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

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

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

) and the mode

profile at z = 30 nm of the input SPP mode. The upper

and lower E

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

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

distribution at output 1. Figure 3(b)

shows the mode profile at z = 30 nm in output 1. Figu-

Figure 2: (a) E

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

distribution in output 1, (b) mode

profile at z = 30 nm and (c) E

distribution in output 2.

re 3(c) shows the E

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

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

component

of the TM polarized light. Figure 4(c) shows the E

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

Figure 4: The output mode characteristics when the TM

polarized light is launched to the dielectric channel

waveguide with no strip: (a) E

distribution in output 1, (b)

mode profile at z = 30 nm and (c) E

distribution in output

Figure 5: The output mode characteristics when the TE

polarized light is launched to the dielectric channel

waveguide with no strip: (a) E

distribution in output 1, (b)

mode profiles at z = ± 30 nm and (c) E

distribution in output

Figure 5(a) shows the E

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

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

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

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

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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