Abstract

We present an efficient method for the absorption of slow group velocity electromagnetic waves in photonic crystal waveguides (PCWs). We show that adiabatically matching the low group velocity waves to high group velocity waves of the PCW and extending the PCW structure into the perfectly matched layer (PML) region results in a 15dB reduction of spurious reflections from the PML. We also discuss the applicability of this method to structures other than PCWs.

© 2011 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).
  4. E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.
  5. H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis beaming from subwavelength aperture,” J. Appl. Phys. 104, 073108 (2008).
    [CrossRef]
  6. A. F. Matthews, “Experimental demonstration of self-collimation beaming and splitting in photonic crystals at microwave frequencies,” Opt. Commun. 282, 1789–1792 (2009).
    [CrossRef]
  7. B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
    [CrossRef] [PubMed]
  8. M. Askari and A. Adibi, “Wide bandwidth photonic crystal waveguide bends,” Proc. SPIE 7609, 760918 (2010).
    [CrossRef]
  9. M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
    [CrossRef]
  10. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
    [CrossRef]
  11. M. Askari, B. Momeni, M. Soltani, and A. Adibi, “Systematic design of wide bandwidth photonic crystal waveguide bends with high transmission and low dispersion,” J. Lightwave Technol. 28, 1707–1713 (2010).
    [CrossRef]
  12. S. Assefa, S. J. McNab, and Y. A. Vlasov, “Transmission of slow light through photonic crystal waveguide bends,” Opt. Lett. 31, 745–747 (2006).
    [CrossRef] [PubMed]
  13. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34, 1072–1074 (2009).
    [CrossRef] [PubMed]
  14. N. Skivesen, A. Tetu, M. Kristensen, J. Kjems, L. H. Frandsen, and P. I. Borel, “Photonic-crystal waveguide biosensor,” Opt. Express 15, 3169–3176 (2007).
    [CrossRef] [PubMed]
  15. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Antennas Propag Mag. 14, 302–307 (1966).
    [CrossRef]
  16. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  17. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  18. A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided Wave Lett. 9, 502–504 (1999).
    [CrossRef]
  19. M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Compon. Lett. 11, 152–154 (2001).
    [CrossRef]
  20. R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).
  21. D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980).
    [CrossRef]
  22. A. Taflove, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech, 1995).
  23. Y-C. Hsue and T.-J. Yang, “Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite photonic crystal,” Phys. Rev. E 70, 016706 (2004).
    [CrossRef]
  24. B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87, 171104–13 (2005).
    [CrossRef]

2010 (2)

2009 (2)

A. F. Matthews, “Experimental demonstration of self-collimation beaming and splitting in photonic crystals at microwave frequencies,” Opt. Commun. 282, 1789–1792 (2009).
[CrossRef]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34, 1072–1074 (2009).
[CrossRef] [PubMed]

2008 (2)

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis beaming from subwavelength aperture,” J. Appl. Phys. 104, 073108 (2008).
[CrossRef]

M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (1)

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87, 171104–13 (2005).
[CrossRef]

2004 (1)

Y-C. Hsue and T.-J. Yang, “Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite photonic crystal,” Phys. Rev. E 70, 016706 (2004).
[CrossRef]

2001 (2)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Compon. Lett. 11, 152–154 (2001).
[CrossRef]

1999 (1)

A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided Wave Lett. 9, 502–504 (1999).
[CrossRef]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1987 (2)

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

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

1980 (1)

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Antennas Propag Mag. 14, 302–307 (1966).
[CrossRef]

Adibi, A.

M. Askari, B. Momeni, M. Soltani, and A. Adibi, “Systematic design of wide bandwidth photonic crystal waveguide bends with high transmission and low dispersion,” J. Lightwave Technol. 28, 1707–1713 (2010).
[CrossRef]

M. Askari and A. Adibi, “Wide bandwidth photonic crystal waveguide bends,” Proc. SPIE 7609, 760918 (2010).
[CrossRef]

M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
[CrossRef]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
[CrossRef] [PubMed]

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87, 171104–13 (2005).
[CrossRef]

Askari, M.

Assefa, S.

Baba, T.

Bayindir, M.

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Biswas, R.

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Borel, P. I.

Bulu, I.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis beaming from subwavelength aperture,” J. Appl. Phys. 104, 073108 (2008).
[CrossRef]

Caglayan, H.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis beaming from subwavelength aperture,” J. Appl. Phys. 104, 073108 (2008).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Eftekhar, A.

M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
[CrossRef]

Fan, S.

A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided Wave Lett. 9, 502–504 (1999).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Fisher, R.

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980).
[CrossRef]

Frandsen, L. H.

Hamachi, Y.

Ho, K. M.

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Hsue, Y-C.

Y-C. Hsue and T.-J. Yang, “Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite photonic crystal,” Phys. Rev. E 70, 016706 (2004).
[CrossRef]

Huang, J.

Joannopoulos, J. D.

A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided Wave Lett. 9, 502–504 (1999).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

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

John, S.

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

Kjems, J.

Koshiba, M.

M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Compon. Lett. 11, 152–154 (2001).
[CrossRef]

Kristensen, M.

Kubo, S.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Matthews, A. F.

A. F. Matthews, “Experimental demonstration of self-collimation beaming and splitting in photonic crystals at microwave frequencies,” Opt. Commun. 282, 1789–1792 (2009).
[CrossRef]

McNab, S. J.

Meade, R. D.

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

Mekis, A.

A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided Wave Lett. 9, 502–504 (1999).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Merewether, D. E.

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980).
[CrossRef]

Mohammadi, S.

Momeni, B.

M. Askari, B. Momeni, M. Soltani, and A. Adibi, “Systematic design of wide bandwidth photonic crystal waveguide bends with high transmission and low dispersion,” J. Lightwave Technol. 28, 1707–1713 (2010).
[CrossRef]

M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
[CrossRef]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
[CrossRef] [PubMed]

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87, 171104–13 (2005).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Ozbay, E.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis beaming from subwavelength aperture,” J. Appl. Phys. 104, 073108 (2008).
[CrossRef]

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Pollock, R.

R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).

Rakhshandehroo, M.

Sasaki, S.

M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Compon. Lett. 11, 152–154 (2001).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Siqalas, M. M.

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Skivesen, N.

Smith, F. W.

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980).
[CrossRef]

Soltani, M.

Taflove, A.

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

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Temelkuran, B.

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Tetu, A.

Tsuji, Y.

M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Compon. Lett. 11, 152–154 (2001).
[CrossRef]

Tuttle, G.

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Vlasov, Y. A.

Winn, J. N.

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

Yablonovitch, E.

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

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Yang, T.-J.

Y-C. Hsue and T.-J. Yang, “Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite photonic crystal,” Phys. Rev. E 70, 016706 (2004).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Antennas Propag Mag. 14, 302–307 (1966).
[CrossRef]

Yegnanarayanan, S.

M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
[CrossRef]

Yokohoma, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87, 171104–13 (2005).
[CrossRef]

IEEE Antennas Propag Mag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Antennas Propag Mag. 14, 302–307 (1966).
[CrossRef]

IEEE Microw. Guided Wave Lett. (1)

A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided Wave Lett. 9, 502–504 (1999).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Compon. Lett. 11, 152–154 (2001).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980).
[CrossRef]

J. Appl. Phys. (1)

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis beaming from subwavelength aperture,” J. Appl. Phys. 104, 073108 (2008).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (1)

A. F. Matthews, “Experimental demonstration of self-collimation beaming and splitting in photonic crystals at microwave frequencies,” Opt. Commun. 282, 1789–1792 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phy. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohoma, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phy. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Phys. Rev. E (1)

Y-C. Hsue and T.-J. Yang, “Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite photonic crystal,” Phys. Rev. E 70, 016706 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

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

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

Proc. SPIE (2)

M. Askari and A. Adibi, “Wide bandwidth photonic crystal waveguide bends,” Proc. SPIE 7609, 760918 (2010).
[CrossRef]

M. Askari, B. Momeni, S. Yegnanarayanan, A. Eftekhar, and A. Adibi, “Efficient coupling of light into the planar photonic crystal waveguides in the slow group velocity regime,” Proc. SPIE 6901, 69011A (2008).
[CrossRef]

Other (4)

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

E. Ozbay, B. Temelkuran, M. Bayindir, R. Biswas, M. M. Siqalas, G. Tuttle, and K. M. Ho, “Highly directional resonant antennas built around photonic crystals,” in 1999 IEEE LEOS Annual Meeting Conference Proceedings (IEEE, 1999), pp. 8–11.

R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).

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

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Figures (7)

Fig. 1
Fig. 1

(a) Structure used in our simulations showing the location of the source and the observation surface. The PC structure is formed by a triangular lattice of air holes in silicon. The radius of each hole (r) is 30% of the lattice constant (a). The PCW is formed by removing one row of air holes. The origin of the coordinate system is in the middle of the slab at the slab-PCW interface. The observation surface is at a distance x from the slab-PCW interface. (b) Dispersion diagram of the TM modes (i.e., magnetic field normal to the plane of periodicity) of the PCW. Also identified in the figure are even and odd modes of the PCW as well as the high and low group velocity regions of the even mode.

Fig. 2
Fig. 2

Comparison of reflection from a PCPML [19] (blue dashed curve) and an HPML [16] (red solid curve). The length of these PMLs are 15 a and 0.5 a , respectively, with a being the lattice constant. All parameters of the PCW structure are the same as those in the caption of Fig. 1.

Fig. 3
Fig. 3

Dispersion diagram of the PCW of Fig. 1a at different values of conductivity (σ). The curves shown have conductivity σ = 0 (red plus signs) and σ = 0.03 (blue circles). The modes of the two structures are almost the same for ω n > 0.275 . However, there is a significant difference at ω n < 0.275 , which corresponds to the low group velocity region.

Fig. 4
Fig. 4

(a) Dispersion diagram of a PCW with σ = 0.03 . The field profiles are calculated at (b)  κ a = 2.0942 and ω n = 0.275 , (c) κ a = 2.138 and ω n = 0.266 , and (d) κ a = 2.447 and ω n = 0.266 . All parameters of the PCW are the same as those in the caption of Fig. 1.

Fig. 5
Fig. 5

Dispersion of the PCW, in Fig. 1a, for different values of r / a : r / a = 0.30 (red squares), r / a = 0.28 (blue circles), and r / a = 0.26 (green diamonds).

Fig. 6
Fig. 6

Simulation structure with AM-PCPML. The figure shows the adiabatic region, where the low group velocity modes of the PCW with r / a = 0.30 are matched to high group velocity modes of the PCW with an r / a = 0.26 , and the PCPML ( r / a = 0.26 ) region.

Fig. 7
Fig. 7

Comparison of reflections from different PMLs: HPML (red solid curve), PCPML (blue dashed curve), and AM-PCPML (green dash-dot curve) applied to the PCW shown in Fig. 1a.

Equations (4)

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t 2 < t 1 x / v g 2 < ( 2 L x ) / v g 1 v g 1 / v g 2 < ( 2 L x ) / x .
v g 1 / v g 2 < 3.
v g 1 / v g 2 < 59.
E y , ref = E y , total E y , inc .

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