Abstract

We propose that 2D rectangular lattice photonic crystals composed of dielectric rods can be utilized for wide-range and tunable diffraction management. The control of diffraction for a normally incident beam is achieved by either properly choosing the operating frequency or changing the refractive index of the dielectric rods. The convergent, collimated, and divergent beam behaviors corresponding to a wide range of diffraction are clearly illustrated using FDTD simulations. The tunability of diffraction around the frequency of super-collimation is also analyzed and demonstrated.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  4. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
    [CrossRef]
  5. J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, “Super-collimation with high frequency sensitivity in 2D photonic crystals induced by saddle-type van Hove singularities,” Opt. Express 21, 30140–30147 (2013).
    [CrossRef]
  28. M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).
  29. T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005).
    [CrossRef]
  30. J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
    [CrossRef]
  31. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
    [CrossRef]
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    [CrossRef]

2013 (1)

2012 (3)

Y. Shen, P. G. Kevrekidis, N. Whitaker, and B. A. Malomed, “Spatial solitons under competing linear and nonlinear diffractions,” Phys. Rev. E 85, 026606 (2012).
[CrossRef]

J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
[CrossRef]

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

2011 (1)

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

2008 (3)

2007 (3)

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays,” Opt. Express 15, 9547–9552 (2007).
[CrossRef]

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (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]

2006 (2)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[CrossRef]

2005 (2)

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005).
[CrossRef]

2004 (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

2003 (4)

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

2002 (2)

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

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

2001 (2)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

2000 (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

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

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]

1995 (1)

J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
[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]

1987 (2)

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

J. Sajeev, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

Alic, N.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Baba, T.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Bassi, P.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Belabas, N.

J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

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]

Chen, L.

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]

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

Chigrin, D. N.

Christodoulides, D. N.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

de Sterke, C. M.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Delansay, P.

J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

Eggleton, B. J.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Egorov, O.

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

Egorov, O. A.

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

Enoch, S.

Etrich, C.

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

Fainman, Y.

Fan, S.

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (2007).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Fujita, S.

Garanovich, I. L.

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays,” Opt. Express 15, 9547–9552 (2007).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Grillet, C.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

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]

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Ikeda, K.

Iliew, R.

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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, X.

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, “Super-collimation with high frequency sensitivity in 2D photonic crystals induced by saddle-type van Hove singularities,” Opt. Express 21, 30140–30147 (2013).
[CrossRef]

Z. Xu, B. Maes, X. Jiang, J. D. Joannopoulos, L. Torner, and M. Soljačić, “Nonlinear photonic crystals near the supercollimation point,” Opt. Lett. 33, 1762–1764 (2008).
[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]

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (2007).
[CrossRef]

Joannopoulos, J. D.

Z. Xu, B. Maes, X. Jiang, J. D. Joannopoulos, L. Torner, and M. Soljačić, “Nonlinear photonic crystals near the supercollimation point,” Opt. Lett. 33, 1762–1764 (2008).
[CrossRef]

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (2007).
[CrossRef]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

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

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

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]

Kevrekidis, P. G.

Y. Shen, P. G. Kevrekidis, N. Whitaker, and B. A. Malomed, “Spatial solitons under competing linear and nonlinear diffractions,” Phys. Rev. E 85, 026606 (2012).
[CrossRef]

Kitamura, M.

J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
[CrossRef]

Kivshar, Y. S.

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays,” Opt. Express 15, 9547–9552 (2007).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Lederer, F.

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Levenson, J. A.

J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
[CrossRef]

Lin, X.

Lipson, M.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Luo, C.

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

Maes, B.

Malomed, B. A.

Y. Shen, P. G. Kevrekidis, N. Whitaker, and B. A. Malomed, “Spatial solitons under competing linear and nonlinear diffractions,” Phys. Rev. E 85, 026606 (2012).
[CrossRef]

Matsumoto, T.

McPhedran, R. C.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Minot, C.

J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
[CrossRef]

Moison, J.-M.

J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
[CrossRef]

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

Norton, A.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Notomi, M.

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

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]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Pendry, J. B.

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

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Sajeev, J.

J. Sajeev, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Saperstein, R. E.

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]

Segev, M.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

Shen, Y.

Y. Shen, P. G. Kevrekidis, N. Whitaker, and B. A. Malomed, “Spatial solitons under competing linear and nonlinear diffractions,” Phys. Rev. E 85, 026606 (2012).
[CrossRef]

Shim, J.-I.

J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

Soljacic, M.

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, “Super-collimation with high frequency sensitivity in 2D photonic crystals induced by saddle-type van Hove singularities,” Opt. Express 21, 30140–30147 (2013).
[CrossRef]

Z. Xu, B. Maes, X. Jiang, J. D. Joannopoulos, L. Torner, and M. Soljačić, “Nonlinear photonic crystals near the supercollimation point,” Opt. Lett. 33, 1762–1764 (2008).
[CrossRef]

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (2007).
[CrossRef]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

Sotomayor Torres, C.

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

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]

Staliunas, K.

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

Steel, M. J.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Sukhorukov, A. A.

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays,” Opt. Express 15, 9547–9552 (2007).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Tamamura, T.

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

Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Tayeb, G.

Tomita, A.

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

Torner, L.

Whitaker, N.

Y. Shen, P. G. Kevrekidis, N. Whitaker, and B. A. Malomed, “Spatial solitons under competing linear and nonlinear diffractions,” Phys. Rev. E 85, 026606 (2012).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Xu, Z.

Yablonovitch, E.

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

Yamaguchi, M.

J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
[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. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (2007).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

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, X.

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]

Zhou, C.

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (2007).
[CrossRef]

Zoli, R.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

Appl. Phys. Lett. (3)

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. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Appl. Phys. Lett. 91, 031105 (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]

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

J.-I. Shim, M. Yamaguchi, P. Delansay, and M. Kitamura, “Refractive index and loss changes produced by current injection in InGaAs(P)-InGaAsP multiple quantum-well (MQW) waveguides,” IEEE J. Sel. Top. Quantum Electron. 1, 408–415 (1995).
[CrossRef]

Nat. Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, 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]

Nature (3)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. A (2)

C. Etrich, R. Iliew, K. Staliunas, F. Lederer, and O. A. Egorov, “Ab initio dissipative solitons in an all-photonic crystal resonator,” Phys. Rev. A 84, 021808(R) (2011).
[CrossRef]

J.-M. Moison, N. Belabas, J. A. Levenson, and C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86, 033811 (2012).
[CrossRef]

Phys. Rev. B (2)

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

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

Phys. Rev. E (3)

Y. Shen, P. G. Kevrekidis, N. Whitaker, and B. A. Malomed, “Spatial solitons under competing linear and nonlinear diffractions,” Phys. Rev. E 85, 026606 (2012).
[CrossRef]

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. M. de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71, 056608 (2005).

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Phys. Rev. Lett. (9)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

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

J. Sajeev, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

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]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

Other (1)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

Top panel, diagram of EFCs in the second TE band of the 2D rectangular lattice PhC described in the main text, with the arrows showing the magnitude and direction of group velocities. Bottom panel, distribution of κ0, the curvature of EFCs at the ΓX1 axis. The circular point labels the position of ωsc, where κ0=0.

Fig. 2.
Fig. 2.

FDTD simulations of monochromatic beams passing through a block of PhC along the direction of ΓX1. (a) Schematic diagram of the simulation setup. (b)–(d) Snapshots of Hz when the beam is passing through the PhC, with the operating frequencies being (b) ω=0.376(2πc/a), (c) ω=0.381(2πc/a), and (d) ω=0.386(2πc/a).

Fig. 3.
Fig. 3.

Beam profile at the right boundary of PhC at different frequencies. The white-dashed line labels the position of ω=0.381(2πc/a), where the beam is collimated within the block of PhC. The inset shows a snapshot of beam propagation with ω=0.370(2πc/a). The white segment indicates the position of ω=0.370(2πc/a) and the transverse spatial range of the inset.

Fig. 4.
Fig. 4.

Variation of ωsc and κ0 at ω=0.381(2πc/a) with respect to the relative change of the refraction index of the dielectric rods Δn/n.

Fig. 5.
Fig. 5.

Beam profiles at the right boundary of PhC with different choices of Δn/n. The frequency is ω=0.381(2πc/a), at which the beam is collimated when Δn/n=0.

Equations (3)

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

κ0=2kxky2|ky=0=ω,yyυg|ky=0,
Hz(y)=Hz0·exp[i2πy2/aRy2/(2W2)]·exp(iωt),
η=Δκ0Δn/n|ω=ωsc=Δκ0Δω/ωsc|ω=ωsc·Δωsc/ωscΔn/n.

Metrics