Design of a high transmission Y-junction in photonic crystal waveguides

ARTICLE IN PRESS Physica B 405 (2010) 1832–1835

Contents lists available at ScienceDirect

Physica B journal homepage: www.elsevier.com/locate/physb

Design of a high transmission Y-junction in photonic crystal waveguides Wu Yang a,b, Xiaoshuang Chen a,, Xiaoyan Shi c, Wei Lu a, a b c

National Laboratory for Infrared Physics Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yutian Road, Shanghai 200083, China College of Science, Henan University of Technology, Zhengzhou 450001, China College of Science, Information Engineering University of PLA, Zhengzhou 450001, China

a r t i c l e in f o

a b s t r a c t

Article history: Received 27 October 2009 Received in revised form 2 January 2010 Accepted 6 January 2010

A new high transmission Y-junction based on two-dimensional photonic crystal waveguides of triangular lattice is designed. The Y-junction is designed by moving the corner rods of Y-junction into a resonant cavity and placing additional rods between the resonant cavity and the output waveguides. By changing the radius of the additional rods, the transmission coefficient of the Y-junction can be optimized. The coupled mode theory is used to explain the transmission properties. Two-dimensional numerical simulation is performed to verify the Y-junction structure with near-complete transmission. & 2010 Elsevier B.V. All rights reserved.

Keywords: Photonic crystal Transmission and absorption

1. Introduction Since John and Yablonovitch’s proposed the concept of photonic crystals (PCs) in 1987 [1,2], the photonic crystals (PCs) have attracted considerable interest, due to the capability of controlling electromagnetic wave by photonic band gap. Photonic crystal waveguides (PCWs), formed by line defects in photonic crystals, are expected to provide low loss transmission and wellconfined branches when PCWs are operated at wavelengths within the photonic band gap. They can play an important roles in future optical circuits. Waveguide branches can split the input power into the output waveguides without significant reflection or radiation losses. Highly efficient transmission of light around sharp corners in photonic band gap has been demonstrated [3,4]. T-junctions and Y-junctions in PCWs have been proposed and shown high transmission performance [5–10]. Park et al. proposed a power splitter based on directional coupling in 2D-PC with the transmission coefficient up to 47.6% for each output [11]. The losses of the power splitter may be due to some reflection from the ends of the waveguide. Generally speaking, a common Y-junction structure has poor transmission coefficient without tuning structural [5,12]. Due to the three-fold rotational symmetry, 1201 Y-branches in photonic crystal with triangular lattice have low transmittance not exceed 4/9 [5]. Recently, a super defect, a middle rod and four scatterer rods at its corners were designed in PCWs to improve the transmission coefficient [6]. In this paper, we present a new Y-junction by photonic crystal with

 Corresponding authors.

E-mail addresses: [email protected] (X. Chen), [email protected] (W. Lu). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.01.056

triangular lattice composed of dielectric rods in air. Two methods are used to improve transmission coefficient of the Y-junction. One is moving the corner rods of Y-junction and the other is placing two additional rods. The new structure displays near-zero reflection, and the transmission coefficient is higher than 49.5% for each output port. The results are verified by the twodimensional numerical simulation.

2. Coupled mode theory approach The Y-junction is treated as a cavity that couples with the input and output waveguides. The model is shown in Fig. 1. The resonance in the cavity determines the transmission properties of Y-junction, which can be analyzed by coupled-mode theory [5,13]: X1 X dA Þþ Sþi ¼ jo0 AA ti dt i i sffiffiffiffiffiffiffiffi 2 A Si ¼ S þ i þ

ti

sffiffiffiffi! 2

ti

ð1Þ

ð2Þ

where S + i and S  i are the incoming and outgoing wave amplitudes of waveguides, respectively, A is the amplitude of the resonant, o0 is the resonant frequency, ti is the amplitude decay rate of the resonance into the ith port. When the electromagnetic wave is incident from port 1, the reflection coefficient R and the transmission coefficients T2 and T3 into the

ARTICLE IN PRESS W. Yang et al. / Physica B 405 (2010) 1832–1835

1833

Fig. 2. The Y-junction with the moved corner rods (ellipse) and the placed additional rods (square).

Fig. 1. Scheme of the coupled mode model for the Y-junction in photonic crystal with triangular. S + i and S-i are the incoming and outgoing wave amplitudes of waveguides, ti is the amplitude decay rate of the resonance into the ith port.

other two ports can be expressed by 2    jðoo0 Þ þ 1  1  1    t t t 1 2 3 R ¼    jðoo Þ þ 1 þ 1 þ 1  0  t t t 

ð3Þ

2    2   ffiffiffiffiffiffiffiffiffi ffi p   t t 1 2  T2 ¼   jðoo Þ þ 1 þ 1 þ 1  0  t1 t2 t3 

ð4Þ

2    2   ffiffiffiffiffiffiffiffiffi ffi p   t t 1 2  T3 ¼   jðoo Þ þ 1 þ 1 þ 1  0  t1 t2 t3 

ð5Þ

1

2

3

Eq. (6). By the above design, we can obtain high transmission coefficient.

If the following condition: 1

t1

¼

1

t2

þ

1

t3

Fig. 3. Schematic picture of the 110a  100a computational cell. The field amplitude is monitored at points A and B.

ð6Þ

is satisfied, zero reflection can be achieved at the resonant frequency o0 [5]. Y-branches in photonic crystal with triangular lattice have three-fold rotational symmetry. Therefore the decay rates into the three ports are equal, i.e., t1 = t2 = t3, which leads to a transmission coefficient of 4/9 at resonance [5]. The transmission coefficient is only a slowly varying function of the ratio t1/t2. When t1/t2 is varied from 0.26 to 0.97, the transmission coefficient is higher than 45%. The detailed discussion can be found in Ref. [5]. Here, a new Y-junction in photonic crystal with triangular lattice is designed by two steps. Firstly, we move the corner rods of Y-junction into a resonant cavity. Secondly, two additional rods are placed between the cavity and the output waveguides based on the coupled mode theory (see Fig. 2). The displacement of the moved corner rods is 0.5 multiple lattice constant from initial position. The movement of the corner rods can cause the increasing the volume of the cavity and make the cavity mode resonant with the waveguide modes. Moreover, the additional rods can slightly reduce the coupling between the cavity and the output waveguides in order to satisfy the condition described by

3. Numerical simulations and discussion We performed numerical simulation of the Y-junction in twodimensional PCWs with triangular lattice composed of dielectric rods in air (e = 1). Photonic band gap is found in the TM modes. The dielectric constant and the radius of the rods are 11.56 and 0.2a (a is lattice constant), respectively. The present PCWs are formed by removing single row rods in the PCs. A broad band gap is obtained with the single guided mode spanning from 0.34o oa/2pco0.44. The transmission of the structure is calculated by the finitedifference time-domain (FDTD) method with perfectly matchedlayer boundary conditions [14,15]. A dipole located at the entrance of the waveguide creates a pulse with a Gaussian envelope in time. The field amplitude is monitored at two points of the waveguide, one is in front of the Y-junction (point A) and the other is behind the Y-junction (point B) as indicated in Fig. 3. Although most of the light reaching the edge of the computational cell is absorbed by the boundaries, some light is reflected back from the ends of the waveguide [5]. By using a sizable computational cell of 120a  110a and positioning each monitor

ARTICLE IN PRESS 1834

W. Yang et al. / Physica B 405 (2010) 1832–1835

Fig. 4. The transmission coefficient of different radius of the placed additional rods.

Fig. 5. The transmission coefficient of different radius of the placed additional rods without moving the corner rods. The inset shows the configuration of the Yjunction without moving the corner rods.

point appropriately, we can distinguish and separate all the different pulses propagating in the cell [3]. In the calculation, four pulses are sent down the waveguide, and each covers different ranges of frequencies. By the Fourier transform, the transmission coefficient is obtained for each frequency of the pulses. The combined transmission and the reflection coefficient add up to unity to within an accuracy of 0.1%. It indicates that our calculation gives an accurate description to the response function of the waveguide branch. The radius of the placed additional rods rt (see Fig. 2) is varied in order to obtain the optimization performance (the radius of the moved corner rods are fixed, i.e., r =0.2a). Fig. 4 displays the transmission coefficient of Y-junction with different radius rt. When rt = 0.07a, an optimum transmission is obtained. The transmission coefficient is higher than 49.5% within the frequency range between o = 0.375(2pc/a) and 0.385(2pc/a) (see Fig. 4 solid line). When rt is bigger or smaller than 0.007a, e.g., rt =0.10a and 0.04a, the transmission coefficient of Y-junction is reduced obviously (see Fig. 4 dot line and dash line). The calculation results can be qualitatively explained by the coupled-mode theory presented above. In the case of rt = 0.07a, the rate-matching condition described by Eq. (6) is satisfied.

Fig. 6. Steady-state electric field distribution, at a frequency o = 0.38(2pc/a) for the structure with the radius of the moved corner rods being r =0.2a.

Fig. 7. The transmission coefficient with different radius of the moved corner rods.

Therefore, the optimum transmission coefficient is obtained. Here, it should be pointed out that the movement of corner rods is necessary. We calculated the transmission coefficient with different radius of the placed additional rods without moving the corner rods, as shown in Fig. 5. From Fig. 5, it is clearly seen that the transmission coefficient is low in comparison with Fig. 4. This is due to the fact that the resonance frequency of the cavity is not in the frequency range of the waveguide mode. In Fig. 6, we show the steady-state field distribution at o = 0.38(2pc/a) for the photonic structure with rt = 0.07a. The fields are completely confined in the waveguide regions and split equally into the output waveguides. When the radius of the moved corner rods is changed slightly, the transmission coefficient is still high. The reason is that the variety of the volume of the cavity is too small to change transmission coefficient. There is only a change in the frequency range of the transmission coefficient, as shown in Fig. 7.

4. Conclusion In this paper, we have proposed a new Y-junction in PCWs by moving the corner rods into a resonant cavity and placing

ARTICLE IN PRESS W. Yang et al. / Physica B 405 (2010) 1832–1835

additional rods between the resonant cavity and the output waveguides. Two-dimensional numerical simulation is performed to identify the structure with near-complete transmission. The transmission coefficient in each output port is higher than 49.5% within the frequency range between o = 0.375(2pc/a) and 0.385(2pc/a). The transmission properties can be qualitatively explained by the coupled-mode theory.

Acknowledgments This work is partially supported by multiple Grants from the State Key Program for Basic Research of China (2007CB613206, 2006CB921704), National Natural Science Foundation of China (10725418, 10734090, 10474108 and 60576068), Key Fund of Shanghai Science and Technology Foundation (08JC14 21100), Foundation of Henan University of Technology (09XJC007), and Knowledge Innovation Program of the Chinese Academy of Sciences.

1835

References [1] S. John, Phys. Rev. Lett. 58 (1987) 2486. [2] E. Yablonovitch, Phys. Rev. Lett. 58 (1987) 2059. [3] A. Mekis, J.C. Chen, I. Kurland, S. Fan, P.R. Villeneuve, J.D. Joannopoulos, Phys. Rev. Lett. 77 (1996) 3787. [4] S.-Y. Lin, E. Chow, V. Hietala, P.R. Villeneuve, J.D. Joannopoulos, Science 282 (1998) 274. [5] S. Fan, S.G. Johnson, J.D. Joannopoulos, C. Manolatou, H.A. Haus, J. Opt. Soc. Amer. B. 18 (2001) 162. [6] F. Monifi, M. Djavid, A. Ghaffari, M.S. Abrishamian, J. Opt. Soc. Amer. B 25 (2008) 1805. [7] J.S. Jensen, O. Sigmund, J. Opt. Soc. Amer. B 22 (2005) 1191. [8] Y. Watanabe, N. Ikeda, Y. Takata, Y. Kitagawa, N. Ozaki, Y. Sugimoto, K. Asakawa, J. Phys. D Appl. Phys. 41 (2008) 175109. [9] P.I. Borel, L.H. Frandsen, A. Harpøth, M. Kristensen, J.S. Jensen, O. Sigmund, Electron. Lett. 41 (2005) 69. [10] A. Ghaffari, M. Djavid, M.S. Abrishamian, Physica E 41 (2009) 1495. [11] I. Park, H.-S. Lee, H.-J. Kim, K.-M. Moon, S.-G. Lee, B.-H. O, S.-G. Park, E.-H. Lee, Opt. Express 12 (2004) 3599. [12] S. Boscolo, M. Midrio, T.F. Krauss, Opt. Lett. 27 (2002) 1001. [13] H.A. Haus, Waves and Fields in Optoelectronics, Prentice-Hall, London, 1984. [14] A. Taflove, Computational Electrodynamics: The Finite-Difference TimeDomain Method, Artech House, Norwood, MA, 1995. [15] J.C. Chen, K. Li, Microwave Opt. Tech. Lett. 10 (1995) 319.