Optical switching in metal-slit arrays
on nonlinear dielectric substrates
S. Carretero-Palacios,
1,
* Alexander Minovich,
2
Dragomir N. Neshev,
2
Yuri S. Kivshar,
2
F. J. Garcia-Vidal,
3
L. Martin-Moreno,
1
and Sergio G. Rodrigo
1
1
Instituto de Ciencia de Materiales de Aragon and Departamento de Fisica de la Materia Condensada,
CSIC-Universidad de Zaragoza, E-50009, Zaragoza, Spain
2
Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, Australia
3
Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, Madrid 28049, Spain
*Corresponding author: sol@unizar.es
Received October 29, 2010; revised November 1, 2010; accepted November 10, 2010;
posted November 29, 2010 (Doc. ID 129143); published December 15, 2010
We propose a scheme for an optical limiter and switch of the transmitted light intensity in an array of subwavelength
metallic slits placed on a nonlinear Kerr-type dielectric substrate of finite thickness, where the geometrical
parameters are designed for operation at telecom wavelengths. Our approach is based on the abrupt changes of
the output light intensity observed in these systems near transmission minima. © 2010 Optical Society of America
OCIS codes: 240.6680, 190.5940, 250.5403.
Nanostructuring of metal surfaces appears exceptionally
attractive for novel nonlinear photonic applications due
to a strong enhancement of the electromagnetic (EM)
field near corrugated surfaces. Prominent examples
include surface-enhanced Raman scattering [1] and
plasmon-enhanced high-harmo nic generation [2]. How-
ever, the drawback of using metallic elements is the
introduction of stron g loss. Therefore, when metals are
involved, only schemes utilizing short device lengths
can be tolerated in practice to observe noticeable non-
linear phenomena, while any schemes relying on phase
accumulation are intrinsically excluded.
A proposed platform for enhanced nonlinear optical
manipulation is the array of subwavelength apertures in
metal films [3,4]. Nonlinear properties of subwavelength
metallic apertures in combination with nonlinear dielec-
trics have been studied for their potential uses in
enhanced nonlinear beam manipulation [5,6], optical
bistability [7,8], and switching [9,10]. Such geom etries
rely on the phenomenon of enhanced optical transmis-
sion [ 11–13] associated with distinct resonances in the
linear transmission spectrum.
Here we present a proposal for (i) an optical limiter
(OL) of the transmitted intensity, in which the output in-
tensity decreases when the incident one increases, and
(ii) an optical switch (OS), where the output intensity in-
creases abruptly under a small change of the incident
power. These two operating modes are found in an array
of metallic slits placed on a nonlinear Kerr-type dielectric
layer, at the telecom regime. The inset of Fig. 1 shows
schematically the structure analyzed, as well as the direc-
tion of illumination considered. We assume air at the
illuminated and transmission regions, and also inside
the slits.
We study the nonlinear optical response at a fixed
wavelength close to the transmission minimum [see Fig. 1
(top)], where sharp variations in the spectrum take place
within a short wavelength range. We assume nonlinear
response only in the dielectric layer, while the nonlinear
susceptibility in the metal [14] is neglected. In the MKS
system of units, the optical response of the dielectric
material due to a third-order nonlinear susceptibility is
described by the relations of both displacement (
~
D) and
polarization (
~
P) vectors with the electric field (
~
E)[15]:
~
D ¼ ε
o
~
E þ
~
P, where
~
P ≃ ε
0
½χ
ð1Þ
~
E þ χ
ð3Þ
ð
~
E ·
~
EÞ
~
E and ε
0
is
the dielectric constant of vacuum. The scalar quantities
χ
ð1Þ
and χ
ð3Þ
represent the linear and third-order nonlinear
susceptibilities, respectively. Since the change of the di-
electric constant yielded by the local EM field is percen-
tually small, it is common to approximate the refractive
index as n ¼ n
0
þ n
2
I, where I ¼ n
0
cε
0
jEð
~
rÞj
2
=2, n
0
is
the linear refractive index, and n
2
¼
3χ
ð3Þ
4n
2
0
cε
0
[15] is the Kerr
coefficient.
We have employed the finite–difference time–domain
method to simulate both the linear [16] and nonlinear
optical response of the structure [17]. The system is
Fig. 1. (Color online) Linear transmittance through a gold slit
array (P ¼ 520 nm, a ¼ 300 nm, h ¼ 350 nm) on a dielectric
substrate of finite thickness (n
0
¼ 2:8 and d ¼ 1650 nm).
(a)–(c) Modulus of the electric field, j
~
E j, evaluated at the x–z
plane for two unit cells at λ
max
¼ 1437 nm, λ
min
¼ 1451 nm, and
λ
1
¼ 1465 nm, respectively. The dashed white lines mark the
end of the dielectric layer.
December 15, 2010 / Vol. 35, No. 24 / OPTICS LETTERS 4211
0146-9592/10/244211-03$15.00/0 © 2010 Optical Society of America
illuminated with a normal incident p-polarized plane
wave. Unless otherwise stated, the duration of the pulse
is τ ∼ 2:4 ps. This pulse is slowly switched on and off, so it
has a smooth Fourier transform (in this case, with spec-
tral bandwidth of ∼3 nm). We have checked that, under
such excitation, the process of third-harmonic generation
forms less than 1% of the total output energy and, there-
fore, only the optical properties at the fundamental
frequency are considered.
The dielectric constant of gold (ε
m
) is obtained from
the experimental values tabulated in [18] and fitted to
a Drude–Lorentz model [19]. The nonlinear dielectric
is assumed to be isotropic, homogeneous, and disper-
sionless. Furthermore, absorptio n in the dielectric is ne-
glected in our simulations. The linear refractive index is
chosen to be n
0
¼ 2:8, a typical value for materials with
large Kerr coefficients, following Miller’s rule [15].
To illustrate our proposal, we have chosen the following
set of parameters: a 1650 nm thickness dielectric slab, ar-
ray period p ¼ 520 nm, metal film thickness h ¼ 350 nm,
and slit width a ¼ 300 nm. The precise values of these
parameters are arbitrary but are chosen in order to
(i) be within the range accessible to experiments and
(ii) provide a sharp transmission minimum at near-IR, in
this case, λ
min
¼ 1451 nm [Fig. 1 (top)]. The spectral posi-
tion of this minimum depends on the geometrical param-
eters in a complex way. Thus, the consideration of other
ranges of working wavelen gths would require a fine tuning
of geometrical parameters (i.e., other λ
min
) through com-
putation of the linear transmittance. In Figs. 1(a)–1(c) we
plot the modulus of the electric field, j
~
E j (evaluated at the
x–z plane for two unit cells) for three different wave-
lengths: λ
max
¼ 1437 nm, λ
min
, and λ
1
¼ 1465 nm, respec-
tively. For λ
1
and λ
min
, we observe field enhancement
inside the slits and around their corners, while, at λ
max
,
a guided mode appears inside the dielectric layer.
Next, we study the changes in the transmission
through the metal slits with increase of the light intens ity
for four different wavelengths redshifted compared to
λ
min
. We scale both the incident (I
in
) and transmitted
(I
out
) intensities by n
2
, so our results are valid for differ-
ent (current or future) nonlinear materials. Also, n
2
I
out
reflects the average change of the refractive index,
Δn, in the dielectric film (we will discuss spatial distri-
bution of Δn later on). Figure 2 presents, with solid sym-
bols, the results for n
2
I
out
as a function of n
2
I
in
, together
with the corresponding linear results (n
2
I
out
Lin
). As ex-
pected, at low input intensities the transmission follows
the linear dependence. However, as the intensity is in-
creased, the transmission saturates and then drops. This
behavior corresponds to a nonlinear intensity limiter.
For highe r I
in
, the transmission exhibits a steep rise,
switching to a high-transparency state . This can be
heuristically understood by noting that nonlinear effects
correspond to an increase of n and that, in the linear re-
gime, the increase of n shifts the transmission spectrum
to longer wavelengths. In the OL regime, as the incident
intensity increases, the linear transmittance decreases.
Eventually, after the minimum transmittance is reached,
the output intensity would be boosted by both the in-
crease of the incident intensity and the corresponding
increase in linear transmittance, leading to a large incre-
ment of I
out
within a narrow range of incident intensities.
Clearly, the incident intensities to achieve OL or OS
strongly depend on the incident wavelength. The vertical
scale in Fig. 2 breaks in the region of n
2
I
out
¼ð8–12Þ × 10
−4
in order to mark up the features’ visibility at low output
intensities. In Fig. 2, the switching is seen for two wave-
lengths, λ
1
¼ 1465 nm and λ
2
¼ 1475 nm, in the range of in-
tensities chosen, with the final I
out
being much larger than
I
out
Lin
. Precisely, OL occurs for all considered wavelengths
(and also OS, although this is not shown in the figure for
the two largest wavelengths), but the input intensities for
minimum output increase as the working wavelength se-
parates from λ
min
. Figure 2 also shows that the considered
nonlinear effects are still present for shorter pulses
(τ ∼ 500 fs, although the OL is less pronounced and the
OS occurs within a wider range of I
in
), which, in real ex-
periments, would reduce the influence of the free carrier
absorption or thermal effects.
In Fig. 3, panels (a)–(d) show the local change in the
refractive index within the nonlinear dielectric slab (eval-
uated at the x–z plane for two unit cells) for the structure
in Fig. 1 and for four different input intensities at λ
1
¼
1465 nm at a moment just before the plane wave is
switched off (∼2:4 ps). The intensity values cover both
the linear regime as well as the intensity range when the
OL and the OS occur. Importantly, the variation of the re-
fractive index is not uniform and resembles the profiles of
the modulus of the electric field in the linear regime
[Figs. 1(a)–1(c)] at the related wavelengths.
Let us now discuss possible materials to operate the OL
and OS. Chalcogenide glasses, such as As
2
Se
3
, possess
n
0
≈ 2:8 and high n
2
≈ 1:1 × 10
−4
cm
2
=GW [ 20], featuring
low linear and two-photon absorption at IR wavelengths.
However, in real experiments, dielectric slabs made of
these materials support a maximum change in the refrac-
tive index, Δn
max
≈ 0:0001, before being damaged, a
threshold much smaller than the change of the refrac-
tive index here obtained when metals are involved
Fig. 2. (Color online) Transmitted intensity versus inci-
dent intensity for: solid symbols, λ
1
¼ 1465 nm, λ
2
¼ 1475 nm,
λ
3
¼ 1485 nm, and λ
4
¼ 1495 nm. Linear output in each case
is given by solid, dashed, dotted, and dashed–dotted lines, re-
spectively. Open symbols, λ
1
¼ 1465 nm, for a short pulse of
∼500 fs duration (spectral bandwidth of ∼12 nm).
4212 OPTICS LETTERS / Vol. 35, No. 24 / December 15, 2010
(Δn
max
≈ 0:1 in some regions of Fig. 3). Nevertheless,
semiconductors could appear as better candidates, since
they have similar linear and nonlinear refractive indices to
that of chalcogenides but sup port a much higher Δn
max
≈
0:1, as reported in [21,22]. In any case, appropriate candi-
dates for real experiments must have both high Δn and n
2
and also must behave as Kerr-type materials with low ab-
sorption in a wide range of local intensities.
In conclusion, we have theoretically studied the non-
linear response of a slit array deposited on a dielectric
substrate with Kerr nonlinearity. We have described both
a nonlinear intensity limiter and an optical switch, at the
telecom range. The physical mechanism of both opera-
tion modes is based on sharp variations in the linear
transmission close to the transmission minima present
in arrays of subwavelength apertures in metal films.
We acknowledge the support from the Spanish Minis-
try of Science and Innovation (the projects MAT2008-
06609-C02 and CSD2007-046-Nanolight.es), the Consejo
Superior de Investigaciones Cientificas (project Intra-
mural 2008601253), and the Australian Research Council.
References
1. S. Nie and S. R. Emory, Science 275, 1102 (1997).
2. S. Kim, J. H. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim,
Nature 453, 757 (2008).
3. G. A. Wurtz and A. V. Zayats, Laser Photon. Rev. 2, 125
(2008).
4. S. Xie, H. Li, H. Xu, X. Zhou, S. Fu, and J. Wu, Opt. Commun.
283, 998 (2010).
5. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, Opt. Express
15, 9541 (2007).
6. M. A. Vincenti, A. D’Orazio, M. Buncick, N. Akozbek,
M. J. Bloemer, and M. Scalora, J. Opt. Soc. Am. B 26, 301
(2009).
7. J. A. Porto, L. Martín-Moreno, and F. J. García-Vidal, Phys.
Rev. B 70, 081402 (2004).
8. G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97,
057402 (2006).
9. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, Opt. Express
15, 12368 (2007).
10. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning,
Y. Zhou, and G. Yang, Opt. Lett. 33, 869 (2008).
11. T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and
P. A. Wolff, Nature 391, 667 (1998).
12. A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and
H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
13. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and
L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
14. P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein,
Opt. Lett. 35, 1551 (2010).
15. R. W. Boyd, Nonlinear Optics (Academic, 2003).
16. A. Taflove and S. Hagness Computational Electrody-
namics: The Finite-Difference Time-Domain Method
(Artech House, 2000).
17. P. Tran, Phys. Rev. B 52, 10673 (1995).
18. E. D. Palik, Handbook of Optical Constants of Solids II,
E. D. Palik, ed. (Academic, 1991).
19. S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno,
Phys. Rev. B 77, 075401 (2008).
20. V. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch,
M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton,
D.-Y. Choi, S. Madden, and B. Luther-Davies, Opt. Express
15, 9205 (2007).
21. W. C. Hurlbut, Y.-S. Lee, K. L. Vodopyanov, P. S. Kuo, and
M. M. Fejer, Opt. Lett. 32, 668 (2007).
22. L. Brzozowski, E. H. Sargent, A. S. Thorpe, and
M. Extavour, Appl. Phys. Lett. 82, 4429 (2003).
Fig. 3. (Color online) Local change in the refractive index, Δn,
within the dielectric slab for the same structure considered
in Fig. 1 at λ
1
¼ 1465 nm. For different input intensities
(a) n
2
I
in
¼ 5:5 × 10
−4
, (b) n
2
I
in
¼ 27:5 × 10
−4
, (c) n
2
I
in
¼ 55 ×
10
−4
, and (d) n
2
I
in
¼ 61:6 × 10
−4
.
December 15, 2010 / Vol. 35, No. 24 / OPTICS LETTERS 4213
