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
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
H
Et 

  (1)
when using the FDTD grid in 3D , Time dependence
Maxwell’s equations for a material can be written in fol-
lowing form:
E
Ht 

 
which leads to (2):
y
x
z
y
x
z
y
xz
y
xz
yx
z
yx
z
E
H
E
yz t
HE
H
yz t
H
EE
zx t
E
HH
zx t
EE
H
x
yt
HHE
x
yt








 


 



 



 


 


 
(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.
REFERENCES
[1] S. G. Johnson, “Photonic Crystals: From Theory to Prac-
tice,” Massachusetts University, 2001.
[2] S. H. Known, M. Kamp, A. Forchel, M. K. Seo and Y. H.
Lee, “Elimination of Crosstalk in Waveguide Intersec-
tions of Triangular Lattice Photonic Crystals,” Optics
Express, Vol. 16, No. 15, 2008, pp. 11399-11404.
doi:10.1364/OE.16.011399
[3] B. E. A. Saleh, Introduction to Nanophotonics (Photonic
Crystals) Transfer Matrix Method (TMM), Module 1
[4] S. G. Johnson and J. D. Joannopoulos, “Designing Syn-
thetic Optical Media: Photonic Crystals,” Acta Materialia
Inc, 2003, pp. 5823-5835.
[5] W. Jiang, “Study of Photonic Crystal Based Waveguide
and Channel Drop Filter and Localization of Light in
Photonic Crystal” Institute for Fusion Studies and De-
partment of Physics, University of Texas, 2000.
[6] S. Foqani, H. Kaatuzan and M. Danaie, “Simulation and
Design of A Wide-Band T-Shaped Photonic Crystal Split-
ter,” Optica A pplicata, Vol. XL, No. 4, 2010, pp. 863-872
[7] M. Danaie, A. R. Attari, M. M. Mirsalehi, S. Naseh and P.
nanostruct, “Design of A High Efficiency Wide-band 60
Bend for TE Polarization,” 2008.
[8] T. Sundstrom, “Analysis of Photonic Crystal Waveguides
by the Use of FDTD with Regularization,” Master’s De-
gree Project, Sweden, 2004.
[9] H. Kaatuzain, “Theory and Technology of Fabrication of
Semiconductor Devices,” Amir Kabir University Press,
1st Edition, Persian, 2008.
[10] K. Fasihi and S. Mohammadnejad, “A Flexible Design of
Waveguide Intersections with Low Cross-Talk in Hex-
agonal Photonic Crystal Structures,” Applied Electronics,
2009.