Abstract

Magneto-optical and regular photonic crystals with triangular lattice are designed to construct one-way waveguides. Accordingly, two types of efficient beam splitters with one-way input channels are proposed and investigated. One of the proposed beam splitters is a 1×2 splitter, which achieves 50/50 splitting based on the structural symmetry. Since both output channels are one-way waveguides, this splitter is immune to interferences at the output ends. The other is a 1×3 beam splitter, in which one output channel is a regular waveguide and the others are one-way waveguides. It is shown that the 1×3 splitter can provide equal splitting ratios in the guiding band if defects with proper parameters are introduced in the splitting region.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

D. Yang, H. Tian, and Y. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun. 285, 3752–3757 (2012).
[CrossRef]

2011

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

2010

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

M. Zhang, R. Malureanu, A. C. Krger, and M. Kristensen, “1×3 beam splitter for TE polarization based on self-imaging phenomena in photonic crystal waveguides,” Opt. Express 18, 14944–14948 (2010).
[CrossRef]

2009

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

X. Y. Ao, Z. F. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80, 033105 (2009).
[CrossRef]

2008

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

J. J. Feng, C. H. Zhou, B. Wang, J. J. Zheng, W. Jia, H. C. Cao, and P. Lu, “Three-port beam splitter of a binary fused-silica grating,” Appl. Opt. 47, 6638–6643 (2008).
[CrossRef]

2005

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

2004

2003

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, “Efficient photonic crystal Y-junctions,” J. Opt. A 5, S76–S80 (2003).
[CrossRef]

2002

2001

2000

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys. A 71, 11–17 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

1999

Ao, X. Y.

X. Y. Ao, Z. F. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Baba, T.

Baets, R.

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

Beckx, S.

Bogaerts, W.

Borel, P. I.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3 dB photonic crystal waveguide splitter,” Opt. Lett. 29, 1623–1625 (2004).
[CrossRef]

Boscolo, S.

Cao, H. C.

Chan, C. T.

X. Y. Ao, Z. F. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Chen, X. L.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Chena, Y. F.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

Dumon, P.

Fan, S. H.

Feng, J. J.

Frandsen, L. H.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3 dB photonic crystal waveguide splitter,” Opt. Lett. 29, 1623–1625 (2004).
[CrossRef]

Fu, J. X.

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Gan, L.

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Goldman, J. R.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys. A 71, 11–17 (2000).
[CrossRef]

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Harpøth, A.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3 dB photonic crystal waveguide splitter,” Opt. Lett. 29, 1623–1625 (2004).
[CrossRef]

He, C.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Ikeda, M.

Jensen, J. S.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

Ji, Y.

D. Yang, H. Tian, and Y. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun. 285, 3752–3757 (2012).
[CrossRef]

Jia, W.

Joannopoulos, J. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

S. H. Fan, S. G. Johnson, and J. D. Joannopoulos, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165(2001).
[CrossRef]

Johnson, S. G.

Karle, T. J.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, “Efficient photonic crystal Y-junctions,” J. Opt. A 5, S76–S80 (2003).
[CrossRef]

Krauss, T. F.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, “Efficient photonic crystal Y-junctions,” J. Opt. A 5, S76–S80 (2003).
[CrossRef]

S. Boscolo, M. Midrio, and T. F. Krauss, “Y junctions in photonic crystal channel waveguides: high transmission and impedance matching,” Opt. Lett. 27, 1001–1003 (2002).
[CrossRef]

Krger, A. C.

Kristensen, M.

Ladd, T. D.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys. A 71, 11–17 (2000).
[CrossRef]

Li, X. F.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Li, Z. Y.

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Lian, J.

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Lin, Z. F.

X. Y. Ao, Z. F. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Liu, R. J.

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Lu, M. H.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Lu, P.

Malureanu, R.

Midrio, M.

Moerman, I.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, “Efficient photonic crystal Y-junctions,” J. Opt. A 5, S76–S80 (2003).
[CrossRef]

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering (Wiley, 1998).

Qian, X. S.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Shen, L. F.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

Sigmund, O.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

Soljacic, M.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

Thorhauge, M.

Tian, H.

D. Yang, H. Tian, and Y. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun. 285, 3752–3757 (2012).
[CrossRef]

Wan, W. W.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Wang, B.

Wang, Y. G.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

Wang, Z.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

Wang, Z. Y.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

Wiaux, V.

Wilson, R.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, “Efficient photonic crystal Y-junctions,” J. Opt. A 5, S76–S80 (2003).
[CrossRef]

Wouters, J.

Yamaguchi, F.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys. A 71, 11–17 (2000).
[CrossRef]

Yamamoto, Y.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys. A 71, 11–17 (2000).
[CrossRef]

Yang, D.

D. Yang, H. Tian, and Y. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun. 285, 3752–3757 (2012).
[CrossRef]

Yin, R. C.

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Yonekura, J.

Yu, Z. H.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

Zhang, M.

Zhang, X. M.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

Zheng, J. J.

Zheng, X. D.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

Zhou, C. H.

Zhuang, Y. X.

Appl. Opt.

Appl. Phys. A

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys. A 71, 11–17 (2000).
[CrossRef]

Appl. Phys. Lett.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

C. He, X. L. Chen, M. H. Lu, X. F. Li, W. W. Wan, X. S. Qian, R. C. Yin, and Y. F. Chena, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

J. X. Fu, J. Lian, R. J. Liu, L. Gan, and Z. Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Electron. Lett.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69–71 (2005).
[CrossRef]

J. Appl. Phys.

Z. Y. Wang, L. F. Shen, X. M. Zhang, Y. G. Wang, Z. H. Yu, and X. D. Zheng, “Photonic crystal cavity with one-way rotating state and its coupling with photonic crystal waveguide,” J. Appl. Phys. 110, 043106 (2011).
[CrossRef]

J. Lightwave Technol.

J. Opt. A

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, “Efficient photonic crystal Y-junctions,” J. Opt. A 5, S76–S80 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Nature

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Opt. Commun.

D. Yang, H. Tian, and Y. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun. 285, 3752–3757 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Phys. Rev. B

X. Y. Ao, Z. F. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Phys. Rev. Lett.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
[CrossRef]

Other

D. M. Pozar, Microwave Engineering (Wiley, 1998).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Simulated electric-field amplitudes for the proposed 50/50 splitter. The frequency is 4.3 GHz. The arrows indicate the direction of the energy flow. (b) Projected band structures for Al and MO PhCs. The solid and dashed curves with asterisks represent the dispersion relations for the input waveguide, and the curves with solid and open circles represent ones for the left and right output waveguides, respectively. (c) Ez amplitudes of two guiding modes in the input waveguide for the frequency 4.55 GHz. Upper two panels, kx=0.13(2π/a); lower two panels, kx=0.45(2π/a).

Fig. 2.
Fig. 2.

(a) Transmission efficiencies at the left (solid curves) and right (dotted curves) output ports in the presence of an obstacle (PEC rod). Circles, squares, and triangles correspond to the obstacle at xo=2.5a, 3.5a, and 7.5a, respectively. Inset shows the transmission efficiency for xo=7.5a over the whole guiding band. (b) Simulated electric-field amplitudes for the splitter with the obstacle at xo=3.5a. The frequency is 4.3 GHz.

Fig. 3.
Fig. 3.

(a) Simulated electric field amplitudes for a 1×3 splitter at frequency 4.3 GHz. (b) Transmission efficiencies and their (absolute) difference as a function of frequency. The parameters of defect rods are rd(1)=0.065a, rd(2)=0.09a, yd(1)=0.39a, and yd(2)=1.36a.

Equations (1)

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μ˜=[μ±iκ0iκμ0001]μ0,

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