Analysis of Surface Plasmon-Polariton Modes with Metallic
Structures and Polarized Light across Gapped Plasmonic
Waveguides
Guhwan Kim, Sung-Ryoung Koo and Myung-Hyun Lee
*
Department of Electrical and Computer Engineering, Sungkyunkwan University, Suwon, 16419, South Korea
Keywords: Surface Plasmon Polariton, Plasmonic Waveguide, Plasmonic Signal.
Abstract: We analyzed output Surface Plasmon-Polariton (SPP) modes with gold structures in a gap when polarized
light propagated across Gapped SPP Waveguides (G-SPPWs). The G-SPPWs consist of input and output
insulator-metal-insulator typed SPPWs with a gap. The dielectric channel waveguide is laid across the gap.
Gold was used as the metal of the SPPWs. Low loss polymers were used as the upper and lower cladding
layers and the core of the dielectric channel waveguide, respectively. The input SPP mode intersects at the
gap with the polarized light launched to the dielectric channel waveguide. When the TE polarized light is
applied, lossy short-range SPP (SRSPP) modes are overlapped in the output SPPW. For the TM polarized
light, the output SPP mode has low loss though there are mode fluctuations. When horizontal and vertical
gold strips are placed in the gap and the TE polarized light is applied, the propagation loss increases
significantly depending on the shape of the gold strips due to TE-induced symmetric surface charges. Inverted
plasmonic signals can be generated from optical signals by the SPP modulation using excited SRSPP modes.
The modulation efficiency can be increased by introducing photonic crystal or plasmonic resonance in the
gap.
1 INTRODUCTION
To accommodate the ever-increasing amount of data
traffic, dielectric-based photonic devices have been
introduced owing to the tremendous data carrying
capacity and far faster-operating speed than
electronic devices. However, it is hard to integrate
relatively large photonic devices and nano-scaled
electronic devices on the same dimension due to the
fact that the scale of the dielectric photonic devices is
limited to about half of the wavelength by the
diffraction limit of light. Plasmonics can offer a
solution to the operating speed limitation in
electronics and the size limitation in photonics.
Surface Plasmon-Polaritons (SPPs) are TM
polarized electromagnetic waves coupled to
oscillations of electron plasma in a metal, propagating
along the interface between two media with positive
and negative permittivity, respectively. A thin metal
film of finite width surrounded by a homogeneous
dielectric can be used as a plasmonic waveguide
supporting long-range SPP (LRSPP) which has low
propagation loss and compatibility with the
conventional photonic devices. Various plasmonic
devices based on waveguides have been researched
and plasmonic modulators also have been studied.
Such devices can be used as a component in
plasmonic integrated circuits.
The tunneling property of SPP across an
interruption in Insulator-Metal-Insulator (IMI) typed
slab waveguides embedded in a dielectric medium is
investigated and discontinuous SPP waveguides with
a gap (G-SPPWs) are suggested and demonstrated to
control the guided SPP with external energy
conveniently. The optimum structure for G-SPPWs in
terms of the coupling and propagation losses are also
researched.
Some research groups have presented the method
of manipulating SPP using the control of free
electrons inside a metal, e.g. electric current and
magneto-optical effect. In this paper, we analyzed
output SPP modes affected by polarized light across
the gap in order to clarify the experimental
observation which plasmonic signals are invertedly
copied from an optical signal. The SPP mode
characteristics and the propagation loss in the output
SPPW were calculated with the G-SPPW and the
dielectric channel waveguide for various cases
180
Kim, G., Koo, S. and Lee, M.
Analysis of Surface Plasmon-Polariton Modes with Metallic Str uctures and Polarized Light across Gapped Plasmonic Waveguides.
DOI: 10.5220/0009353201800184
In Proceedings of the 8th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2020), pages 180-184
ISBN: 978-989-758-401-5; ISSN: 2184-4364
Copyright
c
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
according to the polarization and the shape of the
inserted metal strips.
The rest of this paper is organized as follows. First,
we describe the design and simulation details for the
mode analysis in Section 2. Section 3 presents the
simulation results and discussion. In section 4, the
conclusions are provided.
2 DESIGN AND SIMULATION
DETAILS
Figure 1(a) shows the schematic diagram of a G-
SPPW and a dielectric channel waveguide across the
gap. The G-SPPW consists of the input and output
IMI typed SPPWs with a gap. The gap length is set to
be 8 μm since the coupling loss at the output SPPW
begin to increase rapidly when the length is over 8
μm. The dielectric channel waveguide is laid across
the gap and polarized light is launched to the
dielectric channel waveguide. Gold was used as the
metal of the SPPWs with 4 μm width and 20 nm
thickness. The lengths of the input and output SPPWs
are 10 μm and 14 μm, respectively. Low loss
polymers were used as the 30 μm-thick upper and
lower dielectric cladding layers and the core of the
dielectric channel waveguide with 10 x 6 μm
2
cross-
section, respectively. Figure 1(b) and (c) show
schematic views from the x-y plane of horizontal and
vertical gold strips in the gap. The horizontal strips,
spaced about 1 μm, consist of two gold strips with 1
μm wid-
Figure 1: Schematic diagrams of simulated (a) G-SPPWs
and dielectric channel waveguide and inserted 20 nm thick-
(b) horizontal and (c) vertical gold strips.
th, 20 nm thickness and 6 μm length. The vertical
strips, evenly spaced about 1.5 μm, consist of three
gold strips with 1 μm width, 20 nm thickness and 4
μm length. The refractive indices of the gold for the
SPPWs, the low loss polymer for the clad and the low
loss polymer for the core are 0.550-11.4912i, 1.450
and 1.460 at a wavelength of 1.55 μm, respectively.
We used FDTD of Lumerical Inc. to solve
Maxwell’s equations in finite-difference time-domain
method and calculated the SPP mode characteristics
at the wavelength of 1.55 μm for optical
communication applications. In the simulation, the
mode source was used to excite a fundamental
LRSPP mode in the input SPPW. The fundamental
TE or TM mode source were used in the dielectric
channel waveguide with the length of 28 μm. The SPP
and polarized light intersect at the center of the gap.
Perfectly matched layers were used in the 3-
dimensional simulation space as a boundary
condition to absorb electromagnetic waves incident to
the layers, reducing unwanted reflection at the layers.
To analyze the SPP mode characteristics in the output
SPPW, we put two frequency-domain field monitors
that collect the field profile across x = 8 μm (output
1) and 18 μm (output 2) plane, respectively.
3 RESULTS AND DISCUSSION
Figure 2(a) and (b) show the spatial distribution of the
normal electric field component (E
z
) and the mode
profile at z = 30 nm of the input SPP mode. The upper
and lower E
z
distributions are spatially symmetric
with respect to the z-axis as shown in Figure 2(a). The
normal electric field component develops an
extremum at the center of the top and bottom
interfaces and the mode profile is very similar to that
of the long-range ss
b
0
mode, which indicates the
fundamental LRSPP mode was excited in the input
SPPW.
We calculated the output SPP mode without strip
when polarized light wasn’t launched. Figure 3(a)
shows the E
z
distribution at output 1. Figure 3(b)
shows the mode profile at z = 30 nm in output 1. Figu-
Figure 2: (a) E
z
distribution and (b) mode profile at z = 30
nm of the input SPP mode.
Analysis of Surface Plasmon-Polariton Modes with Metallic Structures and Polarized Light across Gapped Plasmonic Waveguides
181
Figure 3: The output mode characteristics when polarized
light isn’t launched to the dielectric channel waveguide
with no strip: (a) E
z
distribution in output 1, (b) mode
profile at z = 30 nm and (c) E
z
distribution in output 2.
re 3(c) shows the E
z
distribution at output 2. The SPP
mode at output 1 is symmetric as shown in Figure 3(a)
and the mode profile is also similar to that of the input
SPP mode in Figure 2(a). As shown in Figure 3(c),
the output SPP mode is maintained as it propagates
along the output SPPW, which means that although
there is a dielectric gap between the input and output
SPPWs, the LRSPP is excited again in the output
SPPW after the input SPP mode jumps over the gap.
Figure 4 shows the output SPP mode
characteristics when SPP and TM polarized light
propagate simultaneously along G-SPPWs without
strip and the dielectric channel waveguide,
respectively. Figure 4(a) shows the E
z
distribution at
output 1. Figure 4(b) shows the SPP mode profile at z
= 30 nm (red line) in output 1. The black line
represents the output SPP mode when the TM
polarized light wasn’t launched to the dielectric
channel waveguide. The top and bottom output SPP
modes are symmetric as shown in Figure 4(a) and
there are mode fluctuations due to the E
z
component
of the TM polarized light. Figure 4(c) shows the E
z
distribution at output 2 and indicates the fluctuating
output SPP mode is stabilized as it propagates in the
output SPPW.
Figure 5 shows the SPP mode characteristics at
output 1 and 2 when SPP and TE polarized light
propagate simultaneously along G-SPPWs without
strip and the dielectric channel waveguide,
respectively. The output SPP mode is affected by the
TE polarized light even though the electric field of the
TE polarized light oscillates along the x-axis and
doesn’t have the normal electric field component (E
z
).
Figure 4: The output mode characteristics when the TM
polarized light is launched to the dielectric channel
waveguide with no strip: (a) E
z
distribution in output 1, (b)
mode profile at z = 30 nm and (c) E
z
distribution in output
2.
Figure 5: The output mode characteristics when the TE
polarized light is launched to the dielectric channel
waveguide with no strip: (a) E
z
distribution in output 1, (b)
mode profiles at z = ± 30 nm and (c) E
z
distribution in output
2.
Figure 5(a) shows the E
z
distribution at output 1.
Figure 5(b) shows the SPP mode profiles at z = ± 30
nm (red and blue lines) in output 1. Top and bottom
SPP modes (red and blue lines) are asymmetric and
the intensity differences from the black line are
opposite to each other, which denotes that the output
SPP mode contains asymmetric short-range SPP
(SRSPP) modes as well as the fundamental LRSPP
mode. The electric field of SRSPP mode has a quite
large loss because the fields are confined mainly into
the metal and induces symmetric surface charge
densities at top and bottom interfaces. The
propagation length of SRSPP is limited to few
microns. On the other hand, LRSPP mode has a low
propagation loss and induces antisymmetric surface
charge density at top and bottom interfaces, which is
well matched with the absorption tendency of
metallic nanoparticles according to the surface charge
distribution. Figure 5(c) shows the E
z
distribution at
output 2 after 10 µm propagation from output 1. It is
noticeable that the output SPP mode becomes the
fundamental LRSPP mode again as it propagates in
the output SPPW.
We also put horizontal and vertical gold strips in
the gap to analyze whether metal structures inserted
in the gap affect the output SPP mode. For the TM
polarized light, there is no remarkable difference in
the result of the case where the gold strips are not
inserted, which reveals that SPP doesn’t interact with
TM polarized light which brings out antisymmetric
surface charges like LRSPP. But for the TE polarized
Figure 6: The output mode characteristics when the TE
polarized light is launched to the dielectric channel
waveguide with horizontal strips: (a) E
z
distribution in
output 1, (b) mode profiles at z = ± 30 nm.
PHOTOPTICS 2020 - 8th International Conference on Photonics, Optics and Laser Technology
182
Figure 7: The output mode characteristics when the TE
polarized light is launched to the dielectric channel
waveguide with vertical strips: (a) E
z
distribution in output
1, (b) mode profiles at z = ± 30.
light, the output SPP mode profile is slightly different
depending on the shape of gold strips. Figure 6 and 7
show the E
z
distribution and mode profiles of the
output SPP mode in output 1 when horizontal and
vertical gold strips are inserted in the gap,
respectively. The main difference between the two
SPP mode profiles occurs near right and left edges (y
= ± 2 µm). For vertical strips, the top and bottom
intensity differences from the black line are obviously
larger than that of horizontal strips, which indicates
that the electric field of the output SPP mode is more
concentrated to the corner of the output SPPW than
when horizontal strips are put in the gap. The fact that
the more electric field of an SPP mode is concentrated
at the corners represents the electric fields are highly
confined inside the metal and fields at top and bottom
interfaces are coupled weakly, resulting in a higher
propagation loss.
To investigate the propagation characteristics of
the output SPP mode for each simulated case, we
calculated the propagation losses during 10 µm
propagation from output 1 to output 2. As shown in
Figure 8, when polarized light isn’t launched without
strip, the SPP mode propagates in the output SPPW
with low attenuation of 0.0235 dB since the input SPP
mode tunnels the gap and the LRSPP mode is re-
excited in the output SPPW. The loss of the output
SPP mode when the TM polarized light is launched
to the dielectric waveguide with no strip is 0.0245 dB
and very similar to that of the LRSPP, which signifies
the LRSPP mode is maintained in the output SPPW
without forming lossy SPP modes although there are
mode fluctuations. The output SPP mode when the
TE polarized light is applied without strip has a larger
propagation loss of 0.0313 dB than the previous two
cases. The difference in propagation loss arises from
the radiation of higher-order SPP modes. Even
though the gold strips are inserted into the gap, the
loss is very similar to that of the LRSPP mode when
the TM polarized light is applied. The loss increases
when gold strips are put in the gap and the TE
Figure 8: Comparison of the loss during 10 µm propagation
from output 1 to output 2 for each case.
polarized light is launched to the dielectric channel
waveguide. Especially when vertical strips are placed
in the gap rather than horizontal strips, the loss
increases significantly since the electric fields
concentrated to the corners of output SPPW are
confined inside the gold SPPW more, such SPP
modes have a large propagation loss. The propagation
losses when vertical and horizontal strips are put in
the gap are 0.0638 and 0.0436 dB, respectively.
Only when the TE polarized light is launched to
the dielectric channel waveguide, asymmetric higher-
order SPP modes are excited and the propagation loss
increases in the output SPPW, which implies that the
TE polarized light across the gap can modulate the
amplitude of SPP waves. As previous studies have
shown, propagating SPP can be manipulated via the
control of free electrons in the metal. The propagation
loss of the output SPP mode increases since the
surface charges induced by TE polarized light is
symmetric with respect to the z-axis. When the
metallic structures are put in the gap, the propagation
loss in the output SPPW increases remarkably
depending on the shape of the metallic structures as
shown in Figure 8. Compared with horizontal strips,
vertical strips have the more edges at which a
polarized light induce surface charges. As symmetric
surface charges are induced at metallic edges more,
output SPP mode has more propagation loss. Given
these results, TE polarized optical signals applied to
the gap can invertedly generate modulated plasmonic
signals from optical signals. Introducing metallic
structures such as a photonic crystal in the gap will
make the modulation depth much larger, resulting in
a lowered modulating power.
4 CONCLUSIONS
We analyzed output SPP modes with the shape of
gold structures inserted in the gap when polarized
Analysis of Surface Plasmon-Polariton Modes with Metallic Structures and Polarized Light across Gapped Plasmonic Waveguides
183
light is launched to the dielectric channel waveguide
laid across the gap. There is no significant effect on the
output SPP mode when the TM polarized light is
launched to the dielectric channel waveguide. Only
when the TE polarized light is applied, lossy higher-
order SPP modes are excited in the output SPP mode
and the propagation loss increases remarkably
depending on the shape of the gold strips, which
suggests that modulating guided SPP mode is possible
using the excited higher-order SPP modes. These
phenomena can be applied to plasmonic signal
generator in which plasmonic signals are invertedly
generated from optical signals. Introducing metallic
structures such as a photonic crystal in the gap will
increase the modulation efficiency when plasmonic
signals are copied from optical signals in the G-
SPPWs.
ACKNOWLEDGEMENTS
This work was supported by the National Research
Foundation of Korea (NRF) grant funded by the Korea
government (MSIP) (No. NRF-2017R1A2B2009128).
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