Abstract

The finite-difference time-domain method is employed for the analysis of coupling of the surface modes of two truncated one-dimensional photonic crystals separated by a gap. The wave vector, field distributions, and existence conditions of the coupled surface modes are investigated. The wave vector of symmetric gap modes increases with decreasing gap width, while that of antisymmetric modes decreases—exactly opposite of the situation for surface plasmons on metallic half-spaces separated by a dielectric gap. Photonic crystal gap modes could easily and effectively be used as nondissipating gap-mode waveguides.

© 2005 Optical Society of America

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  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  4. P. Yeh, Optical Waves in Layered Media (Wiley, 1977).
  5. J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994).
    [CrossRef]
  6. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528–530 (1993).
    [CrossRef] [PubMed]
  7. F. Ramos-Mendieta, P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
    [CrossRef]
  8. P. Etchegoin, R. T. Phillips, “Photon focusing, internal diffraction, and surface states in periodic dielectric structures,” Phys. Rev. B 53, 12674–12683 (1996).
    [CrossRef]
  9. R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
    [CrossRef]
  10. J. M. Elson, P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
    [CrossRef]
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    [CrossRef]
  12. W. M. Robertson, M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
    [CrossRef]
  13. W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
    [CrossRef]
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    [CrossRef]
  15. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. G. Mur, “Total-field absorbing boundary conditions for the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. 40, 100–102 (1998).
    [CrossRef]
  24. A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).
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    [CrossRef] [PubMed]

2004 (5)

2003 (3)

F. Villa, J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun. 223, 109–115 (2003).
[CrossRef]

K. Tanaka, M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

J. A. Gaspar-Armenta, F. Villa, T. Lopez-Rios, “Surface waves in finite one-dimensional photonic crystals: mode coupling,” Opt. Commun. 216, 379–384 (2003).
[CrossRef]

2001 (1)

M. Qiu, S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[CrossRef]

1999 (3)

W. M. Robertson, M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
[CrossRef]

F. Ramos-Mendieta, P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

1998 (1)

G. Mur, “Total-field absorbing boundary conditions for the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. 40, 100–102 (1998).
[CrossRef]

1996 (3)

J. M. Elson, P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
[CrossRef]

F. Ramos-Mendieta, P. Halevi, “Propagation constant—limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1–5 (1996).
[CrossRef]

P. Etchegoin, R. T. Phillips, “Photon focusing, internal diffraction, and surface states in periodic dielectric structures,” Phys. Rev. B 53, 12674–12683 (1996).
[CrossRef]

1994 (1)

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994).
[CrossRef]

1993 (1)

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
[CrossRef]

1987 (2)

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

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

Allan, D. C.

Arjavalingam, G.

Boardman, A. D.

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

Borrelli, N. F.

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
[CrossRef]

Digonnet, M. J. F.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[CrossRef]

Elson, J. M.

J. M. Elson, P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
[CrossRef]

Etchegoin, P.

P. Etchegoin, R. T. Phillips, “Photon focusing, internal diffraction, and surface states in periodic dielectric structures,” Phys. Rev. B 53, 12674–12683 (1996).
[CrossRef]

Fan, S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[CrossRef]

Gaspar-Armenta, J. A.

F. Villa, J. A. Gaspar-Armenta, “Photonic crystal to photonic crystal surface modes: narrow-bandpass filters,” Opt. Express 12, 2338–2354 (2004).
[CrossRef] [PubMed]

F. Villa, J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun. 223, 109–115 (2003).
[CrossRef]

J. A. Gaspar-Armenta, F. Villa, T. Lopez-Rios, “Surface waves in finite one-dimensional photonic crystals: mode coupling,” Opt. Commun. 216, 379–384 (2003).
[CrossRef]

Gramotnev, D. K.

Hagness, S.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method2nd. ed. (Artech House, 2000).

Halevi, P.

F. Ramos-Mendieta, P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

F. Ramos-Mendieta, P. Halevi, “Propagation constant—limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1–5 (1996).
[CrossRef]

He, S.

M. Qiu, S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[CrossRef]

Joannopoulos, J. D.

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

John, S.

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

Kim, H. K.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[CrossRef]

Kino, G. S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[CrossRef]

Koch, K. W.

Koshiba, M.

Lopez-Rios, T.

J. A. Gaspar-Armenta, F. Villa, T. Lopez-Rios, “Surface waves in finite one-dimensional photonic crystals: mode coupling,” Opt. Commun. 216, 379–384 (2003).
[CrossRef]

May, M. S.

W. M. Robertson, M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

Meade, R. D.

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Mortensen, N. A.

Mur, G.

G. Mur, “Total-field absorbing boundary conditions for the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. 40, 100–102 (1998).
[CrossRef]

Phillips, R. T.

P. Etchegoin, R. T. Phillips, “Photon focusing, internal diffraction, and surface states in periodic dielectric structures,” Phys. Rev. B 53, 12674–12683 (1996).
[CrossRef]

Pile, D. F. P.

Qiu, M.

M. Qiu, S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[CrossRef]

Ramos-Mendieta, F.

F. Ramos-Mendieta, P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

F. Ramos-Mendieta, P. Halevi, “Propagation constant—limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1–5 (1996).
[CrossRef]

Rappe, A. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
[CrossRef]

Robertson, W. M.

Saitoh, K.

Shin, J.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[CrossRef]

Smith, C. M.

Taflove, A.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method2nd. ed. (Artech House, 2000).

Tanaka, K.

K. Tanaka, M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka, M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

Tran, P.

J. M. Elson, P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
[CrossRef]

Villa, F.

F. Villa, J. A. Gaspar-Armenta, “Photonic crystal to photonic crystal surface modes: narrow-bandpass filters,” Opt. Express 12, 2338–2354 (2004).
[CrossRef] [PubMed]

F. Villa, J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun. 223, 109–115 (2003).
[CrossRef]

J. A. Gaspar-Armenta, F. Villa, T. Lopez-Rios, “Surface waves in finite one-dimensional photonic crystals: mode coupling,” Opt. Commun. 216, 379–384 (2003).
[CrossRef]

West, J. A.

Winn, J. N.

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Yablonovitch, E.

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

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1977).

Appl. Phys. Lett. (2)

W. M. Robertson, M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

K. Tanaka, M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Total-field absorbing boundary conditions for the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. 40, 100–102 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994).
[CrossRef]

Opt. Commun. (3)

J. A. Gaspar-Armenta, F. Villa, T. Lopez-Rios, “Surface waves in finite one-dimensional photonic crystals: mode coupling,” Opt. Commun. 216, 379–384 (2003).
[CrossRef]

F. Ramos-Mendieta, P. Halevi, “Propagation constant—limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1–5 (1996).
[CrossRef]

F. Villa, J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun. 223, 109–115 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Lett. A (1)

M. Qiu, S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[CrossRef]

Phys. Rev. B (4)

F. Ramos-Mendieta, P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

P. Etchegoin, R. T. Phillips, “Photon focusing, internal diffraction, and surface states in periodic dielectric structures,” Phys. Rev. B 53, 12674–12683 (1996).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Electromagnetic bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961–10964 (1991).
[CrossRef]

J. M. Elson, P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

Other (4)

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

P. Yeh, Optical Waves in Layered Media (Wiley, 1977).

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method2nd. ed. (Artech House, 2000).

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

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Figures (4)

Fig. 1
Fig. 1

Period of the superlattices is d = 0.3λvac. I consider alternate layers of vacuum with width 0.8d and dielectric permittivity εvac = 1 (unshaded layers) and a high-index medium with width 0.2d and ε2 = 13 (shaded layers). The termination factor, τ, is considered to be the same for each superlattice. A dielectric gap of width g separates the two photonic crystal half-spaces.

Fig. 2
Fig. 2

(a), (b) Total electric field distribution for a photonic crystal surface-polariton gap mode (symmetric electric field propagating from left to right) with gap width g = 0.5d = 0.1λvac. The absence of the gap mode observed in the region x > 450 is due to the mode’s being excited at the left edge of the window and propagating only a finite distance during the finite time iterations performed. (b) Electric field along the vacuum–photonic crystal interface.

Fig. 3
Fig. 3

(a) Dispersion of the wave vector due to varying gap width. Circles represent wave vectors for antisymmetric excitation (with respect to the electric field), and crosses denote symmetric excitation. (b) Dispersion of the wave vector for varying excitation frequency for the symmetric (upper dashed curve) and antisymmetric (lower dashed curve) modes with g = 0.5d [i.e., data points with g/d = 0.5 in Fig. 3(a)]. The solid curve denotes the symmetric and antisymmetric modes with g = 2d.

Fig. 4
Fig. 4

Electric field distribution for the gap width g/d = 0.05 = 0.015λvac showing (a) the electric field propagating into the photonic crystal half-spaces and (b) the electric field along the vacuum–photonic crystal interface. We can see that this is not a true eigenmode of the structure since the amplitude is clearly decaying along the direction of propagation (b).

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