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11-26-2012
Ultra-thin perfect absorber employing a tunable phase change Ultra-thin perfect absorber employing a tunable phase change
material material
Mikhail A. Kats
Deepika Sharma
Jiao Lin
Patrice Genevet
Romain Blanchard
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Recommended Citation Recommended Citation
Kats, Mikhail A.; Sharma, Deepika; Lin, Jiao; Genevet, Patrice; Blanchard, Romain; Yang, Zheng; and
Qazilbash, M. Mumtaz, Ultra-thin perfect absorber employing a tunable phase change material (2012).
Applied Physics Letters
, 101.
https://doi.org/10.1063/1.4767646
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Ultra-thin perfect absorber employing a tunable phase change material
Mikhail A. Kats,
1
Deepika Shar ma,
1,2
Jiao Lin,
1,3
Patrice Genevet,
1
Romain Blanchard,
1
Zheng Yang,
1
M. Mumtaz Qazilbash,
4,5
D. N. Basov,
4
Shriram Ramanathan,
1
and Federico Capasso
1
1
School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
2
Department of Physics and Mathematics, University of Eastern Finland, Joensuu 80101, Finland
3
Singapore Institute of Manufacturing Technology, Singapore 638075, Singapore
4
Department of Physics, University of California—San Diego, La Jolla, California 92093, USA
5
Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
(Received 5 August 2012; accepted 4 September 2012; published online 26 November 2012)
We show that perfect absorption can be achieved in a system comprising a single lossy dielectric layer of
thickness much smaller than the incident wavelengthonanopaquesubstratebyutilizingthenontrivial
phase shifts at interfaces between lossy media. This design is implemented with an ultra-thin ( k/65)
vanadium dioxide (VO
2
) layer on sapphire, temperature tuned in the vicinity of the VO
2
insulator-to-
metal phase transition, leading to 99.75% absorption at k ¼ 11.6 lm. The structural simplicity and large
tuning range (from 80% to 0.25% in reflectivity) are promising for thermal emitters, modulators, and
bolometers.
V
C
2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.4767646]
In optics, resonant optical cavity configurations have
been used for detectors and modul ators to achieve enhanced
absorption at selected wavelengths and a high on-off ratio,
respectively. The design of such devices benefits from criti-
cal coupling, a phenomenon which facilitates efficient power
transfer to a resonator, which occurs when the internal losses
of a resonant cavity are equal to the mirror losses, i.e., due to
light escaping from the device facets.
1
One implementation
of this concept is the asymmetric Fabry-Perot (FP) cavity in
which the dielectric forming the cavity is typically at least a
quarter-wave in thickness and is surrounded by mirrors with
unequal reflectivities, in which the back reflector is often a
Bragg mirror.
2–7
This geometry has been used for reflection
modulators,
2,5,6
for resonant-cavity enhanced (RCE) photo-
detectors,
3,4
and for enabling strong coupling between light
and matter.
7
More recently, the concept of critical coupling
has been reformulated in terms of the time reversal of lasing
at threshold or “coherent perfect absorption.”
8–10
Another
example of critically coupled resonators is the class of per-
fect absorbers comprising plasmon ic nanostructures, which
have been demonstrated over a wide range of frequencies,
with typical experimental absorption values of 90%
(Refs. 11–14) and reaching as high as 99%.
15
Unlike the
asymmetric FPs, these nanostructured devices are very thin
compared to the wavelength of light, but have complex
nanofabrication requirements, which may limit practical de-
vice applications. It is sometimes assumed that perfect
absorbers based on dielectric cavities cannot be made much
thinner than the operating wavelength, and that plasmon ic
nanostructures are required to overcome this limitation.
10
In this Letter, we demonstrate a perfect absorber com-
prising an unpatterned, ultra-thin ( k/65) film of vanadium
dioxide (VO
2
) on an sapphire substrate. By utilizing an inter-
mediate state of the insulator-metal phase transition (IMT) in
VO
2
, which exhibits multiple co-existing phases, an effective
medium with tunable optical properties is formed. In particu-
lar, the absorption coefficient can be very large in proximity
to the IMT. We show that thermal control of the phase
co-existence in the VO
2
film enables switching of the
absorption from 20% to 99.75% at k ¼ 11.6 lm. The
absorption in our device is greatly enhanced via critical cou-
pling to a cavity resonance, which is shown to exist when the
ultra-thin film has a large imaginary part of the refractive
index. Our device combines the deep-subwavelength thick-
ness characteristic of nanostructure-based perfect absorbers
with the wide tuning capability typical of asymmetric FP
cavities, while comprising only a single film deposited on a
reflecting substrate. This structural simplicity represents a
significant advantage for the implementation of modulators,
thermal emitters, and bolometers.
We consider light incident from air (n
1
¼ 1) onto a
dielectric film with complex refractive index n
2
þ ik
2
, depos-
ited on a substrate with index n
3
þ ik
3
(Fig. 1(a)). The reflec-
tion can be calculated as the coherent sum of the partial
waves reflected from the first interface (with reflection coef-
ficient r
0
) and those reflected from the cavity after 1, 2,…, m
roundtrips with reflection coefficients r
1
, r
2
,…, r
m
. We can
then write the total reflectivity R ¼jrj
2
, in terms of the
reflection coefficient
16
r ¼
X
1
m¼0
r
m
¼
r
12
þ r
23
e
2ib
1 þ r
12
r
23
e
2ib
; (1)
where r
pq
¼ð
~
n
p
~
n
q
Þ=ð
~
n
p
þ
~
n
q
Þ and t
pq
¼ 2
~
n
p
=ð
~
n
p
þ
~
n
q
Þ
are the Fresnel reflection and transmission coefficients as the
wave encounters medium q from medium p,
~
n
p
¼ n
p
þ ik
p
is
the complex refractive index of medium p, b ¼
2p
k
0
~
n
2
h,
r
0
¼ r
12
, and r
m
¼ t
12
r
23
m
r
21
ðm1Þ
t
21
e
2mib
for m > 0.
When k
2
n
2
, Eq. (1) describes the reflection proper-
ties of a simple asymmetric FP cavity with small optical
losses. On resonance, light is stored for many optical cycles
and can be gradually absorbed as it circulates; most FP mod-
ulators and RCE detectors operate in this manner. Such a
cavity is illustrated in Fig. 1(a), with a dielectric film depos-
ited on a reflecting substrate. In the partial wave picture, the
first reflection r
0
has a phase shift of ’p with respect to the
0003-6951/2012/101(22)/221101/5/$30.00
V
C
2012 American Institute of Physics101, 221101-1
APPLIED PHYSICS LETTERS 101, 221101 (2012)
incident wave and thus the corresponding phasor points to
the left, predominantly along the real axis in the complex
plane (Fig. 1(b)). The front facet reflection can be cancelled
out if the partial waves emerging from the film each have a
phase shift of ’0 and the phasor trajectory terminates at the
origin; this occurs when the thickness h of the dielectric is an
odd integer multiple of k=4n (if the reflection phase from the
substrate is p) and the reflectivity jr
12
j
2
is equal to the effec-
tive bottom mirror reflectivity jr
23
e
2ib
j
2
, as can be seen from
Eq. (1).
5
The phasor diagram in Fig. 1(d) suggests another route to
achieving the perfect absorption condition. The exact phasor
trajectory does not matter as long as it returns to the origin.
One of the possible trajectories in which the phase of r
0
is not
p is shown in Fig. 1(d). The interface reflection phase shifts
become substantially different from 0 and p when at least one
of the materials has k comparable to n. As a result, an absorp-
tion resonance can exist for a film that is much thinner than
the wavelength of light, and critical coupling to this ultra-thin
resonance yields a perfectly absorbing state (Fig. 1(c)). This
effect has been recently utilized for the coloring of metals
with nanometer-thick semiconductor films.
40
Our perfect
absorber utilizes this condition to enhance absorption, using
the intermediate state in the IMT in VO
2
to introduce a large,
controllable degree of loss.
VO
2
is a correlated oxide that undergoes a thermally
triggered IMT near room temperature (T
c
340 K), which
takes the material from an insulating state (band gap of
0.6 eV) to a metallic one. The IMT occurs gradually as the
temperature is increased: nanoscale islands of the metallic
phase emerge in the surrounding insulating VO
2
, which then
grow and connect in a percolation process, leading to a fully
metallic state where the band gap has collapsed.
17–19
This
metal-dielectric phase co-existence within the phase transi-
tion results in widely tunable optical properties; in fact, the
naturally occurring nanoscale structures in the IMT region
can be viewed as a reconfigurable disordered metamaterial.
The IMT has been utilized for optical switching
20,21
and has
enabled several tunable devices comprising metallic nano-
structures on VO
2
films.
22–24
VO
2
is also the target of active
research for the realization of novel electronic switching
devices that may complement MOSFET technology.
19
To implement an absorber that can be tuned between
low and perfect absorption states, we deposited a crystalline
film of VO
2
with a thickness of 180 nm on a c-plane sapphire
substrate. The absorption was investigated via normal inci-
dence measurements using a Fourier transform infrared
(FTIR) spectrometer and mid-IR microscope (Fig. 2(a)). The
reflection spectrum was collected while gradually increasing
the sample temperature from 297 K to 360 K at 1 K incre-
ments (Fig. 2(b)).
39
The 297 K curve is representative of the
reflection spectrum at a temperature significantly below T
C
.
Since insulating VO
2
is relatively transparent at photon ener-
gies below its band-gap, the primary features of the room
temperature reflection spectrum are due to the underlying
sapphire. Sapphire is highly absorptive at k 5–10 lm de-
spite its large band gap due to the presence of several phonon
modes, which also result in high reflectivity between 10 and
15 lm.
18,25
The VO
2
thickness is much smaller than the
wavelength of the incident light, so no FP fringes are
observed. The small features at 3 lm, 4.5 lm, and 6 lm
correspond to ambient atmospheric absorption lines. At high
temperatures (e.g., 360 K curve in Fig. 2(b)), the VO
2
is
entirely in the metallic phase and displays relatively high
reflectivity, which slowly increases with increasing wave-
length, as expected for a Drude-like metal.
The reflectivity spectrum does not transition monotoni-
cally from that of the low-temperature state to that of the high-
temperature one due to the complex interplay between the
effective medium formed when the VO
2
is in an intermediate
FIG. 1. (a) The reflection process from a quarter-wave film with low losses (k
2
n
2
) on a perfectly reflecting substrate at normal incidence, showing the partial
waves. Many multiple reflections are involved because of the small losses. (b) Phasor addition diagram (the reflected partial waves are represented in the com-
plex plane) demonstrating that a properly engineered quarter wave film on a reflecting substrate can result in zero reflection via destructive interference, corres-
ponding to complete absorption. This occurs for a particular value of k
2
, which is relatively small, leading to a small imaginary part of r
0
, and corresponding to
critical coupling. The phase of the first partial wave r
0
is ’ p with respect to the incident wave, but the phase of all of the other partial waves is ’0: (c) Reflec-
tion process from a highly absorbing (k
2
n
2
), ultra-thin film in a reflecting substrate. (d) Phasor diagram demonstrating that a zero-reflection (and hence perfect
absorption) condition is achievable if the complex refractive index of the film has a large imaginary component. In this case, the phase of r
0
deviates significantly
from p (the phasor is not along the horizontal axis) and a small number of reflections is sufficient to cancel r
0
and maximize absorption.
221101-2 Kats et al. Appl. Phys. Lett. 101, 221101 (2012)
state and the underlying sapphire substrate. In particular, we
focus on the feature at k 11.6 lm; at this wavelength, the
reflectivity is 0.7 with the VO
2
in the insulating state (at
room temperature) due to the high reflectivity of the underly-
ing sapphire, and 0.8withtheVO
2
in the metallic state
(T ¼ 360 K). At T ¼ 343 K, however, the reflectivity abruptly
drops to approximately 0.0025, corresponding to a reduction
by a factor 280 with respect to the low-temperature insulat-
ing state and by a factor 320 with respect to the high-
temperature metallic state. Since the sapphire substrate is opa-
que at this wavelength, this corresponds to a 99.75% absorb-
ance within the VO
2
film and the top part of the substrate (1-
2 lm), as discussed later in the text. The reflectivity spectrum
has a hysteresis of approximately 5 K (Fig. 2(c)), comparable
to the dc resistance hysteresis width of the VO
2
film (inset of
Fig. 2(c)). The normalized dc resistance R(T)/R(298 K) exhib-
its a change of more than three orders of magnitude between
298 K and 393 K.
To obtain the theoretical reflectivity of our device, we
used Eq. (1) with the temperature-dependent complex refrac-
tive index for VO
2
(for increasing temperature) experimen-
tally obtained by ellipsometry in Ref. 17 and the index for
sapphire from Ref. 26. The calculated spectra match well
with the experimental data across the entire k ¼ 2–15 lm
range (Figs. 2(b) and 2(d)), though the temperatures at which
the various spectral features occur differ by 2
–5
. We attrib-
ute the latter to the differences in the growth conditions and
film thicknesses between our VO
2
sample and the one meas-
ured in Ref. 17.
27
The predicted reflectivity minimum is
0.0007 at k ¼ 11.75 lm and T 342 K, compared to the
experimental data, which showed a minimum value of
0.0025 at k ¼ 11.6 lm and T ¼ 343 K.
To better understand the conditions leading to perfect
absorption, we performed a set of calculations in which the
VO
2
film was replaced with an unknown homogeneous
dielectric of the same thickness, assuming only that it can be
described by some complex refractive index
~
n ¼ n þ ik.In
Fig. 3, we plotted the calculated reflectivity using Eq. (1) at
k ¼ 11.75 lm as a function of n and k, covering a wide range
of potential values of
~
n for the material comprising the thin
film. The complex index of sapphire at this wavelength was
taken to be 0.1 þ 0.8i.
26
We found that for
~
n ffi 3:25 þ 1:5i,
the calculated reflectivity drops to zero indicating critical cou-
pling, with 90% of the light absorbed in the 180 nm film and
the remaining 10% absorbed in the top layer (1–2 lm) of
the underlying sapphire. This reflectivity minimum is very
broad in n - k space, making the phenomenon very robust; as
a result, small changes in the composition (and hence
~
n)of
the lossy dielectric will not significant impact device
FIG. 2. (a) Experimental setup. A sapphire
substrate coated with h ¼ 180 nm of VO
2
is
placed on a temperature-controlled stage
mounted inside an infrared (IR) microscope
and illuminated at normal incidence using a
mid-IR source. A mercury-cadmium-telluride
(MCT) detector is used to collect the reflected
light. (b) Experimental reflectivity spectrum
at temperatures from 297 K to 360 K. At
343 K, the reflectivity drops to 0.0025 at
k ¼ 11.6 lm. (c) Experimental reflectivity
from the sample at k ¼ 11.6 lmasafunction
of increasing (red) and then decreasing (blue)
temperature. A 5Khysteresisisseeninthe
reflectivity. Inset: Normalized dc resistance
of the VO
2
thin film sample as a function of
temperature showing nearly four orders of
magnitude of change in the resistance and
hysteretic behavior. (d) Calculated reflectivity
spectrum at temperatures from 295 K to
360 K using experimental values for the com-
plex refractive indices of VO
2
(Ref. 17)and
sapphire.
26
The reflectivity of bare sapphire
is shown in black.
FIG. 3. (a) Map of the calculated reflectivity as a function of n and k, the
real and imaginary parts of the complex refractive index ~n; of a uniform
dielectric film of 180 nm thickness on sapphire for k ¼ 11.75 lm. The reflec-
tivity drops to zero for ~n ffi 3:25 þ 1:5i. The black dashed line marks the tra-
jectory of the complex refractive index of VO
2
with increasing temperature.
The VO
2
index passes very close to the minimum reflectivity point in n-k pa-
rameter space (black dashed line).
221101-3 Kats et al. Appl. Phys. Lett. 101, 221101 (2012)
