Mode matching between waveguide and periodic dielectric
waveguide
Ruei-Chang Lu,
Department of Electronic Engineering, National I-lan University, Taiwan
rclu@niu.edu.tw
+88639357400
Yu-Lung Chang,
Department of Electronic Engineering, National I-lan University, Taiwan
yu@niu.edu.tw
+88639357401
Dont-Know I,
Department of Electronic Engineering, National I-lan University, Taiwan
know@niu.edu.tw
+88639357402
Abstract This paper discusses mode matching between waveguide and periodic dielectric
waveguide. We used the dispersion relationship to find a line that similar a waveguide. By
changing the radius of periodic dielectric waveguide, we can obtain the mode matching to reduce
between waveguide and periodic dielectric waveguide. We can use the band gap property to
design a polarization beam splitter.
Keywords periodic dielectric waveguide, dispersion, polarization beam splitter
1. Introduction
Since Yablonovitch [1] and John [2] proposed the concept of photonic crystal, it has been widely
used in optic communication system, such as muti-mode interference, wavelength splitter,
direction coupler, and polarization beam splitter. Recently, a structure called periodic dielectric
waveguide (PDWG) is similar to one dimensional photonic crystal. PDWG has the advantages of
both compactness and flexibility. Devices based on PDWG [3-5] are widely studied, too. Luan and
Chang helped us to understand the transmission characteristic in PDWG [6]. However, when we
want to connect PDWG to other devices, a serious problem is mode matching. Mode mismatch
will affect the transmission efficiency. The radiated light propagates out of the PDWG. Therefore,
the power loses.
Direction coupler is an important device in optic communication systems [7-10]. In this paper,
we proposed a new type direction coupler to design a polarization beam splitter. Owing to the
coupling length of the transverse magnetic (TM) and transverse electric (TE) are different, the
coupling device are too long. So we used the direction coupler with one waveguide and one
PDWG. PDWG exist a band gap for TE, but not for TM. Band gap is a useful property to control
the light can guide or not. While the light lunched to the direction coupler, TM mode coupler to the
PDWG. And TE mode still guide to standard waveguide. And the totally size of the device are not
too long. But there is a mode matching problem between the waveguide and PDWG. Wang et al.
[11] changed the input waveguide that can be obtained the mode matching to reduce radiation
losses. On the other, we increase the radius of PDWG. From the dispersion relationship, we can
find a line similar standard waveguide. At that time the dispersion of PDWG equal conventional
waveguide.
2. Structure
A conventional direction coupler is formed by two parallel identical waveguides. From the
coupling theorem we can know that the light will couple from one waveguide to another. The
coupling length for totally transfer is described as following [12]:
Lc 


(1)
Wherein,  is the difference between the first two basic wave propagation constants.
In this paper, we propose a novel direction coupler, which has one index-guided waveguide and
one PDWG, as show in Figure 1. Owing to the mode matching question, the coupler efficiency
reduced.
Figure 1 The structure of proposed polarization splitter based on direction coupler is formed by
one index-guided waveguide and one periodic dielectric waveguide.
In order to solve mismatching problem, we used dispersion relationship to find a line closed to
the line of standard waveguide show in Figure 2. That means the line of PDWG like the line of
conventional waveguide. In the structure, the direction coupler just like formed by two
conventional waveguide. So the transmission characteristic gets better. Therefore we changed the
radius of periodic dielectric waveguide. And then from the dispersion relationship, the dash line
with the symbol of circle (r =0.43a) is close to the solid line (w =0.6a). The radiation loss will be
reduced.
Figure 2 TM mode dispersion relationships between index-guided waveguide and periodic
dielectric waveguide. When the radius of PDWG r equals to 0.43a, its dispersion line is close to the
Because of we regard PDWG as conventional waveguide. And PDWG has a band gap at the normalize
dispersion line of used index-guided waveguide width w = 0.6a.
frequency range from 0.18 to 0.23 for TE, but not for TM as show in Figure 3. Therefore, we operated
the normalize frequency at 0.2. That mean we lunched the light for TE cannot couple to PDWG, and
couple to conventional waveguide. On the other hand, the light for TM can couple to PDWG. So we
design a new type polarization beam splitter in this structure as show in Figure 4. However, we
successfully avoided the problem that coupling length is different for TE and TM. That’s why we
replace conventional waveguide with the PDWG.
Figure 3 TE mode dispersion relationships between index-guided waveguide and
periodic dielectric waveguide. There is a band gap at normalized frequency from
0.18 to 0.23.
Figure 4 The propagation principle of the proposed polarization splitter. The random polarized
light is lunched from the index-guided waveguide. Then, TM mode couples to PDWG, but TE
mode not, due to the band gap of the PDWG.
In our design, the parameter of dielectric constant is ε= 11.56, lattice constant a is 1μm, the width of
waveguide w =0.6a, the radius of PDWG is 0.43 a, and the distance between conventional waveguide
and PDWG is 2.7a. We define the transmission power ratio η2, the light is guided from port1 to port2.
Similarly, when the light is guided from port1 to port3, the transmission power is η3.
2 
Pport2
3 
Pport1
Pport3
Pport1
(2)
In order to understand the direction coupler is good or not, we defined the crosstalk show in Figure 5.
Crosstalk  (
PTEm
a j,TM
o rm a j o r
PT Em
a j,TM
o rm i n o r
)
(3)
5 The symbols used to calculate transmission ratio and crosstalk.
3.Figure
Simulation
We show the transmission power ratio of different ports versus TE mode and TM mode in Figure 6(a)
and (b). The transmission power ratio η2 is 99.9%, the light is confined the conventional waveguide. On
the other hand, the transmission power ratio η3 is 83.9% and. We also calculated the coupling length Lc
is 23μm. We make a table 1 that lists the value of the transmission power ratio and crosstalk.
Figure 6 Field intensity distribution of the proposed polarization splitter. (a) TE mode
propagates in the index-guided waveguide because of the band gap. The transmission power ratio
η2 is 99.9%. (b) TM mode couples to PDWG. The transmission power ratio η3 is 83.9% and the
coupling length Lc is 23μm.
Table 1 The transmission ratio and crosstalk of the proposed polarization splitter for both TE
and TM mode.
Transmission ratio
Crosstalk
TE mode
99.9%
47.3 dB
TM mode
83.9%
9.4 dB
4. Conclusion
In this paper, we used the dispersion relationship of PDWG to find a line (r =0.43a) that equal to
standard waveguide (w =0.6a). Therefore, we solved the mode matching question. We used the
important property band gap to design a polarization beam splitter. The transmission power ratio is
99.9% for TE mode, and 83.9% for TM mode.
Reference
1. E. Yablonovitch. 1987. Inhibited spontaneous emission in solid state physics and electronics.
Physical Review Letters 58(20):2059-2062.
2. S. John. 1987. Strong localization of photons in certain disordered lattices. Physical Review Letters
58(23):2486-2489.
3. Wanwen Huang, Yao Zhang, and Baojun Li. 2008. Ultracompct wavelength and polarization
splitters in periodic dielectric waveguides. Optics Express 16(3):1600-1609.
4. Yao Zhang, Hongxiang Lei and Baojun Li. 2010. Polarization beam splitter with wide bandwidth
in air-hold-based periodic dielectric waveguides. Optics Communications 283(10):2140-2145.
5. Rongkuo Zhao, Tainrui Zhai, Zhaona Wang, and Dahe Liu. 2009. Guided resonances in periodic
dielectric waveguide. Journal of Lightwave Technology 27(20):4544-4547.
6. Pi-Gang Luan and Kao-Der Chang. 2006 Transmission characteristic of finite periodic dielectric
waveguides. Optics Express 14(8):3263-3272.
7. Quan Xu, Kang Xie, Jun Tang, and Jiang Ping. 2011. Direction coupler design based on coupled
cavity waveguide in photonic crystal. Optik-International Journal for Light and Electron
Optics 122(13):1132-1135.
8. Cuesta-Soto, F., Martínez, A., Garcia-Banos, B., and Marti, J. 2004. Numerical analysis of
all-optical switching based on a 2-D nonlinear photonic crystal directional coupler. Selected Topics
in Quantum Electronics 10(5):1101-1106.
9. Wang, C. C., & Chen, L. W. 2010. Channel drop filters with folded directional couplers in
two-dimensional photonic crystals. Physica B: Condensed Matter 405(4):1210-1215.
10. Martinez, A., Cuesta, F., & Marti, J. 2003. Ultrashort 2-D photonic crystal directional
couplers. Photonics Technology Letters IEEE 15(5): 694-696.
11. Ruei-Chang Lu, Chun-Min Wang, Yu-Pin Liao, and Keh-Yi Lee. 2011. Mode matching for
periodic dielectric waveguide. American Journal of Engineering and Technology Research
11(12):1276-1280.
12. Savović, S., Djordjevich, A., Drljača, B., and Kovačević, M. S. 2009. Comparison of methods for
calculating coupling length in step-index optical fibers. Acta Physica Polonica A, 116(4):652-654.