Abstract

We investigate discrepancy and similarity in dispersion relations between transverse-electric (TE) and transverse-magnetic (TM) polarizations in rectangular, square and triangular two-dimensional photonic crystals. It is found that the square lattice is the most appropriate candidate to realize polarization-independent, i.e. absolute self-collimation (ASC) in the first photonic band since it possesses not only a relatively broad angular range for self-collimation but also a small difference in dispersion relations between TE and TM modes. By tailoring the shape of air voids in the square-lattice-based structure, the electric-field vector can be rotated to reduce the discrepancy between TE and TM modes whereby the frequency bandwidth of ASC can be enlarged to ~4.8%. The ASC phenomenon is demonstrated by numerical experiments based on a finite-difference time-domain (FDTD) technique with negligible propagation losses.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  6. H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
    [CrossRef]
  11. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008

Yi Xu, Xiao-Jun Chen, Sheng Lan, Qi Guo, Wei Hu, and Li-Jun Wu, "The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry," J. Opt. A 10085201 (2008).
[CrossRef]

2007

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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]

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

2006

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. SoljaÈiÆ, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimeter-scale supercollimation in a large-area two-dimensional photonic crystal" Nature Mater. 5, 93-96 (2006).
[CrossRef]

2005

L. Wu, M. Mazilu, J. F. Gallet, and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106-211109 (2005).
[CrossRef]

2004

2003

2002

J. Witzens, M. Loncar, and A. Schere, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism Phenomena in Planar Photonic Crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
[CrossRef]

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
[CrossRef]

2001

1999

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

1998

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

1987

E. Yablonovitch, "Inhibited spontaneous emission in solidstate physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices," Phys. Rev. Lett.,  58, 2486-2489 (1987).
[CrossRef] [PubMed]

Baba, T.

T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl.Phys. 40, 5920-5924 (2001).
[CrossRef]

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Borel, P. I.

Chen, C.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, D. M. Pustai, C. 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] [PubMed]

Chigrin, D. N.

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. SoljaÈiÆ, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimeter-scale supercollimation in a large-area two-dimensional photonic crystal" Nature Mater. 5, 93-96 (2006).
[CrossRef]

Dunbar, L. A.

Enoch, S.

Frandsen, L. H.

Gallet, J. F.

L. Wu, M. Mazilu, J. F. Gallet, and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106-211109 (2005).
[CrossRef]

Harpoth, A.

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. SoljaÈiÆ, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimeter-scale supercollimation in a large-area two-dimensional photonic crystal" Nature Mater. 5, 93-96 (2006).
[CrossRef]

Jensen, J. S.

Joannopoulos, J. D.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[CrossRef] [PubMed]

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

John, S.

S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices," Phys. Rev. Lett.,  58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[CrossRef] [PubMed]

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

Ju, Y. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Karle, T.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism Phenomena in Planar Photonic Crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Kawakami, S.

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Kawakamib, S.

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

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Kazumi, W.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
[CrossRef]

Kim, S. B.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kim, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kimerling, L. C.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
[CrossRef]

Kosada, H.

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Kosaka, H.

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

Krauss, T. F.

L. Wu, M. Mazilu, J. F. Gallet, and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106-211109 (2005).
[CrossRef]

L. Wu, M. Mazilu, and T. F. Krauss, "Beam Steering in Planar-Photonic Crystals: From Superprism to Supercollimator," J. Lightwave Technol. 21, 561-566 (2003).
[CrossRef]

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism Phenomena in Planar Photonic Crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Kristensen, M.

Kwon, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Le, N.

Lee, Y. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Loncar, M.

J. Witzens, M. Loncar, and A. Schere, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

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

Martin, R.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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.

L. Wu, M. Mazilu, J. F. Gallet, and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106-211109 (2005).
[CrossRef]

L. Wu, M. Mazilu, and T. F. Krauss, "Beam Steering in Planar-Photonic Crystals: From Superprism to Supercollimator," J. Lightwave Technol. 21, 561-566 (2003).
[CrossRef]

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism Phenomena in Planar Photonic Crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Miao, B.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, D. M. Pustai, C. 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] [PubMed]

Notomi, M.

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

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Ohsaki, D.

T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl.Phys. 40, 5920-5924 (2001).
[CrossRef]

Park, H. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

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

Peter, B.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
[CrossRef]

Prather, D. W.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, D. M. Pustai, C. 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] [PubMed]

Pustai, D. M.

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. SoljaÈiÆ, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimeter-scale supercollimation in a large-area two-dimensional photonic crystal" Nature Mater. 5, 93-96 (2006).
[CrossRef]

Sato, T.

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

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Schere, A.

J. Witzens, M. Loncar, and A. Schere, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Schneider, G. J.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, D. M. Pustai, C. 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] [PubMed]

Sharkawy, A.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, D. M. Pustai, C. 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] [PubMed]

Shi, S.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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. Shi, D. M. Pustai, C. 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] [PubMed]

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N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakamib, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. SoljaÈiÆ, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimeter-scale supercollimation in a large-area two-dimensional photonic crystal" Nature Mater. 5, 93-96 (2006).
[CrossRef]

Tayeb, G.

Tomita, A.

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

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Torres, C. M. S.

Venkataraman, S.

Witzens, J.

J. Witzens, M. Loncar, and A. Schere, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Wu, L.

L. Wu, M. Mazilu, J. F. Gallet, and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106-211109 (2005).
[CrossRef]

L. Wu, M. Mazilu, and T. F. Krauss, "Beam Steering in Planar-Photonic Crystals: From Superprism to Supercollimator," J. Lightwave Technol. 21, 561-566 (2003).
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L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism Phenomena in Planar Photonic Crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
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Xiaoman, D.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
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H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Yasha, Y.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
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Appl. Phys. Lett.

Y. Yasha, B. Peter, W. Kazumi, D. Xiaoman, J. D. Joannopoulos, and L. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation," Appl. Phys. Lett.,  81, 4112-4114 (2002).
[CrossRef]

L. Wu, M. Mazilu, J. F. Gallet, and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106-211109 (2005).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakamib, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction in a three-dimensionally periodic," Appl. Phys. Lett. 81, 2352-2354 (2002).
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L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism Phenomena in Planar Photonic Crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
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IEEE J. Sel. Top. Quantum Electron.

J. Witzens, M. Loncar, and A. Schere, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
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N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. 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).
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Opt. Express

Opt. Lett.

Phys. Rev. B

H. Kosada, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

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E. Yablonovitch, "Inhibited spontaneous emission in solidstate physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
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[CrossRef] [PubMed]

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[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) The sketch map of dispersion surfaces for TE and TM polarizations in the square lattice with r/a=0.3 in the first Brillouin Zone. The black surface stands for the TE mode and the red one for the TM mode. The vertical green bar represents the frequency difference at a specific k-vector. (b) The dispersion discrepancy in rectangular, square and triangular lattices versus the filling factor.

Fig. 2.
Fig. 2.

The distributions of the time-averaged E-field energy density (ε|E|2) for the TM mode at the M point in the first band of square-lattice-based structures with different voids. The unit of the length is in a. The white dotted lines depict the outlines of voids. The radius of the circular-void in (a) is arbitrarily chosen to be 0.3a. The filling factor for all the structures is kept the same as in (a). As can be seen, the energy density distributes similarly in all the structures.

Fig. 3.
Fig. 3.

The distributions of the time-averaged E-field energy density (ε|E|2) for the TE mode. All the structural parameters are the same as in the Fig. 2. The white arrows stand for the in-plane E-field vectors. The insets in each figure stand for one lattice cell.

Fig. 4.
Fig. 4.

The ASC bandwidth for square-lattice-based structures versus the filling factor. (a)-(d) is for circular-, rectangular-, elliptic- and pill-void structure, respectively. The specific shapes of each void are shown in the insets.

Fig. 5.
Fig. 5.

The band structure (a) and EFCs (b) for the pill-void square lattice with d2=0.6a, d1=0.2a. The red/black color indicates TM/TE modes. The light blue box in (a) represents the operating region. The cyan circle is the light cone at a frequency of 0.188×2p c/a and the grey 45°- taper stand for the angular range for the incident k-vectors. As can be seen, the propagation direction of the energy, which is shown in the yellow bulk arrow, is along the GM direction in PhCs when the divergence of the incident beams is within 45° (i.e. ±22.5°).

Fig. 6.
Fig. 6.

The spatial evolutions of beams incident from air (left) into PhCs (right) for (a) TM and (c) TE polarizations at a frequency of 0.188×2π c/a. The input interface shown in the inset has been modified to improve the transmission. The output medium is dielectric. (b) (d) The steady field distributions at different propagation distances. The oscillation of field distributions can be attributed to the modulation of the periodic PhC, in which the difference between TE and TM modes is due to the different length of the coupled k-vector along the ΓM direction (refer to kTE and kTM in the Fig. 5 (b)).

Equations (3)

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X j i = ( v T E ) j i ( v T M ) j i , X j ¯ = 1 n i = 1 n χ j i , j = 1 m
S j 2 = 1 n 1 i = 1 n ( X j i X j ¯ ) 2 , j = 1 m
D D = ( j = 1 m S j 2 ) / m ,

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