M. C. Lin and R. F. Jao, “Quantitative analysis of photon density of states for a realistic superlattice with omnidirectional light propagation,” Phys. Rev. E 74,046613 (2006).

[CrossRef]

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72,056609 (2005).

[CrossRef]

P. Halevi and A. S. Sánchez, “Spontaneous emission in a high-contrast one-dimensional photonic crystal,” Opt. Commun. 251,109–114 (2005).

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. B 21,289–295 (2004).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65,155120, 2002.

[CrossRef]

X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with psudogaps,” Phys. Rev. Lett. 88,093902 (2002)

[CrossRef]
[PubMed]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

Z. Y. Li and Y. Xia, “Omnidirectional absolute band gaps in two-dimensional photonic crystals,” Phys. Rev. B 64,153108 (2001).

[CrossRef]

D. Hermann, M. Frank, K. Busch, and P. wölfle, “Photonic band structure computations,” Opt. Express 8,167–172 (2001).

[CrossRef]
[PubMed]

W. Zhang, C. T. Chan, and P. Sheng, “Multiple scattering theory and its application to photonic band gap systems consisting of coated spheres,” Opt. Express 8,203–208 (2001).

[CrossRef]
[PubMed]

R. Hillebrand, W. Hergert, and W. Harms, “Theoretical band gap studies of two-dimensional photonic crystals with varying column roundness,” Phys. stat. sol. (b) 217,981–989 (2000).

[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” J. Lightwave Tech. 18,102–110 (2000).

[CrossRef]

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48,973–980 (2000).

[CrossRef]

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161,668–679 (2000).

[CrossRef]

D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149,363–376, 1999.

[CrossRef]

O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures,” Phys. Rev. Lett. 82,315–318 (1999).

[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150,468–481 (1999).

[CrossRef]

J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” Opt. Soc. Am. B 15,2316–2324 (1998).

[CrossRef]

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58,3896–3908 (1998).

[CrossRef]

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58,7252–7259 (1998).

[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58,6791–6794 (1998).

[CrossRef]

A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati, “Dipole relaxation in dispersive photonic band-gap structures,” Phys. Rev. A 55,1454–1461 (1997).

[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386,143–149 (1997).

[CrossRef]

G. Tayeb and D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14,3323–3332 (1997).

[CrossRef]

A. Figotin and Y. A. Godin, “The Computation of Spectra of Some 2D Photonic Crystals,” J. Comput. Phys. 136,585–598, 1997.

[CrossRef]

J. M. Elson and 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]

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54,2356–2368 (1996).

[CrossRef]
[PubMed]

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44,2688–2695 (1996).

[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51,16635–16642 (1995).

[CrossRef]

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51,4672–4675 (1995).

[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52,8992–9002 (1995).

[CrossRef]

T. Suzuki and P. K. L. Yu, “Emission power of an electric dipole in the photonic band structure of the fcc lattice,” J. Opt. Soc. Am. B 12,570–582 (1995).

[CrossRef]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69,2772–2775 (1992).

[CrossRef]
[PubMed]

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46,612–622 (1992).

[CrossRef]
[PubMed]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45,13962–13972 (1992).

[CrossRef]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B 44,8565–8571 (1991).

[CrossRef]

A. O. Barut and J. P. Dowling, “Quantum electrodynamics based on self-energy: Spontaneous emission in cavities,” Phys. Rev. A 36,649–654 (1987).

[CrossRef]
[PubMed]

D. Kleppner, “Inhibited Spontaneous Emission,” Phys. Rev. Lett. 47,233–236 (1981).

[CrossRef]

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69,681 (1946).

A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati, “Dipole relaxation in dispersive photonic band-gap structures,” Phys. Rev. A 55,1454–1461 (1997).

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150,468–481 (1999).

[CrossRef]

A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati, “Dipole relaxation in dispersive photonic band-gap structures,” Phys. Rev. A 55,1454–1461 (1997).

[CrossRef]

A. O. Barut and J. P. Dowling, “Quantum electrodynamics based on self-energy: Spontaneous emission in cavities,” Phys. Rev. A 36,649–654 (1987).

[CrossRef]
[PubMed]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58,6791–6794 (1998).

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46,612–622 (1992).

[CrossRef]
[PubMed]

W. Zhang, C. T. Chan, and P. Sheng, “Multiple scattering theory and its application to photonic band gap systems consisting of coated spheres,” Opt. Express 8,203–208 (2001).

[CrossRef]
[PubMed]

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51,16635–16642 (1995).

[CrossRef]

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48,973–980 (2000).

[CrossRef]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161,668–679 (2000).

[CrossRef]

D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149,363–376, 1999.

[CrossRef]

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46,612–622 (1992).

[CrossRef]
[PubMed]

A. O. Barut and J. P. Dowling, “Quantum electrodynamics based on self-energy: Spontaneous emission in cavities,” Phys. Rev. A 36,649–654 (1987).

[CrossRef]
[PubMed]

J. M. Elson and 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]

A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati, “Dipole relaxation in dispersive photonic band-gap structures,” Phys. Rev. A 55,1454–1461 (1997).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65,155120, 2002.

[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386,143–149 (1997).

[CrossRef]

A. Figotin and Y. A. Godin, “The Computation of Spectra of Some 2D Photonic Crystals,” J. Comput. Phys. 136,585–598, 1997.

[CrossRef]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures,” Phys. Rev. Lett. 82,315–318 (1999).

[CrossRef]

A. Figotin and Y. A. Godin, “The Computation of Spectra of Some 2D Photonic Crystals,” J. Comput. Phys. 136,585–598, 1997.

[CrossRef]

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161,668–679 (2000).

[CrossRef]

X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with psudogaps,” Phys. Rev. Lett. 88,093902 (2002)

[CrossRef]
[PubMed]

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65,155120, 2002.

[CrossRef]

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72,056609 (2005).

[CrossRef]

P. Halevi and A. S. Sánchez, “Spontaneous emission in a high-contrast one-dimensional photonic crystal,” Opt. Commun. 251,109–114 (2005).

[CrossRef]

R. Hillebrand, W. Hergert, and W. Harms, “Theoretical band gap studies of two-dimensional photonic crystals with varying column roundness,” Phys. stat. sol. (b) 217,981–989 (2000).

[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45,13962–13972 (1992).

[CrossRef]

R. Hillebrand, W. Hergert, and W. Harms, “Theoretical band gap studies of two-dimensional photonic crystals with varying column roundness,” Phys. stat. sol. (b) 217,981–989 (2000).

[CrossRef]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” J. Lightwave Tech. 18,102–110 (2000).

[CrossRef]

R. Hillebrand, W. Hergert, and W. Harms, “Theoretical band gap studies of two-dimensional photonic crystals with varying column roundness,” Phys. stat. sol. (b) 217,981–989 (2000).

[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58,6791–6794 (1998).

[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51,16635–16642 (1995).

[CrossRef]

J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” Opt. Soc. Am. B 15,2316–2324 (1998).

[CrossRef]

J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” Opt. Soc. Am. B 15,2316–2324 (1998).

[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45,13962–13972 (1992).

[CrossRef]

M. C. Lin and R. F. Jao, “Quantitative analysis of photon density of states for a realistic superlattice with omnidirectional light propagation,” Phys. Rev. E 74,046613 (2006).

[CrossRef]

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-Interscience, New York2002).

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386,143–149 (1997).

[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, New Jersey1995).

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58,3896–3908 (1998).

[CrossRef]

A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati, “Dipole relaxation in dispersive photonic band-gap structures,” Phys. Rev. A 55,1454–1461 (1997).

[CrossRef]

C. Kittel, Introduction to Solid State Physics (Wiley, New York1976).

D. Kleppner, “Inhibited Spontaneous Emission,” Phys. Rev. Lett. 47,233–236 (1981).

[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” J. Lightwave Tech. 18,102–110 (2000).

[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150,468–481 (1999).

[CrossRef]

J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” Opt. Soc. Am. B 15,2316–2324 (1998).

[CrossRef]

Z. Y. Li and Y. Xia, “Omnidirectional absolute band gaps in two-dimensional photonic crystals,” Phys. Rev. B 64,153108 (2001).

[CrossRef]

M. C. Lin and R. F. Jao, “Quantitative analysis of photon density of states for a realistic superlattice with omnidirectional light propagation,” Phys. Rev. E 74,046613 (2006).

[CrossRef]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69,2772–2775 (1992).

[CrossRef]
[PubMed]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B 44,8565–8571 (1991).

[CrossRef]

O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures,” Phys. Rev. Lett. 82,315–318 (1999).

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, New Jersey1995).

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54,2356–2368 (1996).

[CrossRef]
[PubMed]

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48,973–980 (2000).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65,155120, 2002.

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161,668–679 (2000).

[CrossRef]

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48,973–980 (2000).

[CrossRef]

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58,7252–7259 (1998).

[CrossRef]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69,2772–2775 (1992).

[CrossRef]
[PubMed]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B 44,8565–8571 (1991).

[CrossRef]

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69,681 (1946).

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54,2356–2368 (1996).

[CrossRef]
[PubMed]

J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” Opt. Soc. Am. B 15,2316–2324 (1998).

[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52,8992–9002 (1995).

[CrossRef]

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51,4672–4675 (1995).

[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin2001).

P. Halevi and A. S. Sánchez, “Spontaneous emission in a high-contrast one-dimensional photonic crystal,” Opt. Commun. 251,109–114 (2005).

[CrossRef]

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72,056609 (2005).

[CrossRef]

O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures,” Phys. Rev. Lett. 82,315–318 (1999).

[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58,6791–6794 (1998).

[CrossRef]

O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures,” Phys. Rev. Lett. 82,315–318 (1999).

[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58,6791–6794 (1998).

[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45,13962–13972 (1992).

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

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

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

J. M. Elson and 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]

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” J. Lightwave Tech. 18,102–110 (2000).

[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386,143–149 (1997).

[CrossRef]

X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with psudogaps,” Phys. Rev. Lett. 88,093902 (2002)

[CrossRef]
[PubMed]

X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with psudogaps,” Phys. Rev. Lett. 88,093902 (2002)

[CrossRef]
[PubMed]

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58,7252–7259 (1998).

[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, New Jersey1995).

Z. Y. Li and Y. Xia, “Omnidirectional absolute band gaps in two-dimensional photonic crystals,” Phys. Rev. B 64,153108 (2001).

[CrossRef]

X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with psudogaps,” Phys. Rev. Lett. 88,093902 (2002)

[CrossRef]
[PubMed]

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44,2688–2695 (1996).

[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York1984).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York1984).

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51,16635–16642 (1995).

[CrossRef]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modeling,” IEE Proc. -Sci. Meas. Technal. 149,293–296 (2002).

[CrossRef]

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48,973–980 (2000).

[CrossRef]

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44,2688–2695 (1996).

[CrossRef]

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161,668–679 (2000).

[CrossRef]

D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149,363–376, 1999.

[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150,468–481 (1999).

[CrossRef]

A. Figotin and Y. A. Godin, “The Computation of Spectra of Some 2D Photonic Crystals,” J. Comput. Phys. 136,585–598, 1997.

[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” J. Lightwave Tech. 18,102–110 (2000).

[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386,143–149 (1997).

[CrossRef]

P. Halevi and A. S. Sánchez, “Spontaneous emission in a high-contrast one-dimensional photonic crystal,” Opt. Commun. 251,109–114 (2005).

[CrossRef]

D. Hermann, M. Frank, K. Busch, and P. wölfle, “Photonic band structure computations,” Opt. Express 8,167–172 (2001).

[CrossRef]
[PubMed]

W. Zhang, C. T. Chan, and P. Sheng, “Multiple scattering theory and its application to photonic band gap systems consisting of coated spheres,” Opt. Express 8,203–208 (2001).

[CrossRef]
[PubMed]

J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” Opt. Soc. Am. B 15,2316–2324 (1998).

[CrossRef]

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69,681 (1946).

A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati, “Dipole relaxation in dispersive photonic band-gap structures,” Phys. Rev. A 55,1454–1461 (1997).

[CrossRef]

A. O. Barut and J. P. Dowling, “Quantum electrodynamics based on self-energy: Spontaneous emission in cavities,” Phys. Rev. A 36,649–654 (1987).

[CrossRef]
[PubMed]

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54,2356–2368 (1996).

[CrossRef]
[PubMed]

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46,612–622 (1992).

[CrossRef]
[PubMed]

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65,155120, 2002.

[CrossRef]

J. M. Elson and 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]

M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58,6791–6794 (1998).

[CrossRef]

Z. Y. Li and Y. Xia, “Omnidirectional absolute band gaps in two-dimensional photonic crystals,” Phys. Rev. B 64,153108 (2001).

[CrossRef]

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51,4672–4675 (1995).

[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52,8992–9002 (1995).

[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51,16635–16642 (1995).

[CrossRef]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B 44,8565–8571 (1991).

[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45,13962–13972 (1992).

[CrossRef]

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58,7252–7259 (1998).

[CrossRef]

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72,056609 (2005).

[CrossRef]

M. C. Lin and R. F. Jao, “Quantitative analysis of photon density of states for a realistic superlattice with omnidirectional light propagation,” Phys. Rev. E 74,046613 (2006).

[CrossRef]

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64,046603 (2001).

[CrossRef]

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58,3896–3908 (1998).

[CrossRef]

R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, “Density of states functions for photonic crystals,” Phys. Rev. E 69,016609, 2004.

[CrossRef]

X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with psudogaps,” Phys. Rev. Lett. 88,093902 (2002)

[CrossRef]
[PubMed]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69,2772–2775 (1992).

[CrossRef]
[PubMed]

O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures,” Phys. Rev. Lett. 82,315–318 (1999).

[CrossRef]

D. Kleppner, “Inhibited Spontaneous Emission,” Phys. Rev. Lett. 47,233–236 (1981).

[CrossRef]

R. Hillebrand, W. Hergert, and W. Harms, “Theoretical band gap studies of two-dimensional photonic crystals with varying column roundness,” Phys. stat. sol. (b) 217,981–989 (2000).

[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin2001).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, New Jersey1995).

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

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-Interscience, New York2002).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York1984).

C. Kittel, Introduction to Solid State Physics (Wiley, New York1976).