Birck and NCN PublicationsBirck Nanotechnology Center
Extraordinary infrared transmission through a
periodic bowtie aperture array
Edward C. Kinzel
Purdue University - Main Campus, firstname.lastname@example.org
Birck Nanotechnology Center, School of Materials Engineering, Purdue University, email@example.com
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact firstname.lastname@example.org for
Kinzel, Edward C. and Xu, Xianfan, "Extraordinary infrared transmission through a periodic bowtie aperture array" (2010).Birck and
NCN Publications.Paper 686.
Extraordinary infrared transmission through a
periodic bowtie aperture array
Edward C. Kinzel and Xianfan Xu*
School of Mechanical Engineering and Birck Nanotechnology Center, Purdue University,
West Lafayette, Indiana 47907, USA
* Corresponding author: email@example.com
Received December 14, 2009; revised February 19, 2010; accepted February 22, 2010;
posted March 3, 2010 (Doc. ID 121434); published March 26, 2010
The discovery of extraordinary transmission through periodic aperture arrays has generated significant in-
terest. Most studies have used circular apertures and attributed enhanced transmission to surface plasmon
polariton (SPP) resonances and/or Rayleigh–Wood anomalies (RWA). Bowtie apertures concentrate light and
have much longer cutoff wavelengths than circular apertures and can be designed to be strongly resonant.
We demonstrate here that the total transmission through a bowtie aperture array can exceed 85% (4? the
open area). Furthermore, we show that the high transmission is due to waveguide modes as opposed to the
commonly believed SPP/RW phenomena. This work is focused on IR wavelengths near 9 ?m; however, the
results are broadly applicable and can be extended to optical frequencies. © 2010 Optical Society of America
OCIS codes: 240.0240, 240.6680, 050.1220.
Classical aperture theory predicts that transmission
through a subwavelength hole scales with ?d/??4,
where d is the diameter of the aperture and ? is the
free-space wavelength of light [1,2]. The discovery of
the extraordinary transmission through subwave-
length hole arrays has generated significant interest
[3–5]. However, debate still exists as to the exact
physical mechanism behind the enhancement . A
number of studies have shown that the transmission
enhancement occurs near the Bragg condition of the
propagating surface plasmon polaritons (SPPs) [7,8].
This occurs for conditions similar to the Rayleigh–
Wood anomaly (RWA), which happens when higher
diffraction orders are directed along the surface .
In either case, energy is trapped at the surface and,
once trapped, tunnels through the hole array before
being scattered. In addition to propagating SPP
modes, localized surface plasmon resonances also
have been shown to play a role . It has also been
noted that the cutoff wavelength is considerably
longer for a waveguide defined in a real metal than in
PEC due to hybridization with SPP modes in the
holes [11,12]. If the apertures are not symmetric, the
transmission becomes polarization dependent [5,13].
90% transmission has been achieved through annu-
lar aperture arrays [14,15]. Larger, open apertures
such as circles [16,17], rectangles , and crossed
dipoles  have also been investigated, showing the
influence of both aperture shape and surface reso-
nances in the mid- and long-IR wavelengths.
In this Letter we investigate transmission through
a periodic array of bowtie apertures. The transmis-
sion modes are optimized to obtain high transmission
around ?=9 ?m. The high transmission in IR has the
potential as a high-efficiency IR coupler for detection
devices. The bowtie aperture is also polarization se-
lective, therefore useful where polarization selectiv-
ity is of interest such as IR polarimetry imaging .
The fundamental principles in IR are similar to those
in visible wavelengths, and therefore the bowtie ap-
erture arrays studied in this work are scalable to vis-
Bowtie apertures are one type of ridge aperture
[2,19–22]. A key advantage of the ridge aperture is
that the cutoff wavelength is much longer than that
in the circular or rectangular aperture while provid-
ing electric field confinement. Ridge apertures can
also be designed to provide strong resonant effects
that permit enhanced transmission even for an iso-
lated aperture [21,22]. Field concentration and en-
hancement in bowtie apertures have been experi-
mentally demonstrated (in visible wavelengths),
including near-field scanning microscopy (NSOM)
measurements  and nanolithography .
The geometry of the bowtie aperture array studied
in this work is shown in Fig. 1, with periodicity px
and py. The aperture profile described by Fig. 1 is se-
lected to capture the profile produced by FIB milling.
The geometry is defined by outline dimensions a and
b with a gap defined by d, and the apertures are
milled in a free-standing gold film with thickness
t=1.25 ?m. The array presented in this study is char-
acterized by a=3.20 ?m, b=1.80 ?m, px=4.35 ?m,
py=2.85 ?m, d=0.11 ?m, ?=2.5°, r1=4.00 ?m, r2
=0.25 ?m, r3=0.13 ?m, and r4=0.05 ?m. These di-
mensions are determined by fitting scanning electron
milled bowtie aperture array (not drawn to scale). Insets,
an SEM image taken at 52° and a cross-section on the yz
plane through the gap of one of the apertures.
Simulated geometry of focused-ion-beam (FIB)
OPTICS LETTERS / Vol. 35, No. 7 / April 1, 2010
0146-9592/10/070992-3/$15.00© 2010 Optical Society of America
microscopy images of the apertures designed to maxi-
mize transmission near ?=9 ?m.
A 170?160 ?m array (40?56 apertures) was
milled using an FEI Nova 200 dual-beam FIB (30 kV,
3 nA Ga+ beam current). Transmission through the
array was measured with a Bruker Vector 22 FTIR
with an IRScope I and is plotted in Fig. 2. The polar-
ization of the light was selected by placing a holo-
graphic wire-grid linear polarizer in the optical path.
The maximum transmission of y-polarized light
through the array is measured to be 85% and occurs
at the wavelength of 9.4 ?m. If the transmission is
normalized to the open area of the arrays, the maxi-
mum transmission is ?400%. The measured polar-
x-polarized light is greater than 300 for 8.5 ?m??
finite-element method solver  were performed to
design and optimize the aperture arrays prior to fab-
rication. Periodic boundary conditions were employed
to simulate an infinite array except for the isolated
aperture case, where absorbing boundaries were
used. The permittivity of gold is taken from . We
start by calculating the transmission through an iso-
lated aperture, which is determined by integrating
the Poynting vector over the exit plane of the aper-
ture and normalizing it to the intensity on the open
area. Figure 3(a) shows that at resonance the light
diffracted from the aperture exceeds the light inci-
dent on its open area by a factor of 3 for y-polarized
light. The peak at ?=4 ?m corresponds to the first
Fabry–Perot resonance of the TE10waveguide mode.
Figures 3(b) and 3(c) show the field structure ex-
tracted from the lowest-order eigenmode simulation
of an isolated aperture. This mode occurs at ?
=10.4 ?m and corresponds to the cutoff condition for
the TE10waveguide mode. At cutoff, the propagation
constant approaches zero and the magnetic field
within the aperture is almost completely directed in
the z direction. As shown in Figs. 3(b) and 3(c), the
electric field is well confined in the gap while the
magnetic field forms inductive loops circulating
through the open arms of the aperture. These fields
are almost completely polarized in the yz and xz
planes, respectively, which makes the coupling to the
resonant mode very polarization dependent. Because
the electric field is confined to the gap region (much
smaller than the free-space wavelength), the aper-
ture radiates similar to a Hertzian dipole.
When apertures are assembled to form an array,
they constructively interfere to provide the T00dif-
fraction order under normal incidence (this is the
only diffraction order for ??px). Figure 4 shows the
simulated transmission through an infinite array of
apertures. The numerical results are in good agree-
ment with the experimental results (Fig. 2). Figure
bowtie aperture array at 0° and 90° polarizations. The in-
set is an SEM image of the array.
Experimental results for the normally illuminated
aperture: (a) transmission spectra, field distributions from
eigenmode simulation; (b) electric field in the yz plane and
(c) magnetic field in the xz plane.
(Color online) Simulated response from an isolated
bowtie apertures: (a) transmission spectra with close-up of
SPP/RWA in inset, (b) electric field in the yz plane (c) mag-
netic field in the xz plane, both for the TE10 mode, and (d)
electric field on the yz plane for the SPP/RWA.
(Color online) Simulation results of an array of
April 1, 2010 / Vol. 35, No. 7 / OPTICS LETTERS
4(a) also shows the Fabry–Perot peak at about 4 ?m, Download full-text
which was also seen in the experimental data and in
the simulation result of a single bowtie aperture [Fig.
3(a)]. The resonant peak is blueshifted from the case
of the isolated aperture. This is due to inductive cou-
pling between adjacent apertures. Figures 4(b) and
4(c) show the electric and magnetic field structures
for this resonance extracted from an eigenmode
simulation. As was the case for the isolated aperture,
the electric field remains well confined in the gap re-
gion in each aperture. The magnetic field is aligned
with the z direction within the aperture, indicating a
TE10mode, and circulates between adjacent aper-
tures, further reducing its confinement. This mag-
netic coupling greatly increases the effective area of
the aperture, permitting more incident radiation to
transmit through the array. The spacing between the
apertures is critical to maximize this effect.
The isotropic nature of the transmission from an
isolated aperture suggests the possibility of grating
phenomena when ? or ?SPP=py(in the IR, ?SPP??,
since the imaginary part of the permittivity of metal
is sufficiently large). The simulation results do show
a weak RWA/SPP feature at ?=2.85 ?m [inset of Fig.
4(a)]. Figure 4(d) shows the field distribution corre-
sponding to this mode. The magnitude of the RWA/
SPP is small compared with the waveguide mode at
9.4 ?m. This is further exacerbated by the roughness
of the film, which serves to scatter the surface mode,
making it difficult to detect in the experiment.
In summary, this work demonstrates extraordinary
IR transmission through a bowtie aperture array.
The high transmission is shown to be the result of
coupling to and from resonant waveguide modes for
both a bowtie array and a single bowtie aperture
with surface-mode phenomena playing a negligible
role. The mode structures of the apertures are shown
to be inductively coupled to each other when the ap-
ertures are placed in the array, which contribute to
the extraordinary transmission of the aperture array.
Support to this work by the Air Force Office of Sci-
entific Research STTR program (contract FA9550-09-
C-0058, Program Manager Dr. Gernot Pomrenke),
National Science Foundation (NSF) (DMI-0707817),
and Defense Advanced Research Projects Agency
(DARPA) (grant N66001-08-1-2037, Program Man-
ager Dr. Thomas Kenny) is gratefully acknowledged.
The authors also thank John Coy of the Purdue Uni-
versity Birck Nanotechnology Center for assistance
in taking the FTIR measurements and Dr. Axel Reis-
inger of QmagiQ LCC and Prof. W. J. Chappell of
Purdue University for helpful discussions.
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