Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity
Hideki T. Miyazaki*
Materials Engineering Laboratory, National Institute for Materials Science,
1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
International Center for Young Scientists, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
(Received 30 August 2005; published 7 March 2006)
We demonstrate controlled squeezing of visible light waves into nanometer-sized optical cavities. The
light is perpendicularly confined in a few-nanometer-thick SiO2film sandwiched between Au claddings in
the form of surface plasmon polaritons and exhibits Fabry-Perot resonances in a longitudinal direction. As
the thickness of the dielectric core is reduced, the plasmon wavelength becomes shorter; then a smaller
cavity is realized. A dispersion relation down to a surface plasmon wavelength of 51 nm for a red light,
which is less than 8% of the free-space wavelength, was experimentally observed. Any obvious break-
downs of the macroscopic electromagnetics based on continuous dielectric media were not disclosed for
DOI: 10.1103/PhysRevLett.96.097401 PACS numbers: 78.67.?n, 71.36.+c, 71.45.Gm, 73.20.Mf
Surface plasmons, electromagnetic
coupled to free electron plasma in metals [1,2], are nowa-
days familiar to us in biomolecule detection. Since the
discovery of the single-molecule sensitivity of Raman
scattering at the contact point of silver nanoparticles ,
plasmon resonance at small gaps in metallic subwave-
length structures has attracted attention in terms of en-
hanced spectroscopy. Various geometries have been
extensively studied both theoretically [4,5] and experimen-
tally [6–10]. However, the vital problem of reproducible
fabrication ofnanometer-sized gapshasbeen left unsolved.
In this Letter, we propose a clear-cut architecture of plas-
mon cavity resonators, in which a nanometer-thick dielec-
tric film is employed as the gap. The spatial extent of the
energy can be reduced perpendicularly by metal claddings
 and longitudinally by large wave vectors of the sup-
ported plasmons . We demonstrate the resonant con-
finement ofvisible light wavesin a dielectric core asthin as
3.3 nm and as short as 55 nm. The minimum wavelength of
the plasmon polariton observed is 51 nm for a red light,
which is less than 8% of the free-space wavelength. A soft
x-ray wavelength for a visible frequency is almost within
our reach .
The structure of our resonator is simple; it is a so-called
MIM (metal-insulator-metal) waveguide with a finite
length. Consider a dielectric sheet with a thickness of T
between two noble metal slabs. Here we restrict our dis-
cussion to Au=SiO2=Au systems. Figure 1 depicts the
analytical dispersioncurves  ofpropagating TM(trans-
verse magnetic) modes for various T values. When two
insulator-metal interfaces are brought closer to each other,
the dispersion curve of a single interface splits into high-
and low-energy modes. Figure 1 shows only the low-
energy ones for simplicity. Surface plasmons can be ex-
cited from a free space without momentum matching sim-
ply by perpendicular incidence to the end face .
However, due to the matching of the field symmetry,
only the low-energy mode is excited. Here we utilize this
When T ? 100 nm, the dispersion is not so different
from that of a single interface. However, when T is re-
duced, the interaction of two interfaces gets stronger and
the dispersion curve of the lower mode becomes flat.
Particularly, for T values less than 10 nm, we can obtain
plasmons with small wavelengths (?p) on the order of
10 nm, i.e., extreme ultraviolet wavelengths, for free-space
wavelengths (?) ranging from visible to near-infrared; they
FIG. 1 (color).
TM modes propagating in the z direction. The geometry, the
coordinate system, and the field components of the TM mode are
illustrated in the inset. The black solid curve shows the disper-
sion for a single interface, and colored ones those for low-energy
modes for various T values. We used the value of 2.1 and the
reported values  for the dielectric constants of SiO2and Au,
Dispersion relations of MIM waveguides for
PRL 96, 097401 (2006)
10 MARCH 2006
© 2006 The American Physical Society
open a routeto nanocavities. Moreover,small T valueslead
to higher amplitude of excited fields . This can also be
understood from the viewpoint of the plasmon density of
states inversely proportional to the slope of the dispersion
curves . While reproducible realization of gaps nar-
rower than 10 nm by current lithography-based technolo-
gies is difficult , deposition of nanometer-thick thin film
is sufficiently feasible with conventional techniques.
In the course of the investigation on the extraordinary
transmission through nanohole arrays , Fabry-Perot
resonance in narrow slits has been unveiled [18–21]. The
plasmon modes supported by the slits are reflected by the
end faces, so that the electric field becomes the maximum
at the ends, and can form standing waves between two
surfaces. In other words, a MIM waveguide with a finite
length (L) works as a resonator . Our original point is
to realize this slit by depositing a dielectric thin film. Since
the nanometer-thick dielectric sheet functions as a cavity
resonator for plasmons, we would like to call such a
structure a nanosheet plasmon cavity.
Figure 2 shows the theoretical results of the energy
density distribution in a cavity at a typical first-order
resonance (order number: m ? 1). In this Letter, we used
the two-dimensional (2D) boundary element method 
for calculation. Perpendicular (x) and longitudinal (z) en-
ergy confinement is clearly visualized. Furthermore, the
field distribution suggests that the simple standing wave
picture inside a MIM waveguide is surely applicable. Note
that the electric field is maximized near the entrance and
the exit surfaces (z ? 0 and L). Consequently, we can
expose molecules approximately to the maximum field
by just letting the molecules adsorbed on the end face of
the SiO2sheet. This is a novel feature, which was not
present in conventional optical cavities, and is especially
important for the application to enhanced Raman
MIM geometries have not attracted attention as trans-
mission lines due to their limited propagation lengths :
The imaginary part of the dielectric constant of the metal
induces Joule heating losses. Nonetheless, giant Raman
enhancements were demonstrated in dimers of silver nano-
particles , which can be regarded as MIM configura-
tions. From this fact, we expect that the profit from the
strong energy confinement of MIM cavities can outweigh
the disadvantage of losses.
To fabricate the cavities, Au=SiO2=Au multilayers were
first deposited on fused silica substrates by magnetron
sputtering. The thickness of the Au layers was fixed to
150 nm and those of the SiO2film were T ? 56, 14, and
3.3 nm. Transmission electron microscopy was employed
to measure T and to inspect the morphology of SiO2layers.
The result is exemplified in the inset in Fig. 3. Next the
Au=SiO2=Au multilayers were processed with a focused
FIG. 2 (color).
guide with a finite length. The first-order resonance for T ?
3:3 nm and L ? 65 nm. The thickness of the Au slabs in the x
direction is 150 nm. A TM (x)-polarized plane wave of ? ?
970 nm is incident from the left. The dashed lines are the borders
between Au, SiO2, and free space. Right: Electric and magnetic
fields at z ? 2 nm and L=2, respectively. These are typical
profiles of the MIM guided mode. Below: Fields at x ? 0. The
electric field shows the maximum amplitudes near both end
faces, and the magnetic field exhibits a peak at the center; a
typical standing wave of m ? 1. The fields are the snapshots at
the moment of the maximum amplitude. The energy density and
the fields are normalized by those of the incident wave. The
energy was calculated taking account of the frequency dispersion
of the dielectric constant of Au [16,28]. Each corner of the model
has a radius of 0.25 nm to avoid unphysically singular values.
Energy density distribution in a MIM wave-
sheet plasmon cavity. T ? 14 nm, L ? 107 nm, and W ?
3 ?m. Scale bar, 500 nm. Inset: The transmission electron
micrograph of the cross section for T ? 3:3 nm. Scale bar,
20 nm. Although the SiO2film is wavy due to the surface
roughness of the first Au layer, this feature had no influence
on the optical properties in this study. The SiO2film looks
duplicated because the microscope specimen has a finite thick-
ness and the vicinities of convex and concave points of the film
Scanning electron micrograph of a fabricated nano-
PRL 96, 097401 (2006)
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ion beam from the normal direction, so that rectangular
cavities with widthsofW and lengths of Lare left unmilled
as shown in Fig. 3. For each T value, about 20–30 cavities
with different L values (L ? 55–483 nm) were arrayed
along one of the edges of the substrate. The structures
are assumed to be infinitely long in the y direction in
Figs. 1 and 2. To minimize the discrepancy of the experi-
mental samples from the theoretical models, W was set to
3 ?m, which is sufficiently long compared with ?p.
Resonance in a nanostructure can be probed with far-
field signals in most cases [4–9]. In this study, the en-
trance surfaces of the cavities were vertically illuminated
with a nearly collimated white light, and the backscattering
spectrum only from a selected area around the center of
each single cavity was measured, as depicted in Fig. 4(b).
The measured quantity is hereafter simply called reflec-
tance. Representative results are displayed in Fig. 4(a).
Dips were observed in the reflection spectra for TM polar-
ization, and they systematically shifted as a function of L.
Calculated results of the reflectance and the field enhance-
ment at the center of the entrance surface are compared in
Fig. 4(c). It is obvious that the reflection dips are the signs
of the resonances. At the peaks of the field enhancement
spectra, standing waves as exemplified in Fig. 2 were
confirmed by the calculation of the field distributions. In
addition, Fig. 4(c) manifests the agreement of the dip
positions in the experimental reflection spectra with those
by the calculation. By comparison with the calculation, the
major dips in Fig. 4(a) were assigned to the resonances of
m ? 1–4. Similar results were obtained also for T ? 56
and 3.3 nm. In contrast, remarkable features were not
found in the reflection for TE (transverse electric) po-
larization. Thus, the Fabry-Perot resonance of plasmon
polaritons in the fabricated cavities was successfully dem-
onstrated. Several minor dips discernible in the spectra for
small L values in Fig. 4(a) were not reproduced by the
calculation. These could be due to the transverse modes in
the y direction.
At the mth resonance in a cavity with a length of L, the
corresponding wave vector of the propagating plasmon, k,
is expressed as k ? 2?=?p? m?=L. Therefore, the dis-
persion relations of the plasmon in the cavities can be
experimentally determined . In Fig. 5, the reflection
dips observed were plotted. The resonances of various
orders for various L values formed single dispersion curves
unique to each T value. Furthermore, the experimental
results showed fairly good agreement with the analytical
dispersion curves  of MIM waveguides. This also
proves that the macroscopic electromagnetics, in which
the spatial dispersion effects  are neglected, is appli-
cable to a 3-nm-thick core so far as far-field responses are
discussed. Nanometric slits can be regarded as media with
a large refractive index n . The dashed lines in Fig. 5
indicate the dispersions for representative n values. A red
light of ? ? 651 nm in vacuum is confined in the cavity as
FIG. 4 (color).
T ? 14 nm and TM polarization. The individual spectra are
offset by 0.04 from one another for visibility. Arrows indicate
the major dips. (b) Schematic drawing illustrating the incident,
the collected scattered light, and the measurement area (diame-
ter: 2 ?m). (c) Calculated reflectance (upper) and intensity
enhancement at the center of the entrance surface (lower) for
TM polarization for representative T and L values. The field is
normalized by that of the incident light. The thin lines indicate
the experimental reflection spectra for similar parameters (left:
L ? 106 nm; right: 61 nm). The reflection dips and the field
peaks are denoted by arrows. The fields in Fig. 2 correspond to
the m ? 1 peak in the right panel. The Q values of the reso-
nances are 10–20.
(a) Measured reflectance for various L values.
FIG. 5 (color).
Solid curves: Analytical dispersion of MIM waveguides. Dashed
lines: Propagation in the media with refractive indices of n
drawn for reference. The non-negligible discrepancy between
the analytical model and the experiment for T ? 14 nm proba-
bly originates from an error in the thickness measurement.
Experimentally obtained dispersion relations.
PRL 96, 097401 (2006)
10 MARCH 2006
a surface plasmon polariton with a wavelength of ?p?
51 nm. This wavelength is equivalent to that for n ’ 13.
Such a large index is unattainable by bulk materials.
Larger wavevectors enable ustorealize smaller cavities.
The minimum modal volume in this study is V ?
0:00095 ?m3? 0:0012?3? 1:6TLW . This value
was estimated according to the definition of Foresi et al.
 with a slight modification; we used the maximum
energy density on the z axis for the normalization instead
of the maximum density in the whole space, because the
maximum but singular value at the edge of the Au clad-
dings gives an unrealistically small V value. Despite the
large width of W ? 3 ?m, the estimated modal volume is
very small. For cavities of W ’ ?p, further reduction of
more than one order is possible. Although the Q value is
small, Q=V values comparable to those of the conventional
optical resonators might be obtained because of the very
In summary, we proposed the nanosheet plasmon cavity
as a new configuration of optical resonators and demon-
strated energy confinement in volumes much smaller than
the free-space wavelengths (’0:001?3). Although the esti-
mated intensity enhancements for the fabricated cavities
resulted in modest values as high as jEj2’ 103[Fig. 4(c)],
a further enhancement should be possible for periodically
arrayed cavities by the interaction with the plasmons along
the entrance and the exit surfaces . Reduction of the
width W would also lead to a larger field enhancement by
the energy confinement in a much smaller volume. For a
thinner core, a breakdown of the macroscopic electromag-
netics is expected; it would probably result in enhanced
losses  and resultant deterioration in resonances. Wave
vector dependence of the dielectric functions should be
We are grateful to H. Miyazaki, K. Miyano, H. Tamaru,
K. Ohtaka, and T. Ochiai for discussion and the Materials
Analysis Station of the National Institute for Materials
Science and N. Ishikawa for technical support. This work
was supported by PRESTO of the Japan Science and
Technology Agency and by Special Coordination Funds
for Promoting Science and Technology from the Ministry
of Education, Culture, Sports, Science and Technology.
*Electronic address: MIYAZAKI.Hideki@nims.go.jp
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