Abstract

We present a high-efficiency antireflection structure for both TE and TM polarizations in two-dimensional self-collimating square lattice photonic crystal consisting of air holes in silicon. The design parameters of the optimal antireflection structure can be obtained by using the concept of Fresnel coefficients and the finite-difference time-domain simulations. The photonic crystal operating in almost identical self-collimation frequencies for two polarizations exhibits a large reflection coefficient for TE and a very small one for TM polarization. In this case, the antireflection structure for TE can also improve the transmission for TM polarization. To confirm a highly efficient antireflection structure designed, we investigate the transmission data of three finite photonic crystal samples consisting of 36, 38 and 40 unit cells for the cases without and with the antireflection structures through finite-difference time-domain simulations.

© 2010 Optical Society of America

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  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]
  2. J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in Planar Photonic Crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
    [CrossRef]
  3. X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
    [CrossRef]
  4. S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, "Dispersion-based beam splitter in photonic crystals," Opt. Lett. 29, 617-619 (2004).
    [CrossRef] [PubMed]
  5. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
    [CrossRef]
  6. M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
    [CrossRef]
  7. J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, "Efficient beaming of self-collimated light from photonic crystals," Opt. Express 16, 20354-20367 (2008).
    [CrossRef] [PubMed]
  8. V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdr’e, M. V. Kotlyar, L. O’Faolin, and T. F. Krauss, "Selfcollimating photonic crystal polarization beam splitter," Opt. Lett. 32, 530-532 (2007).
    [CrossRef] [PubMed]
  9. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114 (2007).
    [CrossRef]
  10. T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, "Asymmetric Mach-Zehnder filter based on selfcollimation phenomenon in two-dimensional photonic crystals," Opt. Express 18, 5384-5389 (2010).
    [CrossRef] [PubMed]
  11. Y. Zhang, Y. Zhang, and B. Li, "Optical switches and logic gates based on self-collimated beams in twodimensional photonic crystals," Opt. Express 15, 9287-9292 (2007).
    [CrossRef] [PubMed]
  12. X. Chen, Z. Qiang, D. Zhao, H. Li, Y. Qiu, W. Yang, and W. Zhou, "Polarization-independent drop filters based on photonic crystal self-collimation ring resonators," Opt. Express 17, 19808-19813 (2009).
    [CrossRef] [PubMed]
  13. T. Baba and D. Ohsaki, "Interfaces of Photonic Crystals for High Efficiency Light Transmission," Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. S.-G. Lee, J.-s. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Reflection minimization at two-dimensional photonic crystal interfaces," Opt. Express 16, 4270-4277 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  22. J.-M. Park, S.-G. Lee, H. Y. Park, J.-E. Kim, and M.-H. Lee, "High-efficiency antireflection structures for terahertz self-collimating photonic crystals," J. Opt. Soc. Am. B 26, 1967-1974 (2009).
    [CrossRef]
  23. K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302 (1966).
  24. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
    [CrossRef]
  25. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  26. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
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  29. S. Adachi, "Model dielectric constants of Si and Ge," Phys. Rev. B 38, 12966-12976 (1988).
    [CrossRef]
  30. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
    [CrossRef] [PubMed]

2010 (2)

2009 (3)

2008 (3)

2007 (5)

V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdr’e, M. V. Kotlyar, L. O’Faolin, and T. F. Krauss, "Selfcollimating photonic crystal polarization beam splitter," Opt. Lett. 32, 530-532 (2007).
[CrossRef] [PubMed]

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

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

Y. Zhang, Y. Zhang, and B. Li, "Optical switches and logic gates based on self-collimated beams in twodimensional photonic crystals," Opt. Express 15, 9287-9292 (2007).
[CrossRef] [PubMed]

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

2005 (2)

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

2004 (2)

S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, "Dispersion-based beam splitter in photonic crystals," Opt. Lett. 29, 617-619 (2004).
[CrossRef] [PubMed]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

2003 (2)

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

2002 (1)

J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in Planar Photonic Crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

2001 (2)

T. Baba and D. Ohsaki, "Interfaces of Photonic Crystals for High Efficiency Light Transmission," Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

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]

1994 (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1988 (1)

S. Adachi, "Model dielectric constants of Si and Ge," Phys. Rev. B 38, 12966-12976 (1988).
[CrossRef]

1966 (1)

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302 (1966).

Adachi, S.

S. Adachi, "Model dielectric constants of Si and Ge," Phys. Rev. B 38, 12966-12976 (1988).
[CrossRef]

Adibi, A.

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

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]

Baehr-Jones, T.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Botten, L. C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, "Antireflection coatings for twodimensional photonic crystals using a rigorous impedance definition," Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
[CrossRef] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chen, C.

Chen, H.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Chen, J.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Chen, X.

X. Chen, Z. Qiang, D. Zhao, H. Li, Y. Qiu, W. Yang, and W. Zhou, "Polarization-independent drop filters based on photonic crystal self-collimation ring resonators," Opt. Express 17, 19808-19813 (2009).
[CrossRef] [PubMed]

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

Choi, J.-s.

Dossou, K. B.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, "Antireflection coatings for twodimensional photonic crystals using a rigorous impedance definition," Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Dunbar, L. A.

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
[CrossRef] [PubMed]

Fan, S.

X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Hochberg, M.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Jiang, X.

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

Joannopoulos, J. D.

Johnson, S. G.

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]

Kee, C.-S.

T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, "Asymmetric Mach-Zehnder filter based on selfcollimation phenomenon in two-dimensional photonic crystals," Opt. Express 18, 5384-5389 (2010).
[CrossRef] [PubMed]

S.-G. Lee, J.-s. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Reflection minimization at two-dimensional photonic crystal interfaces," Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Kim, J.-E.

T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, "Asymmetric Mach-Zehnder filter based on selfcollimation phenomenon in two-dimensional photonic crystals," Opt. Express 18, 5384-5389 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, "Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures," Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

J.-M. Park, S.-G. Lee, H. Y. Park, J.-E. Kim, and M.-H. Lee, "High-efficiency antireflection structures for terahertz self-collimating photonic crystals," J. Opt. Soc. Am. B 26, 1967-1974 (2009).
[CrossRef]

S.-G. Lee, J.-s. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Reflection minimization at two-dimensional photonic crystal interfaces," Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, "Efficient beaming of self-collimated light from photonic crystals," Opt. Express 16, 20354-20367 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Kim, M.-W.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, "Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures," Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

Kim, T.-T.

T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, "Asymmetric Mach-Zehnder filter based on selfcollimation phenomenon in two-dimensional photonic crystals," Opt. Express 18, 5384-5389 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, "Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures," Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[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]

Lawrence, F. J.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, "Antireflection coatings for twodimensional photonic crystals using a rigorous impedance definition," Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Le Thomas, N.

Lee, M.-H.

Lee, S.-G.

T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, "Asymmetric Mach-Zehnder filter based on selfcollimation phenomenon in two-dimensional photonic crystals," Opt. Express 18, 5384-5389 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, "Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures," Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

J.-M. Park, S.-G. Lee, H. Y. Park, J.-E. Kim, and M.-H. Lee, "High-efficiency antireflection structures for terahertz self-collimating photonic crystals," J. Opt. Soc. Am. B 26, 1967-1974 (2009).
[CrossRef]

S.-G. Lee, J.-s. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Reflection minimization at two-dimensional photonic crystal interfaces," Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, "Efficient beaming of self-collimated light from photonic crystals," Opt. Express 16, 20354-20367 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Li, B.

Li, H.

Li, Z.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Loncar, M.

J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in Planar Photonic Crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Martijn de Sterke, C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, "Antireflection coatings for twodimensional photonic crystals using a rigorous impedance definition," Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Momeni, B.

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

Notomi, M.

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]

Oh, S. S.

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[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]

Ozbay, E.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Park, H. Y.

T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, "Asymmetric Mach-Zehnder filter based on selfcollimation phenomenon in two-dimensional photonic crystals," Opt. Express 18, 5384-5389 (2010).
[CrossRef] [PubMed]

J.-M. Park, S.-G. Lee, H. Y. Park, J.-E. Kim, and M.-H. Lee, "High-efficiency antireflection structures for terahertz self-collimating photonic crystals," J. Opt. Soc. Am. B 26, 1967-1974 (2009).
[CrossRef]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, "Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures," Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

S.-G. Lee, J.-s. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Reflection minimization at two-dimensional photonic crystal interfaces," Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, "Efficient beaming of self-collimated light from photonic crystals," Opt. Express 16, 20354-20367 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Park, J.-M.

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
[CrossRef] [PubMed]

Prather, D. W.

Pustai, D. M.

Qiang, Z.

Qiu, Y.

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]

Scherer, A.

J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in Planar Photonic Crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Sharkawy, A.

Sherer, A.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Shi, S.

Shirane, M.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
[CrossRef] [PubMed]

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]

Tokushima, M.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

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]

Ushida, J.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
[CrossRef] [PubMed]

Witzens, J.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in Planar Photonic Crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Yamada, H.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

Yang, F.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Yang, W.

Yao, P.

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

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302 (1966).

Yu, X.

X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Zabelin, V.

Zhang, J.

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

Zhang, Y.

Zhao, D.

X. Chen, Z. Qiang, D. Zhao, H. Li, Y. Qiu, W. Yang, and W. Zhou, "Polarization-independent drop filters based on photonic crystal self-collimation ring resonators," Opt. Express 17, 19808-19813 (2009).
[CrossRef] [PubMed]

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

Zheng, H.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Zhou, W.

Appl. Phys. Lett. (9)

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. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007).
[CrossRef]

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

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, "Antireflection coatings for twodimensional photonic crystals using a rigorous impedance definition," Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, "Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures," Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in Planar Photonic Crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302 (1966).

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. D: Appl. Phys. (1)

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, "Resonant cavity based compact efficient antireflection structures for photonic crystals," J. Phys. D: Appl. Phys. 40, 5873-5877 (2007).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Baba and D. Ohsaki, "Interfaces of Photonic Crystals for High Efficiency Light Transmission," Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. B (1)

S. Adachi, "Model dielectric constants of Si and Ge," Phys. Rev. B 38, 12966-12976 (1988).
[CrossRef]

Phys. Rev. E (1)

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Science (1)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337-339 (2010).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999), pp. 63-74.

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics, Bristol, 2001), Chaps. 2 and 3.
[CrossRef]

S.-G. Lee, M. Yi, J. Ahn, J.-E. Kim, and H. Y. Park, "Optimization of Photonic Crystal Interfaces for High Efficient Coupling of Terahertz Waves," in International Conference on Infrared and Millimeter Waves/THz Electronics (IRMMW-THz 2008) (IEEE, 2008), pp. 1-2.

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Figures (6)

Fig. 1.
Fig. 1.

Schematics of the ARC structure: (a) In the 1D case, the ARC parameters are the refractive index n 2 and the thickness h of ARC structure. (b) In the 2D PhC case, the ARC parameters are the radius of air holes rarc and the distance darc between the ARC (enclosed by the dark green rectangle) and the 2D semi-infinite PhC. For the 2D PhC case of (b), schematics of the rij modified properly: (c) r 123 is the reflection coefficient of the ARC embedded in Si. (d) r 34 is that of the semi-infinite 2D SC PhC when the light is incident upon it from the Si. In (a)–(d), the thick and thin red arrows indicate the incident and reflected beams, respectively.

Fig. 2.
Fig. 2.

(a) SC frequencies within the second photonic band for TE and TM polarizations and the corresponding reflectances, as a function of the air hole radius. (b) Values of ARC parameters and the reflectances without and with the designed ARCs applied. Considered here are 2D square lattice SC PhCs of air holes in Si with the refractive index of n = 3.518.

Fig. 3.
Fig. 3.

Reflectance maps as a function of the parameters darc and rarc for (a) TE and (b) TM polarizations, where rsc = 0.34 a and ωsc = 0.275 (2πc/a). Here, the dark green solid circles indicate the reflectances at the above-two common ARC parameters for both TE and TM polarizations. Reflectance maps as a function of the parameters ω and r for (c) TE and (d) TM polarizations, where rarc = 0.225 a and darc = 0.94 a. In (a)–(d), the dark gray solid circles indicate the reflectance at a specific position consisting of rsc = 0.34 a, ωsc = 0.275 (2πc/a), rarc = 0.225 a and darc = 0.94 a.

Fig. 4.
Fig. 4.

Reflectance maps as a function of the parameters rarc and r for (a) TE and (b) TM polarizations, where ωsc = 0.275 (2πc/a) and darc = 0.94 a. Reflectance maps as a function of the parameters darc and r for (c) TE and (d) TM polarizations, where ωsc = 0.275 (2πc/a) and rarc = 0.225 a. In (a)–(d), the dark gray solid circles indicate the reflectances at a specific position consisting of rsc = 0.34 a, ωsc = 0.275 (2πc/a), rarc = 0.225 a and darc = 0.94 a.

Fig. 5.
Fig. 5.

Reflectance maps as a function of the parameters rarc and ω for (a) TE and (b) TM polarizations, where rsc = 0.34 a and darc = 0.94 a. Reflectance maps as a function of the parameters darc and ω for (c) TE and (d) TM polarizations, where rsc = 0.34 a and rarc = 0.225 a. In (a)–(d), the dark gray solid circles indicate the reflectances at a specific position consisting of rsc = 0.34 a, ωsc = 0.275 (2πc/a), rarc = 0.225 a and darc = 0.94 a.

Fig. 6.
Fig. 6.

Time-averaged power transmission spectra of three finite PhC samples consisting of 36, 38 and 40 unit cells (ucs) for (a) TE and (b) TM polarizations for the case without any ARC. Time-averaged power transmissions for (c) TE and (d) TM polarizations for the case with the designed ARCs applied at the input and output ends of the PhCs. Here, the condition of simulation parameters is as follows: rsc = 0.34 a, ωsc = 0.275 (2πc/a), rarc = 0.223 a and darc = 0.939 a.

Tables (1)

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Table 1. Transmitted powers (%).

Equations (3)

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r = r 12 + r 23 e 2 i β 1 + r 12 r 23 e 2 i β ,
r 12 = r 23 ,
e i ( 2 β + δ 23 δ 12 ) = 1 ,

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