Abstract

We report that self-collimated beams from a photonic crystal can be refracted to any direction in air by introducing an additional layer composed of dielectric rods at a photonic crystal surface. The refraction angle can be tuned from negative to positive value by adjusting the period of the additional layer. The refracted beam power can be also controllable by varying the radii of rods in the layer and the distance between the layer and the surface. The grating-induced omnidirectional refraction of self-collimated beams could provide an efficient way to manipulate light propagation and increase the possibility of application of self-collimated beams.

© 2013 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. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv´, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93–96 (2006).
    [CrossRef]
  3. Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
    [CrossRef]
  4. S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
    [CrossRef]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef]
  6. C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  7. S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
    [CrossRef]
  8. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  9. W. Jiang, R. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
    [CrossRef]
  10. 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]
  11. 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]
  12. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
    [CrossRef]
  13. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3253 (2003).
    [CrossRef]
  14. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
    [CrossRef]
  15. T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Asymmetric Mach–Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals,” Opt. Express 18, 5384–5389 (2010).
    [CrossRef]
  16. T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Ring-type Fabry–Perot filter based on the self-collimation effect in a 2D photonic crystal,” Opt. Express 18, 17106–17113 (2010).
    [CrossRef]
  17. S.-G. Lee, S.-H. Kim, T.-T. Kim, J.-E. Kim, H. Y. Park, C.-S. Kee, and , “Resonant transmission of self-collimated beams through coupled zigzag-box resonators: slow self-collimated beams in a photonic crystal,” Opt. Express 20, 8309–8316 (2012).
    [CrossRef]
  18. X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E 70, 055601 (2004).
    [CrossRef]
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  20. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 181, 173–190 (2001).
    [CrossRef]
  21. A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos–Hanchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93, 131901 (2008).
    [CrossRef]
  22. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]
  23. 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]
  24. 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]
  25. W. Dai and C. M. Soukoulis, “Converging and wave guiding of Gaussian beam by two-layer dielectric rods,” Appl. Phys. Lett. 93, 201101 (2008).
    [CrossRef]

2012 (1)

2011 (1)

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
[CrossRef]

2010 (3)

2009 (1)

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]

2008 (3)

W. Dai and C. M. Soukoulis, “Converging and wave guiding of Gaussian beam by two-layer dielectric rods,” Appl. Phys. Lett. 93, 201101 (2008).
[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]

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos–Hanchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93, 131901 (2008).
[CrossRef]

2006 (2)

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

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

2005 (2)

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

W. Jiang, R. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[CrossRef]

2004 (1)

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E 70, 055601 (2004).
[CrossRef]

2003 (3)

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

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

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

2002 (2)

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

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 181, 173–190 (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]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[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]

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]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Chen, R.

W. Jiang, R. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[CrossRef]

Choi, J.-S.

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]

Dahlem, M. S.

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

Dai, W.

W. Dai and C. M. Soukoulis, “Converging and wave guiding of Gaussian beam by two-layer dielectric rods,” Appl. Phys. Lett. 93, 201101 (2008).
[CrossRef]

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]

Fan, S.

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E 70, 055601 (2004).
[CrossRef]

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

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]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[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.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

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

Ippen, E. P.

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

Jiang, W.

W. Jiang, R. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

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

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

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 181, 173–190 (2001).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

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

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 181, 173–190 (2001).
[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.

Kim, J.-E.

S.-G. Lee, S.-H. Kim, T.-T. Kim, J.-E. Kim, H. Y. Park, C.-S. Kee, and , “Resonant transmission of self-collimated beams through coupled zigzag-box resonators: slow self-collimated beams in a photonic crystal,” Opt. Express 20, 8309–8316 (2012).
[CrossRef]

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
[CrossRef]

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

T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Ring-type Fabry–Perot filter based on the self-collimation effect in a 2D photonic crystal,” Opt. Express 18, 17106–17113 (2010).
[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]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated 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]

Kim, S.-H.

Kim, T.-T.

Kivshar, Y. S.

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos–Hanchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93, 131901 (2008).
[CrossRef]

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv´, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93–96 (2006).
[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]

Lee, S.-G.

Lu, X.

W. Jiang, R. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[CrossRef]

Lu, Z.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

Luo, C. Y.

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

Matthews, A. F.

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos–Hanchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93, 131901 (2008).
[CrossRef]

Murakowski, J. A.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

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

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.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
[CrossRef]

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

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Park, H. Y.

S.-G. Lee, S.-H. Kim, T.-T. Kim, J.-E. Kim, H. Y. Park, C.-S. Kee, and , “Resonant transmission of self-collimated beams through coupled zigzag-box resonators: slow self-collimated beams in a photonic crystal,” Opt. Express 20, 8309–8316 (2012).
[CrossRef]

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
[CrossRef]

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

T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Ring-type Fabry–Perot filter based on the self-collimation effect in a 2D photonic crystal,” Opt. Express 18, 17106–17113 (2010).
[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]

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

Pendry, J.

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

Petrich, G. S.

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

Prather, D. W.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

Rakich, P. T.

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

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (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]

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]

Schneider, G. J.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

Schuetz, C. A.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

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]

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]

Shi, S.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[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]

Soljaciv´, M.

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

Soukoulis, C. M.

W. Dai and C. M. Soukoulis, “Converging and wave guiding of Gaussian beam by two-layer dielectric rods,” Appl. Phys. Lett. 93, 201101 (2008).
[CrossRef]

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

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Taflove, A.

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

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. Soljačiv´, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93–96 (2006).
[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]

Yu, X.

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E 70, 055601 (2004).
[CrossRef]

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

Appl. Phys. Lett. (7)

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 self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[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]

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos–Hanchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93, 131901 (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]

W. Dai and C. M. Soukoulis, “Converging and wave guiding of Gaussian beam by two-layer dielectric rods,” Appl. Phys. Lett. 93, 201101 (2008).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Nat. Mater. (1)

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

Opt. Express (5)

Phys. Rev. B (6)

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
[CrossRef]

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

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

W. Jiang, R. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[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]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

Phys. Rev. E (1)

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E 70, 055601 (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]

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef]

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]

Other (1)

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

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Figures (7)

Fig. 1.
Fig. 1.

EFCs for E-polarized lights of frequencies f=0.100(c/a), 0.180(c/a), 0.194(c/a), and 0.210(c/a) in the first band.

Fig. 2.
Fig. 2.

(a) TIR of a self-collimated beam at (10) PC–air interface. Dark red and blue color represent the maximum and the minimum values of the electric field parallel to the rod axis, respectively. Arrows denote the propagation direction of the beam. (b) An EFC diagram for a light of frequency f=0.194c/a in the PC (red contours) and air (black circle). Black and blue arrows denote wave vectors of the incident and reflected beams, respectively. TIR takes place because the EFC in air does not meet the kx-conservation line.

Fig. 3.
Fig. 3.

Additional layer of dielectric rods is placed at the truncated (10)-surface of a PC. d is the distance between the layer and the PC surface. p and ra are a period and the radius of rods in the layer, respectively.

Fig. 4.
Fig. 4.

EFCs with f=0.194(c/a) in the PC (red contours) and air (black circle). Black and blue arrows denote wave vectors of incident and reflected beams, respectively. Note that kxinc=0.359(2π/a). The vertical dashed lines denote the kx-conservation lines and purple arrows represent wave vectors of refracted beams when (a) p/a=2.0 and (b) p/a=3.8.

Fig. 5.
Fig. 5.

φm as a function of p/a for m=1,2, and 3 when f0=0.194(c/a) and kxinc=0.359(2π/a). Solid circles represent refraction angles obtained from FDTD simulations at selected values of p/a. Theoretical and simulated values are in a good agreement.

Fig. 6.
Fig. 6.

Simulated spatial distributions of steady-state electric fields of the beams with a frequency f=0.194c/a for (a) negative refraction at p/a=2.0, (b) positive refraction at p/a=3.2, (c) dual-beam refraction at p/a=4.0, and (d) triple-beam refraction at p/a=5.7. The value of d/a is 1. Black thin arrows indicate refraction directions predicted from Eq. (1). Incident beams are denoted by thick arrows.

Fig. 7.
Fig. 7.

(a) Dependence of the normalized refracted beam power in air, Pr, on the distance between the additional layer and the PC surface, d/a, when p/a=2.0 and ra/a=0.55 and (b) dependence of Pr on ra/a when p/a=2.0 and d/a=1.2.

Equations (1)

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φm=sin1(kxinc+2πm/p2πf0/c).

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