Optics and Photonics Journal, 2013, 3, 240-242
doi:10.4236/opj.2013.32B056 Published Online June 2013 (http://www.scirp.org/journal/opj)
Coupling Device with Resonant Cavities Based on Periodic
Dielectric Waveguides
Ruei-Chang Lu, Yu-Lung Jang
Department of Electronic Engineering, National I-Lan University, Chinese Taipei
Received 2013
ABSTRACT
In this paper, we propose a coupling device based on periodic dielectric waveguide. In order to reduce the device size,
two resonant cavities are added so th at the ligh t can be coupled b etween two periodic d ielectric wavegu ides. Plane wav e
expansion method and two dimension finite difference time domain methods are used to analyze this device. The cou-
pled transmission ratio of this device at the wavelength of 1550 nm is above 94%.
Keywords: Periodic Dielectric Waveguides; Direction Coupler
1. Introduction
Periodic dielectric waveguides (PDWGs) have been
studied much in recent years. The structure of PDWG is
similar to that of photonic crystal waveguide (PCWG).
PDWG can be formed by dielectric cylinder array in air
or air-hole array in a dielectric [1,2]. They are dielectric
structures with lattice periodicity in one, two or three
dimensions. Though the guiding methods are not the
same, PDWG and PCWG can form similar device in
optics communication, such as, multimode-interference
(MMI)[3], optical power splitter based on T-junction [4]
or Y-junction, polarizatio n device [5], channel drop filter
[6], direction coupler, etc. These device based on PDWG
have the advantages of the structure compactness and
flexibility. In order to reduce device size, we design a
coupling device with two resonant cav ities. The resonant
cavity is a kind of point defects. By introducing point
and/or line defects in direction coupler, the light from the
PDWG can be guided to the other one.
2. Design
The coupling device we designed has two resonant cavi-
ties to couple the pro pagating light between two PDWGs,
as show in Figure 1. In our design, the simulated para-
metric of dielectric constant is
ε = 11.56 (i.e. the index
of refraction is n = 3.4), the radius of the cylinder is set r
= 0.45 *a, and the radius of cavity is R = 1.70 * a, where
a is the center to center distance between two adjacent
cylinders. We set the distance of the two PDWGs 4.5 a,
because the distance between these two PDWGs should
be far enough not to couple each other. The distance of
the two central cavities is 2 * rd, and rd = 1.75 * a. When
the light is guided form port 1 to port 2, we define the
transmission power ratio η2. Similarly, when the light is
guided from port 1 to port 3, the transmission ratio is η3.
3. Simulation and Results
The band of TE mode was calculated by plane wave ex-
pansion method (PWE). Figure 2 shows the band struc-
ture for the a × 14.5 a supercell by the dash frame. The
shaded region represents extended mode region. In the
band structure, we use the frequency from 0.10 to 0.16.
In this frequency range, two modes are very closed. That
means the light can not coupled to the other one. Unless
the device is long enough. However, using FDTD simu-
lation result, it shows the transmission ratio of different
ports versus normalized frequency a/
 in Figure 3. We
can see that most power guided to port 3 at a/
 = 0.145
and port 2 at a/
 = 0.155. Figure 4 shows the corre-
sponding propagating field of these two cases. With a =
225 nm, the input wavelength of Figure 4(a) is 1550 nm,
Figure 1. Schematic diagram of the device.

R.-C. LU, ET AL. 241
Figure 2. A diagram of two rows PDWGs. The dash frame
shows the supercell for PWE method. Between the two
dashes line is our operating frequency from 0.10 to 0.16.
The shaded region repre se nts extended mode region.
Figure 3. The relationship of transmission ratio and fre-
quency.
(a)
(b)
(c)
(d)
Figure 4. (a) Propagation field for input wavelength 1550
nm; (b) The light round the two resonant cavities with dif-
ferent directions; (c) Propagation field for input wavelength
1450 nm; (d) The light round the two resonant cavities with
the same direction.
and we can see that the light is guid ed mainly into port 3
with normalized transmission power 94%. The input

R.-C. LU, ET AL.
242
wavelength of Figure 4(c) is 1450 nm, and we can see
that the light is guided mainly into port 2 with lower
transmission power 82%.
We explain this wave how to propagate from port 1 to
port 3 in Figure 4(b). The light surrounded to the two
resonant cavities, upper cavity and lower cavity. The
upper cavity is counter clockwise and the lo wer cavity is
clockwise. There is a 180° phase difference between the
two resonant cavities. Due to the electric field with posi-
tive and negative caused to offset by the amplitude. So
the light can not travel to port 4.
Another case is shown in Figure 4(d), there are
clockwise in both resonant cavities. The above cavity
couple to right PDWG but the light propagates several
nanometers to couple to below cavity immediately. The
same condition occur to the below cav ity that port 4 gets
about 5% loss come from the below cavity.
4. Conclusions
In order to reduce device size, we have proposed a cou-
pling device with two cavities in PDWG. PDWG just
likes a grating pattern, as a = 225 nm, we can guide the
light to different ports at 1550 nm and 1450 nm using
plane wave expansion method and finite-difference
time-domain method. The proposed device can be used
in the future optical communication systems.
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