has been made,
an important requirement
for
power
efficient, high
-
speed,
active metasurface
s
is electrostatic
control of scattered phase
at multiple wavelengths
, which has not been adequately addressed
experimentally
in the
mid
-
IR
.
In
gaining active control of phase,
one
can engineer arbitrary phase fronts in
both
space and time, thereby opening the door to
reconfigurable metasurface devices
.
This is
particularly necessary as classic techniques for phase
modulation including liquid crystals
a
nd acousto
-
optic modulators
are
generally
poorly
-
suited for the IR due to parasitic
absorption in the materials used
34, 35
, in addition to being relatively bulky and energy
-
expensive in comparison to electrostatic modulators
.
Similarly, though 60° phase
modulation based on a VO
2
phase transition has been demonstrated at 10.6 μm, the p
hase
transition occurs over relatively long time scales
and
the design
is
limited in application
due to the
restricted
tunability range
36
.
Finally,
recent works on the electrostatic control
of phase in the mid
-
IR using graphene
-
integrated or ITO
-
integrated resonant geometries
are limi
ted to
only
55° electrostatic phase tunability at 7.7 μm
37
and 180°
tunability
at
5.95
μm
38
, respectively.
In this work, we
overcome these limitations and
experimentally
demonstrate
widely
-
tunable phase modulation
in excess of 200
°
with
over 25
0 nm
bandwidth
usi
ng an electrostatically gate
-
tunable
graphene
-
gold metasurface
(see Figure
1)
. We highlight a smooth
phase
transition over
206
°
at 8.7
0
μ
m
and sharper, but larger,
phase
modulation of
237
°
at 8.5
0
μm
, opening up the possibility of designing high
efficie
ncy, reconfigurable metasurface devices
with nanosecond switching times
.
By
measuring this active tunability over multiple wavelengths in a Michelson interferometer
measurem
ent apparatus, we present evidence that this approach is suitable for devices
that can operate at multiple wavelengths in the mid
-
IR.
Our tunable phase metasurface design is based on a
metasurface unit
cell that
supports a gap plasmon mode
,
also referred
to as a patch antenna
or ‘perfect absorber’
mode,
which has been
investigated
previously by many groups
39
-
42
, shown schemati
cally
in Figure 1a
.
Absorption and phase are calculated as a function of Fermi energy (E
F
)
using COMSOL FEM
and Lumerical FDTD software
(see Methods for calculation
details).
A 1.2
μ
m length gold resonator on graphene is coupled to a gold back
-
plane,
separated by 500
nm SiN
x
.
At the appropriate balance of geometric and materials
parameters, this structure results in
near
-
unity absorption on resonance, and a phase shift
of 2
π
.
This may be considered from a theoretical perspective as
the
tuning of parame
ters
to satisfy critical coupling to the
metas
urface
40
.
This
critical coupling
occurs when the
resistive and radiative damping modes of the structure are equal
, thereby eff
iciently
transforming incoming
light
to resistive losses and suppressing reflection
.
This
condition
is possible at
subwavelength spacing
between the gold dipole resonator and back
-
plane
,
when the resonator is able to couple to its
image dipole moment in th
e back
-
reflector,
generating
a strong magnetic moment. The magnetic moment
,
in turn
,
produces scattered
fields
that
are
out of phase with the light reflected from the ground plane, leading to
destructive interference and total absorption.
This may be considered the plasmonic
equivalent of the patch antenna mode.
In order to enhance the sensitivity of the structure to the tunable permittivity of
the graphene, t
hese unit cells are arrayed together with a small (50
nm) gap size to result
in s
ignificant field enhancement at the position of the graphene
, as shown in Figures 1b
and 1c
.
This is critical for enhancing the
in
-
plane component of the
electric field to result
in sensitivity to the graphene’s optical constants.
Therefore, as the Fermi e
n
ergy of the
graphene is modulated, changing both the inter
-
and intra
-
band contributions to its
complex permittivity, the resonan
t
peak position and amplitude are shifted
, as shown in
Figure
s
1
d
and
1
e.
Specifically, the intraband contribution to the perm
ittivity is shifted to
higher energies as the plasma frequency of the graphene,
ω
p
increases
with the charge
carrier density
as
ω
p
n
1
4
. Additionally, as E
F
increases, Pauli blocking prevents the
excitation of interband transitions to energies above 2E
F
, thereby shifting these tr
ansitions
to higher energy
.
The net effect of these two contributions is
a decrease of the graphene
permittivity
w
ith increasing car
rier density,
leading to a shift of the
gap mode
resonance
to higher energy.
By taking advantage of
graphene’s tunable optical response
, we
obtain an
optimize
d
design
capable of a continuously shifted
resonan
ce
peak from
8.81
μm
at E
F
=
0
eV
or Charge Neutral Point
(CNP)
to
8.24 μm
at E
F
= 0.5eV
;
a
peak shift
range
of 570
nm
. Correspondingly,
this peak shift
indicate
s
that at a fixed
operation wavelength of
8.50 μm,
the scatter
ed phase can be modulated by 225
°
, as seen in Figure 1f
.
This trend
persists
at
longer wavelengths, with greater than 180
°
modulation achieved between 8.50
and 8.75
μm
.
At shorter wavelengths, such as 8.20
μm
, minimal tuning is observed
because this falls outside of the tuning range of the resonance.
It is notew
orthy that this
phase
transition
occurs
sharply as a function of E
F
at 8.50
μm
because it falls in the
middle of our tuning range
, and becomes smoother at longer wavelengths.
We
therefore
illustrate this
smooth
resonan
ce
detuning
at a wavelength of 8.70
μm
in Figure 1b and 1c
,
wherein we plot the magnitude of the electric field at different Fermi energies of the
graphene.
On resonance
(Figure 1
b
), the field is strongly
localized to the
gap, and then as
the Fermi energy is increased
(Figure 1c
)
,
this localiz
ation decreases as the g
ap mode
shifts to shorter wavele
ngths.
Field profiles at 8.50
μm
are presented in Supporting
Information Section I
.
These different responses are summarized at three wavelengths
(8.2, 8.5, and 8.7
μm
) in Figure 1f
, where the phase r
esponse is plotted as a function of
E
F
.
We experimentally demonstrate the tunable absorption and phase of our designed
structure using Fourier
-
Transform Infrared Microscopy and a mid
-
IR Michelson
interferometer, respectively, schematically shown in Figure 2a.
Graphene
-
gold antenna
arrays are fab
ricated on a 500
nm free
-
standing SiNx membrane with a gold back
-
plane
.
A Scanning Electron Micros
cope (SEM) image of the resonat
or arrays is presented in
Figure 2b.
An electrostatic
gate voltage is applied between the graphene and gold
reflector
via the
d
oped
silicon frame
to modulate the Fermi energy
.
Tunable absorption
resul
ts are presented in Figure 2c
demonstrating
490
nm
of tunability
from
a resonance
peak of 8.63 μm at
the
C
NP
of the graphene
to
8.14 μm at
E
F
= 0.42
eV
, corresponding to
voltages of
+90 V and
-
80V
.
This
blue
-
shifting
is consistent with the
decrease
in
graphene permittivity with increasing carrier concentration, and a
grees well with
simulation predictions.
Discrepancies between simulation and experiment are explained
by fabrication imp
erfections, as well as inhomogeneous graphene quality and minor
hysteretic effects in the gate
-
modulation due to the SiN
x
and atmospheric impurities
43
.
The m
inor feature at 7.6 μ
m is an atmospheric
arti
fact.
The shoulder noted especially at
longer wavelengths is a result of the angular spread of the FTIR beam, wherein
the use of
a
15X
Cassegrain
objective results in off
-
normal illumination of the sample
, explained
further in
Supporting Information Section II
.
We note that the processing of
our sample
in combination with the surface charge accumulated as a result of the SiN
x
surface results
in a significant hole
-
doping of the graphene
, as has been observed in previous
experiments
44
.
Due to this heavy doping, we are unable to experimentally observe the
exact CNP of the graphene using standard gate
-
dependent transport measurement
techniques, a
nd therefore determine this by compariso
n
to simulation.
We then calculate
the Fermi energy at each voltage using a standard parallel plate capacitor model.
To experimentally characterize the phase modulation of scattered light achievable
in our graphene
-
gold resonant structure, we use a custo
m
-
built mid
-
IR
, free
-
space
Michelson Interferometer
, for which a schematic is presented in Figure 3a and explained
in depth in the Methods section
.
The integrated quantum cascade laser source, MIRcat,
from Daylight Solutions provides
an opera
ting
wavelength range from 6.9 μm to 8.8 μ
m,
allowing us to characterize the phase modulation
from our metasurface
at multiple
wavelengths
.
The reference and sample legs
of
the
interferometer
have
independent
automated translations
in order to collect interfero
grams at
each wavelength
as a function
of gate voltage.
A comparison of the relative phase difference between interferograms taken for
different sample biases
is conducted to capture the phase shift
as a function of E
F
.
A
t
each
Fermi energy
, an inter
ferogram for different reference mirror displacements is taken.
Due
to the different absorptivity at each doping level
, each biases’ inte
rfer
ogram is
normalized to it
s own peak value.
We then take
the midp
oint of the normalized
interfer
ogr
am amplitude as a
reference,
and
a
relative phase shift from one bias to t
he
other is calculated by recording
the displacement between the two interf
er
ograms at the
reference amplitude. Factoring that the sample leg is an optical double
pass,
the relative
phase difference
is given by
equation 1
:
=
!"#
!
!
(Equation 1)
Where
Δ
Φ
is the phase difference between different sample responses in degrees,
Δ
x is
the displacement between interferograms, and
λ
is the wavelength of operation.
Data
collected
for three Fermi en
ergies at 8.70
μ
m and fitted to
a linear regression for
extracting phase based on
the above equation are
presented
in Figure 3b.
For
straightforward
comparison, the phase modulation is presented relative to zero phase
difference at E
F
= 0 eV.
Linear
regression fits to the data
for all Fermi energies measured
at 8.70
μ
m are presented in Figure 3c, and the extracted phase as a function of E
F
is
presented in Figure 3d
.
Discrepancies between the experimental data and fits, particularly
at CNP, can be expl
ained by the decreased
reflection
signal from the s
ample due its
strong absorption
on resonance
.
To further highlight the broad utility of our device, p
hase modulation results are
presented in Figure 4
a
at multiple
wavelen
gths: 8.20
, 8.50
, and 8.7
0
μ
m
. At
an
operating
wavelength of 8.7
0
μ
m
,
continuous control of phase is achieved
from 0
°
rel
ative at
CNP
to 206
°
at E
F
= 0.4
4
eV
with excellent agreement to simulation.
At 8.50
μ
m
, this
range
increases to 237
°
,
much greater than any observed in th
is wavelength range previously,
though as noted above, the transition is very sharp
. At the shorter wavelength
of 8.20
μ
m,
a modulation range
of 38
°
is
achieved,
with excellent agreement to simulation
,
demonstrating the different trends in phase control th
is structure presents at different
wavelengths
.
Simulation parameters are presented in the Methods section.
Deviation is
primarily
due to
hysteresis effects and sample inhomogeneity.
We summarize the
experimental and simulation results at all wavelengths between 8.15
μ
m and 8.75
μ
m in
Figure 4b
, wherein we plot the tuning range at each wavelength
, defined as the maximum
difference of scattered phase
between CNP and E
F
= 0.44 eV
. This F
ermi energy range is
limited by electrostatic breakdown of the SiN
x
gate dielectric
.
The data from wavelengths
not presented in Figure 4a are included in
Supporting Information Section III
.
We can
therefore highlight two features of this structure: at long
er wavelengths, we observe
experimentally a smooth transition of phase over more than 200
°
, and at slightly shorter
wavelengths, we can accomplish a very large phase tuning range with the tradeoff of a
large transition slope. It is also noteworthy that mor
e than 200
°
active tunability is
achieved between 8.50
μ
m and 8.75
μ
m, which is sufficient for active metasurface
devices
in the entire wavelength range.
To illustrate the applicability of
our design to
reconfigurable metasurface
s
,
we
calculate the efficiency of beam
steering to different reflected angles as a function of
active phase ran
ge for a linear array
of independently gate
-
tunable elements as shown
schematically in Figure 5a
.
We choose a linear array
with polarization orthogona
l to the
steering direction
to ensure minimal coupling between neighboring elements and a pitch
of 5.5
0
μ
m to suppress spurious diffracted orders
at
a
wavelength
s
of 8.
5
0
μ
m.
To
quantify the beam steering feasibility of
this
metasurface,
we
frame the analysis in the
formalism of antenna array theory, where the array
can be considered as a
discretized
aperture. The far
-
field radiation pattern of such a discretized aperture can be analytically
calculated by independently considering the physic
al array configuration (radiating
element layout) and the radiating element properties, such as its amplitude, phase and
element far
-
field radiation pattern. For a general two dimensional array, the far
-
field
radiation pattern is given by the array factor
weighted by the element’s radiation pattern.
The element pattern can be considered a weighting factor in the calculation of the far
-
field radiation pattern, where the array factor is only a function of the element placement
and assumed isotropic radiators
with a complex amplitude and phase. For relatively
omnidirectional radiating elements, as in our case, the array factor captures the primary
radiation pattern features, such as the main beam direction, main beam half power beam
width
(angular width of the
main beam noted at half the main beam peak intensity)
, and
major side lobes, reasonably well
. The array factor for a general two
-
dimensional
configuration
is given as:
45
퐴퐹
,
=
!"
!
!
!"
!
!
!"
!
!
!
!
!
!
!
!
(
1
)
!"
=
!"
!
sin
!
cos
!
+
!"
!
sin
!
sin
!
(
2
)
!"
=
!"
!
=
!"
!
sin
cos
+
!"
!
sin
sin
(
3
)
where
θ
0
and
φ
0
are
the elevation and azimuthal values of the main beam pointing
direction
, respectively,
α
mn
represents the element
imparted phase that controls the beam
direction,
γ
mn
represents the path length phase difference due to the element position
!"
!
and the unit vector
from the array center to an observation angle,
,
.
β
is the free
space propagation constant,
I
mn
is the complex element amplitude and the double
summations represent the row and column element placement of a general two
-
dimensional array.
Consid
ering only the array factor, we
can analytically capture the beam steering
characteristics of a metasurfac
e as a function of the achievable element phase tuning
range.
In the microwave regime, where the achievable element phase tuning range is
greater than 270
°
, beam attributes such as its pointing direction and side lobe levels, can
be quantified as a
function of the phase discretization; the phenomenon is known as
quantization error
46
. Independent of qua
ntization errors, it is informative to understand
the consequence of an element phase tuning range well below the desired ideal 360
°
. We
define a figure of merit, the
beam efficiency
η
,
to be the
ratio of the
power in the half
power beam width
for a limite
d phase tuning range
relative to the total radiated power
steered to a given angle
for an ideal case
(tuning range of 360
°
)
. In our analysis we
consider maximum p
hase tuning ranges as lo
w as 20
0
°
and desired scan angles up to
+/
-
30°
relative to
surface nor
mal.
For phase ranges below
20
,
the undesirable side lobes
will equal or exceed the intensity of the
primary
beam
and main beam pointing errors
exceeding one degree can exists
; therefore
,
we restrict our
analysis for phase ranges
greater than 200°
.
In a
simplified analysis, a one
-
dimensional array is assumed (Fig. 5a).
Since the focus of the analysis is only on the consequence of a limited element phase
tuning range, the element amplitude is assumed to be equal
and unity
. Assuming a fine
enough gating ste
p size, a virtually continuous sampling of a given element phase tuning
range, is possible and therefore quantization error is not an issue. In this analysis, for a
calculated element phase value that was unachievable, the closest phase value achievable
wa
s assigned. Namely, either an element phase value of 0
°
or the maximum phase for the
considered element phase
tuning range.
As shown in Figure 5b, regardless of the element
phase tuning range, the main beam scanning direction of zero degrees represents the
trivial case where a zero difference in beam efficiency is expected because all elements
exhibit the same reflected phase (zero phase gradient along the metasurface).
The
analysis illustrates the trade space and suggests, for the experimentally verified 2
37
°
of
element phase tuning at 8.50
μ
m, that beam ste
ering efficiency is on average 50% up to a
scan angle of ±30°
.
Below this, lower efficiency steering is observed; however, we note
that down to 200°, the steered
main
beam signal
still
exceeds
the intens
ity in the other
lobes
. We note that the fluctuating trends observed as a function of reflection angle are a
result of the incomplete phase range, which manifests differently depending on the
deviation from the ideal phase gradient
needed
.
This clearly il
lustrates the necessity of
achieving at least
200
°
in active phase
control in order to create viable reconfigurable metasurfaces. In addition, it is noteworthy
that this calculation includes an assumption of all intermediate phase values being
available, meaning that a smoothly varying phase response as a
function of gate voltage
is necessary, as demonstrated in our device.
This highlights the potential applications of
our structure to metasurface devices, in which independently gateable elements can be
used to generate arbitrary phase gradients in time an
d space
.
In conclusion, we have demonstrated for the first time electrostatic tunability of
phase from graphene gold antennas of 237° at a waveleng
th of 8.5 μm, more than 55°
greater
than has been demonstrated in the mid
-
IR
in a different materials system
. We
additionally demonstrate phase modulation at multiple wavelengths, exceeding 200° from
8.5
0
to 8.75 μm.
By calculating from antenna theory the fraction of power reflected to the
desired angle as opposed to spurious side
-
lobes, we show that this design
will enable
beam
steering with acceptable
signal to noise
ratio
.
We therefore
conclude
that this
design is
feasible
for reconfigurable metasurfaces.
Methods:
Device Fabrication
:
Graphene was grown
on 50
μ
m thick Cu
foil using previous
ly established
CVD
methods
24, 47, 48
.
Following growth, the
graphene was spin
-
coated with 2 layers of
poly(methyl methacrylate) (PMMA).
Cu foil was etched away in iron ch
loride solution,
and the graphene was transferred to a
suspended SiN
x
membrane
obtained commercially
from Norcada, part #NX10500E
.
A back
-
reflector
/back
-
gate
of
2
nm Ti/
200
nm Au
wa
s
evaporated on the back
of the membrane
by electron beam deposition.
100keV
electron
beam
lithography wa
s then used to fabricate
the device. First,
arrays of
gold resonators
were
patterned in 300
nm thick 950 PMMA (MicroChem) developed in 3:1
isopropanol:methyl isobutyl ketone (MIBK) for
one
minute.
The sample wa
s then etch
ed
for
five
sec
onds in a RIE
oxygen plasma at 20mTorr and 80W to
partially
remove the
exposed graphene.
3
nm Ti/60
nm Au was
then deposited by electron beam evaporation,
and l
iftoff was
done in acetone heated to 60
°
C.
A second electron beam lithography step
was used to define contacts of 10 nm Ti/150 nm Au.
Wire bonding was
done to
electrically address
the electrode
.
Electromagnetic Simulations:
We use commercially available finite element methods software (COMSOL)
to
solve for the
two
-
dimens
i
onal
complex electromagnetic field of our structures. Graphene
is modeled as a thin film of thickness
δ
with a relative permittivity from the
Kubo
fo
r
mula
ε
G
= 1 + 4
π
i
σ
/
ωδ
ε
0
.
σ
(
ω
) is the complex optical constant of graphene
evaluated
within the local
random phase approximation
23
.
The value of
δ
is chosen to be 0.1
n
m
which shows good convergence w
ith respect to a zero
-
thickness limit.
The complex
dielectr
i
c constant of SiN
x
was
fit using IR ellipsometry based on the model in
ref
49
.
Three
-
dimensional simulations are performed using finite difference time domain
(FDTD) simulations
(Lumerical). Graphene is modeled as a surface
conductivity adapted
again from
ref
23
.
We use a scattering rate of 20 fs for the graphene, which provides the
optimum fit to
experimental results and is consistent with previous experimental works
using patterned CVD graphene on SiN
x
.
44
Interferometry
Measurements:
A custom built mid
-
IR
, free
-
space Michelson
i
nterferometer was used to
characterize the electrically tunable optical reflection phase from the graphene
-
gold
metasurface. The integrated quantum cascade laser source, MIRcat, from Daylight
Solu
tions provided an opera
ting wavelength range from 6.9 μ
m to 8.8
μ
m, which was a
sufficiently large enough wavelength range to characterize the absorption spectra and
phase of the designed metasurface. A ZnSe lens with a focal length of 75 mm was used to
fo
cus the beam onto the sample. The near
-
field beam waist was 2.5 mm and the far
-
field
beam waist was 90 μ
m and was measured with a NanoScan beam profiler. The reference
and sample legs have independent automated translations, namely, the reference mirror is
mounted on a Newport VP
-
25XA automated linear translation stage with a typical bi
-
directional repeatability of +/
-
50
nm and the sample stage is automated in all three
dimensions to give submicron alignment accuracy with the
Newport
LTA
-
HS. The
propagatin
g beams from the sample and reference legs combine after a two inch
Germanium beam splitter. Two ZnSe lenses, one with a focal length of 100 mm and
another with 1000 mm image the beam at the sample plane with
a ~10 times
expansion.
Control of the source,
translation stages, pyroelectric power detector and the Keithley
source used to bias the metasurface is conducted through a Labview automation script.
Acknowledgements:
This work was supported b
y the U.S. Department of Energy
(DOE) Office of Science,
un
der Grant No. DE
-
FG02
-
07ER46405.
M.C.S. acknowledges support by the Resnick
Sustainability Institute. This research used facilities of the DOE ‘
Light
-
Material
Interactions in Energy Conversion' Energy Frontier Research Center
.
References:
1.
Sun, S. L.; Yang, K. Y.; Wang, C. M.; Juan, T. K.; Ch
en, W. T.; Liao, C. Y.; He, Q.;
Xiao, S. Y.; Kung, W. T.; Guo, G. Y.; Zhou, L.; Tsai, D. P.
Nano Lett
2012,
12, (12), 6223
-
6229.
2.
Arbabi, A.; Horie, Y.; Bagheri, M.; Faraon, A.
Nat Nanotechnol
2015,
10, (11),
937
-
U190.
3.
Khorasaninejad, M.; Chen, W. T.;
Devlin, R. C.; Oh, J.; Zhu, A. Y.; Capasso, F.
Science
2016,
352, (6290), 1190
-
1194.
4.
Ni, X.; Emani, N. K.; Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M.
Science
2012,
335, (6067), 427.
5.
Yu, N.; Aieta, F.; Genevet, P.; Kats, M. A.; Gaburro, Z.; Capasso, F.
Nano Lett
2012,
12, (12), 6328
-
33.
6.
Chen, W. T.; Yang, K. Y.; Wang, C. M.; Huang, Y. W.; Sun, G.; Chiang, I. D.; Liao,
C. Y.; Hsu, W. L.; Lin, H. T.; Sun, S.; Zhou, L.; Liu, A. Q.; Tsa
i, D. P.
Nano Lett
2014,
14,
(1), 225
-
230.
7.
Ni, X.; Kildishev, A. V.; Shalaev, V. M.
Nature Communications
2013,
4, 2807.
8.
Ni, X.; Wong, Z. J.; Mrejen, M.; Wang, Y.; Zhang, X.
Science
2015,
349, (6254),
1310
-
4.
9.
Minovich, A. E.; Miroshnichenko, A. E.
; Bykov, A. Y.; Murzina, T. V.; Neshev, D.
N.; Kivshar, Y. S.
Laser Photonics Rev
2015,
9, (2), 195
-
213.
10.
Genevet, P.; Capasso, F.
Rep Prog Phys
2015,
78, (2).
11.
Yu, N. F.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J. P.; Capasso, F.; Gaburro,
Z.
Science
2011,
334, (6054), 333
-
337.
12.
Zhao, Y.; Liu, X. X.; Alu, A.
J Optics
-
Uk
2014,
16, (12).
13.
Chen, H. T.; Taylor, A. J.; Yu, N. F.
Rep Prog Phys
2016,
79, (7
).
14.
Augustine, M. U.; Zubin, J.; Luca Dal, N.; Nader, E.; Boardman, A. D.; Egan, P.;
Alexander, B. K.; Vinod, M.; Marcello, F.; Nathaniel, K.; Clayton, D.; Jongbum, K.;
Vladimir, S.; Alexandra, B.; Jason, V.; Carl, P.; Anthony, G.; Evgenii, N.; Linxiao,
Z.;
Shanhui, F.; Andrea, A.; Ekaterina, P.; Natalia, M. L.; Mikhail, A. N.; Kevin, F. M.; Eric,
P.; Xiaoying, L.; Paul, F. N.; Cherie, R. K.; Christopher, B. M.; Dorota, A. P.; Igor, I. S.;
Vera, N. S.; Debashis, C.
J Optics
-
Uk
2016,
18, (9), 093005.
15.
Park, J.; Kang, J. H.; Liu, X.; Brongersma, M. L.
Scientific reports
2015,
5,
15754.
16.
Dicken, M. J.; Aydin, K.; Pryce, I. M.; Sweatlock, L. A.; Boyd, E. M.; Walavalkar,
S.; Ma, J.; Atwater, H. A.
Opt Express
2009,
17, (20), 18330
-
18339.
17.
Li, Z.; Yu,
N.
Appl Phys Lett
2013,
102, (13), 131108.
18.
Yao, Y.; Kats, M. A.; Shankar, R.; Song, Y.; Kong, J.; Loncar, M.; Capasso, F.
Nano
Lett
2014,
14, (1), 214
-
219.
19.
Ou, J. Y.; Plum, E.; Zhang, J. F.; Zheludev, N. I.
Nat Nanotechnol
2013,
8, (4),
252
-
255.
20
.
Zheludev, N. I.; Kivshar, Y. S.
Nat Mater
2012,
11, (11), 917
-
924.
21.
Ma, F. S.; Lin, Y. S.; Zhang, X. H.; Lee, C.
Light
-
Sci Appl
2014,
3.
22.
de Abajo, F. J. G.; Koppens, F. H. L.; Chang, D. E.; Thongrattanasiri, S.
Aip Conf
Proc
2011,
1398.
23.
Falkovsky, L. A.
Journal of Physics: Conference Series
2008,
129, (1), 012004.
24.
Brar, V. W.; Jang, M. S.; Sherrott, M.; Lopez, J. J.; Atwater, H. A.
Nano Lett
2013,
13, (6), 2541
-
2547.
25.
Koppens, F. H. L.; Chang, D. E.; de Abajo, F. J. G.
Nano Lett
20
11,
11, (8), 3370
-
3377.
26.
Bonaccorso, F.; Sun, Z.; Hasan, T.; Ferrari, A. C.
Nat Photonics
2010,
4, (9),
611
-
622.
27.
Geim, A. K.; Novoselov, K. S.
Nat Mater
2007,
6, (3), 183
-
91.
28.
Fei, Z.; Rodin, A. S.; Andreev, G. O.; Bao, W.; McLeod, A. S.; Wagner,
M.; Zhang,
L. M.; Zhao, Z.; Thiemens, M.; Dominguez, G.; Fogler, M. M.; Castro Neto, A. H.; Lau, C.
N.; Keilmann, F.; Basov, D. N.
Nature
2012,
487, (7405), 82
-
85.
29.
Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.;
Grigorieva
, I. V.; Dubonos, S. V.; Firsov, A. A.
Nature
2005,
438, (7065), 197
-
200.
30.
Li, Z. Q.; Henriksen, E. A.; Jiang, Z.; Hao, Z.; Martin, M. C.; Kim, P.; Stormer, H.
L.; Basov, D. N.
Nat Phys
2008,
4, (7), 532
-
535.
31.
Yao, Y.; Kats, M. A.; Genevet, P.; Yu, N
. F.; Song, Y.; Kong, J.; Capasso, F.
Nano
Lett
2013,
13, (3), 1257
-
1264.
32.
Liu, M.; Yin, X. B.; Ulin
-
Avila, E.; Geng, B. S.; Zentgraf, T.; Ju, L.; Wang, F.; Zhang,
X.
Nature
2011,
474, (7349), 64
-
67.
33.
Phare, C. T.; Lee, Y. H. D.; Cardenas, J.; Lipson
, M.
Nat Photonics
2015,
9, (8),
511
-
+.
34.
Resler, D. P.; Hobbs, D. S.; Sharp, R. C.; Friedman, L. J.; Dorschner, T. A.
Optics
letters
1996,
21, (9), 689
-
691.
35.
Shim, S. H.; Strasfeld, D. B.; Fulmer, E. C.; Zanni, M. T.
Optics letters
2006,
31,
(6), 838
-
840.
36.
Shelton, D. J.; Coffey, K. R.; Boreman, G. D.
Opt Express
2010,
18, (2), 1330
-
1335.
37.
Dabidian, N.; Dutta
-
Gupta, S.; Kholmanov, I.; Lai, K. F.; Lu, F.; Lee, J.; Jin, M. Z.;
Trendafilov, S.; Khanikaev, A.; Fallahazad, B.; Tutuc, E.; Belkin, M. A
.; Shvets, G.
Nano
Lett
2016,
16, (6), 3607
-
3615.
38.
Park, J.; Kang, J.
-
H.; Kim, S. J.; Liu, X.; Brongersma, M. L.
Nano Lett
2016
.
39.
Aydin, K.; Ferry, V. E.; Briggs, R. M.; Atwater, H. A.
Nature Communications
2011,
2.
40.
Wu, C. H.; Neuner, B.; Shvets, G.; John, J.; Milder, A.; Zollars, B.; Savoy, S.
Phys
Rev B
2011,
84, (7).
41.
Landy, N. I.; Sajuyigbe, S.; Mock, J. J.; Smith, D. R.; Padilla, W. J.
Phys Rev Lett
2008,
100, (20).
42.
Avitzour, Y.; Urzhumov, Y. A.; Shvets, G
.
Phys Rev B
2009,
79, (4).
43.
Levesque, P. L.; Sabri, S. S.; Aguirre, C. M.; Guillemette, J.; Siaj, M.; Desjardins,
P.; Szkopek, T.; Martel, R.
Nano Lett
2011,
11, (1), 132
-
137.
44.
Jang, M. S.; Brar, V. W.; Sherrott, M. C.; Lopez, J. J.; Kim, L.; Kim, S
.; Choi, M.;
Atwater, H. A.
Phys Rev B
2014,
90, (16).
45.
Stutzman, W. L.; Thiele, G. A.,
Antenna Theory and Design
. John Wiley & Sons:
1998.