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Journal ArticleDOI

Non-universal behavior of leaky surface waves in a one dimensional asymmetric plasmonic grating

22 Jul 2015-Journal of Applied Physics (AIP Publishing)-Vol. 118, Iss: 4, pp 043103
TL;DR: In this article, a non-universal behavior of leaky surface plasmon waves on asymmetric (Si/Au/analyte of different height) 1D grating through numerical modeling is investigated.
Abstract: We report on a non-universal behavior of leaky surface plasmon waves on asymmetric (Si/Au/analyte of different height) 1D grating through numerical modelling. The occurrence of the leaky surface wave was maximized (suppressing the Fabry–Perot cavity mode), which can be identified in a reflection spectrum through characteristic minimum. Beyond a specific analyte height (h), new sets of surface waves emerge, each bearing a unique reflection minimum. Furthermore, all of these minima depicted a red-shift before saturating at higher h values. This saturation is found to be non-universal despite the close association with their origin (being leaky surface waves). This behavior is attributed to the fundamental nature and the origin of the each set. Additionally, all of the surface wave modes co-exit at relatively higher h values.

Summary (1 min read)

INTRODUCTION

  • From early 1980s,1,2 surface plasmon3,4 based optical sensors have been exhibiting a great potential in evaluating physical, chemical, and biological parameters.
  • These applications are dependent on the sensitivity of surface plasmon polaritons (SPPs) to the refractive index (RI) of the medium adjacent to the metal surface.
  • 3,4,13,18 Among the various types, grating structure can be compact and robust, which are desirable characteristics for integration into other devices6 apart from the tunability of the spectral response through geometrical parameters.
  • The grating parameters were optimized10,19 to maximize the absorption of propagating SPPs (surface wave).

GRATING STRUCTURE AND COMPUTATIONAL DETAILS

  • Svempati01@qub.ac.uk and tahir.awan@uog.edu.pk b)S. Vempati and T. Iqbal contributed equally to this work, also known as Electronic addresses.
  • The gradient condition increases the number of data points as the spatial distribution of the field becomes more complicated.
  • The source-field and the reflection in the far-field were at a distance of 1500 nm and 1000 nm when measured from the top of the analyte, respectively.
  • In the present case, the relevant parameters were optimized (results not shown here) in such a way that the FP-like resonances were suppressed in the region of spectral interest10,19 while maximizing the absorption for surface waves.

RESULTS AND DISCUSSION

  • The activation of surface modes requires either evanescent or grating coupling, where the latter introduces additional wave-vector along the parallel direction.
  • It is notable that the grating parameters were optimized such that the slits are in anti-resonant condition at the wavelengths in which the RS (iii) associated with the two interfaces occur (1st and 2nd order FP modes 1150 nm and 509 nm, respectively).
  • As h value increases, the minimum becomes prominent and red-shifts, where the shift is governed by the effective RI.
  • Significant changes in the effective RI induce additional (k1, k2, and k3) sets of surface wave modes on Au/analyte interface.
  • Since k1, k2, and k3 are not integer multiples of k0, the possibility of the former being higher order surface modes of the latter can be ruled out.

CONCLUSIONS

  • It is known that the surface plasmons are quite sensitive to the changes in the RI, so is the case with surface waves on 1D asymmetric grating.
  • Essentially, the resonance wavelength red-shifts with increasing h value while after a certain h value, new sets of surface waves emerge.
  • The authors believe that this study not only provides new insights in designing the plasmonic sensors but also has fundamental importance in the context of behavior of plasmonic surface waves.

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Non-universal behavior of leaky surface waves in a one dimensional asymmetric
plasmonic grating
Sesha Vempati, Tahir Iqbal, and Sumera Afsheen
Citation: Journal of Applied Physics 118, 043103 (2015);
View online: https://doi.org/10.1063/1.4927269
View Table of Contents: http://aip.scitation.org/toc/jap/118/4
Published by the American Institute of Physics

Non-universal behavior of leaky surface waves in a one dimensional
asymmetric plasmonic grating
Sesha Vempati,
1,a),b)
Tahir Iqbal,
2,a),b)
and Sumera Afsheen
3
1
UNAM-National Nanotechnology Research Center, Bilkent University, Ankara 06800, Turkey
2
Department of Physics, Institute of Natural Sciences, University of Gujrat, Hafiz Hayat Campus,
Gujrat 50700, Pakistan
3
Department of Zoology, Institute of Life Sciences, University of Gujrat, Hafiz Hayat Campus,
Gujrat 50700, Pakistan
(Received 6 May 2015; accepted 10 July 2015; published online 22 July 2015)
We report on a non-universal behavior of leaky surface plasmon waves on asymmetric (Si/Au/
analyte of different height) 1D grating through numerical modelling. The occurrence of the leaky
surface wave was maximized (suppressing the Fabry–Perot cavity mode), which can be identified
in a reflection spectrum through characteristic minimum. Beyond a specific analyte height (h),
new sets of surface waves emerge, each bearing a unique reflection minimum. Furthermore, all of
these minima depicted a red-shift before saturating at higher h values. This saturation is found to
be non-universal despite the close association with their origin (being leaky surface waves). This
behavior is attributed to the fundamental nature and the origin of the each set. Additionally, all of
the surface wave modes co-exit at relatively higher h values.
V
C
2015 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4927269]
INTRODUCTION
From early 1980s,
1,2
surface plasmon
3,4
based optical
sensors have been exhibiting a great potential in evaluating
physical, chemical, and biological parameters.
59
These sen-
sors are 1D or 2D gratings
5,1014
apart from gold colloids/its
variations,
6,15
ring resonators,
8,16
evanescent field optical
waveguides,
17
etc. These applications are dependent on the
sensitivity of surface plasmon polaritons (SPPs) to the refrac-
tive index (RI) of the medium adjacent to the metal sur-
face.
3,4,13,18
Among the various types, grating structure can
be compact and robust, which are desirable characteristics
for integration into other devices
6
apart from the tunability
of the spectral response through geometrical parame-
ters.
1012,1921
Especially, 1D grating can support waveguide,
propagating SPPs and/or surface wave modes.
10,14,19
The
grating parameters can be tuned to maximize any of the
above modes, which may be featured in the optical proper-
ties. In the present report, we limit our interest to the asym-
metric grating,
22
which supports leaky surface waves
predominantly. The asymmetric grating depicts minima in
the reflection spectrum corresponding to the SPPs due to the
interaction between longitudinal and transverse resonant
modes.
10,19,23
The applications of gratings are not limited to
the detection of RI,
5,1013,18
but extends to the estimation of
analyte height (h)
10,24
where the latter is quite interesting,
and the least explored as far as we can ascertain. In the con-
text of detection of h, the spectral shift of surface wave reso-
nance can be quantified, similar to that of RI. Notably, in an
earlier study,
10
the detection of “h” is investigated, however,
up to a maximum of 500 nm for a specific design employing
predominantly surface waves. Importantly, beyond the above
mentioned h value, some key observations were made, viz.,
(a) the spectral shift of the minimum that corresponds to the
surface wave saturates after a certain h, (b) because of the
changes in the effective RI (increasing h value) additional
sets (3) of surface waves emerge, and (c) the new sets ex-
hibit saturation behavior with increasing h, however qualita-
tively not similar to the earlier occurred set.
In this report, finite element method is adopted to ana-
lyze the behavior of the surface waves of Au grating on Si
substrate. The grating parameters were optimized
10,19
to
maximize the absorption of propagating SPPs (surface
wave). The spectral shift for each set of surface wave is pur-
sued for various h values. The non-universal behavior of the
saturation with respect to h is interpreted based on the origin
and fundamental nature of the each set of surface wave.
GRATING STRUCTURE AND COMPUTATIONAL
DETAILS
Fig. 1(a) shows the schematic of a 1D Au grating on Si-
substrate, where K—periodicity, t—thickness, a—slit width,
and h—analyte height for a fixed RI of 1.33. The source-
field is a plane wave of TM-polarization (two in plane field
components E
x
and E
y
, whereas H
z
orthogonal to the
FIG. 1. (a) Schematic of the grating structure, where K—periodicity, a
the slit width, and t—thickness, and (b) TM-polarization of the
illumination.
a)
Authors to whom correspondence should be addressed. Electronic
addresses: svempati01@qub.ac.uk and tahir.awan@uog.edu.pk
b)
S. Vempati and T. Iqbal contributed equally to this work.
0021-8979/2015/118(4)/043103/4/$30.00
V
C
2015 AIP Publishing LLC118, 043103-1
JOURNAL OF APPLIED PHYSICS 118, 043103 (2015)

simulation plane) at normal incidence (y-axis, Fig. 1(b)).
The optical properties of Si and Au were adopted from
Ref. 25. The reflection spectrum is obtained via finite ele-
ment method from COMSOL multiphysics
26
in the presence
of perfectly matched layers on top and bottom of the compu-
tational domains with periodic boundary conditions. We
have used a resolution of 1 nm for the narrow regions while
the whole model was meshed with maximum element size of
20 nm. The details are as follows. Maximum element size
scaling factor, 1 nm; element growth rate, 1.3 nm; mesh cur-
vature factor, 0.3; and mesh curvature cut off, 0.001 nm. The
element shape was triangular (quad), which allows an accu-
rate description of the plane wave.
27
The gradient condition
increases the number of data points as the spatial distribution
of the field becomes more complicated. For instance, an
evanescent wave is professionally explained when a gradient
in mesh resolution is used. Furthermore, the gradient mesh is
useful to simulate the interaction of photons with real metal
surfaces, since the skin depth and field enrichment results in
a quick onset of very large field gradients over a tiny dis-
tance. The source-field and the reflection in the far-field were
at a distance of 1500 nm and 1000 nm when measured from
the top of the analyte, respectively. The spectra were
acquired (600–900 nm) by considering the component of the
Poynting vector propagating along the incident field direc-
tion at various h values (220–2200 nm). Fabry–Perot (FP)-
like resonance modes are dependent on slit width and depth
of the grating, which however can interfere with the Wood’s
anomaly (onset of the 1st order diffracted wave which propa-
gates along the grating surface) producing other modes.
19
In the present case, the relevant parameters were optimized
(results not shown here) in such a way that the FP-like
resonances were suppressed in the region of spectral inter-
est
10,19
while maximizing the absorption for surface waves.
The resulting parameters were K ¼ 630 nm, a ¼ 160 nm, and
t ¼ 220 nm, and the whole structure is referred to as K630-
a160-t220-h(220–2200) for convenience.
RESULTS AND DISCUSSION
The activation of surface modes requires either evanes-
cent or grating coupling, where the latter introduces addi-
tional wave-vector along the parallel direction.
11,12,14,20,21
Narrow slits support TM waveguide mode propagating
inside the slits in contrast to cylindrical apertures.
11,12,1921
A metal grating surrounded by a dielectric medium supports
three resonant states (RS), which can be identified in a reflec-
tion spectrum. These RS are (i) waveguide formed within the
metal strips (broad band resonance, metal-insulator-metal
structure),
10
similar to FP cavity mode, (ii) propagating
SPPs, and (iii) involve the whole grating periodicity depend-
ing on the availability of FP cavity modes. RS (iii) are bound
to the surface of the grating however, can generate a leaky
mode by coupling through the slits depending on the avail-
ability of a FP-like cavity mode.
10
Essentially, for wave-
lengths close to K, the reflection minimum of 1D grating
follows the dispersion relation of bound surface waves.
19,28
These surface waves become leaky for k < 2K where their
dispersion is determined by the geometrical parameters and
the finite conductivity
29
of the metal.
14,19
Note that the dis-
persion of the leaky surface waves is quite different from
that of unperturbed surface plasmons. On the other hand,
because of the asymmetry, SPP modes are excited at the
input and output interfaces in addition to FP cavity modes.
Importantly, coupling among FP and SPP modes can gener-
ate hybrid modes carrying the characteristics of constitu-
ents.
10,19
It is notable that the grating parameters were
optimized such that the slits are in anti-resonant condition at
the wavelengths in which the RS (iii) associated with the two
interfaces occur (1st and 2nd order FP modes 1150 nm and
509 nm, respectively).
10,19
Also, the presence of a substrate
does not significantly alter the physics of the structure, other
than inducing a spectral shift of FP and plasmonic
resonances.
19
Fig. 2 shows the reflection spectra from K630-a160-
t220-h(220–2200) grating. Due to the asymmetry,
22
the
resonance modes seen in the reflection spectra are highly
dependent on the contrast of RI of the (two) surrounding
media (i.e., analyte and Si). For h ¼ 220 nm, the analyte just
fills the cavity of Au strips and shows a local minimum at
630 nm. As h value increases, the minimum becomes
prominent and red-shifts, where the shift is governed by the
effective RI. The red-shift can be calibrated against h and
used to determine the thickness of the analyte.
10
However, in
Ref. 10, the spectral shift of the said minimum is shown until
h ¼ 500 nm. Further increase in h, for example, h 800 nm
[Ref. 30], a new resonance (k
1
) feature starts to emerge
and becomes prominent with increasing h. While for
h > 1000 nm and h > 1400 nm, we can see the additional
minima, which are referred to as k
2
and k
3
, respectively.
The resonance wavelengths k
0
, k
1
, k
2
, and k
3
can be attrib-
uted to RS (iii), while we will see in the following that this
attribution is really the case.
FIG. 2. Reflection spectra from K630-a160-t220-h(220-2200) grating. The h
value is annotated on the corresponding spectrum. The surface wave reso-
nance wavelengths are identified with k
0
, k
1
, k
2
, and k
3
if available.
043103-2 Vempati, Iqbal, and Afsheen J. Appl. Phys. 118, 043103 (2015)

To identify the origin of these SPP modes at the reso-
nance wavelengths k
0
, k
1
, k
2
, and k
3
, magnetic field
distributions (jMj) for h ¼ 220–2200 nm were shown in
Figs. 3(a)–3(d), respectively. The presence of the surface
wave can be seen for all 25 cases corresponding to the min-
ima in Fig. 2. From Fig. 3(a), it is clear that at 630 nm,
jMj related to the surface wave is distributed on Au/analyte
interfaces, which sustains for increasing the h value. It is
quite interesting to note that this behavior is similar for
other sets of surface waves, viz., k
1
, k
2
, and perhaps k
3
in
Figs. 3(b)–3(d), respectively. Significant changes in the
effective RI induce additional (k
1
, k
2
, and k
3
) sets of surface
wave modes on Au/analyte interface. As expected, all these
RSs red-shift with increasing h before saturation. Since k
1
,
k
2
, and k
3
are not integer multiples of k
0
, the possibility of
the former being higher order surface modes of the latter can
be ruled out. On the other hand, if the contrast between the
RI on either side of the grating is decreased, then the reso-
nance wavelengths of the two interfaces become comparable.
In this case, the magnitude of “asymmetry”
22
decreases and
the grating can be approximated to “symmetric”
20
-type,
which supports the SPPs at both the interfaces simultane-
ously. Under these circumstances, the SPPs on both the sides
can couple through the slits, provided a FP mode is available
within that wavelength range. This coupling creates two
degenerate SPP modes propagating all at once on both the
interfaces.
21
However, this is not the case here as we can see
from Fig. 3 that the surface wave mode exists only on Au/
analyte side for the given h values. In other words, this mode
does not exist on both the sides at once due to the lack of
coupling between the two interfaces, which is achieved by
depleting the FP mode within the wavelength range of inter-
est. To emphasize, FP mode within the slit is highly depend-
ent on the geometry (k ¼ 2t effective RI) of the single
slit
10
although the effective RI changes with h. Having said
that as the h increases further (>2200 nm), there is a
possibility that the FP mode may occur (due to the change in
the effective RI) and hence a coupling between the SPPs
on either side may be expected. Keeping this coupling aside,
it is convincing that the modes at k
0
, k
1
, k
2
, and k
3
are in
fact surface modes and exist on Au/analyte interface.
Furthermore, from Fig. 3, the wavelengths listed under k
0
and k
1
do not spectrally shift at higher h values. This
saturation-like behavior is discussed in the following.
The spectral location of the resonance wavelengths k
0
,
k
1
, k
2
, and k
3
against h were plotted in Fig. 4. The curves
were individually normalized with respect to the maximum
on both the axes. This double normalized plot clearly indi-
cated that the curves do not trace each other (not shown
here), which is nothing but a non-universal saturation behav-
ior. We treat this behavior as “non-universal” by given the
fact that all the modes are surface waves and expected
FIG. 3. False colored magnetic field
plots (6301100 nm
2
) from the gra-
ting K630-a160-t220-h(220-2200). k
0
,
k
1
, k
2
, and k
3
are the surface wave res-
onance wavelengths (in nm) with
respect to h shown in (a)–(d), respec-
tively. Same color scale is given for all
cases.
FIG. 4. Spectral position of surface wave resonance modes (k
0
, k
1
, k
2
, and
k
3
) from K630-a160-t220-h(220-2200) with varying h values. Single expo-
nential fit and their parameters were also shown for first three resonance
modes where R
2
0.99 for all fittings.
043103-3 Vempati, Iqbal, and Afsheen J. Appl. Phys. 118, 043103 (2015)

to respond universally to changes in the effective RI. The
saturation behavior resembles a single exponential type
(y ¼ y
0
þ A*exp( x/t)) and the fits are shown on Fig. 4 for
all cases, including the fit-output. Starting with the time con-
stants of the fits, they sharply increase, i.e., t
0
< t
1
< t
2
, where
t
0
,t
1
,t
2
are referred to k
0
, k
1
, and k
2
, respectively. It is inter-
esting to note that t
1
and t
2
are nearly twice and thrice that of
t
0
(within the error limits), respectively, and of course
require further investigation for clear understanding of this
relation. At the same time, k
1
, k
2
,and k
3
may not be the
higher order modes of k
0
. By considering the first two reso-
nance wavelengths in each set, the differential red-shifts
with respect to h are (dk/dh) 0.59, 0.23, and 0.09 for
k
0
, k
1
, and k
2
, respectively. Apparently, dk/dh may approach
zero for k
i
(i > 3) and h values exceeding 2200 nm, i.e., no
red-shift with increasing h, which essentially suggests two
plausible reasons. (1) No change in the effective RI with h
and, (2) the surface waves become insensitive. By given the
basic nature of effective RI,
31
it is possible to entangle these
two complex possibilities through a logical elimination-
approach. If (1) is true then k
1
, k
2
, and k
3
would not appear
and hence the possibility-(2) is the most likely factor. In
what follows is the discussion on the insensitivity of the sur-
face modes. From Fig. 4, it can be expected that for k
1
, k
2
,
and k
3
, the saturation will take place, however, at relatively
higher h values. Interestingly, despite being non-universal, the
y
0
of k
1
, k
2
,andk
3
will match to that of k
0
at a certain analyte
height, where the y
0
(825 nm) is the characteristic wave-
length of the present grating design. This characteristic wave-
length (y
0
) depends on the grating parameters, which were
optimized to suppress the FP modes while supporting the sur-
face waves within the wavelength range. Hence, for any of the
surface waves, the red-shift can be expected until this value is
approached. It is notable that insensitive”shouldbereferred
to the context where the effective RI introduces the second set
of surface waves not to the zero shift of plasmon resonance
with change in effective RI. Surface wave plasmon resonance
shifts with change in the effective RI.
CONCLUSIONS
It is known that the surface plasmons are quite sensitive to
the changes in the RI, so is the case with surface waves on 1D
asymmetric grating. These surface waves can be employed to
estimate the height of analyte as well, where the changes in the
effective RI are calibrated. Essentially, the resonance wave-
length red-shifts with increasing h value while after a certain h
value, new sets of surface waves emerge. As expected, the res-
onance wavelength of these new sets also red-shifts with h.
Notably, the red-shift saturates exponentially in all cases how-
ever, with different time constants, i.e., the surface waves
respond non-universally to the changes in the effective RI.
Although the saturation profiles were not universal, the y
0
values from the fitting may be equal to each other at much
higher h values. This might be a characteristic wavelength of
the present design. These modes stopped responding once the
characteristic wavelength is reached, i.e., 825 nm for the
present design. This wavelength depends on the grating param-
eters those were optimized to suppress the FP modes within
the wavelength range. Also, when a mode is at the onset of the
saturation (characteristic wavelength) k
0
(k
1
), the grating starts
to support k
1
(k
2
). On the other hand, t
1
and t
2
are nearly twice
and thrice that of t
0
, respectively, where k
1
, k
2
,andk
3
may be
not the higher order modes of k
0
. We believe that this study
not only provides new insights in designing the plasmonic sen-
sors but also has fundamental importance in the context of
behavior of plasmonic surface waves.
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043103-4 Vempati, Iqbal, and Afsheen J. Appl. Phys. 118, 043103 (2015)
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, a simple 1D grating device fabrication on ∼50nm gold (Au) film deposited on glass, which is employed as a high performance refractive index (RI) sensor by exploiting the surface plasmon polaritons (SPP) excited by the grating devices along the Au/analyte interface.
Abstract: We report a simple 1D grating device fabrication on ∼50 nm gold (Au) film deposited on glass, which is employed as a high performance refractive index (RI) sensor by exploiting the surface plasmon polaritons (SPP) excited by the grating device along the Au/analyte interface. A finite element analysis (FEA) method is employed to maximize the sensitivity of the sensor for a fixed period and thickness of a gold film and its close correspondence with experiment has given the insight for high sensitivity and enhanced transmission. Significantly, in the context of economic design and performance, it is shown that an optimally designed and fabricated 1D grating can be as sensitive as 524 nm/RIU (linearity RI = 1.33303 to 1.47399), which is remarkably higher than existing reports operating in a similar wavelength region.

43 citations


Cites background from "Non-universal behavior of leaky sur..."

  • ...The SPPs are sensitive to the small variations in the refractive index (RI) at the surface of the metal that supports themwhich is the basis formost of the biosensing applications [3, 4]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the effect of different gold grating structures on light absorption in solar cell was investigated by finite elemental analysis using COMSOL multiphysics-RF module, and it was deduced from the results that a grating device with slit width of 250-350nm is the most efficient which reveals the fact that such device offers intermediate scattering from the grating structure and supports fundamental plasmonic mode.
Abstract: Effect of different gold (Au) grating structures on light absorption in solar cell is investigated by finite elemental analysis using COMSOL multiphysics-RF module. The geometry of the solar cell consists of a 50-nm Au film on the substrate of amorphous silicon (a-Si). An optimum value of the slit width (w) of the Au grating has been obtained whereas periodicity of the grating structure remained the same. The periodicity in the grating device was chosen in such a way that the excitation of the surface plasmon polritons (SPPs) lies in the IR or NIR region where most of the spectrometers work well in practical life. Far-field transmission spectra were extracted from the grating device when illuminating with p-polarized light through the substrate side. Near-field plots of the Fano resonance (dip) associated with the excitation of the surface plasmon polritons (SPPs) were carefully examined to understand the underlying physics. It was deduced from the results that a grating device with slit width of 250–350 nm is the most efficient which reveals the fact that such device offers intermediate scattering from the grating structure and supports fundamental plasmonic mode. Hence, such devices absorb more light being most efficiently and find application in solar cell.

41 citations

Journal ArticleDOI
Tahir Iqbal1
TL;DR: In this paper, the propagation length of surface plasmon polaritons (SPPs) was investigated experimentally using a 1D metallic grating fabricated on a higher refractive index substrate (Gallium Phosphide, GaP).

31 citations

Journal ArticleDOI
TL;DR: In this article, the successful excitation of surface plasmon polaritons (SPPs) through 1D metallic grating on higher refractive index GaP substrate was investigated experimentally and numerically.
Abstract: This paper reports the successful excitation of surface plasmon polaritons (SPPs) through 1D metallic grating on higher refractive index GaP substrate. Coupling efficiency (η) of a free-space transverse-magnetic (TM) plane-wave mode into a SPP mode is crucial for many plasmonic devices. This η predominantly depends on the fabrication (milling) parameters and the factors (under- and over-milling) affecting the η is investigated experimentally and numerically. First of all, η is estimated by measuring the transmission spectra obtained through the plasmonic grating structures by varying the slit width (a) for a fixed period (Λ) and the thickness (t) of the gold (Au) film in which the grating is formed. The wave vector of the incident light is tuned to match the wave vector of the SPP, to get maximum η. For an optimum Au film thickness, a slit width of half of the periodicity of 770 nm in the grating device yields a maximum η. Such grating devices support only a fundamental plasmonic mode because the profile/shape of the slit in the grating device is more like a sinusoidal nature. Furthermore, such grating offers intermediate scattering to the incident light and the SPP as well which in-truns couple more incident energy to the SPPs. Moreover, over-milling results in decreased η where the crystalline plane of the substrate is disturbed. Finite element method (FEM) in COMSOL modeling is used to understand the underlying physics. This study is very useful for the development of the device application in real word.

27 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical model is proposed for the study of Transverse-electric (TE) surface plasmon polaritons (SPPs) in nonlinear multi-layer graphene-based waveguides.
Abstract: In this article, an analytical model is proposed for the study of Transverse-electric (TE) surface plasmon polaritons (SPPs) in nonlinear multi-layer graphene-based waveguides. Each graphene sheet has been located between two different Kerr-type layers. As special cases of the general, proposed structure, two new nonlinear graphene-based waveguides are introduced and investigated in this paper. The obtained results show that the propagation properties of these exemplary structures are adjustable via chemical potential and nonlinear coefficients. A large value of the effective index, i.e. neff=82 is obtained for the chemical potential of 0.15 ev and the nonlinear ratio of 0.8 for the second structure at the frequency of 61 THz. The presented study suggests a novel platform in graphene plasmonics, which can be used for the design of innovative THz devices.

20 citations

References
More filters
Journal ArticleDOI
TL;DR: This paper introduces the localized surface plasmon resonance (LSPR) sensor and describes how its exquisite sensitivity to size, shape and environment can be harnessed to detect molecular binding events and changes in molecular conformation.
Abstract: Recent developments have greatly improved the sensitivity of optical sensors based on metal nanoparticle arrays and single nanoparticles. We introduce the localized surface plasmon resonance (LSPR) sensor and describe how its exquisite sensitivity to size, shape and environment can be harnessed to detect molecular binding events and changes in molecular conformation. We then describe recent progress in three areas representing the most significant challenges: pushing sensitivity towards the single-molecule detection limit, combining LSPR with complementary molecular identification techniques such as surface-enhanced Raman spectroscopy, and practical development of sensors and instrumentation for routine use and high-throughput detection. This review highlights several exceptionally promising research directions and discusses how diverse applications of plasmonic nanoparticles can be integrated in the near future.

6,352 citations

Journal ArticleDOI
TL;DR: In this paper, it has been shown that the non-radiative mode excited by light can also radiate under certain conditions if they are excited by electrons (grazing incidence of electrons on a rough surface or at normal incidence on a grating).
Abstract: There are two modes of surface plasma waves: 1) Non-radiative modes with phase velocities Cü/k smaller than the velocity of light c. They cannot decay into photons in general. 2) Radiative modes with (o/k > c which couple directly with photons 1. The following paper is concerned with the excitation of these modes by light and their decay into photons. It has been shown that the radiative mode on thin silverand potassium-films can be excited by light and that the mode reradiates light almost into all directions with an intensity maximum at the plasma frequency cOp 2. It had been further observed that the non-radiative modes radiate under certain conditions if they are excited by electrons (grazing incidence of electrons on . a rough surface3 or at normal incidence on a grating 4) . The mechanism of this emission is in these cases always the same: The \"wave vector\" of the roughness of the surface or its irregularity changes the plasmon wave vector k so that a) in the case of the radiative mode light emission is found in directions in addition to that of reflexion and transmission, b) in the case of the non-radiative mode its wave vector is reduced so that the condition /c0, the wave vector of the inhomogeneous wave is (co/c) • Vsq' sin 0O (fq = 2.16 for quartz) and thus can excite a non radiative mode on the boundary of the prism for j/fq sin 0O > 1 or 90° > @o > 43°. If one vaporises a silver film directly on the quartz surface the inhomogeneous light wave penetrates into the silver film and excites a nonradiative mode on the boundary silver/air. The excitation will be highest for those frequencies which fulfill the dispersion relation of these surface plasmons.

2,790 citations

Journal ArticleDOI
TL;DR: The surface plasmon resonance (SPR) is a new optical technique in the field of chemical sensing as discussed by the authors, which can be used for gas detection, together with results from exploratory experiments with relevance to biosensing.

2,243 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films, and the physical mechanisms operating in the different structures considered are analyzed within a common theoretical framework.
Abstract: This review provides a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical transmission in periodic hole arrays, discovered over a decade ago. It is shown that surface electromagnetic modes play a key role in the emergence of the resonant transmission. These modes are also shown to be at the root of both the enhanced transmission and beaming of light found in single apertures surrounded by periodic corrugations. This review describes both the theoretical and experimental aspects of the subject. For clarity, the physical mechanisms operating in the different structures considered are analyzed within a common theoretical framework. Several applications based on the transmission properties of subwavelength apertures are also addressed.

1,160 citations

Journal ArticleDOI
TL;DR: A theoretical and experimental investigation of the possibilities of using surface plasmon resonance for gas detection is presented in this paper, where an organic layer that reversibly absorbs the anaesthetic gas halothane is used.

743 citations

Frequently Asked Questions (17)
Q1. What have the authors contributed in "Non-universal behavior of leaky surface waves in a one dimensional asymmetric plasmonic grating" ?

In this paper, the surface plasmon polaritons ( SPPs ) on 1D asymmetric grating on Si substrate were analyzed. 

Due to the asymmetry,22 the resonance modes seen in the reflection spectra are highly dependent on the contrast of RI of the (two) surrounding media (i.e., analyte and Si). 

the resonance wavelength red-shifts with increasing h value while after a certain h value, new sets of surface waves emerge. 

3,4,13,18 Among the various types, grating structure can be compact and robust, which are desirable characteristics for integration into other devices6 apart from the tunability of the spectral response through geometrical parameters. 

Having said that as the h increases further (>2200 nm), there is apossibility that the FP mode may occur (due to the change in the effective RI) and hence a coupling between the SPPs on either side may be expected. 

To emphasize, FP mode within the slit is highly dependent on the geometry (k¼ 2t effective RI) of the single slit10 although the effective RI changes with h. 

A metal grating surrounded by a dielectric medium supports three resonant states (RS), which can be identified in a reflection spectrum. 

RS (iii) are bound to the surface of the grating however, can generate a leaky mode by coupling through the slits depending on the availability of a FP-like cavity mode.10 Essentially, for wavelengths close to K, the reflection minimum of 1D grating follows the dispersion relation of bound surface waves. 

These surface waves become leaky for k< 2K where their dispersion is determined by the geometrical parameters andthe finite conductivity29 of the metal. 

These RS are (i) waveguide formed within the metal strips (broad band resonance, metal-insulator-metal structure),10 similar to FP cavity mode, (ii) propagating SPPs, and (iii) involve the whole grating periodicity depending on the availability of FP cavity modes. 

On the other hand, because of the asymmetry, SPP modes are excited at the input and output interfaces in addition to FP cavity modes. 

the red-shift saturates exponentially in all cases however, with different time constants, i.e., the surface waves respond non-universally to the changes in the effective RI. 

In other words, this mode does not exist on both the sides at once due to the lack of coupling between the two interfaces, which is achieved by depleting the FP mode within the wavelength range of interest. 

The source-field and the reflection in the far-field were at a distance of 1500 nm and 1000 nm when measured from the top of the analyte, respectively. 

This characteristic wavelength (y0) depends on the grating parameters, which were optimized to suppress the FP modes while supporting the surface waves within the wavelength range. 

dk/dh may approach zero for ki (i> 3) and h values exceeding 2200 nm, i.e., no red-shift with increasing h, which essentially suggests two plausible reasons. 

By considering the first two resonance wavelengths in each set, the differential red-shifts with respect to h are (dk/dh) 0.59, 0.23, and 0.09 for k0, k1, and k2, respectively.