October 10, 2008 / Vol. 6, No. 10 / CHINES E OPTICS LETTERS 709
A compact T-branch beam splitter based on anomalous
reflection in two-dimensional photonic crystals
Yifeng Shen (
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, Jian Sun (
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, Xiaopeng Shen (
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, Juan Wang (
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,
Lulu Sun (
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, Kui Han (
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, and Guozhong Wang (
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1
Department of Physics, China University of Mining and Technology, Xuzhou 221008
2
School of Physics and telecommunication, Wenzhou University, Wenzhou 325035
3
State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and
Information Technology, Chinese Academy of Sciences, Shanghai 200050
Received March 13, 2008
We project a compact T-branch b eam splitter with a micron scale using a two-dimensional (2D) photonic
crystal (PC). For TE polarization, one light beam can be split into two sub- beams along opposite directions.
The propagating directions of the two splitting beams remain unchanged when the incident angle varies
in a certain range. Coupled-mode theory is used to analyze the truncating interface structure in order to
investigate the energy loss of the splitter. Simulation results and theoretical analysis show that choosing
an appropriate location of the truncating interface (PC-air interface) is very important for obt aining high
efficiency due to the effect of defect mo des. The most advantage of this kind of beam splitter is being
fabricated and integrated easily.
OCIS codes: 230.1360, 120.1680.
doi: 10.3788/COL20080610.0709.
Since its inceptio n, pho tonic crystal (PC) has attracted
much interest due to its ability to control the flow o f
light
[1,2]
. In recent years, there have been lots of re-
searches on self-collimation effect
[3−14]
, which means a
beam of electromagnetic wave can propagate with al-
most no diffraction in a perfectly periodic PC. When
a self-collimated beam propagating in a PC incidents
upon the interface between the PC and a homogeneous
dielectric (i.e., air), it will be reflected and the direc tion
of the reflected beam is almost independent of the ori-
entation of the interface (namely, the reflected beam’s
direction has little business with the incident angle in
a certain range). This phenomenon is called anomalous
reflection. Yu et al. designed a beam bend device using
this effect
[13]
. But they did not consider the localized
light scattering of the defect air-holes at the truncating
surface. These defect modes may be str ong enough to
lead heavy energy loss especially for large incident an-
gles. Recently Chen et al. have given a study on the line
defect mode by c oupled-mode theory
[14]
. But they did
not consider the case for defect modes caused by surface
truncation.
In this letter, using a two-dimensional (2D) PC, we
propose a micr on scale T-branch beam splitter bas e d on
anomalous reflection effect. For TE polarization (TE
polarization has a magnetic field H parallel to the axis
of the air holes), one be am can be separa ted into two
branches along opposite directio ns
[15]
. The magnetic-
field distribution was simulated by the finite-difference
time-domain (FDTD) method
[16]
. In addition, we inves-
tigate the e ffect on the intensity of the two sub-beams
for different shapes and locations of the be am splitter.
Simulation results show that choosing an appropriate
location of the truncating interface (PC-air interface)
is very imp ortant to obtain a high reflection due to the
effect of defect modes. Detailed analyses for defect modes
are considered. The well-known coupled-mode theory is
used to analyze the truncating interface structure by con-
sidering the coupling between the self-collima ted modes
and the surface defect modes.
Reference [12 ] introduced a PC structure which con-
sists of a square lattice of air holes introduced into sili-
con material (with a refractive index n =
√
12). This PC
structure has a good self-collimation character along Γ-M
direction in the frequency range from 0.186 to 0.192c/a,
where c and a represe nt the light velo c ity and lattice
constant, respectively. In the context, we also adopt this
PC structure and keep the work fr e quency f = 0.190c/a
in the FDTD simulation. The PC structure consists of
a 18
√
2a × 45
√
2a square lattice of air holes introduced
into a high index material Si (n =
√
12) and the holes
have a radius of 0.35a, where n is the dielectric index.
A 2D X-Y orthogonal coordinate system is established
as shown in Fig. 1, whose origin locates at the center
of one air hole. Obviously, the X-direction is along the
Γ-M direction. We introduce a triangular air area (the
white isosceles triangle region in Fig. 1), which behaves
as a beam splitter, into the P C structure. Parameters
of the isosceles triangle are set as follows: the vertex is
(−0.6a, 0), the vertex angle is defined as 2θ, where θ is
in a range from 35
◦
to 45
◦
, and the height is set as a
constant of 10a for the convenience of discussion. The
device can be easily realized by etching away the trian-
gular Si-a ir holes area in the fabrication process.
In the structure of Fig. 1, a continuous Gaussian type
source (the black cross) with a 6a width is pla ced at
(−16.5a, 0) and the work frequency is set as 0.190c/a.
The light beam propagates along the Γ-M direction
keeping a self-collimating character. In the context we
only consider the TE polarization. Thr e e power mon-
itors (marked as I, II, III) are introduced into the PC
structure, which are located at (−8.5a, 0), (1.5a, 19a),
1671-7694/2008/100709-04
c
2008 Chinese Optics Letters