Abstract

This paper systematically investigates the self-collimation behavior in silicon-based triangular-lattice annular photonic crystals (PCs). It is found that, in comparison with normal air-hole PCs, annular PCs more easily suppress the separation between TE-2 and TM-2 bands along the Γ-M direction by increasing the inner radius of annular air rings. Such a feature is quite beneficial in the formation of a flat equi-frequency contour for both polarizations at the same frequency, which means a polarization-insensitive self-collimation (PISC) effect. Further analysis has shown that, to support PISC, the minimum ratio between the inner and outer radii of annular air rings will gradually increase as the outer radius changes from 0.25a to 0.49a. When the ratio is fixed, the annular air rings with larger outer radius will provide wider common frequency area to realize PISC. We have also investigated the transmission feature for different annular PCs and chosen an optimal structure to illustrate the PISC effect. Finally, a polarization beam splitter has been proposed and demonstrated based on the unique PISC and band-gap feature in triangular-lattice annular PCs.

© 2013 Optical Society of America

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2012

L. Y. Jiang, H. Wu, W. Jia, and X. Y. Li, “Polarization-independent negative refraction effect in SiO2-GaAs annular photonic crystals,” J. Appl. Phys. 111, 023508 (2012).
[CrossRef]

L. Y. Jiang, H. Wu, and X. Y. Li, “Dual-negative-refraction and imaging effects in normal two-dimensional photonic crystals with hexagonal lattices,” Opt. Lett. 37, 1829–1831 (2012).
[CrossRef]

2011

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. LonCar, “High-Q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[CrossRef]

2009

J. Hou, D. S. Gao, H. M. Wu, and Z. P. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282, 3172–3176 (2009).
[CrossRef]

Y. Xu, X. J. Chen, S. Lan, Q. F. Dai, Q. Guo, and L. J. Wu, “Polarization-independent self-collimation based on pill-void photonic crystals with square symmetry,” Opt. Express 17, 4903–4912 (2009).
[CrossRef]

2008

2007

V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdr, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. 32, 530–532 (2007).
[CrossRef]

Y. L. Zhang, Y. Zhang, and B. J. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15, 9287–9292 (2007).
[CrossRef]

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

2006

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

2005

2004

2003

X. F. Yu and S. H. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3523 (2003).
[CrossRef]

D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
[CrossRef]

2002

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2001

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

2000

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

1999

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

1998

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russel, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

1996

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

1987

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Bhatia, C. S.

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russel, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russel, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef]

Chen, C. H.

Chen, C. P.

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Chen, X. J.

Chen, X. Y.

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

Chigrin, D.

Citrin, D. S.

Dai, Q. F.

Danner, A. J.

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Deng, J.

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Deotare, P. B.

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. LonCar, “High-Q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[CrossRef]

Dunbar, L. A.

Enoch, S.

Etrich, C.

Fan, S. H.

X. F. Yu and S. H. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3523 (2003).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Fink, Y.

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Frandsen, L. H.

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

Gao, D. S.

J. Hou, D. S. Gao, H. M. Wu, and Z. P. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282, 3172–3176 (2009).
[CrossRef]

Guo, Q.

Han, K.

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Hou, J.

J. Hou, D. S. Gao, H. M. Wu, and Z. P. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282, 3172–3176 (2009).
[CrossRef]

Houdr, R.

Hvam, J. M.

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

Iliew, R.

Jia, W.

L. Y. Jiang, H. Wu, W. Jia, and X. Y. Li, “Polarization-independent negative refraction effect in SiO2-GaAs annular photonic crystals,” J. Appl. Phys. 111, 023508 (2012).
[CrossRef]

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Jiang, L. Y.

L. Y. Jiang, H. Wu, and X. Y. Li, “Dual-negative-refraction and imaging effects in normal two-dimensional photonic crystals with hexagonal lattices,” Opt. Lett. 37, 1829–1831 (2012).
[CrossRef]

L. Y. Jiang, H. Wu, W. Jia, and X. Y. Li, “Polarization-independent negative refraction effect in SiO2-GaAs annular photonic crystals,” J. Appl. Phys. 111, 023508 (2012).
[CrossRef]

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Jiang, X. Y.

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

Joannopoulos, J. D.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef]

Johnson, S. G.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russel, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef]

Kosaka, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Kotlyar, M. V.

Krauss, T. F.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Kurt, H.

Lan, S.

Le Thomas, N.

Lederer, E.

Li, B. J.

Li, H. P.

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Li, X. Y.

L. Y. Jiang, H. Wu, and X. Y. Li, “Dual-negative-refraction and imaging effects in normal two-dimensional photonic crystals with hexagonal lattices,” Opt. Lett. 37, 1829–1831 (2012).
[CrossRef]

L. Y. Jiang, H. Wu, W. Jia, and X. Y. Li, “Polarization-independent negative refraction effect in SiO2-GaAs annular photonic crystals,” J. Appl. Phys. 111, 023508 (2012).
[CrossRef]

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Liu, L.

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

LonCar, M.

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. LonCar, “High-Q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[CrossRef]

Luo, C. Y.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Martin, R.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

McCutcheon, M. W.

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. LonCar, “High-Q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Miao, B. L.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Michel, J.

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Murakowski, J.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

D. W. Prather, S. Y. Shi, D. M. Pustai, C. H. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

O’Faolain, L.

Ou, H. Y.

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

Pendry, J. B.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Pertsch, T.

Prather, D. W.

Pu, M. H.

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

Pustai, D. M.

Russel, P. S. J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russel, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef]

Sahadevan, A. M.

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Schneider, G. J.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

D. W. Prather, S. Y. Shi, D. M. Pustai, C. H. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004).
[CrossRef]

Sharkawy, A.

Shen, X. P.

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Shen, Y. F.

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Shi, S. Y.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Sotomayor Torres, C.

Staliunas, K.

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Tayeb, G.

Thomas, E. L.

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Tokushima, M.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

Tomita, A.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Venkataraman, S.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Wu, H.

L. Y. Jiang, H. Wu, W. Jia, and X. Y. Li, “Polarization-independent negative refraction effect in SiO2-GaAs annular photonic crystals,” J. Appl. Phys. 111, 023508 (2012).
[CrossRef]

L. Y. Jiang, H. Wu, and X. Y. Li, “Dual-negative-refraction and imaging effects in normal two-dimensional photonic crystals with hexagonal lattices,” Opt. Lett. 37, 1829–1831 (2012).
[CrossRef]

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Wu, H. M.

J. Hou, D. S. Gao, H. M. Wu, and Z. P. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282, 3172–3176 (2009).
[CrossRef]

Wu, L. J.

Xiao, Z. W.

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yamada, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Yang, H.

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

Yao, P. J.

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Yu, X. F.

X. F. Yu and S. H. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3523 (2003).
[CrossRef]

Yvind, K.

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

Zabelin, V.

Zhang, J.

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

Zhang, Y.

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. LonCar, “High-Q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[CrossRef]

Y. L. Zhang, Y. Zhang, and B. J. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15, 9287–9292 (2007).
[CrossRef]

Zhang, Y. L.

Zhao, D. Y.

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

Zheng, J.

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Zhou, Z. P.

J. Hou, D. S. Gao, H. M. Wu, and Z. P. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282, 3172–3176 (2009).
[CrossRef]

Acta Phys. Sinica

X. P. Shen, K. Han, Y. F. Shen, H. P. Li, Z. W. Xiao, and J. Zheng, “Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals,” Acta Phys. Sinica 55, 2760–2764(2006).

Appl. Phys. Lett.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

X. F. Yu and S. H. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3523 (2003).
[CrossRef]

D. Y. Zhao, J. Zhang, P. J. Yao, X. Y. Jiang, and X. Y. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007).
[CrossRef]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

W. Jia, J. Deng, A. M. Sahadevan, H. Wu, L. Y. Jiang, X. Y. Li, C. S. Bhatia, H. Yang, and A. J. Danner, “Design and fabrication of high efficiency power coupler between different photonic crystal waveguides,” Appl. Phys. Lett. 98, 241102 (2011).
[CrossRef]

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. LonCar, “High-Q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[CrossRef]

J. Appl. Phys.

L. Y. Jiang, H. Wu, W. Jia, and X. Y. Li, “Polarization-independent negative refraction effect in SiO2-GaAs annular photonic crystals,” J. Appl. Phys. 111, 023508 (2012).
[CrossRef]

J. Phys. D

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Opt. Commun.

J. Hou, D. S. Gao, H. M. Wu, and Z. P. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282, 3172–3176 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Phys. Rev. Lett.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Science

Y. Fink, J. N. Winn, S. H. Fan, C. P. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russel, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef]

Other

S. G. Johnson and J. D. Joannopoulos, “MIT Photonic-Bands package,” The MIT Photonic-Bands Package Home Page, http://ab-initio.mit.edu/mpb/ (2008).

M. H. Pu, L. Liu, L. H. Frandsen, H. Y. Ou, K. Yvind, and J. M. Hvam, “Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA20.

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Figures (12)

Fig. 1.
Fig. 1.

Representative model for a triangular-lattice annular PC. The annular air rings with outer radius R and inner radius r are arranged in a triangular lattice (a is the lattice constant) and embedded in a silicon background.

Fig. 2.
Fig. 2.

TE (solid lines) and TM (dashed lines) band structures of the triangular-lattice annular PC when R=0.35a and (a) r=0, (b) r=0.1a, (c) r=0.2a, and (d) r=0.3a, respectively. The yellow area (or gray area for black and white version) represents the band gap of TE polarization.

Fig. 3.
Fig. 3.

TE-2 and TM-2 EFCs of the triangular-lattice annular PC when R=0.35a and (a) r=0, (b) r=0.2a, and (c) r=0.3a, respectively.

Fig. 4.
Fig. 4.

To realize PISC, the minimum possible value of the ratio between the inner and outer radii of the annular air rings when the outer radius R varies from 0.25a to 0.49a.

Fig. 5.
Fig. 5.

TE (solid lines) and TM (dashed lines) band structures of the triangular-lattice annular PC when r=0.9R and (a) R=0.3a, (b) R=0.4a, and (c) R=0.49a, respectively.

Fig. 6.
Fig. 6.

TE-2 and TM-2 EFCs of the triangular-lattice annular PC when r=0.9R and (a) R=0.3a, (b) R=0.4a, and (c) R=0.49a, respectively.

Fig. 7.
Fig. 7.

(a1) and (a2) Normalized transmittance in a 19-layer triangular-lattice annular PC when R=0.35a and r=0.86R, r=0.9R, and r=R for different polarizations. (b1) and (b2) Normalized transmittance in a 19-layer triangular-lattice annular PC slab when r=0.9R and R=0.25a, R=0.35a, and R=0.45a for different polarizations.

Fig. 8.
Fig. 8.

TE-2 (a1) and TM-2 (a2) EFCs of the triangular-lattice annular PC when R=0.45a and r=0.9R. (b) Combined TE-2 and TM-2 and the air background EFCs at normalized frequency 0.279ωa/2πc.

Fig. 9.
Fig. 9.

(a) Relationship between cutoff value δy and transmittance. (b) and (c) show the magnetic/electric field distributions in the whole X–Y plane for both polarizations when δy=0.09a. The subfigure on the top of (b) or (c) is the cross-section normalized absolute magnetic/electric field at the location of the monitor. The solid lines represent the termination of the PC, and the dashed line represents the location of the monitor. The normalized frequency used in simulations is 0.279ωa/2πc.

Fig. 10.
Fig. 10.

Schematic of a polarization beam splitter based on different triangular-lattice annular PCs. The main triangular-lattice annular PC has the same structure as in Fig. 8, while the defect triangular-lattice annular PC enclosed by the dashed line has a different inner radius r of air rings. The inset on the right side of the defect PC gives a simple schematic diagram to illustrate the working mechanism.

Fig. 11.
Fig. 11.

TE (solid lines) and TM (dashed lines) band structures of the defect triangular-lattice annular PC when R=0.45a and r=0.33a. The yellow area (or gray area for black and white version) represents the band gap of TE polarization.

Fig. 12.
Fig. 12.

(a) Relationship between the inner radius r and the extinction coefficient at two outputs. (b) and (c) show the absolute magnetic/electric field distributions in the whole X–Y plane for both polarizations when r=0.347a. The subfigure near the output shows the cross-section normalized magnetic/electric field at the location of the monitor, which is marked by the dashed line and is 2a away from the output surface. The cutoff value at all terminations is still 0.09a.

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