Abstract

In this paper, we have systematically investigated the polarization-insensitive and broad-angle self-collimation behavior in a square-lattice two-dimensional photonic crystal (PhC) with rectangular air holes. By analyzing the band structures and the corresponding equi-frequency contours (EFCs), it is found that such PhC can show special dispersion properties when the half-length L and half-width W of rectangular air holes are appropriately changed. First, compared with conventional square-lattice PhCs with circular or square air holes, such PhC is easier to support polarization-insensitive self-collimation (PISC) based on the EFCs for the second band. Meanwhile, the PISC behavior such as working frequency range and effective incident angle can be more flexibly adjusted by changing the structural parameters of rectangular air holes. Second, such PhC can show long flat EFCs for the TM-3 band. This is quite helpful for supporting broad-angle self-collimation. In particular, when L=0.5a and W/L=0.8, this PhC will degenerate to a one-dimensional grating PhC. It can show good all-angle self-collimation behavior with an improved relative bandwidth (about 19.98%) compared with previous works. It also presents advantages in practical applications due to a relatively convenient fabrication process.

© 2013 Optical Society of America

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    [CrossRef]

2012 (2)

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]

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[CrossRef]

2010 (5)

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

J. M. Park, S. G. Lee, H.-R. Park, and M. H. Lee, “Self-collimating photonic crystal antireflection structure for both TE and TM polarizations,” Opt. Express 18, 13083–13093 (2010).
[CrossRef]

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12, 035102 (2010).
[CrossRef]

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[CrossRef]

2009 (3)

2008 (3)

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

R. Iliew, C. Etrich, T. Pertsch, E. Lederer, and K. Staliunas, “Subdiffractive all-photonic crystal Fabry–Perot resonators,” Opt. Lett. 33, 2695–2697 (2008).
[CrossRef]

2007 (4)

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. 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]

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]

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]

2006 (2)

L. C. Botten, T. P. White, C. M. de Sterke, and R. C. McPhedran, “Wide-angle coupling into rod-type photonic crystals with ultralow reflectance,” Phys. Rev. E 74, 026603 (2006).
[CrossRef]

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. Sin. 55, 2760–2764 (2006).

2004 (2)

2003 (3)

2002 (1)

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 (1)

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]

1999 (1)

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]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. 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 (2)

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]

Botten, L. C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

L. C. Botten, T. P. White, C. M. de Sterke, and R. C. McPhedran, “Wide-angle coupling into rod-type photonic crystals with ultralow reflectance,” Phys. Rev. E 74, 026603 (2006).
[CrossRef]

Cen, Y.

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

Chen, C. H.

Chen, J.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. 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, L. F.

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

Chen, X. J.

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]

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

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.

Chuang, Y. C.

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12, 035102 (2010).
[CrossRef]

Dai, Q. F.

de Sterke, C. M.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

L. C. Botten, T. P. White, C. M. de Sterke, and R. C. McPhedran, “Wide-angle coupling into rod-type photonic crystals with ultralow reflectance,” Phys. Rev. E 74, 026603 (2006).
[CrossRef]

Dong, J. W.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[CrossRef]

Dossou, K. B.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Dunbar, L. A.

Enoch, S.

Etrich, C.

Fan, D. Y.

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

Fan, S.

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

A. Mekis, J. C. Chen, I. Kurland, S. 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]

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.

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]

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

Hamam, R. E.

Han, K.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

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. Sin. 55, 2760–2764 (2006).

He, X. J.

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[CrossRef]

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.

Hu, W.

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

Ibanescu, M.

Iliew, R.

Jiang, L. Y.

Jiang, P.

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[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.

R. E. Hamam, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Broadband super-collimation in a hybrid photonic crystal structure,” Opt. Express 17, 8109–8118 (2009).
[CrossRef]

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]

A. Mekis, J. C. Chen, I. Kurland, S. 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.

R. E. Hamam, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Broadband super-collimation in a hybrid photonic crystal structure,” Opt. Express 17, 8109–8118 (2009).
[CrossRef]

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]

Kosaka, H.

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. 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]

Lan, S.

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]

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

Lawrence, F. J.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Le Thomas, N.

Lederer, E.

Lee, M. H.

Lee, S. G.

Leng, F. C.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[CrossRef]

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. Sin. 55, 2760–2764 (2006).

Li, X. Y.

Liang, W. Y.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[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]

Mazilu, M.

McPhedran, R. C.

L. C. Botten, T. P. White, C. M. de Sterke, and R. C. McPhedran, “Wide-angle coupling into rod-type photonic crystals with ultralow reflectance,” Phys. Rev. E 74, 026603 (2006).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. 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]

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.

Park, H.-R.

Park, J. M.

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.

Pustai, D. M.

Qian, L. J.

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[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. Sin. 55, 2760–2764 (2006).

Shen, Y. F.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

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. Sin. 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]

Soljacic, M.

Sotomayor Torres, C.

Staliunas, K.

Suleski, T. J.

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12, 035102 (2010).
[CrossRef]

Sun, J.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

Sun, L. L.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

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]

Tang, G.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

Tayeb, G.

Tomita, A.

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. 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]

Wang, H. Z.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[CrossRef]

Wang, J.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

Wang, L. G.

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

Wang, T. B.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[CrossRef]

White, T. P.

L. C. Botten, T. P. White, C. M. de Sterke, and R. C. McPhedran, “Wide-angle coupling into rod-type photonic crystals with ultralow reflectance,” Phys. Rev. E 74, 026603 (2006).
[CrossRef]

Wu, H.

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.

Wu, Z. H.

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[CrossRef]

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. Sin. 55, 2760–2764 (2006).

Xie, K.

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[CrossRef]

Xu, Y.

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]

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

Yablonovitch, E.

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

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[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]

Yin, C. P.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[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. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3523 (2003).
[CrossRef]

Zabelin, V.

Zhang, H.

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

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.

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. Sin. 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]

Zhu, H. Y.

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

Acta Phys. Sin. (1)

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. Sin. 55, 2760–2764 (2006).

Appl. Phys. Lett. (4)

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[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]

X. F. Yu and S. 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]

J. Lightwave Technol. (1)

J. Opt. (3)

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12, 035102 (2010).
[CrossRef]

H. Zhang, Y. Cen, L. F. Chen, H. Y. Zhu, L. J. Qian, and D. Y. Fan, “Full-angle collimations of two-dimensional photonic crystals with ultrahigh-index background materials,” J. Opt. 12, 045103 (2010).
[CrossRef]

Z. H. Wu, K. Xie, H. J. Yang, P. Jiang, and X. J. He, “All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals,” J. Opt. 14, 015002 (2012).
[CrossRef]

J. Opt. A (1)

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A 10, 085201 (2008).
[CrossRef]

J. Phys. D (2)

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D 43, 075103 (2010).
[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]

Opt. Commun. (1)

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 (5)

Opt. Lett. (5)

Photonic. Nanostruct. (1)

J. Sun, Y. F. Shen, J. Chen, L. G. Wang, L. L. Sun, J. Wang, K. Han, and G. Tang, “Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab,” Photonic. Nanostruct. 8, 163–171 (2010).
[CrossRef]

Phys. Rev. B (1)

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. E (1)

L. C. Botten, T. P. White, C. M. de Sterke, and R. C. McPhedran, “Wide-angle coupling into rod-type photonic crystals with ultralow reflectance,” Phys. Rev. E 74, 026603 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

A. Mekis, J. C. Chen, I. Kurland, S. 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]

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]

Other (1)

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).

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of a two-dimensional square-lattice PhC with rectangular air holes arranged in the x and y plane and embedded in a silicon background. As shown in the subfigure on the top right side, the half-length and half-width of rectangular air holes can be represented by L and W, while a is the lattice constant. The subfigure on the bottom right side shows the 1st Brillouin Zone of square lattice PhCs.

Fig. 2.
Fig. 2.

Band structures of the square-lattice PhC with rectangular air holes when different half-length L and half-width W of the rectangular air hole are considered.

Fig. 3.
Fig. 3.

Corresponding TE-2 and TM-2 EFCs of the square-lattice PhCs as shown in Fig. 2.

Fig. 4.
Fig. 4.

Relationship between L and effect range of W/L to support PISC for a square-lattice PhC with rectangular air holes.

Fig. 5.
Fig. 5.

Normalized transmittance of TE and TM modes in a 20-layer square-lattice PhC with rectangular air holes when L=0.3a and W/L=0.2, 0.4, and 0.6, respectively.

Fig. 6.
Fig. 6.

Normalized transmittance of TE and TM modes in a 20-layer square-lattice PhC with rectangular air holes when W/L=0.4 and L=0.2a, 0.3a, and 0.4a, respectively.

Fig. 7.
Fig. 7.

Normalized transmittance (a) and corresponding EFCs [(b) and (c)] of TE and TM modes in a 20-layer square-lattice PhC with rectangular air holes when L=0.35a and W/L=0.46.

Fig. 8.
Fig. 8.

(a1) and (b1) Magnetic and electric field distributions for TE and TM polarizations when normalized frequency is 0.27ωa/2πc. (a2) and (b2) The cross-sectional normalized absolute amplitude of magnetic/electric field at the output surface (dashed lines) of PhC. (a3) and (b3) The combined TE-2/TM-2 and the air background EFCs at normalized frequency 0.27ωa/2πc.

Fig. 9.
Fig. 9.

EFCs for TM-2 and TM-3 bands in a two-dimensional square-lattice PhC with rectangular air holes when W/L=0.8 and L changes from 0.47a to 0.5a.

Fig. 10.
Fig. 10.

Combined EFCs for TM-3 band and air background at different working frequencies when W/L=0.8 and L changes from 0.47a to 0.5a.

Fig. 11.
Fig. 11.

(a) PhC model (L=0.5a, W/L=0.8) for angular test of self-collimation. (b1), (b2), and (b3) show the electric field distributions in the whole x and y plane for TE polarization when the incident angle is 0°, 45°, and 85°, respectively. The dashed lines represent the terminations of PhCs. (c1), (c2), and (c3) show the cross-sectional-normalized absolute electric field at the output termination of PhC. The working frequency is 0.495ωa/2πc.

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