University of Nebraska - Lincoln
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Faculty Publications from the Department of
Electrical and Computer Engineering
Electrical & Computer Engineering, Department of
2013
Enhanced optical bistability with lm-coupled
plasmonic nanocubes
Christos Argyropoulos
Duke University, christos.argyropoulos@unl.edu
Cristian Ciraci
Duke University
David R. Smith
Duke University
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Argyropoulos, Christos; Ciraci, Cristian; and Smith, David R., "Enhanced optical bistability with 6lm-coupled plasmonic nanocubes"
(2013). Faculty Publications om the Department of Electrical and Computer Engineering. 412.
h7p://digitalcommons.unl.edu/electricalengineeringfacpub/412
Enhanced optical bistability with film-coupled plasmonic nanocubes
Christos Argyropoulos, Cristian Ciracì, and David R. Smith
Citation: Appl. Phys. Lett. 104, 063108 (2014); doi: 10.1063/1.4866048
View online: https://doi.org/10.1063/1.4866048
View Table of Contents: http://aip.scitation.org/toc/apl/104/6
Published by the American Institute of Physics
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Enhanced optical bistability with film-coupled plasmonic nanocubes
Christos Argyropoulos,
a)
Cristian Cirac
ı, and David R. Smith
Center for Metamaterials and Integrated Plasmonics, Department of Electrical and Computer Engineering,
Duke University, Durham, North Carolina 27708, USA
(Received 7 December 2013; accept ed 5 February 2014; published online 13 February 2014)
Colloidally synthesized nanocubes strongly coupled to conducting films hold great promise for
enhancing different nonlinear optical processes. They exhibit a robust and sensitive scattering
response that can be easily controlled by their geometrical and material parameters. Strong local
field enhancement is generated at the gap regions between the nanocubes and the metallic film. We
show that strong optical bistability and all-optical switching behavior can be obtained by loading
these nanogaps with Kerr nonlinear materials. Relatively low input intensities are required to
obtain these nonlinear effects. The proposed design can lead to efficient, low-power, and ultrafast
all-optical memories and scattering nanoswitches.
V
C
2014 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4866048]
Integrated photonic devices that possess a bistable
response are the key elements for all-optical computing
applications. The weak nature of the nonlinear optical inter-
actions places a huge limit to the practical implementation of
optical bistability; extremely high pump intensities are in
fact required to obtain noticeable effects.
1
Although it is pos-
sible to relax the requirement on the input intensity by using
very high quality factor cavities, i.e., extended Fabry–P
erot
gratings and photonic-crystal resonators,
2–6
this is extremely
detrimental to the operational bandwidth of the device and
its integration to nanoscale dimensions.
Recently, significant research efforts have been devoted
to control and enhance light-matter interactions at subwave-
length scales by means of plasmonic platforms
7,8
In particu-
lar, extreme coupling between nanoparticles or nanoparticles
and conducting films has shown to increase local field inten-
sities up to three orders of magnitude with respect to the inci-
dent radiation.
8
In addition, the development of bottom-up
fabrication techniques has granted simple and cheap access
to nanometric-gap structures.
9,10
Colloidally synthesized
metal nanoparticles can, for example, be adsorbed on large
area self-assembly organic layers only few nanometer s thick,
deposited on conducting substrates.
11
The resonance of such
systems is strongly dependent on the dielectric thickn ess and
requires very small separation distances in order to span the
entire visible spectrum. By using colloidal silver nanocubes,
it is possible to introduce a better control on the resonances
and even push them down to the near-infrared.
The efficient local field enhancement and flexible tuna-
bility serve as an excellent platform to boost several nonlin-
ear optical processes,
12
which can make nonlinear optical
effects accessible with much lower input intensities and
within nanosized structures, in contrast to the previous
designs. Different nonlinear materials may be included
within the plasmonic “hot-spot” field regions, leading to
effectively enhanced nonlinear optical processes, such as
second harmonic generation (v
ð2Þ
media)
13–18
and optical
bistability (v
ð3Þ
media).
19–26
Although the intrinsic absorption of metals is considered
to be detrimental for most linear applications, it is generally
far less critical for nonlinear applications, where conversion
rates are expected to be a few percent. Moreover, the role of
metals in nonlinear optics applications goes beyond their
ability to support surface plasmon modes that allow the light
to become strongly confined in deeply subwavelength vol-
umes. Metals possess third-order nonlinear susceptibilities
that are orders of magnitude larger than dielectric materi-
als.
1,27
As a result, a major research effort has been targeted
toward metallo-dielectric composi tes
28,29
and metamaterial
composites,
30–32
including structured films and surfaces.
33–36
However, bulk metallic structures are characterized by high
reflectivity and the fields cannot efficiently couple inside
them, leading to poor field enhancement and, as a result,
weak nonlinear optical effects.
Although, moderate threshold input pump intensities
were still required in all the previous nonlinear plasmon ic
works, nevertheless, it is expected to achieve even more pro-
nounced low-power nonlinear optical effects, in case the
plasmonic modes can be strongly confined and coupled in
extremely subwavelength regions loaded with nonlinear
materials, such as narrow waveguides, ultrasmall nanocav-
ities, and nanogaps. This will lead to an even better compact-
ness of nonlinear optical designs, bringing the highly
anticipated ultrafast and low-power integrated nanophotonic
logical circuits one step closer to their practical realization.
In this Letter, we will focus our study to film-coupled
nanocubes
11,37–39
loaded with nonlinear materials to achieve
all the aforementioned goals. It will be demonstrated that
this particular plasmonic design constitutes an ideal platform
towards the experimental realization of compact, ultrafast,
and low-power nonlinear plasmonic systems with instantane-
ous nonli near optical responses. Furthermore, the bottom-up
chemical synthesis approach is ideal for large-scale practical
implementation of such structures. The nanocubes are single
crystalline and can be coupled to atomically smooth epitaxi-
ally grown silver films
40
or ultrasmooth template-stripped
a)
Author to whom correspondence should be addressed. Electronic mail:
christos.argyropoulos@duke.edu
0003-6951/2014/104(6)/063108/5/$30.00
V
C
2014 AIP Publishing LLC104, 063108-1
APPLIED PHYSICS LETTERS 104, 063108 (2014)
metallic films.
41
This is expected to drastically reduce the
effective damping constant of the metallic film and enables
experimental results which are in close agreement with the
numerical simulations. This property makes the proposed
plasmonic system even more appealing to enhance different
active and nonlinear optical processes, where the lasing or
nonlinear processes are much more sensitive to losses. In
this work, we will consider Kerr v
ð3Þ
nonlinear materials em-
bedded into the spacing layer between the nanocube and the
metallic film. The nonlinear analys is will be limited to third-
order Kerr nonlinear effects, such as optical hysteresis and
all-optical switching, but the structure is expected to be ad-
vantageous in several other nonlinear applications, i.e., sec-
ond/third-harmonic generation and four-wave mixing.
The proposed plasmonic design is shown in Fig. 1, where
a silver nanocube is positioned above a dielectric-coated me-
tallic (Ag) film. The plasmonic nanocube is strongly coupled
to its electromagnetic mirror image, effectively leading to the
formation of a nanodimer with a deeply subwavelength gap
in which a nanocavity is formed characterized by an excep-
tionally strong field enhancement. The ultrathin dielectric
spacing layer is constituted by a Kerr nonlinear optical mate-
rial (v
ð3Þ
NOM) with relative permittivity e ¼ e
L
þ v
ð3Þ
jEj
2
,
with e
L
¼ 2:2, and v
ð3Þ
¼ 4:4 10
18
m
2
=V
2
, which is typi-
cal nonlinear material values of semiconductors and poly-
mers;
1
jEj is assumed to be the magnitude of the mean value
of the local complex electric field inside the nanogap. Note
that the corners of the nanocubes are slightly rounded in order
to avoid numerical artifacts and to be in agreement with a
potential experimental realization of such plasmonic sys-
tem.
11,39
Silver losses are fully taken into account in our anal-
ysis by using a silver dielectric function obtained from
experimental data.
42
The Ag film is placed over a semi-
infinite glass substrate with refractive index n ¼ 1:47, and the
dimensions of the plasmonic system are chosen (with respect
to the inset of Fig. 1) to be: l ¼ 80 nm, h ¼ 50 nm, and
g ¼ 2 nm. Although the gap is highly subwavelength, the
analysis can still be performed without taking into account
nonlocal
38,43–46
or quantum
47–49
effects which have been
shown to severely affect the scattering response and limit the
field enhancement in similar plasmonic structures with only a
few Angstrom thickness (subnanometer) gaps (typically
g < 0:5 nm).
The three-dimensional (3D) film-coupled plasmonic
nanocube structure of Fig. 1 is simulated using the finite ele-
ment method (COMSOL Multiphysics). In this Letter, the
device is always excited by transverse-magnetic (TM) polar-
ized plane waves impinging at an incident angle of h ¼ 75
8
with respect to normal. However, the scattering response is
fairly independent of the angle of incidence and polarization
of the plane wave excitation, as it was demonstrated earlier
in Refs. 11 and 39. First, we consider the linear operation of
the plasmonic nanocube system, where a conventional
dielectric is loaded at the spacer laye r with relative permit-
tivity e
L
¼ 2:2. We numerically compute the scattering
cross-section (SCS) of this structure and normalize its value
to the dimensions of the nanocube, in order to compute the
SCS efficiency of the entire plasmonic system. The result is
presented in Fig. 2 , where a sharp narrowband scattering
response is obtained with a pronounced scattering peak
around k ’ 1:07 lm. The quality factor of this resonant
response is approximately Q ’ 80, typical value for plas-
monic resonances. Standing waves are rapidly built inside
the nanogap at this frequency point and the computed elec-
tric field enhancement distribution can be seen in the inset of
Fig. 2. The cavi ty plasmonic mode is caused by the built-up
of the standing waves, which directly leads to enhanced
localized electric fields inside the nanogap with a maximum
enhancement factor of about 200, as it is clearly demon-
strated in the inset of Fig. 2. The rapid increase in scattering
efficiency can also be translated into an increase in absorp-
tion strength, leading to efficient plasmonic absorber
designs.
11
Hence, we will employ the large local field enhancement
and high SCS efficiency to boost nonlinear optical processes.
To this end, Kerr nonlinear v
ð3Þ
material is loaded at the
spacer layer between the nanocube and the film with parame-
ters and geometry described before. In general, the intensity
FIG. 1. Schematic of the film-coupled nanocube structure. The substrate is
composed of glass. Kerr nonlinear material is loaded at the spacer layer,
which separates the nanocube with the silver film. The dimensions of the
nonlinear system are: l ¼ 80 nm, h ¼ 50 nm, and g ¼ 2 nm.
FIG. 2. SCS efficiency of the linear nanocube plasmonic system varying
with the input radiation’s wavelength. A dielectric material is loaded at the
spacer layer with relative permittivity e
L
¼ 2:2. The strong field enhance-
ment is depicted in the inset of this figure and is mainly localized in the
spacer layer.
063108-2 Argyropoulos, Ciraci, and Smith Appl. Phys. Lett. 104, 063108 (2014)
dependent permittivity of Kerr nonlinear materials can lead
to optical hysteresis and all-optical switching responses.
1
Here, we apply a mean-field approximation to monitor the
fields inside the nanocavity and we compute the SCS effi-
ciency of this nonlinear plasmonic system for different
applied input intensities. The graphical solution approach is
used to post-process all these results and calculate the solu-
tions of the nonlinear problem.
1
The bistable SCS efficiency
performance of the nonlinear structure under study is com-
puted and plotted in Fig. 3 versus the wavelength of the input
radiation for relatively low input pump intensity
I
in
¼ 1MW=cm
2
. Strong hysteresis in the scattering effi-
ciency is obtained and the nonlinear scattering spectrum is
spread in a relative broad frequency range compared to the
linear results presented in Fig. 2. In the same plot, we also
show the calculated unstable branch of the predicted nonlin-
ear response, plotted as the dashed line. This is another math-
ematical solution of the nonlinear problem, but it is not
reachable from the two stable branches (solid lines in Fig. 3).
An exceptionally strong bistable performance is obtained in
the nonlinear SCS efficiency spectrum, which can become
even wider if we increase the input pump intensity impinging
at the plasmonic nanocube. The input intensity required in
our case is several orders of magnitude lower compared to
nanoantennas embedded or placed over Kerr nonlinear
materials,
22–26,50
where bistability and modulation were pre-
dicted in the scattering or reflection responses with input
intensities with approximate values in the range of
I
in
’ 0:5 1GW=cm
2
. The key distinction of the presented
work compared with the previously published nonlinear plas-
monic systems is that in our plasmonic configuration we can
precisely place the nonlinear material in the nanogap region,
where the highest fields are obtained.
Next, we fix the wavelength of the nonlinear operation
to k ¼ 1:105 lm, slightly above the resonant scattering peak
of the linear operation (Fig. 2). We monitor the scattering
response of the nonlinear plasmonic system as the input radi-
ation intensity is varied. The device always has the same
dimensions and parameters, presented earlier in Fig. 1.
Strong low-power all-optical scattering switching behavior is
obtained, when the input power is increased or decreased,
and the response is plotted in Fig. 4. Note that in case the
gap thickness of the proposed structure is increased, the field
enhancement will be decreased inside the formed nanocav-
ity.
11,39
However, we have calculated that still low input
intensities I
in
’ 3 6MW=cm
2
are needed to excite bistable
performance for the same nonlinear plasmonic system but
with increased gap thickness g ¼ 5 nm.
The reported broad hysteresis loop demonstrates an effi-
cient way to design a compact low-power optical nanoswitch
with high sensitivity to relative low input pump intensities.
When we increase the input intensity of the impinging radia-
tion, the SCS efficiency remains almost constant, taking par-
ticularly low values. However, when the threshold input
intensity value I
up
¼ 820kW=cm
2
is reached, the SCS effi-
ciency experiences an abrupt “jump” and the device now
operates at the upper branch of the scattering hysteresis
curve. If we start to decrease the input intensity, after the
threshold intensity value has been reached, the nonlinear
structure will keep its high SCS efficiency operation, which
will be even further increased in this particular plasmonic
configuration. The SCS efficiency will always be higher than
10 in the upper scattering br anch, which is approximately
four times higher compared to the SCS efficiency of the
lower scattering branch of the hysteresis curve. Only when
we reach low input pump intensities with values less than
I
down
¼ 180kW=cm
2
, the SCS response will return to its ini-
tial low value, similar to the performance in the beginning,
when we just started increasing the input intensity. Indeed,
this nonlinear system can exhibit memory and it can operate
as an efficient nanoswitch with the OFF-mode operation
located at the lower scattering branch (increasing pump in-
tensity) and the ON-mode operation positioned at the high
scattering branch (decreasing pump intensity). If illuminated
with a continuous wave laser, the plasmonic optical switch
can close or open depending on the intensity of the input
radiation,
1,20
similar to the well-established logic circuits in
semiconductor electronic components.
We envision that the integration of these compact non-
linear plasmonic elements with other planar plasmonic
FIG. 3. Strong bistability in the scattering performance of the nonlinear plas-
monic nanocube system with geometry shown in Fig. 1. The SCS efficiency
is plotted versus the wavelength and the device is pumped with low input in-
tensity I
in
¼ 1MW=cm
2
. The unstable branch of the bistable curve is shown
with a dashed line.
FIG. 4. Bistable SCS efficiency as a function of the input pump intensity of
the nonlinear nanocube structure shown in Fig. 1 and monitored at
k ¼ 1:105 lm. The unstable branch of the curve is shown with the dashed
line. Strong scattering hysteresis is obtained with the proposed nonlinear
plasmonic system, leading to efficient all-optical scattering switching
behavior.
063108-3 Argyropoulos, Ciraci, and Smith Appl. Phys. Lett. 104, 063108 (2014)
