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Photonic crystal beam splitters
Optics Communications 259 (2006) 873–875 www.elsevier.com/locate/optcom
Photonic crystal beam splitters Hung-Ta Chien *, Chii-Chang Chen, Pi-Gang Luan Institute of Optical Sciences, National Central University, Jhong-Li 320, Taiwan Received 15 June 2005; received in revised form 22 August 2005; accepted 5 September 2005
Abstract In this work, the beam splitter with two input ports and two output ports in two-dimensional photonic crystals is studied through the finite-difference time-domain method. The beam splitter consists of two orthogonally cross line defects. The diameter of the two diagonal air holes at the intersection of the two line defects was modified. The input light can be identically divided into the two output ports. The beam splitters can be applied in the photonic crystal Mach–Zehnder interferometers or photonic crystal optical switches. 2005 Elsevier B.V. All rights reserved. Keywords: Beam splitters; Photonic crystals
1. Introduction Photonic crystal (PC) slab waveguides have been intensively studied [1–8]. Various optical components can be realized by introducing the defects into the PC structures. Line defects can be used to build the straight or bent waveguides [2,5–8]. The wavelength add-drop devices can be realized by introducing the point defects beside the line defects [2]. The point defect can also be added in the bent PC waveguides to improve the transmission efficiency [9]. The beam splitters in PC structures have been studied by arranging the line defects [10–19]. The performance of the T- or Y-type PC beam splitter with one input port and two output ports have been investigated [13,19]. To build a PC Mach–Zehnder interferometer, a beam splitter with one input port and two output ports should be used to divide the input light into two beams with identical power as the 1 · 2 beam splitter shown in Fig. 1. The two beams should interfere in the second PC beam splitter that consists of two input ports and two output ports. The function of the second beam splitter should act as the glass slide shown in Fig. 1. The directional couplers can be used as the
*
Corresponding author. E-mail address: [email protected] (H.-T. Chien).
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.09.008
second beam splitter. However, the fact that the coupling ratio highly depends on the wavelength is the bottleneck to use the directional coupler as the beam splitter. Recently, we have proposed a PC beam splitter with two input ports and two output ports [17]. The PC structure is formed by periodically arranged dielectric rods in square lattice. A point defect is added into the orthogonally cross line defects. As the beam splitter is used in the PC Mach–Zehnder interferometer, the bandwidth for the extinction ratio larger than 20 dB is 125 nm (from 1.485 to 1.610 lm). This result indicates that the beam splitter can be operated in the wavelength range of fiber optic communication with a large bandwidth. In this study, we propose a novel PC beam splitter structure formed by the periodically arranged air holes in square lattice. In this PC device, the vertical and horizontal confinements of the light can be obtained by the index difference and photonic-bandgap guiding, respectively. The PC beam splitter consists of two orthogonally cross line defects. The diameter of the two diagonal air holes located at the intersection of the cross line defects was modified. By varying the diameter of the two air holes, the input light can be divided into the two outputs with identical power. The interference and the reflection properties of the beam splitter are studied. The results indicate that the PC beam splitter can be used in the PC Mach–Zehnder interferometer or PC
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H.-T. Chien et al. / Optics Communications 259 (2006) 873–875
Fig. 1. Schematic diagram of a Mach–Zehnder interferometer including a 1 · 2 beam splitter, two mirrors, and a 2 · 2 beam splitter.
symmetry of the structure, the properties of the input port 2 are identical as those of the input port 1. A pulse is launched into the input port 1 and the temporal variation of the electromagnetic (EM) field in each input and output port is monitored. The distance between each position where we monitor the EM field to the center of the beam splitter is identical to avoid the unexpected inaccuracy. The transmission and the reflection spectra can be obtained by the Fourier transformation of the monitored signals from time domain to frequency domain. The diameter d is varied and it is found that as d = 0.48–0.54a, the input power can be divided into the output ports with identical power. As d is equal to 0.5a, at the wavelengths of
optical switches for the applications of the optical fiber communication. 2. Simulation procedure and results 2-D finite-difference time-domain (FDTD) method is adopted to calculate the characteristics of the beam splitters. The PC structure consists of air holes arranged in square lattice in the dielectric material where the refractive index is 3.46. Fig. 2 illustrates the structure of the 2 · 2 PC beam splitter. The diameter of air holes is D = 0.9a, where a is the lattice constant. Two orthogonally cross line defects are created in the PC structure by removing the air holes. The width of the line defect, W, is defined by the distance between the centers of the air holes beside the line defects. W is reduced to be 1.4a to ensure the fact that the PC waveguides is single-mode for the wavelength range in the photonic bandgap of the PC structure. The H-polarized light (the electric field lies on the propagation plane) is launched into the line defect. The diameter of the two diagonal air holes at the intersection of the two line defects, d, was varied to study the splitting ratio of the beam splitter. As shown in Fig. 2, by reducing d to be 0.5a, the input light launched from the input port 1 can be separated into the two output ports with identical power. Since the diagonal
Fig. 2. Schematic diagram of 2 · 2 PC beam splitter. W is the width of PC waveguides. D is the diameter of the air holes of the PC structure. d is the diameter of the diagonal air hole at the center of the PC beam splitter.
Fig. 3. (a) Transmission spectra of the two output ports. (b) Reflection and crosstalk spectra.
H.-T. Chien et al. / Optics Communications 259 (2006) 873–875
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3. Conclusion We have proposed a novel PC beam splitter with two input ports and two output ports by combining the orthogonally cross line defects and two point defects with reduced diameter. The PC structure consists of air holes in dielectric material with refractive index 3.46. The proposed structure can be applied in Si or GaAs-based semiconductor materials. The optimized structure is d = 0.5a, where the wavelength range is the widest. The power difference between two outputs is lower than 8% in wavelength from 2.554a to 2.6a. The corresponding wavelength range can be from 1534 to 1562 nm. Therefore, the PC beam splitter can be operated in the C band of the optical fiber communication. The PC beam splitters can be used to realize the optical switches or the Mach–Zehnder modulators in PC structures. Fig. 4. Two output powers versus the phase difference between the two input lights. The sinusoidal relation is the typical response of Mach– Zehnder interferometers.
2.55a and 2.6a, the powers received in the two output ports are identical. Fig. 3(a) shows the transmission spectra of the two output ports as d = 0.5a. The power difference between the two output ports is less than 8% in the wavelength range from 2.554a to 2.6a. This wavelength range is the widest for d = 0.5a, as d is varied between 0.48a and 0.54a. If, in Fig. 3(a), the normalized wavelength of 2.58a corresponds to the wavelength at 1550 nm, the corresponding wavelength range of 2.554a–2.6a is from 1534 to 1562 nm. Therefore, this beam splitter can be used in the C band for optical fiber communication. In Fig. 2, we can observe the fact that as the light is launched into the input port 1, the light also leaks into the input port 2. This behavior causes the crosstalk of the signals. Additionally, as the light is launched into the input port, the beam splitter reflects a few part of the energy. Fig. 3(b) shows the crosstalk spectrum and the reflection spectrum. The crosstalk and the reflection are less than 20 dB (1%) and 14 dB (4%) in the wavelength range that mentioned above, respectively. The crosstalk is better than that reported in [17] to be 12 dB. The reflection is slightly higher than that reported in [17] to be 16 dB. Two lights are launched into the two input ports with a phase difference. Fig. 4 shows the variation of the powers received in the two output ports. The sinusoidal relation between the output powers and the phase difference demonstrates that the PC beam splitter can be used in the PC Mach–Zehnder interferometers.
References [1] E. Chow, S.Y. Lin, S.G. Johnson, P.R. Villeneuve, J.D. Joannopoulos, J.R. Wendt, G.A. Vawter, W. Zubrycki, H. Hou, A. Alleman, Nature 407 (2002) 983. [2] S. Noda, A. Chutinan, M. Imada, Nature 407 (2000) 608. [3] A. Talneau, L. Le Gouezigou, N. Bouadma, C.M. Soukoulis, N. Agio, Appl. Phys. Lett. 80 (2002) 547. [4] N. Kawai, K. Inoue, N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Phys. Rev. Lett. 86 (2001) 2289. [5] M. Tokushima, H. Kosaka, A. Tomita, H. Yamada, Appl. Phys. Lett. 76 (2000) 952. [6] M. Qiu, B. Jaskorzynska, Appl. Phys. Lett. 83 (2003) 1074. [7] M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, Electron. Lett. 37 (2001) 293. [8] M.H. Shih, Woo Jun Kim, Wan Kuang, J.R. Cao, Sang-Jun Choi, John D. OÕBrien, P. Daniel Dapkus, Appl. Phys. Lett. 86 (2005) 191104. [9] A. Chutinan, M. Okano, S. Noda, Appl. Phys. Lett. 80 (2002) 1698. [10] C. Jin, S. Han, X. Meng, B. Cheng, D. Zhang, J. Appl. Phys. 91 (2002) 4771. [11] M. Bayindir, E. Ozbay, B. Temelkuran, M.M. Sigalas, C.M. Soukoulis, R. Biswas, K.M. Ho, Phys. Rev. B 63 (2001) 081107. [12] M. Bayinder, B. Temelkuran, E. Ozbay, Appl. Phys. Lett. 77 (2000) 3902. [13] T. Søndergaard, K.H. Dridi, Phys. Rev. B 61 (2000) 15688. [14] J. Yonekura, M. Ikeda, T. Baba, J. Lightwave Technol. 17 (1999) 1500. [15] C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, J.D. Joannopoulos, J. Lightwave Technol. 17 (1999) 1682. [16] S.G. Johnson, C. Manolatou, S. Fan, R. Villenwuve, J.D. Joannopoulos, H.A. Haus, Opt. Lett. 23 (1988) 1855. [17] C.C. Chen, H.D. Chien, P.G. Luan, Appl. Opt. 43 (2004) 6188. [18] D. Goldring, E. Alperovich, U. Levy, D. Mendlovic, Opt. Express 13 (2005) 2931. [19] S. Boscolo, M. Midrio, T.F. Krauss, Opt. Lett. 27 (2002) 1001.
Photonic crystal beam splitters Hung-Ta Chien *, Chii-Chang Chen, Pi-Gang Luan Institute of Optical Sciences, National Central University, Jhong-Li 320, Taiwan Received 15 June 2005; received in revised form 22 August 2005; accepted 5 September 2005
Abstract In this work, the beam splitter with two input ports and two output ports in two-dimensional photonic crystals is studied through the finite-difference time-domain method. The beam splitter consists of two orthogonally cross line defects. The diameter of the two diagonal air holes at the intersection of the two line defects was modified. The input light can be identically divided into the two output ports. The beam splitters can be applied in the photonic crystal Mach–Zehnder interferometers or photonic crystal optical switches. 2005 Elsevier B.V. All rights reserved. Keywords: Beam splitters; Photonic crystals
1. Introduction Photonic crystal (PC) slab waveguides have been intensively studied [1–8]. Various optical components can be realized by introducing the defects into the PC structures. Line defects can be used to build the straight or bent waveguides [2,5–8]. The wavelength add-drop devices can be realized by introducing the point defects beside the line defects [2]. The point defect can also be added in the bent PC waveguides to improve the transmission efficiency [9]. The beam splitters in PC structures have been studied by arranging the line defects [10–19]. The performance of the T- or Y-type PC beam splitter with one input port and two output ports have been investigated [13,19]. To build a PC Mach–Zehnder interferometer, a beam splitter with one input port and two output ports should be used to divide the input light into two beams with identical power as the 1 · 2 beam splitter shown in Fig. 1. The two beams should interfere in the second PC beam splitter that consists of two input ports and two output ports. The function of the second beam splitter should act as the glass slide shown in Fig. 1. The directional couplers can be used as the
*
Corresponding author. E-mail address: [email protected] (H.-T. Chien).
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.09.008
second beam splitter. However, the fact that the coupling ratio highly depends on the wavelength is the bottleneck to use the directional coupler as the beam splitter. Recently, we have proposed a PC beam splitter with two input ports and two output ports [17]. The PC structure is formed by periodically arranged dielectric rods in square lattice. A point defect is added into the orthogonally cross line defects. As the beam splitter is used in the PC Mach–Zehnder interferometer, the bandwidth for the extinction ratio larger than 20 dB is 125 nm (from 1.485 to 1.610 lm). This result indicates that the beam splitter can be operated in the wavelength range of fiber optic communication with a large bandwidth. In this study, we propose a novel PC beam splitter structure formed by the periodically arranged air holes in square lattice. In this PC device, the vertical and horizontal confinements of the light can be obtained by the index difference and photonic-bandgap guiding, respectively. The PC beam splitter consists of two orthogonally cross line defects. The diameter of the two diagonal air holes located at the intersection of the cross line defects was modified. By varying the diameter of the two air holes, the input light can be divided into the two outputs with identical power. The interference and the reflection properties of the beam splitter are studied. The results indicate that the PC beam splitter can be used in the PC Mach–Zehnder interferometer or PC
874
H.-T. Chien et al. / Optics Communications 259 (2006) 873–875
Fig. 1. Schematic diagram of a Mach–Zehnder interferometer including a 1 · 2 beam splitter, two mirrors, and a 2 · 2 beam splitter.
symmetry of the structure, the properties of the input port 2 are identical as those of the input port 1. A pulse is launched into the input port 1 and the temporal variation of the electromagnetic (EM) field in each input and output port is monitored. The distance between each position where we monitor the EM field to the center of the beam splitter is identical to avoid the unexpected inaccuracy. The transmission and the reflection spectra can be obtained by the Fourier transformation of the monitored signals from time domain to frequency domain. The diameter d is varied and it is found that as d = 0.48–0.54a, the input power can be divided into the output ports with identical power. As d is equal to 0.5a, at the wavelengths of
optical switches for the applications of the optical fiber communication. 2. Simulation procedure and results 2-D finite-difference time-domain (FDTD) method is adopted to calculate the characteristics of the beam splitters. The PC structure consists of air holes arranged in square lattice in the dielectric material where the refractive index is 3.46. Fig. 2 illustrates the structure of the 2 · 2 PC beam splitter. The diameter of air holes is D = 0.9a, where a is the lattice constant. Two orthogonally cross line defects are created in the PC structure by removing the air holes. The width of the line defect, W, is defined by the distance between the centers of the air holes beside the line defects. W is reduced to be 1.4a to ensure the fact that the PC waveguides is single-mode for the wavelength range in the photonic bandgap of the PC structure. The H-polarized light (the electric field lies on the propagation plane) is launched into the line defect. The diameter of the two diagonal air holes at the intersection of the two line defects, d, was varied to study the splitting ratio of the beam splitter. As shown in Fig. 2, by reducing d to be 0.5a, the input light launched from the input port 1 can be separated into the two output ports with identical power. Since the diagonal
Fig. 2. Schematic diagram of 2 · 2 PC beam splitter. W is the width of PC waveguides. D is the diameter of the air holes of the PC structure. d is the diameter of the diagonal air hole at the center of the PC beam splitter.
Fig. 3. (a) Transmission spectra of the two output ports. (b) Reflection and crosstalk spectra.
H.-T. Chien et al. / Optics Communications 259 (2006) 873–875
875
3. Conclusion We have proposed a novel PC beam splitter with two input ports and two output ports by combining the orthogonally cross line defects and two point defects with reduced diameter. The PC structure consists of air holes in dielectric material with refractive index 3.46. The proposed structure can be applied in Si or GaAs-based semiconductor materials. The optimized structure is d = 0.5a, where the wavelength range is the widest. The power difference between two outputs is lower than 8% in wavelength from 2.554a to 2.6a. The corresponding wavelength range can be from 1534 to 1562 nm. Therefore, the PC beam splitter can be operated in the C band of the optical fiber communication. The PC beam splitters can be used to realize the optical switches or the Mach–Zehnder modulators in PC structures. Fig. 4. Two output powers versus the phase difference between the two input lights. The sinusoidal relation is the typical response of Mach– Zehnder interferometers.
2.55a and 2.6a, the powers received in the two output ports are identical. Fig. 3(a) shows the transmission spectra of the two output ports as d = 0.5a. The power difference between the two output ports is less than 8% in the wavelength range from 2.554a to 2.6a. This wavelength range is the widest for d = 0.5a, as d is varied between 0.48a and 0.54a. If, in Fig. 3(a), the normalized wavelength of 2.58a corresponds to the wavelength at 1550 nm, the corresponding wavelength range of 2.554a–2.6a is from 1534 to 1562 nm. Therefore, this beam splitter can be used in the C band for optical fiber communication. In Fig. 2, we can observe the fact that as the light is launched into the input port 1, the light also leaks into the input port 2. This behavior causes the crosstalk of the signals. Additionally, as the light is launched into the input port, the beam splitter reflects a few part of the energy. Fig. 3(b) shows the crosstalk spectrum and the reflection spectrum. The crosstalk and the reflection are less than 20 dB (1%) and 14 dB (4%) in the wavelength range that mentioned above, respectively. The crosstalk is better than that reported in [17] to be 12 dB. The reflection is slightly higher than that reported in [17] to be 16 dB. Two lights are launched into the two input ports with a phase difference. Fig. 4 shows the variation of the powers received in the two output ports. The sinusoidal relation between the output powers and the phase difference demonstrates that the PC beam splitter can be used in the PC Mach–Zehnder interferometers.
References [1] E. Chow, S.Y. Lin, S.G. Johnson, P.R. Villeneuve, J.D. Joannopoulos, J.R. Wendt, G.A. Vawter, W. Zubrycki, H. Hou, A. Alleman, Nature 407 (2002) 983. [2] S. Noda, A. Chutinan, M. Imada, Nature 407 (2000) 608. [3] A. Talneau, L. Le Gouezigou, N. Bouadma, C.M. Soukoulis, N. Agio, Appl. Phys. Lett. 80 (2002) 547. [4] N. Kawai, K. Inoue, N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Phys. Rev. Lett. 86 (2001) 2289. [5] M. Tokushima, H. Kosaka, A. Tomita, H. Yamada, Appl. Phys. Lett. 76 (2000) 952. [6] M. Qiu, B. Jaskorzynska, Appl. Phys. Lett. 83 (2003) 1074. [7] M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, Electron. Lett. 37 (2001) 293. [8] M.H. Shih, Woo Jun Kim, Wan Kuang, J.R. Cao, Sang-Jun Choi, John D. OÕBrien, P. Daniel Dapkus, Appl. Phys. Lett. 86 (2005) 191104. [9] A. Chutinan, M. Okano, S. Noda, Appl. Phys. Lett. 80 (2002) 1698. [10] C. Jin, S. Han, X. Meng, B. Cheng, D. Zhang, J. Appl. Phys. 91 (2002) 4771. [11] M. Bayindir, E. Ozbay, B. Temelkuran, M.M. Sigalas, C.M. Soukoulis, R. Biswas, K.M. Ho, Phys. Rev. B 63 (2001) 081107. [12] M. Bayinder, B. Temelkuran, E. Ozbay, Appl. Phys. Lett. 77 (2000) 3902. [13] T. Søndergaard, K.H. Dridi, Phys. Rev. B 61 (2000) 15688. [14] J. Yonekura, M. Ikeda, T. Baba, J. Lightwave Technol. 17 (1999) 1500. [15] C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, J.D. Joannopoulos, J. Lightwave Technol. 17 (1999) 1682. [16] S.G. Johnson, C. Manolatou, S. Fan, R. Villenwuve, J.D. Joannopoulos, H.A. Haus, Opt. Lett. 23 (1988) 1855. [17] C.C. Chen, H.D. Chien, P.G. Luan, Appl. Opt. 43 (2004) 6188. [18] D. Goldring, E. Alperovich, U. Levy, D. Mendlovic, Opt. Express 13 (2005) 2931. [19] S. Boscolo, M. Midrio, T.F. Krauss, Opt. Lett. 27 (2002) 1001.