Abstract

Investigation on the phase shifts of higher-order reflected light from a two-dimensional photonic crystal (PC) demonstrates that the phase shift of mth order reflected light is symmetric with respect to the line of kx=mπb in the frequency-wave vector domain, where kx and b denote the incident wave vector component along the surface and the period of the PC along the surface, respectively, and m is an integer. Such phase symmetry originates from the periodicity of a PC along the surface. When higher-order propagating waves appear between two band edges of a stop band, the phase change of the 0th order reflection is generally not π as reported before. Moreover, the reflection phase can be adjusted and designed by changing the cylinder radii of the surface layer. It provides a robust way to achieve a giant Goos–Hänchen shift, which is described in detail as an example, and superluminal propagation from a PC.

© 2010 Optical Society of America

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  1. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  2. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).
  3. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  4. G. Nimtz, A. Haibel, and R.-M. Vetter, “Pulse reflection by photonic barriers,” Phys. Rev. E 66, 037602 (2002).
    [CrossRef]
  5. D. R. Solli, C. F. McCormick, and R. Y. Chiao, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
    [CrossRef] [PubMed]
  6. H. G. Winful, “Nature of 'superluminal' barrier tunneling,” Phys. Rev. Lett. 90, 023901 (2003).
    [CrossRef] [PubMed]
  7. L.-G. Wang, H. Chen, and S.-Y. Zhu, “Superluminal pulse reflection and transmission in a slab system doped with dispersive materials,” Phys. Rev. E 70, 066602 (2004).
    [CrossRef]
  8. I. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
    [CrossRef]
  9. X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
    [CrossRef]
  10. L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101-103 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
    [CrossRef] [PubMed]
  13. J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14, 3024-3029 (2006).
    [CrossRef] [PubMed]
  14. R. Gruschinski, G. Nimtz, and A. A. Stahlhofen, “Resonance-like Goos-Hänchen shift induced by nano-metal films,” Ann. Phys. 17, 917-921 (2008).
    [CrossRef]
  15. Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
    [CrossRef]
  16. E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
    [CrossRef]
  17. E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86, 151112 (2005).
    [CrossRef]
  18. M. Golosovsky, Y. Neve-Oz, and D. Davidov, “Phase shift on reflection from metallodielectric photonic bandgap materials,” Phys. Rev. B 70, 115105 (2004).
    [CrossRef]
  19. Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89, 061121 (2006).
    [CrossRef]
  20. G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
    [CrossRef]
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    [CrossRef]
  23. R. M. Bell, J. B. Pendry, L. Martin Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
    [CrossRef]
  24. M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic bandgap confinement via Van Hove saddle point singularities,” Phys. Rev. Lett. 96, 033904 (2006).
    [CrossRef] [PubMed]

2008 (1)

R. Gruschinski, G. Nimtz, and A. A. Stahlhofen, “Resonance-like Goos-Hänchen shift induced by nano-metal films,” Ann. Phys. 17, 917-921 (2008).
[CrossRef]

2006 (4)

J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14, 3024-3029 (2006).
[CrossRef] [PubMed]

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89, 061121 (2006).
[CrossRef]

L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101-103 (2006).
[CrossRef] [PubMed]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic bandgap confinement via Van Hove saddle point singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[CrossRef] [PubMed]

2005 (2)

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[CrossRef]

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86, 151112 (2005).
[CrossRef]

2004 (5)

M. Golosovsky, Y. Neve-Oz, and D. Davidov, “Phase shift on reflection from metallodielectric photonic bandgap materials,” Phys. Rev. B 70, 115105 (2004).
[CrossRef]

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
[CrossRef]

D. R. Solli, C. F. McCormick, and R. Y. Chiao, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[CrossRef] [PubMed]

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Superluminal pulse reflection and transmission in a slab system doped with dispersive materials,” Phys. Rev. E 70, 066602 (2004).
[CrossRef]

D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

2003 (4)

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

I. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

H. G. Winful, “Nature of 'superluminal' barrier tunneling,” Phys. Rev. Lett. 90, 023901 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

1999 (1)

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

1995 (1)

R. M. Bell, J. B. Pendry, L. Martin Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
[CrossRef]

Bardinal, V.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Bell, R. M.

R. M. Bell, J. B. Pendry, L. Martin Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
[CrossRef]

Benisty, H.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Busch, K.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Cassagne, D.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Chan, S. W.

Chen, H.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Superluminal pulse reflection and transmission in a slab system doped with dispersive materials,” Phys. Rev. E 70, 066602 (2004).
[CrossRef]

Chiao, R. Y.

D. R. Solli, C. F. McCormick, and R. Y. Chiao, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[CrossRef] [PubMed]

Dai, Q. F.

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89, 061121 (2006).
[CrossRef]

Davidov, D.

M. Golosovsky, Y. Neve-Oz, and D. Davidov, “Phase shift on reflection from metallodielectric photonic bandgap materials,” Phys. Rev. B 70, 115105 (2004).
[CrossRef]

Diem, M.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Fang, N.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
[CrossRef]

Felbacq, D.

D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

Freymann, G.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Garcia-Martin, A.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Golosovsky, M.

M. Golosovsky, Y. Neve-Oz, and D. Davidov, “Phase shift on reflection from metallodielectric photonic bandgap materials,” Phys. Rev. B 70, 115105 (2004).
[CrossRef]

Gösele, U.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Green, A. A.

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[CrossRef]

Gruschinski, R.

R. Gruschinski, G. Nimtz, and A. A. Stahlhofen, “Resonance-like Goos-Hänchen shift induced by nano-metal films,” Ann. Phys. 17, 917-921 (2008).
[CrossRef]

Haibel, A.

G. Nimtz, A. Haibel, and R.-M. Vetter, “Pulse reflection by photonic barriers,” Phys. Rev. E 66, 037602 (2002).
[CrossRef]

He, J.

He, S.

Hesselink, L.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
[CrossRef]

Ho, K.-M.

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Houdré, R.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Ibanescu, M.

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic bandgap confinement via Van Hove saddle point singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[CrossRef] [PubMed]

Istrate, E.

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86, 151112 (2005).
[CrossRef]

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[CrossRef]

Joannopoulos, J. D.

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic bandgap confinement via Van Hove saddle point singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[CrossRef] [PubMed]

Jouanin, C.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Kivshar, Y. S.

I. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Koch, W.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Krauss, T. F.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Labilloy, D.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Labiloy, D.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Lai, H. M.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Li, Y. W.

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89, 061121 (2006).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Liu, Z.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
[CrossRef]

Martin Moreno, L.

R. M. Bell, J. B. Pendry, L. Martin Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
[CrossRef]

Maystre, D.

McCormick, C. F.

D. R. Solli, C. F. McCormick, and R. Y. Chiao, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[CrossRef] [PubMed]

Meisel, D. C.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Neve-Oz, Y.

M. Golosovsky, Y. Neve-Oz, and D. Davidov, “Phase shift on reflection from metallodielectric photonic bandgap materials,” Phys. Rev. B 70, 115105 (2004).
[CrossRef]

Nimtz, G.

R. Gruschinski, G. Nimtz, and A. A. Stahlhofen, “Resonance-like Goos-Hänchen shift induced by nano-metal films,” Ann. Phys. 17, 917-921 (2008).
[CrossRef]

G. Nimtz, A. Haibel, and R.-M. Vetter, “Pulse reflection by photonic barriers,” Phys. Rev. E 66, 037602 (2002).
[CrossRef]

Oesterle, U.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Pendry, J. B.

R. M. Bell, J. B. Pendry, L. Martin Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
[CrossRef]

Pereira, S.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Reed, E. J.

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic bandgap confinement via Van Hove saddle point singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[CrossRef] [PubMed]

Sargent, E. H.

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86, 151112 (2005).
[CrossRef]

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[CrossRef]

Schilling, J.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Shadrivov, I.

I. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Smaâli, R.

D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

Solli, D. R.

D. R. Solli, C. F. McCormick, and R. Y. Chiao, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[CrossRef] [PubMed]

Stahlhofen, A. A.

R. Gruschinski, G. Nimtz, and A. A. Stahlhofen, “Resonance-like Goos-Hänchen shift induced by nano-metal films,” Ann. Phys. 17, 917-921 (2008).
[CrossRef]

Vetter, R.-M.

G. Nimtz, A. Haibel, and R.-M. Vetter, “Pulse reflection by photonic barriers,” Phys. Rev. E 66, 037602 (2002).
[CrossRef]

Wang, H. Z.

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89, 061121 (2006).
[CrossRef]

Wang, L. G.

Wang, L.-G.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Superluminal pulse reflection and transmission in a slab system doped with dispersive materials,” Phys. Rev. E 70, 066602 (2004).
[CrossRef]

Ward, A. J.

R. M. Bell, J. B. Pendry, L. Martin Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
[CrossRef]

Wegener, M.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Wehrspohn, R. B.

G. Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Weisbuch, C.

D. Labiloy, D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdré, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

Winful, H. G.

H. G. Winful, “Nature of 'superluminal' barrier tunneling,” Phys. Rev. Lett. 90, 023901 (2003).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Yi, J.

Yin, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
[CrossRef]

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372-374 (2004).
[CrossRef]

Zharov, A.

I. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Zhu, S. Y.

Zhu, S.-Y.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of incident and reflected light on a PC structure of square lattice. The black and white denote the substrate medium and air cylinders, respectively.

Fig. 2
Fig. 2

(a1)–(c1) are reflectance of the 0th, 1 st and 2 nd order reflected waves as functions of frequency and k x , respectively. (a2)–(c2) are reflection phase of the 0th, 1 st , and 2 nd order reflected waves as functions of frequency and k x , respectively. (a3) Presents the 0th reflection phase in normalized frequency of 0.315, (b3) presents the 1 st reflection phase in normalized frequency of 0.315, and (c3) presents the 2 nd reflection phase in normalized frequency of 0.552. The corresponding frequencies are marked in (a2)–(c2) with dashed lines. The PC structure (Fig. 1) with r = r s = 0.5 a . Points A, B, and C have the same frequency in (b1).

Fig. 3
Fig. 3

(a)–(c) Sketches of reflection in points A, B, and C of Fig. 2(b1), respectively. Lines with arrows indicate the wave vectors of incident, the 0th, and the 1 st order reflected lights, respectively.

Fig. 4
Fig. 4

With normal incidence, i.e., k x = 0 , (a) is the reflected energy flux including all order propagating waves as a function of frequency; (b) and (c) are reflectance and phase of the 0th reflected wave as functions of frequency, respectively. The reflection bands, in which the total reflection energy flux is greater than 99.9%, are shown by shaded areas.

Fig. 5
Fig. 5

(a1)–(c1) Reflectance of the 0th, 1 st , and 2 nd order reflected waves as functions of frequency and k x , respectively. (a2)–(c2) Reflection phase of the 0th, 1 st , and 2 nd order reflected waves as functions of frequency and k x , respectively. (a3) Presents the 0th reflection phase in normalized frequency of 0.315, (b3) presents the 1 st reflection phase in normalized frequency of 0.315, and (c3) presents the 2 nd reflection phase in normalized frequency of 0.552. The corresponding frequencies are marked in (a2)–(c2) with dashed lines. The PC structure (Fig. 1) with r = 0.5 a and r s = 0.4 a .

Fig. 6
Fig. 6

GH shift of the 0th order reflected wave as a function of frequency and k x . The PC structure with r = 0.5 a , r s = 0.4 a . The incident Gaussian beam width W x = 25 a . The incident wave is an evanescent wave to be neglected. The inset shows the GH shift as a function of k x in a normalized frequency of 0.315.

Equations (4)

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

r ( m ) = u r ( m ) u in = | r ( m ) | e i ϕ ( m ) ,
E ( i ) ( z , x ) = 1 2 π A ( k x ) exp [ i ( k z z + k x x ) ] d k x ,
E ( r ) ( z , x ) = 1 2 π r ( m ) ( k x ) A ( k x ) exp [ i ( k z z + k x x ) ] d k x .
G = + x | E ( r ) ( 0 , x ) | 2 d x + | E ( r ) ( 0 , x ) | 2 d x .

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