Simulation and Design of a Low Crosstalk Hexagonal Photonic Crystal Crossover Waveguide

doi:10.4236/opj.2013.32B049

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Optics and Photonics Journal, 2013, 3, 209-211

doi:10.4236/opj.2013.32B049 Published Online June 2013 (http://www.scirp.org/journal/opj)

Simulation and Design of a Low Crosstalk Hexagonal

Photonic Crystal Crossover Waveguide

Elnaz Pilehvar1, Hassan Kaatuzian1, Mohammad Danaie2

1Photonics Research Lab.(P.R.L.), Dept. of Electrical Engineering, Amirkabir University of Tech., Hafez Ave., Tehran, Iran

2Faculty of Elecrical Engineering, Semnan University, Semnan

Email: [email protected]

Received 2013

ABSTRACT

In this paper, an optical waveguide junction is introduced to reduce crosstalk based on a hexagonal structure of photonic

crystals for TE modes. The wavelength is 1330 nm which is an important wavelength for optical fiber data transmission.

Simulation results show that the proposed design exhibits a reduction of -50 dB in crosstalk. It translates to a consider-

able isolation improvement between two crossover waveguides. FDTD method is used to obtain the transmission coef-

ficient.

Keywords: Cross Talk; TE Mode; Waveguide; Hexagonal Photonic Crystal

1. Introduction

Photonic crystals (PhC) are periodic optical structures

that are designed to affect the light trajectory in dielectric

or semiconductor waveguides[1].They have been devel-

oped as building blocks for integrated photonic systems.

In order to integrate multiple devices in a small region, it

is necessary to have intersections of the waveguides

which connect devices [2].The mentioned intersections

should ideally have zero cross-talk.

Photonic band gap (PBG) is essentially the gap be-

tween the air-line and the dielectric-line in the dispersion

relation of the PBG system [3]. In other word it is range

of frequencies in which light is forbidden to propagate in

crystal [4]. PhC behaves like a perfect mirror for light

with frequency lying inside the band gap [5].

2D-PhC’s, have two basic topologies. The first con-

tains a dielectric substrate in which air holes are intro-

duced periodically .The second one consists of dielectric

rods embedded in air. Rod-type PhC has PBG for trans-

verse magnetic (TM) modes and air-hole type has PBG

for transverse electrical (TE) modes [6].Since the im-

plementation of hole-type PhCs is easier, usually most

structures realized in the literature have used it instead of

the rod type alternative.

A PhC waveguide can be constructed by removing one

row of holes inside the otherwise perfect crystal [5]. For

a two dimensional (2D) triangular lattice of air holes the

hole radius of 0.45 a provides the largest band gap, al-

though having a larger gap is a pre-requirement to

achieving a wide-band single-mode waveguide but to

avoid the structure becoming fragile, in most applications

the radius of the most holes is not chosen larger than 0.3a

[7]. In our design radii of some holes have been changed

to achieve low crosstalk, high throughput for triangular

lattice in TE mode in the important wavelength for opti-

cal fiber data transmission that is 1.33 μ because of low

dispersion [6].Various numerical methods can be used

for analyzing PhC’s. Among this methods, finite-differ-

ence time-domain (FDTD) is mostly used to obtain the

throughput of the waveguide .It calculate the radiation

field in open space by using appropriate boundry condi-

tions [8].The numerical design of FDTD is described in

section II. There is also a simulation and results section

that explains the numerical simulation results. Finally we

have a conclusion section.

2. Numerical Design

The method we use to solve Maxwell’s equation in real

space is called FDTD (Yee 1966). Figure 1 shows the

Yee cell. It depicts the position of the electric and mag-

netic field components [8].

Figure 1. Yee cell that shows the position of the electric and

magnetic field components in 3D.

E. PILEHVAR ET AL.

210





  (1)

when using the FDTD grid in 3D , Time dependence

Maxwell’s equations for a material can be written in fol-

lowing form:





 

which leads to (2):

yz t

zx t

HHE

















 





 







 







 





 





 

(2)

Here



and



are the position dependent permittivity

and permeability of the material respectively. The com-

putational region is divided in XYZ such Yee cells. [8]

3. Simulation and Results

We consider a 2D hexagonal array of air holes in the

dielectric of SiO2 with refractive index of 1.46.[9]. The

radii of holes are r = 0.3 a Where a is the lattice constant.

Here, the PBG is between normalized frequency range of

0.41 to 0.56, which is more than the other materials re-

ported in the literature [2,10]. Figure 2 shows the PBG

for structure used in this paper. The simplest geometry

which can be used as an intersection consists of two

waveguides crossing each other with a 60 degrees angle

which is shown in Figure 3.

Figure 2. The band diagram of the structure used in this

paper.

The Crosstalk is the signals that leaks from a waveguide

to the other. Our purpose is to reduce the cross talk and

increase the transmission. The structure proposed in this

paper is shown in Figure 4. The values of radii are men-

tioned in Table 1. The light with Gaussian envelope is

lunched to the input port from the left. In this paper, we

use a single line defect waveguide formed by enlarging

the innermost holes to shift the frequency of dispersion

curve of the waveguide mode [2] and decrease the reflec-

tive light. All the FDTD simulations are for TE polariza-

tion.

Figures 5(a) and (b) show the transmission and

crosstalk in dB in the intersection of proposed structure

in Figure 4. It can be seen that there is crosstalk (cross-

talk1 + crosstalk2) as -50 dB near the wavelength of 1.33

μm and throughput have been increased in comparison

with the simplest structure in Figure 3.

Figure 3. The simplest geometry can be used as intersection.

Figure 4. Schematic of the proposed structure in the paper.

The values of radii is mentioned in table.

Table 1. Values of radii of the proposed stru cture in Figu re 2.

Parameter R1 R2 R3 R4

Radius/a 0.5 0.3 0.428 0.257

E. PILEHVAR ET AL.

211

(a)

(b)

Figure 5. (a)The transmission and crosstalk in dB after im-

provement the crossover waveguide (b) Zoom in the (a)

diagram.

4. Conclusions

In summery by changing some radii in the crossover we

have successfully decreased in simulation, the crosstalk

near -50 dB around the wavelength of 1.33 μm in the

photonic crystal with air holes in TE polarization. For

analyzing the structure we’ve used FDTD method. to

obtain the throughput and crosstalk in the structure.

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