Effect of Filling-Factor and Angle of Incident on Transmittance of a DielectricSlab Waveguide with Metallic Grating

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Effect of Filling-Factor and Angle of Incident on Transmittance of a Dielectric Slab Waveguide with Metallic Grating

Conference Paper · April 2015

DOI: 10.1063/1.4917134

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Effect of filling-factor and angle of incident on transmittance of a dielectric slab waveguide with metallic grating

T. P. Negara, L. Yuliawati, A. D. Garnadi, S. Nurdiati, and H. Alatas

Citation: AIP Conference Proceedings 1656, 060003 (2015); doi: 10.1063/1.4917134 View online: http://dx.doi.org/10.1063/1.4917134

View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1656?ver=pdfcov Published by the AIP Publishing

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Effect of Filling-Factor and Angle of Incident on Transmittance of a Dielectric Slab Waveguide with Metallic Grating

T. P. Negara

^{1, 2}

, L. Yuliawati

¹

, A. D. Garnadi

^{1, 3}

, S. Nurdiati

³

, and H. Alatas

^{1, 4, #}

1)Research Cluster for Dynamics and Modeling of Complex Systems, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia

2)Department of Computer Science, Pakuan University, Bogor, Indonesia

3)Computational Mathematics Division, Department of Mathematics,

Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia

4)Theoretical Physics Division, Department of Physics,

Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia

#)Corresponding Author: alatas@ipb.ac.id

Abstract. The effect of filling factor on the transmittance characteristics of a slab waveguide with deposited metallic grating on its top is investigated by means of finite difference time domain method under uniaxial perfectly matched layer boundary condition. The system is assumed to be illuminated by a TM electromagnetic waves with oblique incidence. We studied the device transmittance for various angle of incident, while for the associated dielectric section in the grating we consider two different refractive indices. The result shows that the grating filling factor affects the device performance significantly. It is found that for certain values of filling factor and angle of incident, the difference of transmission for those two cases can be relatively large. We show this remarkable behavior is related to the surface plasmons interaction in the non-metallic section of the grating.

Keywords: Slab Waveguide, Metallic Grating, FDTD method, UPML boundary condition.

PACS: 42.82.Et, 41.20.Jb, 42.70.Qs

INTRODUCTION

The role of metallic materials in a nanophotonic structure have attracted many attentions in recent years due to the existence of surface plasmons at its interface with a dielectric material. This phenomenon occured when the corresponding structure is illuminated with transverse magnetic (TM) electromagnetic mode [1].

It was shown that the surface plasmons interaction can lead to a large enhancement of electric field [2], which is related to the surrounding dielectric material.

In other word, this enhancement is strongly depends on the environment of the corresponding metallic structure. Certainly, this phenomenon can be very useful for a highly sensitive optical sensor [3].

In this report, we discuss our recent numerical investigation on a slab waveguide structure with a metallic grating deposited on its top which is consists of array of metallic stripes. We consider the non- metallic section of the grating can be filled with different dielectric materials.

We study the device performance by means of finite difference time domain (FDTD) method [4] with

uniaxial perfectly matched layer (UPML) [5] as the corresponding boundary condition. It is well known that the FDTD algorithm to solve Maxwell’s equation was first proposed by Yee [4].

Our study reveals that the transmission of the electric field is significantly affected by the variation of filling factor which is defined as the ratio between the thickness of dielectric section of the grating with its periodicity. We also demonstrate that the sensitivity of the device alters if the dielectric material in the non- metallic section of the corresponding grating is varied.

This may indicates that the device can be functioned as an optical sensor.

MATHEMATICAL FORMULATION

The propagation of electromagnetic field inside a photonic structure can be quantitatively described by the four Maxwell’s equations. For the TM wave case where the electric field, E

( )

x,y

r

lies in the x−yplane and the magnetic field H

( )

x,y

r

lies in the z plane, the Maxwell’s equations are given as follows:

The 5th Asian Physics Symposium (APS 2012) AIP Conf. Proc. 1656, 060003-1–060003-3; doi: 10.1063/1.4917134

© 2015 AIP Publishing LLC 978-0-7354-1298-9/$30.00

060003-1













∂

−∂

∂

= ∂

∂

∂

x E y E t

Hz x y

0 0

1 µ

ε ⁽¹⁾

y H t

D_{x z}

∂

= ∂

∂

∂

0 0

1 µ

ε ⁽²⁾

x H t

D_{y z}

∂

− ∂

∂ =

∂

0 0

1 µ

ε ⁽³⁾

with the corresponding constitutive relations are given by D_x =ε₀ε_rE_x and D_y =ε₀ε_rE_y. These Maxwell equations are solved numerically using the FDTD method with UPML boundary condition which is represented by an artificial anisotropic absorbing material layer. Among the variant of PML boundary conditions, this UPML gives the most efficient scheme when handling the oblique constinuous waves.

Detailed formulation of the FDTD and UPML can be found in refs. [4, 5].

To characterize the performance of the device, we consider the following definition for its transmission:

( )

(

y t

)

dy dt E

dt dy t y L E T

f

i f

i

t

t h

in t

t h

tr

∫ ∫

∫ ∫

































=

0

2 0

2

, , 0

, , r r

(4)

Here L and h=h_sl denote the device length and the slab waveguide width, respectively, while the parameters t_i and t_f denote the initial and final observation time after steady condition reached, respectively. The fields E_in

(

0,y,t

)

r

and E_tr

(

L,y,t

)

r

are the incoming and outgoing waves at left and right sides of the device, respectively.

DEVICE STRUCTURE

The cross-sectional sketch of the corresponding device is given in fig. 1. We consider the refractive indices of the waveguide and substrate to be 1.45 and 2.21, with the corresponding width h_sl =60µm and

µm,

=80

hsu respectively. The length of the device is µm,

=300

L and the periodicity of the metallic grating is set to Λ=31µm.The filling factor is defined as:

= Λd

f (5)

where d is the thickness of non-metallic section of the grating.

Following ref. [6], we assume the permitivitty of the metallic material in the grating is given by the Drude’s relation as follows:

(

^{v i}

)

v ¹³

30

10 6 . 1

10 52 . 1 1

×

−

− ×

ε = (6)

with ν is the operational frequency and it is set to

=5

ν THz. The device is assumed to be illuminated by an oblique continuous wave with angle of incident is denoted by θ.

RESULT AND DISCUSSION

For the numerical calculation, we consider the number of mesh to be 492×226 with size

µm,

=1

∆

=

∆x y and the time increment is chosen to be ∆t=1.67fs. The initial and final observation time are set to t_i =0.334ps and t_f =2.004ps. These time parameter values are chosen arbitrarily in femtosecond and picosecond order, respectively.

Fig. 1. Cross-sectional sketch of the device

T

θ (degree)

Fig. 2. Characteristics of device transmission, T, with respect to angle of incident variation, θ.

non-metallic section metallic section

y

x Hz

r

θ k

r

Λ d

L Substrate

Slab Waveguide

hsl

hsu

Air

060003-2

Depicted in the Fig. 2 is the device transmission characteristic with respect to the variation of angle of incident for two different dielectric materials filled in the non-metallic section namely n=1.3 (solid square) and n=1.4 (solid circle) with f =0.290. It is clearly shown that at θ =80^o, for both materials a significant transmission discrepancy with ∆T =0.2989 is observed, which is defined as transmittance difference between n=1.3 and n=1.4 cases.

As shown in Fig. 3, the transmission discrepancy

∆T can be further enhanced by varying the filling factor f . It is found that the highest ∆T =0.3466 can be reached at f =0.065.

To explain this interesting phenomenon, it is useful to discuss the field distribution in the non-metallic section of the grating for both dielectric materials which is demonstrated in Figs. 4. It is observed that for

065 .

=0

f and θ=80^o,as depicted in Fig. 4c, the case of n=1.4 shows a more pronounce surface plasmons in comparison with n=1.3given in Fig. 4b.

Obviously, this result may indicates that the surface plasmons in the grating non-metallic section to play a significant role on the device performance.

CONCLUSION

We have discussed the performance of a slab waveguide with a deposited metallic grating on its top.

We show that its transmission can be very sensitive to the filling factor as well as the surrounding dielectric material in the non-metallic section. The highest electric field enhancement is observed for small filling factor. It is explained that this phenomenon occurred due to the significant effect of surface plasmons which

exist in the non-metallic section filled by dielectric material.

ACKNOWLEDGEMENT

This work is funded by the Ministry of Education and Culture, Republic of Indonesia, through “Penelitian Strategis Unggulan” DIPA-IPB grant, under contract no. 0558/023-04.2.01/12/2012.

REFERENCES

1. M. I. Stockman, Opt. Expr. 19, 22029-22106 (2011).

2. M. Maisonneuve, O. d’Allivy Kelly, A-P. Blanchard- Dionne, S. Patskovsky, and M. Meunier, Opt. Expr. 19, 26318-26324 (2011).

3. M. W. Kim, T. T. Kim, J. E. Kim, and H. Y. Park, Opt.

Expr. 17, 12315-12322 (2009).

4. K. Yee, IEEE Trans. Antennas Prop., 14, 302–307 (1966).

5. S. D. Gedney, IEEE Trans. Antennas Prop., 44, 1630- 1639 (1996).

∆T

f

Fig. 3. Transmission discrepancy ∆T with respect to filling factor f.

Fig. 4. (Color online) Electric field distribution in grating for the case of (a) θ=0^o and n=1.3, while θ=80^o for (b) n=1.3 and (c) n=1.4.

x y

x y

x y

(a)

(b)

(c)

060003-3

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