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OPTICS LETTERS / Vol. 33, No. 13 / July 1, 2008
Controlling the phase delay of light transmitted
through double-layer metallic subwavelength
slit arrays
Z. Marcet,1 J. W. Paster,1 D. W. Carr,2 J. E. Bower,3 R. A. Cirelli,3 F. Klemens,3 W. M. Mansfield,3
J. F. Miner,3 C. S. Pai,3 and H. B. Chan1,*
1
Department of Physics, University of Florida, Gainesville, Florida 32611, USA
2
Symphony Acoustics, Rio Rancho, New Mexico 87124, USA
3
Bell Laboratories, Alcatel-Lucent, Murray Hill, New Jersey 07974, USA
*Corresponding author: hochan@phys.ufl.edu
Received April 4, 2008; revised May 14, 2008; accepted May 15, 2008;
posted May 20, 2008 (Doc. ID 94672); published June 19, 2008
We demonstrate that the phase of light transmitted through double-layer subwavelength metallic slit arrays
can be controlled through lateral shift of the two layers. Our samples consist of two aluminum layers, each
of which contains an array of subwavelength slits. The two layers are placed in sufficient proximity to allow
coupling of the evanescent fields at resonance. By changing the lateral shift between the layers from zero to
half the period, the phase of the transmitted electromagnetic field is increased by ␲, while the transmitted
intensity remains high. Such a controllable phase delay could open new capabilities for nanophotonic devices
that cannot be achieved with single-layer structures. © 2008 Optical Society of America
OCIS codes: 310.6628, 050.5080, 240.6690, 240.6680, 310.6860, 310.4165.
Periodical arrays of subwavelength apertures in a
metal film exhibit extraordinarily high optical transmission owing to resonance of the incident light with
surface excitations [1,2]. Surface plasmons, diffracted
evanescent waves, and guided modes have been suggested to play a role in the strong transmission [3–6].
So far, the majority of experiments were performed
on subwavelength structures on a single layer of
metal [1,4,6–8]. Both calculations and experiments
have shown that the high transmission at resonance
is accompanied by dramatic enhancement of the local
electromagnetic field on the metal surfaces [2,6]. By
placing two nanostructured metal films in close
proximity and tailoring the evanescent field coupling
between them [9–16], it might be possible to achieve
novel optical properties and new functionalities that
are not possible with a single layer of metal.
In this Letter, we demonstrate that the phase
delay of light transmitted through double-layer
aluminum slit arrays at resonance can be controlled
via the lateral shift between the two layers. An extra
phase shift of ␲ is introduced while the transmission
intensity is maintained close to the maximum value
共⬃50% 兲. Our samples are made of two identical
layers of aluminum films, each of which contains an
array of subwavelength slits. Each individual aluminum layer supports high transmission at resonance
in the absence of the other. The separation between
the layers is chosen to be small enough to allow
coupling of the strong evanescent fields on the metal
surfaces. In an earlier experiment [15], the magnitude of the peak transmission was found to exhibit a
strong dependence on the lateral shift between the
two layers, with maximum transmission occurring
when the slits on the two layers are perfectly aligned
or when they are shifted by half of the period. Here,
we performed calculations to show that the phase of
the transmitted light differs by ␲ for these two cases.
0146-9592/08/131410-3/$15.00
These numerical results were supported by experiments demonstrating that the transmitted light from
the two regions destructively interferes.
Our samples consist of two layers of aluminum
films, each with a thickness of 0.39 ␮m, fabricated on
a quartz substrate. The two layers are separated by
0.3 ␮m and surrounded by silicon oxide. Each layer
contains a slit array with a periodicity of 2 ␮m and
slit widths of 0.45 ␮m. The insets in Fig. 1a show
cross-sectional images of similar devices fabricated
on a silicon wafer with dimensions similar to the
samples on quartz. In an earlier experiment [15], we
demonstrated that a single-layer subwavelength slit
array with comparable dimensions exhibits transmission enhancement at the resonance wavelength of
⬃3.1 ␮m. Moreover, the optical transmission through
the bilayers strongly depends on the lateral shift
between them. Figure 1a shows the measured transmission of TM polarized light (the electric field is
perpendicular to the slits) for sample I (lateral shift
l = 0 ␮m) and sample II 共l = 0.9 ␮m兲 using a Fourier
transform infrared spectrometer (FTIR). All data
have been normalized using transmission through a
clear region adjacent to the samples consisting of the
quartz wafer and a layer of silicon oxide. For samples
I and II, maximum transmission occurs at ⬃3.2 ␮m
with as high as 50% of the incident radiation being
transmitted. Taking into account the refractive index
of silicon oxide (1.53), the peak transmission occurs
at a wavelength slightly higher than the 2 ␮m periodicity of the structures. Here we present calculations and experiments to show that although the
intensity of the transmitted light is strong in both
structures, the phase varies by ␲ because of the
different manner that the evanescent fields in the
two layers couple.
We performed numerical simulations using
rigorous coupled-wave analysis (RCWA) [17]. The
© 2008 Optical Society of America
July 1, 2008 / Vol. 33, No. 13 / OPTICS LETTERS
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Fig. 2. a, RCWA calculation of the phase of the transmitted light as a function of lateral shift between the two layers. Electromagnetic field distribution around b, single
layer; c, aligned double layer; and d, offset double layer.
The incoming wave is incident from the bottom with unit
amplitude. The magnetic field is directed in and out of the
page with the color bar representing its magnitude and direction. The arrows represent the electric field. For
simplicity, the silicon oxide layers are assumed to extend
through all space.
Fig. 1. (Color online) a, measured transmission through
sample I with aligned double layers (dashed curve) and
sample II with offset double layers (solid curve). Insets:
The cross-sectional side view of structures fabricated on a
silicon wafer with similar dimensions to samples I and II
with the two layers aligned (right) and offset by 0.9 ␮m
(left). Light is incident from the top. b, transmission calculation using RCWA. Inset: Cross-sectional schematic of the
structure used in RCWA calculations.
structure is divided into layers, and the calculation
involves expanding the electromagnetic fields and
the dielectric functions in each layer into spatial
Fourier components with the requirement that they
satisfy Maxwell’s equations and the boundary conditions. We used tabulated values for the dielectric
function of aluminum [18] and kept 100 orders in the
Fourier expansion. The layer geometry of the
samples was slightly simplified in the simulations.
We accounted for the silicon oxide–air interface at
the outgoing region, but at the input side, the silicon
oxide was extended to all space. The calculated transmission for samples I and II are in good agreement
with the data (Fig. 1b), reproducing the magnitude
and wavelength for the peak transmission. Deviations between the experiment and the simulation are
probably owing to additional losses in the sample and
the simplification of the sample geometry.
Figure 2a shows an RCWA calculation of the phase
of the outgoing wave at a wavelength of 3.25 ␮m as a
function of the lateral shift between the two layers.
The phase decreases by ␲ as the lateral shift increases from zero to half the period. Such dependence
can be understood by considering the electromagnetic
field distribution on the metal surface. Figures 2b–2d
show the field calculated using RCWA for three different structures at the instant when the field inside
the slits attains maximum. For a single-layer struc-
ture (Fig. 2b), there are two locations where local
maxima of the magnetic field occur: At the slits (position A) and on the metal surface between two slits
(position B). However, the sign of the field is opposite
at these two locations. Such change of sign is also evident for the electric fields at positions A and B. When
the two layers are brought closer together, the evanescent fields begin to couple. If the two layers are
aligned, coupling of fields at positions A and B between the top and bottom layers leads to high transmission. Conversely, when the two layers are shifted
by half the period, coupling occurs between position A
on the top layer and position B on the bottom layer,
where the sign of the electromagnetic field is opposite. As a result, even though the coupling is effective
and transmission remains strong, the sign of the
transmitted electromagnetic field is reversed.
Depending on the lateral shift, the phase of the
transmitted light at resonance can be varied over a
range of ␲. If the separation between the two layers
is increased to 2 ␮m, the phase of the transmitted
light remains largely constant with lateral shift because the evanescent fields do not couple effectively.
We experimentally verify this phase difference in
the outgoing wave by fabricating sample III that allows light transmitted from the aligned and offset
double-layer structures to destructively interfere. As
shown in the left inset in Fig. 3a, the sample is
divided into a checkerboard pattern of 10 ␮m
⫻ 10 ␮m pixels of alternating aligned and offset
regions. The solid curve in Fig. 3a shows that the
transmission peak at 3.2 ␮m is suppressed by about a
factor of 10. Apart from the destructive interference
between the adjacent pixels, the transmission can
also in part be reduced as a result of the finite pixel
size, as each pixel contains only five subwavelength
slits. To confirm the occurrence of destructive infer-
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OPTICS LETTERS / Vol. 33, No. 13 / July 1, 2008
Fig. 3b), the transmission is reduced to a value
nearly identical to half of a nonpixelated structure
(sample I) (dotted curve in Fig. 3b).
In conclusion, the phase delay of the transmitted
light through double-layer subwavelength slit arrays
can be tuned by the lateral shift of the two layers
while the transmitted intensity remains high
共⬃50% 兲. This controllable phase change could open
up possibilities in the design of tunable subwavelength optical components not achievable with
single-layer structures.
We thank H. J. Lezec and D. B. Tanner for useful
discussions. This project was supported by the National Science Foundation ECS-0621944. Z. Marcet
acknowledges support from South East Alliance for
Graduate Education and the Professoriate.
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Fig. 3. (Color online) a, Solid curve shows the measured
transmission of sample III with 10 ␮m squares of aligned
and offset regions in a checkerboard pattern (top view
shown in left inset with light incident into the page). After
covering the offset pixels with aluminum (right inset), the
transmission peak increases in magnitude (dotted curve).
b, Pixel size is increased to 50 ␮m squares in sample IV.
ence, we deposit aluminum on the offset pixels to
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Measurements show that the peak transmission
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to be 54 ␮m, comparable to the pixel size in sample
IV. After covering the offset regions (right inset in
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