Abstract

A two-dimensional superlattice photonic crystal structure is investigated in which the holes in adjacent rows of a triangular lattice alternate between two different radii. The superimposition of a superlattice on a triangular lattice is shown to reduce the photonic bandgap, introduce band splitting, and change the dispersion contours so that dramatic effects are seen in the propagation, refraction, and dispersion properties of the structure. For single mode propagation, the superlattice shows regions of both positive and negative refraction as well as refraction at normal incidence. The physical mechanisms responsible for these effects are directly related to Brillouin Zone folding effects on the triangular lattice that lowers the lattice symmetry and introduces anisotropy in the lattice.

© 2005 Optical Society of America

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References

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  1. J. P. Dowling and C. Bowen, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345 (1994).
    [Crossref]
  2. S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771 (1996).
    [Crossref] [PubMed]
  3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
    [Crossref]
  4. M. Notomi, “Theory of light propagating in strongly modulated photonic crystal: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10,696 (2000).
  5. J. Bravo-Abad, T. Ochiai, and J. Sànchez-Dehesa, “Anomalous refractive properties of a two-dimensional photonic band-gap prism,” Phys. Rev. B 67, 115,116 (2003).
    [Crossref]
  6. W. Park and C. J. Summers, “Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs,” Opt. Lett. 27(16), 1397 (2002).
    [Crossref]
  7. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
    [Crossref]
  8. L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).
  9. T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38(7), 909 (2002).
    [Crossref]
  10. W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
    [Crossref]
  11. T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325 (2002).
    [Crossref]
  12. W. Park and C. J. Summers, “Optical properties of superlattice photonic crystal waveguides,” Appl. Phys. Lett. 84(12), 2013 (2004).
    [Crossref]
  13. C. J. Summers, C. W. Neff, and W. Park, “Active Photonic Crystal Nano-Architectures,” J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
    [Crossref]
  14. N. W. Ashcroft and N. D. Mermin, Solid State Physics (W. B. Saunders, 1976).
  15. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173 (2001).
    [Crossref]
  16. A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures and Green’s functions using a non-orthogonal FDTD method,” Comput. Phys. Commun. 112(1), 23 (1998).
    [Crossref]
  17. C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51(23), 16,635 (1995).
  18. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
    [Crossref]
  19. J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [Crossref]
  20. L. Zhao and A. Cangellaris, “GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 44, 2555–2563 (1996).
    [Crossref]
  21. P. J. Russell and T. A. Birks, “Bloch wave optics in photonic crystals: physics and applications,” in Photonic band gap materials, C. M. Soukoulis, ed., no. 315 in NATO ASI series. Series E, applied sciences, p. 71 (Kluwer, 1996).

2004 (1)

W. Park and C. J. Summers, “Optical properties of superlattice photonic crystal waveguides,” Appl. Phys. Lett. 84(12), 2013 (2004).
[Crossref]

2003 (2)

C. J. Summers, C. W. Neff, and W. Park, “Active Photonic Crystal Nano-Architectures,” J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
[Crossref]

J. Bravo-Abad, T. Ochiai, and J. Sànchez-Dehesa, “Anomalous refractive properties of a two-dimensional photonic band-gap prism,” Phys. Rev. B 67, 115,116 (2003).
[Crossref]

2002 (5)

W. Park and C. J. Summers, “Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs,” Opt. Lett. 27(16), 1397 (2002).
[Crossref]

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38(7), 909 (2002).
[Crossref]

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

2001 (1)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173 (2001).
[Crossref]

2000 (1)

M. Notomi, “Theory of light propagating in strongly modulated photonic crystal: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10,696 (2000).

1999 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

1998 (2)

A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures and Green’s functions using a non-orthogonal FDTD method,” Comput. Phys. Commun. 112(1), 23 (1998).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

1996 (2)

S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771 (1996).
[Crossref] [PubMed]

L. Zhao and A. Cangellaris, “GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 44, 2555–2563 (1996).
[Crossref]

1995 (1)

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51(23), 16,635 (1995).

1994 (2)

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

J. P. Dowling and C. Bowen, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345 (1994).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (W. B. Saunders, 1976).

Baba, T.

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38(7), 909 (2002).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

Berenger, J.

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

Birks, T. A.

P. J. Russell and T. A. Birks, “Bloch wave optics in photonic crystals: physics and applications,” in Photonic band gap materials, C. M. Soukoulis, ed., no. 315 in NATO ASI series. Series E, applied sciences, p. 71 (Kluwer, 1996).

Bowen, C.

J. P. Dowling and C. Bowen, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345 (1994).
[Crossref]

Bravo-Abad, J.

J. Bravo-Abad, T. Ochiai, and J. Sànchez-Dehesa, “Anomalous refractive properties of a two-dimensional photonic band-gap prism,” Phys. Rev. B 67, 115,116 (2003).
[Crossref]

Cangellaris, A.

L. Zhao and A. Cangellaris, “GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 44, 2555–2563 (1996).
[Crossref]

Chan, C. T.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51(23), 16,635 (1995).

Dowling, J. P.

J. P. Dowling and C. Bowen, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345 (1994).
[Crossref]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

Hietala, V. M.

Ho, K. M.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51(23), 16,635 (1995).

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173 (2001).
[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173 (2001).
[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

Jones, E. D.

Karle, T.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

King, J. S.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

Krauss, T. F.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).

Liddell, C.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

Lin, S.-Y.

Matsumoto, T.

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

Mazilu, M.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (W. B. Saunders, 1976).

Nakamura, M.

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38(7), 909 (2002).
[Crossref]

Neff, C. W.

C. J. Summers, C. W. Neff, and W. Park, “Active Photonic Crystal Nano-Architectures,” J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
[Crossref]

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

Notomi, M.

M. Notomi, “Theory of light propagating in strongly modulated photonic crystal: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10,696 (2000).

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

Ochiai, T.

J. Bravo-Abad, T. Ochiai, and J. Sànchez-Dehesa, “Anomalous refractive properties of a two-dimensional photonic band-gap prism,” Phys. Rev. B 67, 115,116 (2003).
[Crossref]

Park, W.

W. Park and C. J. Summers, “Optical properties of superlattice photonic crystal waveguides,” Appl. Phys. Lett. 84(12), 2013 (2004).
[Crossref]

C. J. Summers, C. W. Neff, and W. Park, “Active Photonic Crystal Nano-Architectures,” J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
[Crossref]

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

W. Park and C. J. Summers, “Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs,” Opt. Lett. 27(16), 1397 (2002).
[Crossref]

Pendry, J. B.

A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures and Green’s functions using a non-orthogonal FDTD method,” Comput. Phys. Commun. 112(1), 23 (1998).
[Crossref]

Russell, P. J.

P. J. Russell and T. A. Birks, “Bloch wave optics in photonic crystals: physics and applications,” in Photonic band gap materials, C. M. Soukoulis, ed., no. 315 in NATO ASI series. Series E, applied sciences, p. 71 (Kluwer, 1996).

Sànchez-Dehesa, J.

J. Bravo-Abad, T. Ochiai, and J. Sànchez-Dehesa, “Anomalous refractive properties of a two-dimensional photonic band-gap prism,” Phys. Rev. B 67, 115,116 (2003).
[Crossref]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

Summers, C. J.

W. Park and C. J. Summers, “Optical properties of superlattice photonic crystal waveguides,” Appl. Phys. Lett. 84(12), 2013 (2004).
[Crossref]

C. J. Summers, C. W. Neff, and W. Park, “Active Photonic Crystal Nano-Architectures,” J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
[Crossref]

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

W. Park and C. J. Summers, “Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs,” Opt. Lett. 27(16), 1397 (2002).
[Crossref]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

Wang, L.

Ward, A. J.

A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures and Green’s functions using a non-orthogonal FDTD method,” Comput. Phys. Commun. 112(1), 23 (1998).
[Crossref]

Wu, L.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).

Yu, Q. L.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51(23), 16,635 (1995).

Zhao, L.

L. Zhao and A. Cangellaris, “GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 44, 2555–2563 (1996).
[Crossref]

Appl. Phys. Lett. (3)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370 (1999).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

W. Park and C. J. Summers, “Optical properties of superlattice photonic crystal waveguides,” Appl. Phys. Lett. 84(12), 2013 (2004).
[Crossref]

Comput. Phys. Commun. (1)

A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures and Green’s functions using a non-orthogonal FDTD method,” Comput. Phys. Commun. 112(1), 23 (1998).
[Crossref]

IEEE J. Quantum Electron. (2)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915 (2002).

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38(7), 909 (2002).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

L. Zhao and A. Cangellaris, “GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 44, 2555–2563 (1996).
[Crossref]

J. Comput. Phys. (1)

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

J. Mod. Opt. (1)

J. P. Dowling and C. Bowen, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345 (1994).
[Crossref]

J. Nonlinear Optical Phys. and Mater. (1)

C. J. Summers, C. W. Neff, and W. Park, “Active Photonic Crystal Nano-Architectures,” J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
[Crossref]

Opt. Express (1)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173 (2001).
[Crossref]

Opt. Lett. (2)

W. Park and C. J. Summers, “Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs,” Opt. Lett. 27(16), 1397 (2002).
[Crossref]

S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771 (1996).
[Crossref] [PubMed]

Phys. Rev. B (5)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10,096 (1998).
[Crossref]

M. Notomi, “Theory of light propagating in strongly modulated photonic crystal: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10,696 (2000).

J. Bravo-Abad, T. Ochiai, and J. Sànchez-Dehesa, “Anomalous refractive properties of a two-dimensional photonic band-gap prism,” Phys. Rev. B 67, 115,116 (2003).
[Crossref]

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51(23), 16,635 (1995).

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751 (1999).
[Crossref]

Phys. Status Solidi B (1)

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, “ZnS-based photonic crystals,” Phys. Status Solidi B 229(2), 949 (2002).
[Crossref]

Other (2)

N. W. Ashcroft and N. D. Mermin, Solid State Physics (W. B. Saunders, 1976).

P. J. Russell and T. A. Birks, “Bloch wave optics in photonic crystals: physics and applications,” in Photonic band gap materials, C. M. Soukoulis, ed., no. 315 in NATO ASI series. Series E, applied sciences, p. 71 (Kluwer, 1996).

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Figures (4)

Fig. 1.
Fig. 1.

Details of the SL structure.(a) An illustration of a SL slab waveguide. (b) A schematic showing the parameters of the structure. (c) Reciprocal lattice representation.

Fig. 2.
Fig. 2.

Photonic band diagrams for SL structures calculated using the PWE method for (a) r 2/r 1=1.0, (b) 0.857, and (c) 0.571.

Fig. 3.
Fig. 3.

Time-averaged magnetic-field energy density of the Hz field component for (a) and (b) the degenerate states at the bottom of the air band at the M point of the triangular lattice and (c) and (d) the 3s and 3p states of the 2D PC-SL with strength 0.571.

Fig. 4.
Fig. 4.

(a) TE polarization equi-frequency contours for the SL structure calculated with the PWE method for a strength of 1.0 (solid line) and 0.857 (dashed line) and with the FDTD method for a radius ratio of 0.857 (scattered dots), gray lines indicate the construction lines for a beam of ωn =0.3185 incident from air onto the PC. (b) Refraction angles with change in incident angle for r 2/r 1=0.857 for a range of ωn with 1% spacing between frequencies (group of lines) and for a 2D slab waveguide structure (scattered plot).

Equations (4)

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S K = j = 1 n f j ( K ) e i K · d j ,
K = n 1 b 1 + n 2 b 2 ,
S K = f 1 ( K ) + ( 1 ) n 1 + n 2 f 2 ( K ) .
ε eff , j = ε b ( 1 ( r 2 r 1 ) 2 ) + ε c , i ( r 2 r 1 ) 2 ,

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