Using transmission electron microscopy (TEM) to analyse the physical-chemical
surface properties of subwavlength structured silver films and
finite-difference time-domain (FDTD) numerical simulations of the optical
response of these structures to plane-wave excitation, we report on the origin
and nature of the persistent surface waves generated by a single slit-groove
motif and recently measured by far-field optical interferometry. The surface
analysis shows that the silver films are free of detectable oxide or sulfide
contaminants, and the numerical simulations show very good agreement with the
results previously reported.Comment: 9 Figure

A. Taflove

B. Fultz

C. F. Bohren

C. O’Dwyer

D. W. Lynch

G. Gay

H. J. Lezec

H. Raether

J. Weiner

M. Sukharev

O. Alloschery

P. Lalanne

T. Seideman

Z. L. Wang

English

arXiv

Crossref

Surface quality and surface waves on subwavelength-structured silver films

Gay, Guillaume

Alloschery, Olivier

Weiner, John

Lezec, H.J.

Dwyer, C., O.

Sukharev, M.

Seideman, T.

HAL: Hyper Article en Ligne

We analyze the physical-chemical surface properties of single-slit, single-groove subwavelength-structured silver films with high-resolution transmission electron microscopy and calculate exact solutions to Maxwell's equations corresponding to recent far-field interferometry experiments using these structures. Contrary to a recent suggestion the surface analysis shows that the silver films are free of detectable contaminants. The finite-difference time-domain calculations, in excellent agreement with experiment, show a rapid fringe amplitude decrease in the near zone (slit-groove distance out to 3–4 wavelengths). Extrapolation to slit-groove distances beyond the near zone shows that the surface wave evolves to the expected bound surface plasmon polariton (SPP). Fourier analysis of these results indicates the presence of a distribution of transient, evanescent modes around the SPP that dephase and dissipate as the surface wave evolves from the near to the far zone

Gay, G.

Alloschery, O.

Weiner, J.

Lezec, H. J.

O'Dwyer, C.

Caltech Authors - Main

Surface quality and surface waves on subwavelength-structured silver films
G. Gay, O. Alloschery, and J. Weiner*
IRSAMC/LCAR, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
H. J. Lezec
Thomas J. Watson Laboratories of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
and Centre National de la Recherche Scientifique, 3, rue Michel-Ange, 75794 Paris cedex 16, France
C. O’Dwyer
Tyndall National Institute, University College Cork, Cork, Ireland
M. Sukharev and T. Seideman
Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA
Received 25 August 2006; published 24 January 2007
We analyze the physical-chemical surface properties of single-slit, single-groove subwavelength-structured
silver films with high-resolution transmission electron microscopy and calculate exact solutions to Maxwell’s
equations corresponding to recent far-field interferometry experiments using these structures. Contrary to a
recent suggestion the surface analysis shows that the silver films are free of detectable contaminants. The
finite-difference time-domain calculations, in excellent agreement with experiment, show a rapid fringe am-
plitude decrease in the near zone slit-groove distance out to 3–4 wavelengths. Extrapolation to slit-groove
distances beyond the near zone shows that the surface wave evolves to the expected bound surface plasmon
polariton SPP. Fourier analysis of these results indicates the presence of a distribution of transient, evanescent
modes around the SPP that dephase and dissipate as the surface wave evolves from the near to the far zone.
DOI: 10.1103/PhysRevE.75.016612 PACS numbers: 42.25.Fx, 73.20.Mf, 78.67.n
The optical response of subwavelength-structured metal-
lic films has enjoyed a resurgence of interest in the past few
years due to the quest for an all-optical solution to the inexo-
rable drive for ever-smaller, more densely integrated devices
operating at ever-higher bandwidth. Two basic questions mo-
tivate research in this field: how to confine micrometer light
waves to subwavelength dimensions 2 and how to transmit
this light without unacceptable loss over at least tens of mi-
crometers 3,4. Although surface waves and in particular
periodic arrays of surface plasmon polaritons SPPs have
received a great deal of attention as promising vehicles for
subwavelength light confinement and transport, detailed un-
derstanding of their generation and early time evolution
within the first few wave periods in and on real metal films
is still not complete 5–8.
Recent measurements 1,9 of far-field interference
fringes arising from surface wave generation in single slit-
groove structures on silver films have characterized the am-
plitude, wavelength, and phase of the surface waves. After a
rapid amplitude decrease within the first 3 m from the gen-
erating groove, waves persisting with near-constant ampli-
tude over tens of micrometers were observed. Such long-
range transport is the signature of a “guided mode” SPP, but
the measured wavelength was found to be markedly shorter
than the expectation from conventional theory 10. One pos-
sible reason advanced for the disparity between experiment
and theory was the presence of an oxide or sulfide dielectric
layer on the silver surface, and it has been suggested 11
that an 11 nm layer of silver sulfide would bring experiment
and theory into agreement. We report here the results of two
investigations: one experimental, into the physical-chemical
surface properties of the silver structures, and the other the-
oretical, into the calculated optical response of the silver slit-
groove structures using the finite-difference time-domain
FDTD technique to numerically solve Maxwell’s equa-
tions. These studies show no evidence of oxide or sulfide
layers on the silver surface and the numerical solutions to
Maxwell’s equations not only show good agreement with
measurements reported in 1 but also point to the important
role played by short-range evanescent components in the
early time evolution of the surface wave.
Three typical structured samples were chosen for exami-
nation with fabrication dates of about 12 months, 6 months,
and 1 week from the date of the transmission electron mi-
croscopy TEM analysis. The structures dating from 6
months and 12 months were part of the series actually used
in the previous reports 1,9. They consist of a 400 nm silver
film evaporated onto a fused silica substrate Corning 7980
uv grade 25 mm2, 1 mm thick, optically polished on both
sides to a roughness of no more than 0.7 nm. The structured
substrates are stored in Fluoroware sample holders, 25 mm
diameter and 1 mm in depth at the center. Electron-
transparent sections for cross-sectional transmission electron
microscopy examination were prepared by sample thinning
to electron transparency using standard focused Ga+-ion
beam FIB milling procedures 12 in a FEI 200 FIB work-
station and placed on a holey carbon support. The TEM char-
acterization was performed using a Philips CM300 Schottky
field emission gun FEG microscope operating at 300 kV.
The FEGTEM has a point resolution of 0.2 nm and an infor-
mation limit of 0.12 nm. The minimum focused electron
beam probe size is 0.3 nm. In dark-field images diffracted*Electronic address: jweiner@irsamc.ups-tlse.fr
PHYSICAL REVIEW E 75, 016612 2007
1539-3755/2007/751/0166124 ©2007 The American Physical Society016612-1
flux passes the objective aperture while the direct straight-
through beam is blocked. The diffracted beam interacts
strongly with the specimen and selection of a particular dif-
fracted beam allows better visual phase differentiation. Typi-
cal regions of Ag layer that were thinned to electron trans-
parency are shown at relatively low magnification in the
bright-field micrograph in Fig. 1. An immediate distinction
can be made between the fused silica substrate A and the
Ag deposit B. Protective capping layers of Au and Pt, ap-
plied at the time of analysis, are marked at C and D, respec-
tively. The latter are used to prevent any “top down” ion
damage of the cross section during the ion beam thinning
preparation. The white line marked by an arrow in Fig. 1 is a
band that contains very fine particles of Au formed during
the initial stages of the deposition of this metal. The fine
particles do not exhibit the same degree of absorption con-
trast as the bulk of the Au above them because the particle
diameters are less than the thickness of the cross-sectional
slice and thus do not extend through the full thickness of the
TEM sample. It is clearly observed that the Au nanoparticles
form a separate layer above the Ag deposit. Local undula-
tions in the Ag layer are observed to be devoid of any oxide
or sulfide layer. Fresnel contrast methods were also used to
examine the upper surface regions of the silver at the detail
shown in Fig. 2. Imaging of layers in cross section always
results in Fresnel fringes. Because the amplitude and phase
changes that occur when an electron is scattered elastically
are characteristic of the atomic number, there will be changes
in the elastic scattering directly related to the form of the
projected scattering potential when there is a composition
change at an interface viewed in projection 13, analogous
to a phase grating filtering of the scattered electronic wave
function. Interface Fresnel effects can thus provide a signa-
ture of the form and magnitude of any compositional discon-
tinuity that is present. The visibility of these fringes depends
on the thickness of the specimen and on the defocus value of
the microscope. From Fig. 2, the critical observation is the
absence of Fresnel effects at the surface of the metal other
than at the localized regions associated with the gold protec-
tive coating. The lack of Fresnel fringes at the upper surface
indicates a lack of variation in the scattering potentials and
hence of the chemical composition at the interface. The sil-
ver surface is not covered by a detectable layer of sulfide or
oxide since their presence would exhibit differences in scat-
tering potential by comparison with the metal itself 14. The
lower detection limit for such compositional differences is a
few tenths of a nanometer layer thickness. The absence of a
dielectric layer is not surprising when account is taken of the
small-volume, air-tight sample storage and the trace frac-
tional concentrations of sulfur-containing contaminants in or-
dinary laboratory air 15.
The optical response of structured metal surfaces is simu-
lated using a finite-difference time-domain approach 16.
The subwavelength slit-groove structures 1,9 are modeled
in two dimensions and excited by TM polarized light. In
metallic regions of space  is a complex, frequency-
dependent function. Within the standard Drude model 17 it
is given as
 = 0 − p2
2 + i , 1
where 0 is the electric permittivity of free space, =
→  the dimensionless infinite-frequency limit of the di-
electric constant, p the bulk plasmon frequency, and  the
damping rate. We numerically fit the real and imaginary parts
of the Drude dielectric constant in the form of Eq. 1 to the
experimental data collected in 18. The Drude parameters
obtained in the wavelength regime ranging from 750 to
900 nm for silver are =3.2938, p=1.35521016 rad s−1,
and =1.99441014 rad s−1, which correspond to Re
=−33.9767 and Im=3.3621 at 0=852 nm. These fitted
parameters are close to those determined in 1 by ellipsom-
etry, Re=−33.27 and Im=1.31. Numerical results were
not sensitive to this range of parameter variability. For refer-
ence we also implement perfect electric conductor PEC
boundary conditions, where the metal dielectric constant is
set to negative infinity, and all electromagnetic field compo-
nents are therefore strictly zero in metal regions. The light
source is a plane wave Einc, incident perpendicular to the
metal surface and depending on time as Einct
=E0ftcos t, where E0 is the peak amplitude of the pulse,
ft=sin2	t /
 is the pulse envelope, and 
 is the pulse
duration ft
=0. Time propagation is performed by a
leapfrogging technique 16. In order to prevent nonphysical
reflection of outgoing waves from the grid boundaries, we
employ perfectly matched layer PML absorbing bound-
aries. To avoid accumulation of spurious electric charges at
the ends of the excitation line and generate a pure plane
FIG. 1. Cross-sectional bright-field through-focal TEM micro-
graph of the Ag layer on a fused silica substrate. Labels refer to
fused silica substrate A, silver layer B, capping gold layer C, and
capping platinum layer D. The darkened features in the Ag layer B
are dislocations and grain boundaries.
FIG. 2. A higher-magnification defocused image of the upper
surface showing the Au-particle-containing protection layer. No
Fresnel fringes are observed at the uppermost Ag surface when
compared with in-focus images. White spaces indicate voids.
GAY et al. PHYSICAL REVIEW E 75, 016612 2007
016612-2
wave with a well-defined incident wavelength, we embed the
ends in the PML regions. Convergence is achieved with a
spatial step size of x=y4 nm and a temporal step size of
t=x / 2c, where c denotes the speed of light in vacuum.
The parallel computation technique used in our simulations
is described in detail in 21. Calculations of the intensity I
Ex
2+Ey
2+Hz
2 are performed and converged along a box
contour.
The collected data are averaged over time and the spatial
coordinates for a range of slit-groove distances. Finally, the
space- and time-averaged intensity is normalized to unit
maximum. Our results are converged to the cw limit with
incident pulse durations 
200 fs. A direct comparison of
the experimental data with both the PEC and the Drude mod-
els is shown in Fig. 3. Clearly, the Drude model agrees very
well with the data, whereas the PEC model predicts oscilla-
tions of the intensity with a noticeably larger wavelength and
smaller amplitude. In order to properly determine the wave-
length of oscillations we use a cosine function with an expo-
nentially decreasing amplitude plus a constant offset to fit the
data shown in Fig. 3. We also extend both the FDTD simu-
lation and the fitting function to a slit-groove distance of
16 m, well beyond the range of experimental data, and take
the Fourier transform of the fitted function over this extended
range. We obtain the associated power spectrum expressed as
a wavelength distribution. The results are shown in Fig. 5
below:
Ifitx = A1 + A2expA3xcosA4x + A5 + A6. 2
The FDTD simulation and analytic fit for larger slit-
groove distances are shown in Fig. 4 for the case of the
Drude model. The fitting function Eq. 2 tracks the FDTD
results over the entire slit-groove distance range. Figure 5
shows the normalized power spectrum corresponding to Eq.
2 as a function of the wavelength. The two power spectrum
plots of Fig. 5 provide the effective wavelength eff at which
surface waves propagate as well as the distribution of modes
around the peak. Note that the Drude model for silver shows
a marked blueshift in peak wavelength and a noticeable
broadening of the distribution compared to the perfect
metal PEC model. The Drude simulation results in eff
=837.482 nm, whereas the PEC gives eff=852.066 nm,
very close to the free-space reference wavelength 0
=852 nm. The effective surface index of refraction, neff
=0 /eff, leads to the following values: neffDrude=1.0173
and neffPEC=0.9999.
In summary, surface analysis by transmission electron mi-
croscopy of subwavelength-structured silver films used to
investigate their optical response 1,9 showed no detectable
evidence of material on the surface other than silver. The
suggestion that an 11 nm sulfide layer may be present so as
to bring the interference pattern calculated by the authors of
Ref. 11 into agreement with experiment is therefore not
confirmed. In contrast to the calculations reported by Ref.
11, the numerical solution of Maxwell’s equations reported
here shows excellent agreement with the fringe amplitude
and wavelength over the near-zone slit-groove range mea-
sured in 1. We emphasize that the amplitude decrease in
this near-zone reflects evanescent mode dephasing and dissi-
pation. It is much faster than loss rates expected from surface
scattering or absorption 1. Extrapolation of the FDTD
simulations beyond the range of the measurements shows
that the initially decreasing amplitude of the fringe settles to
an oscillation with near-constant amplitude and fringe con-
trast. These features resemble the calculations of 11, but the
FIG. 3. Color online Comparison of FDTD simulation and
experiment. Green points are experimental data taken from 1.
Blue solid curve that closely fits the points corresponds to Drude
model; red solid curve with longer fringe wavelength and smaller
amplitude than data corresponds to PEC model.
FIG. 4. Color online Blue solid curve plots the same Drude
model FDTD calculation as in Fig. 3 but extended to 16 m slit-
groove distance. Red dashed curve plots the fitting function of Eq.
2.
FIG. 5. Color online Fourier transform spectra of Eq. 2 for
Drude peaked at 837 nm blue and PEC peaked at 852 nm red
FDTD simulation fits. Indicated peak correspond to neffDrude
=1.017, neffPEC=1.000.
SURFACE QUALITY AND SURFACE WAVES ON … PHYSICAL REVIEW E 75, 016612 2007
016612-3
results reported here accord with experiment without the
need to invoke an 11 nm silver sulfide layer. Fourier analysis
of the FDTD simulations reveal that the most probable wave-
length in the Fourier distribution is 837 nm, within about
2 nm of the expected long-range SPP wavelength of 839 nm.
Similar analysis of the PEC simulations yields a peak wave-
length, as expected, at the free-space wavelength of 852 nm.
Finally, Figs. 4 and 5 point to the important contributions to
the surface wave of transient modes neighboring the SPP at
slit-groove distances within the near zone. The presence of
these modes implies a surface k-mode “wave packet” that
evolves to the final SPP as the wave passes beyond the near
zone. This near zone, however, extends over several wave-
lengths; and therefore any theory of subwavelength array
transmission must take these ephemeral, evanescent modes
into account.
Support from the Ministère délégué à l’Enseignement
supérieur et à la Recherche under the programme ACI
“Nanosciences-Nanotechnologies,” the Région Midi-
Pyrénées Grant No. SFC/CR 02/22, and FASTNet Grant
No. HPRN-CT-2002-00304 EU Research Training Network,
is gratefully acknowledged, as is support from the Caltech
Kavli Nanoscience Institute, the AFOSR under Plasmon
MURI Grant No. FA9550-04-1-0434, the National Energy
Research Scientific Computing Center, the U.S. Department
of Energy under Contract No. DE-AC03-76SF00098, and the
San Diego Supercomputer Center under Grant No.
PHY050001. Discussions with P. Lalanne, M. Mansuripur,
and H. Atwater and computational assistance from Y. Xie are
also gratefully acknowledged.
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