Abstract

We propose a method to design antireflection structures to minimize the reflection of light beams at the interfaces between a two-dimensional photonic crystal and a homogeneous dielectric. The design parameters of the optimal structure to give zero reflection can be obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations. We examine the performance of a Mach-Zehnder interferometer utilizing the self-collimated beams in two-dimensional photonic crystals with and without the optimal antireflection structure introduced. It is shown that the optimal antireflection structure significantly improves the performance of the device.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  4. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
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    [CrossRef]
  6. D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003).
    [CrossRef] [PubMed]
  7. 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).
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  8. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljaciv, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and Erich P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93-96 (2006).
    [CrossRef] [PubMed]
  9. X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  14. Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003).
    [CrossRef]
  15. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
    [CrossRef] [PubMed]
  16. V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
    [CrossRef] [PubMed]
  17. T. Matsumoto, S. Fujita, and T. Baba, "Wavelength demultiplexer consisting of Photonic crystal superprism and superlens," Opt. Express 13, 10768-10776 (2005).
    [CrossRef] [PubMed]
  18. K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
    [CrossRef]
  19. T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
    [CrossRef]
  20. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
    [CrossRef]
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    [CrossRef]
  27. 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]
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    [CrossRef]

2007 (4)

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]

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

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]

2006 (1)

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

2005 (3)

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]

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]

T. Matsumoto, S. Fujita, and T. Baba, "Wavelength demultiplexer consisting of Photonic crystal superprism and superlens," Opt. Express 13, 10768-10776 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (7)

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

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

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

2002 (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]

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (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]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (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]

1998 (1)

H. Kosaka, 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]

1994 (1)

J. -P. Berenger, "A perfectly matched layer for the absorption of electomagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[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]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Baba, T.

T. Matsumoto, S. Fujita, and T. Baba, "Wavelength demultiplexer consisting of Photonic crystal superprism and superlens," Opt. Express 13, 10768-10776 (2005).
[CrossRef] [PubMed]

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. Scherer, "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 electomagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Chen, C.

Chen, 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]

Chigrin, D.

Chung, K. B.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Dahlem, M. S.

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

Dunbar, L. A.

Economou, E. N.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Enoch, S.

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]

Foteinopou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Foteinopoulou, S.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Fujita, S.

Hochberg, M.

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

Hong, S. W.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

Ibanescu, M.

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

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]

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]

H. Kosaka, 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]

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]

H. Kosaka, 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]

Kee, C.-S.

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.

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.

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.

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]

H. Kosaka, 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]

Le Thomas, N.

Lee, S.-G.

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, Z. Y.

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Lin, L. L.

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003).
[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]

Lu, W. T.

V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Matsumoto, T.

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]

Murakowski, J.

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]

H. Kosaka, 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]

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.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Parimi, V. P.

V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Park, H. Y.

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]

Prather, D.

Prather, D.W.

Pustai, D.

Pustai, D. M.

Rakich, P. T.

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

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]

H. Kosaka, 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]

Scherer, A.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "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]

Schneider, G. J.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sharkawy, A.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sotomayor Torres, C.

Soukoulis, C. M.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Sridhar, S.

V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[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]

H. Kosaka, 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]

Tandon, S.

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

Tayeb, G.

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]

H. Kosaka, 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]

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]

Venkataraman, S.

Vodo, P.

V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Witzens, J.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "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]

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]

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.

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]

Appl. Phys. Lett. (8)

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]

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[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]

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]

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]

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]

J. Comput. Phys. (1)

J. -P. Berenger, "A perfectly matched layer for the absorption of electomagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[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]

Nat. Mater. (1)

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

Nature (1)

V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. B (2)

H. Kosaka, 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]

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (2)

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Other (3)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, 1995).

M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Cambridge, 2002).

H. A. Macleod, Thin-film Optical Filters, (Adam Hilger Ltd, Bristol, 1986).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Structural parameters for ARC. (a) In the 1D case, the ARC parameters are the refractive index n 2 and the thickness h of an antireflection layer. (b) In the 2D PC case, the ARC parameters are the radius of rods Rarc and the distance darc between the ARC structure and the crystal truncation. The antireflection structure becomes a part of the host PC when Rarc =R and darc =a/√2.

Fig. 2.
Fig. 2.

(a) |r 12|, the amplitude of the reflection coefficient of the ARC structure, as a function of Rarc . |r 23| represents the amplitude of the reflection coefficient of the semi-infinite square lattice PC consisting of dielectric rods in air. (b) Total reflectance of the PC with the ARC structure is calculated as a function of darc when Rarc =0.2064 a (red solid) and Rarc =0.4347 a (black dotted). The reflectance oscillates with a period of about a half wavelength of the incident beam. Simulations are performed for the light of frequency f=0.194 c/a (wavelength λ=5.1546 a).

Fig. 3.
Fig. 3.

(a) Configuration of the simulations. Periodic boundary condition is used in the x-direction and PMLs are placed at the ends of computational domain in the y-direction. Transmission spectra of two different sized PC samples of 2D square array of dielectric rods in air for the cases (b) without the ARC and (c) with the ARC structure. The red solid and black dotted lines represent the transmission through the PC samples of sizes 12√2 a and 16√2 a, respectively.

Fig. 4.
Fig. 4.

Transmission spectra of a 2D square lattice PC of air holes for the cases of (a) without the ARC and (b) with the ARC structure.

Fig. 5.
Fig. 5.

(a) Schematic diagram of a PC Mach-Zehnder interferometer composed of two 50:50 beam splitters and two perfect mirrors. The radius of rods in the line-defect is 0.275 a. Transmission spectra at the two output ports when (b) the ARC structure is and (c) is not introduced.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

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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