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Optik 125 (2014) 5374–5377

Contents lists available at ScienceDirect

Optik

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esign and analysis of a gallium lanthanum sulfide basedanoplasmonic coupler yielding 67% efficiency

d. Ghulam Saber ∗, Rakibul Hasan Sagorepartment of Electrical and Electronic Engineering, Islamic University of Technology, Board Bazar, Gazipur 1704, Bangladesh

r t i c l e i n f o

rticle history:eceived 29 September 2013

a b s t r a c t

In this paper, we propose a novel ultra-compact nanoplasmonic coupler using gallium lanthanum sulfide(GLS) which yields an efficiency of 67% at the optical communication wavelength. The analysis has been

ccepted 26 May 2014

eywords:urface plasmon polaritonlasmonic waveguideanoplasmonic couplerinite-difference time-domain

done numerically using the finite-difference time-domain method. Our proposed coupler can operateat a broad frequency range and easier to fabricate than couplers with multi-section tappers since it is asimple rectangular-shaped coupler with no variation along the whole length.

© 2014 Elsevier GmbH. All rights reserved.

. Introduction

The field of plasmonics has attracted a lot of research interestn the last few years. The incredible ability of surface-plasmon-olariton (SPP) to overcome the diffraction limit of conventionalptical modes [1] and propagate at the deep sub-wavelength scale2] has been the key reason behind the boom of this field. Plasmonicaveguides, in particular the metal-dielectric-metal (MDM) con-guration can tightly confine the optical mode within the dielectricore. This leads to the potential application in biosensing [3], Braggeflectors [4], subwavelength imaging [5] and metamaterials [6].owever, the MDM configuration has a major drawback. The prop-gation loss of SPP is very high in this configuration of plasmonicaveguide which limits the length of propagation. Even the fab-

ication related disorders have far less impact on the propagationoss than the losses that occur in metallic layers of the MDM wave-uide. This problem can be addressed by using both dielectric andlasmonic waveguide on the same chip. The dielectric waveguideill carry the fundamental optical mode while the plasmonic wave-

uide will address the sub-wavelength scale issue. This calls for theeed of efficient coupling of optical modes from the dielectric wave-uide to the plasmonic waveguide. Therefore, designing efficient

anoplasmonic couplers with different materials and structuresan be a pioneering step in miniaturization of the integrated pho-onic devices.

∗ Corresponding author. Tel.: +880 1671081441/1715170549.E-mail address: gsaber@iut-dhaka.edu (Md.G. Saber).

ttp://dx.doi.org/10.1016/j.ijleo.2014.06.034030-4026/© 2014 Elsevier GmbH. All rights reserved.

Due to the amazing expected features of MDM wave-guide, researchers have started to explore this configurationexperimentally. Dionne et al. [7] have experimentally shownthat quasi-two-dimensional MDM waveguides can guide sub-wavelength modes with significant propagation length.

In the recent time, chalcogenide glasses (ChG) have attracteda lot of research interest due to their photosensitivity to visiblelight and transparent behavior in the mid-infrared region. Theyprovide strong confinement of optical modes and enhanced propa-gation length. Gallium lanthanum sulfide is one of the chalcogenideglasses with high refractive index [8] and a transparency band ran-ging from 500 nm to 10 �m [9]. With this as a background, wehave chosen gallium lanthanum sulfide (GLS) as the material forthe nanoplasmonic coupler.

In the past years, several plasmonic couplers have been pro-posed by different researchers. Veronis et al. [10] proposed acoupler with multi-section tapers. Ginzburg et al. [11] reported a�/4 coupler to couple optical modes from a 0.5 �m to 50 nm wideplasmonic waveguide. Pile et al. [12] presented an adiabatic anda non-adiabatic tapered plasmonic coupler. Wahsheh et al. [13]reported an analysis on nanoplasmonic air-slot coupler and its fab-rication steps.

In this paper, we present a novel design and analysis of ananoplasmonic coupler using GLS based on the finite-differencetime-domain method [14]. To the best of our knowledge, this is

for the first time one proposes and analyzes a nanoplasmonic cou-pler using GLS. We have achieved a coupling efficiency of 67% atthe telecommunication wavelength. The advantage of this designis that it can operate at a wide range of frequencies and is easier to

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The reflection coefficient, return loss and voltage standing waveratio (VSWR) has also been determined in order to analyze theperformance of the coupler. The method we have used for calcu-lating reflection coefficient is as follows. First an optical mode has

Fig. 1. Schematic diagaram of the coupling structure used for the numerical analysis.

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Md.G. Saber, R.H. Sagor /

abricate since it is a simple flat terminal waveguide without anyapering placed at the entry of the MIM plasmonic waveguide.

. Formulation of the materials and the structure

.1. Material models

The frequency dependent permittivity function of single poleorentz model is given by [15],

r(ω) = ε∞ + ωo2(εs − ε∞)

ωo2 + j2ıω − ω2

(1)

here ε∞ is the infinite frequency relative permittivity, εs is theero frequency relative permittivity, j is the imaginary unit, ı is theamping co-efficient and ωo is the frequency of the pole pair.

The frequency dependent permittivity function of Lorentz-rude 6 (six) pole model is given by [15],

r(ω) = 1 − foω2p

ω2 − j�oω+

5∑

i=1

fiω2p

ω2oi

+ j�iω − ω2(2)

here ωp is the plasma frequency, � i is the damping frequency,i is the oscillator strength, j is the imaginary unit and ωoi is theesonant frequency.

We have used single pole-pair Lorentz model to account for theispersive property of gallium lanthanum sulfide (GLS) and six-ole Lorentz-Drude model to integrate the dispersion property ofilver (Ag) in the simulation model. An excellent agreement haseen achieved with the experimental values [16] by fitting GLSo the single pole-pair Lorentz model with ε∞ = 2.7, εs = 2.2572,

= 8 × 1011 rad/s and ωo = 0.70 × 1016 rad/s. The modeling param-ters for Ag that we have used, have been determined by Rakict al. [17].

.2. Structure formulation

We have developed the 2D simulator based on the finite-ifference time-domain method proposed by Yee [14]. A generalDE-FDTD algorithm is used to integrate the frequency depend-nt dispersion properties of the materials. [18,19]. This algorithms useful where materials with different dispersion properties areresent. The perfectly matched layer (PML) has been used to avoideflection of incident wave from the boundaries [20].

Considering the material dispersion, the frequency-dependentlectric flux density can be given as

(ω) = ε0ε∞E(ω) + P(ω) (3)

The general Lorentz model is given by

(ω) = a

b + jcω − dω2E(ω) (4)

hich can be written in time-domain through inverse Fourierransform as

P(t) + cP ′(t) + dP ′′(t) = aE(t) (5)

The FDTD solution for the first order polarization of Eq. (5) cane expressed as

n+1 = C1Pn + C2Pn−1 + C3En (6)

here,

2 2

1 = 4d − 2b�t

2d + c�t, C2 = −2d − c�t

2d + c�t, C3 = 2a�t

2d + c�t

The values of C1, C2 and C3 depend on the material under con-ideration.

125 (2014) 5374–5377 5375

Finally the electric field intensity becomes,

En+1 = Dn+1 −∑N

i Pn+1

εoε∞(7)

where Dn+1 is the update value of the electric flux density calculatedusing the FDTD algorithm.

3. Structure specifications and simulation method

The proposed nanoplasmonic coupler structure that has beenused for simulation is given in Fig. 1. Here the width of the GLSlayer has been taken as 300 nm and the width of the air layer in theMDM waveguide has been taken as 60 nm.

A monochromatic point source has been used to excite the opti-cal modes. Since the coupler can operate at a broad frequency range,we have used input signals of wavelengths ranging from 900 nm to2000 nm. The reason we have limited our simulation within thiswavelength range is that the modeling parameters for the mate-rials we have used is applicable within this wavelength boundaryonly.

In order to get accurate results and maintain the courant stabil-ity criteria [21] we have taken �x = 5 nm, �y = 5 nm and the timestep as �t = (0.95/c

√(1/�x2) + (1/�y2)).

In order to validate our developed simulation model, we haverun a simulation using the given parameters (ε∞ = 2.25, εs = 5.25,ı = 2 × 109 rad/s and ωo = 4 × 1014 rad/s) for a dispersive medium inChapter 9 of the Taflove’s book [21]. The results we obtained arepresented in Fig. 2 and have been compared with the results givenin the book (Fig. 9.3(a)) and we achieved a perfect match.

We have defined the coupling efficiency as the ratio of the trans-mitted power into the MIM waveguide to the incident power in theinput dielectric waveguide. The incident power of the fundamen-tal mode has been measured right before the interface betweendielectric and MDM waveguide and the transmitted power has beenmeasured right after the interface.

20 60 100 140 180-0.75

Distance (micrometer)

Fig. 2. Results obtained using the parameters given in Taflove’s book.

5376 Md.G. Saber, R.H. Sagor / Optik 125 (2014) 5374–5377

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Ref

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Ret

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Loss

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VS

WR

(iii)

Fig. 4. (i) Numerically calculated reflection coefficient, (ii) return loss and (iii) volt-age standing wave ratio (VSWR) of the proposed nanoplasmonic coupler.

Fig. 3. Coupling efficiency of the proposed nanoplasmonic coupler.

een incident in the dielectric waveguide when there is no plas-onic waveguide. The value of the electric field is then recorded

t one point. This represents the value of the incident wave. Thenhe same thing has been done with the plasmonic waveguide. Thisime the electric field represents the value of the incident wavelus the reflected wave since some part of the incident wave wille reflected by the MDM waveguide due to the difference in dis-ersion property of the materials. Therefore, we can calculate theeflected wave by subtracting the incident wave from this value.he reflection coefficient is then calculated by taking the maximumf the ratio of the reflected wave to the incident wave. This haseen done for all the input signal wavelengths for which we haveun the simulation. After determining the reflection coefficient, weave determined the return loss and voltage standing wave ratioVSWR) from it using analytical formulas.

. Results and discussion

The coupling efficiency of the proposed nanoplasmonic couplersing gallium lanthanum sulfide has been determined for different

nput signal wavelengths and presented in Fig. 3. From the figure itan be observed that the coupling efficiency keeps on increasing ase increase the input signal wavelength reaching about 75% at the

nput signal wavelength of 2000 nm. The optical communicationavelength is of particular interest for us and at this wavelength

he coupling efficiency is 67%.We have determined the reflection coefficient of the coupler

umerically which is presented in Fig. 4(i).From the figure it can be observed that the reflection coeffi-

ient is the maximum at the input signal wavelength of 1100 nmnd it starts falling after this point. At the optical communicationavelength the reflection coefficient is 0.19 which indicates the

mount of reflection is very small for the proposed coupler at thisavelength.

From the numerically obtained reflection coefficient, we haveetermined the return loss and the voltage standing wave ratiosing analytic equations which are given in Fig. 4(ii and iii). Theeturn loss is zero at 1100 nm wavelength and it is 14.64 dB athe optical communication wavelength which indicates that thempedance mismatch is low at the wavelength of our interest. TheSWR is the maximum at the input signal wavelength of 1100 nmavelength having a value of 32.4. At the optical communicationavelength VSWR has a value of 1.45 only. Thus it can be realized

hat the impedance mismatch is very low at the optical communi-ation wavelength for our proposed nanoplasmonic coupler.

The electric field distribution inside the coupling structure forLS has been presented in Fig. 5. The GLS waveguide is carrying

he optical mode to couple it to the MDM waveguide. The coupled

ode in the MDM waveguide is clearly visible from the electric

eld distribution plot of the simulated structure.The coupler proposed by Wahsheh et al. [6] provides a theo-

etical efficiency of 50% at the optical communication wavelength

Fig. 5. Electric field distribution in the proposed nanoplasmonic coupler.

whereas our proposed coupler provides a theoretical efficiency of67% at the same input signal wavelength. The proposed couplersof Veronis [10] and Pile [12] contain multi-section tapers which isdifficult to fabricate at the nano-scale. But our proposed structureis easier to fabricate since we have not used any tapered interface.Therefore, it is evident from the obtained results that our proposedcoupler using gallium lanthanum sulfide is better in terms of effi-ciency and easier to fabricate.

5. Conclusion

We present a novel design of a nanoplasmonic coupler using

gallium lanthanum sulfide (GLS). This simple rectangular-shapedcoupler provides a coupling efficiency of 67%. We have also ana-lyzed and presented the reflection coefficient, return loss and VSWRin order to characterize the performance of the proposed coupler.

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rom our results it can be inferred that our proposed design usingLS demonstrates better performance in terms of efficiency andethod of fabrication. This analysis will be helpful in designing

ighly efficient couplers for integrated photonic devices.

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