Proceedings of the International Electrical Engineering Congress 2014

A Comparative Study of Dielectric Materials as Nano-plasmonic Couplers

Md. Ghulam Saber and Rakibul Hasan Sagor Department of Electrical and Electronic Engineering

Islamic University of Technology

Board Bazar, Gazipur 1704, Bangladesh

Email: gsaber@iut-dhaka.edu, sagor@iut-dhaka.edu

Abstract-We present a novel ultra-compact nano-plasmonic coupler using aluminum gallium arsenide (AIGaAs) and silicon­germanium alloy (Si-Ge) as the coupling dielectric materials. The performance of these two materials has been analyzed using the finite-difference time-domain (FDTD) method. The parameters that we have analyzed are coupling efficiency, reflection coeffi­cient, return loss and mismatch loss. At telecom wavelength an efficiency of 51 % has been achieved when AIGaAs is used as the dielectric while for Si-Ge it is 48%. The presented structure also provides advantage in the fabrication process since it is a rectangular shaped waveguide having no tapering. The coupler can operate at a broad range of input signal wavelengths.

Index Terms-Surface-plasmon-polariton; plasmonic coupler; optical communication; plasmonics.

I. INTRODUCTION

The information processing speed has seen tremendous

growth in the last few decades due to the scaling down of

the electronic devices. But the researchers are facing major

difficulties in achieving speed over a few ten of GHz using

the scaling approach in micro and nano-electronics. This is

due to the limitations from RC delay and power consumption

in the devices. Photonics based devices, on the other hand,

offer bandwidth in the THz range but cannot be scaled

down to the size of a present day computer chip due to

diffraction limit of light. The difference in physical dimensions

of electronic and photonic devices creates an incompatibility

between them. Plasmonics bridge the high bandwidth pho­

tonic circuits with the nanometer scale electronic circuits by

coupling the energy of photon with free electrons, generating

a deep sub-wavelength mode known as Surface Plasmon

Polariton (SPP). The birth of plasmonics and transformation

optics are paving the way for a family of novel devices

with unprecedented features such as plasmonic nano-antennas

[1], [2], sub-wavelength waveguides [3] [4], superlenses [5]

[6], light concentrators [7], and hyperlenses [8]. SPP can

propagate at the deep sub-wavelength scale which makes it

a potential candidate for the nanoscale plasmonic-electronic

hybrid integrated circuits. It is being predicted that SPP based

integrated photonic devices will be able to transfer signals at

optical data rate through sub-wavelength channels. Therefore,

plasmonic-electronic hybrid ICs hold promise for potential

application in the field of optical communication.

Since SPPs are generated from the collective oscillations

of free charges when an electromagnetic field is applied,

978-1-4799-3174-3114/$3l.00 ©2014lEEE

plasmonic waveguides require metals which have abundance

of free electrons. However, metals are blighted by losses in the

optical range due to interband electronic transitions. Even the

best conductors suffer from huge losses at the visible and near

infrared region of electromagnetic spectrum [9]. These losses

degrade the performance of the plasmonic devices limiting the

possibility of many applications. The metal-dielectric-metal

configuration of the plasmonic waveguide is advantaged by

high confinement, which allows deep sub-wavelength integra­

tion. However, the losses are higher than other configurations

due to larger overlap of the field with the metallic layers.

One possible solution of this problem is to use both dielectric

waveguide and plasmonic waveguide in the same chip. The di­

electric waveguide will carry the optical mode from the source

and couple it to the plasmonic waveguide and the plasmonic

waveguide will address the nano-scale optoelectronic devices.

However, this requires efficient coupling of the optical mode

to the plasmonic waveguide.

In the past years several researchers have proposed different

coupling techniques. P. Ginzburg et al. [10] reported a ..\/4 coupler to couple optical modes from a 0.5 11m to 50 nm wide

plasmonic waveguide. D. Pile et al. [II] presented an adiabatic

and a non-adiabatic tapered plasmonic coupler. R. Wahsheh

[12] reported an analysis on nanoplasmonic air-slot coupler

and its fabrication steps. G. Veronis et al. [13] proposed a

coupler with multi-section tappers.

Herein, we present a novel ultra-compact nano-plasmonic

coupler using AlGaAs and Si-Ge as the dielectric materials. A

two dimensional simulation model has been developed based

on FDTD method [14] to analyze the proposed structure.

We have achieved a coupling efficiency of 51 % for AIGaAs

and 48% for Si-Ge at the te1ecom wavelength. The coupler

is rectangular in shape and has a flat end terminal which

makes it easier to fabricate. We have determined the reflection

coefficient, return loss and mismatch loss in order to analyze

the performance of the structure for different input signal

wavelengths.

II. CHOICE OF MATERIAL AND STRUCTURE

FORMULATIONS

A. Choice of Material

The most dominant loss occurs in plasmonic waveguides is

due to the interband electronic transitions of the constituent

materials at optical frequencies. Interband transItIOn occurs

when electrons jump to empty higher energy levels due to en­

ergy absorption from incident photons. In dielectric materials,

the valence band electrons absorb photon energy and jump to

the conduction band which results in loss. In order to reduce

the interband transition losses, materials with large bandgap

should be used. The bandgap of AIGaAs varies between 1.42

e V and 2.16 e V while for Si-Ge it varies between 1.12 e V

and 0.67 eV by changing the alloy composition. Since both

of the materials have large bandgaps, the interband transition

losses are negligible.

B. Structure Formulations

The simulation model we have developed is based on the

FDTD method [14]. We have utilized the general auxiliary dif­

ferential equation (AD E) based FDTD [15] approach in order

to incorporate the frequency dependent dispersion properties

of the constituent materials. This algorithm is useful for the

simulation of materials with different dispersion properties.

The perfectly matched layer [16] has been integrated at all

the boundaries in order to prevent back reflections.

Considering the material dispersion, the frequency­

dependent electric flux density can be given as

D(w) = cQcooE(w) + P(w) (I)

The general Lorentz model is given by

a P(w) = b+jcw_dw2E(w) (2)

which can be written in time-domain through inverse Fourier

transform as

bP(t) + cP'(t) + dP"(t) = aE(t) (3)

The FDTD solution for the first order polarization of Eq.

(3) can be expressed as

pn+l = G1pn + G2pn-1 + G3En (4)

h G 4d-2bl!.t2 G -2d-cl!.t G 2al!.t2 w ere, 1 = 2d+cl!.t ' 2 = 2d+cl!.t ' 3 = 2d+cl!.t

The values of G1, G2 and G3 depend on the material under

consideration. Finally the electric field intensity becomes,

N Dn+l _ � P in+1

En+ 1 = ___ ---=-i=---=--I __ (5)

where, N is the number of poles and Dn+1 is the update value

of the electric flux density calculated using FDTD algorithm.

III. METHODOLOGY OF ANALYSIS

The proposed coupling structure is given in Fig. l. The

thickness of air is taken as 60 nm with metallic layers on its

top and bottom having thickness of 500 nm each. The length

of the dielectric waveguide is 2.5 f-Lm while the length of the

plasmonic waveguide is 6 f-LTn . A TM polarized Gaussian pulse has been used as the optical

source. The dielectric waveguide will carry the fundamental

Metal

ty o Dielectric T-y

Air

t 500nm

! 60nm

•

t 500nm Metal

,

Fig. I. Schematic Diagram of the proposed coupler used for simulation.

optical mode up to 2.5 f-Lm and couple it to the plasmonic

waveguide. We have used input signal wavelengths ranging

from 400 nm to 2000 nm. The material modeling parameters

have been obtained from different published results. For AI­

GaAs, we have utilized the parameters obtained by Alsunaidi

et at. [17] while for Si-Ge, we have used the parameters

reported by M.G. Saber et al. [18].

In order to get accurate results and maintain the courant

stability criteria [19] we have taken box = 2 nm, boy = 2 nm and the time step as bot = 0.95 . c-1 . [� + �] -1

. We have defined the coupling efficiency as the ratio of the

transmitted power into the MDM waveguide to the incident

power in the input dielectric waveguide. The incident power of

the optical mode has been measured right before the interface

between dielectric and MDM waveguide and the transmitted

power has been measured right after the interface.

The reflection coefficient, return loss and mismatch loss

have also been determined in order to analyze the performance

of the coupler. The method we have used for calculating

reflection coefficient is as follows. First an optical mode has

been incident in the dielectric waveguide when there is no

plasmonic waveguide. The value of the electric field is then

recorded at one point. This represents the value of the incident

wave. Then the same thing has been done with the plasmonic

waveguide. This time the electric field represents the value

of the incident wave along with the reflected wave since

some part of the incident wave will be reflected by the MDM

waveguide due to the difference in dispersion properties of the

materials. Therefore, we can calculate the reflected wave by

subtracting the incident wave from this value. The reflection

coefficient is then calculated by taking the maximum of the

ratio of the reflected wave to the incident wave. This has been

done for all the input signal wavelengths for which we have

run the simulation. After determining the reflection coefficient,

we have determined the return loss and mismatch loss from it

using analytical formulas.

IV. RESULTS AND DISCUSSIONS

The proposed coupler has been characterized with several

figure of merits which are, coupling efficiency, reflection coef­

ficient, return loss and mismatch loss. The coupling efficiency

.' .'

.' "" _ .. .. ..

••........

.. " .

,"

en ••• - •• ••••• �--

� 40 .. + :::J o

u 35

30 500 1000 1500 2000 Wavelength (nm)

CI) CI) o

80

.....J 40·· .... c +. � .

(a)

:::J • (j) -........ ........ .II •• 0:: 20- ".

'. ' . . . .

o 500 . .

1000 1500 Wavelength (nm)

(c)

" 'AIGaAs

-SiGe

2000

Q) 1 •• 'AIGaAs "0

E -SiGe §,0.8 ctl ::2; � 0.6 '0 tt 80.4 c o :g 0.2

., · . · . · . · . · . · . · . : . · · · · · · · · · . Q)

'$ 0::

o 500 ....

•••...•.......•• 1000 1500

Wavelength (nm)

(b)

· · · · · · · · · · ... ..... 2000

40 "'AIGaAs

-SiGe

� 30 CI) CI) o --I "520 ro E CI) � 10

o 500 1000 1500 Wavelength (nm)

(d)

2000

Fig. 2. (al Coupling efficiency as a function of wavelength. (b) Reflection coefficient as a function of wavelength. (cl Return loss as a function of wavelength. (d) Mismatch loss as a function of wavelength.

as a function of wavelength has been presented in Fig. 2a.

From the figure, it can be observed that for AIGaAs the

coupling efficiency keeps on increasing as we increase the

input signal wavelength with a valley at 800 nm. AIGaAs

offers higher efficiency than Si-Ge at all wavelengths except

800 nm. On the other hand, the coupling efficiency for SiGe

keeps on varying with increasing input signal wavelength with

peak at 1400 nm. The telecom wavelength is of our particular

interest since the lasers used in optical communication are

mostly of 1550 nm wavelength. At this wavelength the

coupling efficiency for AIGaAs is 51 % and for Si-Ge is 48%.

The reflection coefficients of the coupling structure for dif­

ferent wavelengths have been determined numerically which

are presented in Fig. 2b. For AIGaAs, the reflection coeffi­

cient has a peak value of 0.8 at 1550 nm while for other

wavelengths it is mostly around 0.1. In case of Si-Ge, the

reflection coefficient for wavelengths up to 1550 nm is close

to zero, however, it has a peak value of 0.98 at 1750 nm. After

the peak value, the reflection coefficient magnitude again starts

decreasing.

From the numerically determined reflection coefficient, we

have determined the return loss and mismatch loss using the

analytical equations which are given in Fig. 2c and Fig. 2d.

From the Fig. 2c, it can be observed that for both AIGaAs

and Si-Ge, the highest return loss occurs at 400 nm having

values 64 dB and 42 dB respectively. With the increasing

wavelength, the return loss keeps on varying for both the

materials. The lowest return loss occurs at 1550 nm for

AIGaAs and at 1750 nm for Si-Ge.

Mismatch loss indicates the amount of power wasted in

a system due to impedance mismatch or reflections where

discontinuity of material or geometry is present. Since our

proposed coupler has a discontinuity of both shape and ma­

terial at the point of coupling, mismatch loss is an important

parameter for characterizing the coupler. In Fig. 2d, we can

observe that the highest mismatch loss occurs at 1550 nm for

AIGaAs having a value of 10 dB whereas for Si-Ge it occurs

at 1750 nm with a value of 32 dB. Therefore, the performance

of the couplers will degrade significantly if we operate them

at these two particular wavelengths.

The electric field distribution inside the coupling structure

is provided in Fig. 3. The dielectric waveguide is carrying the

optical mode up to 2.5 p,m and coupling it to the plasmonic

waveguide. From the colormap of the figure, it is understood

that the field intensity is higher in the dielectric waveguide

than the plasmonic waveguide. Besides, due to higher losses

in the metallic layer the field intensity decays if one goes into

the top and bottom metallic layers from the dielectric region

of the plasmonic waveguide.

E .s 1: Ol ill J:

2.65 5.3 7.95 Distance (micrometer)

Fig. 3. Electric field distribution inside the coupler.

The air-slot coupler proposed by Rami A. Wahsheh et at. [l2l offers a theoretical efficiency of 50%. On the other hand,

our proposed coupler using AIGaAs exhibits an efficiency of

51 % and for the coupler with Si-Ge, the value is 48%. The

coupling efficiency can be further increased if we use multi­

section tapering for impedance matching. Though in case of

Si-Ge the efficiency is a little less than the coupler proposed

by Rami A. Wahsheh et at. [12], our proposed coupler has

very simple structure which is advantageous to fabrication

process. Therefore, our couplers using AIGaAs and Si-Ge as

the coupling materials provide better performance and ease of

fabrication.

V. CONCLUSION

A comparative study on the performance of two dielectric

materials AIGaAs and Si-Ge as nanoplasmonic couplers is

presented. The materials have been chosen based on the

criteria of bandgap energy. The couplers have been charac­

terized using standard performance parameters like coupling

efficiency, reflection coefficient, return loss and mismatch loss.

Improvements in the performance have been found when the

obtained results have been compared with published works of

other reseachers. It is being expected that the analysis will be

useful in designing efficient couplers for plasmonic application

which will pave the way for miniaturization of the photonics­

based devices. Analyzing the performance of the proposed

couplers after incorporating their nonlinearity properties could

be a future work.

ACKNOWLEDGMENT

The authors would like to acknowledge the support of

Islamic University of Technology.

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