S. J. Cooke and B. Levush, “Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm,” J. Comput. Phys. 157, 350–370 (2000).
[Crossref]
J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]
A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method,” Comput. Phys. Comm. 128, 590–621 (2000).
[Crossref]
P. Yang, K. N. Liou, M. I. Mishchenko, and B.-C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,” Appl. Opt. 39, 3727–3737 (2000).
[Crossref]
S. Ismail-Beigi and T. A. Arias, “New algebraic formulation of density functional calculation,” Comp. Phys. Commun. 128, 1–45 (2000).
[Crossref]
H. A. van der Vorst, “Krylov subspace iteration,” Computing in Sci. and Eng. 2, 32–37 (2000).
[Crossref]
J. Arriaga, A. J. Ward, and J. B. Pendry, “Order N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[Crossref]
K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[Crossref]
W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comput. Phys. 150, 468–481 (1999).
[Crossref]
D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
[Crossref]
D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2D photonic crystals,” J. Lightwave Tech. 17, 2078–2081 (1999).
[Crossref]
T. Suzuki and P. K. L. Yu, “Method of projection operators for photonic band structures with perfectly conducting elements,” Phys. Rev. B 57, 2229–2241 (1998).
[Crossref]
E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band-gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]
W. C. Sailor, F. M. Mueller, and P. R. Villeneuve, “Augmented-plane-wave method for photonic band-gap materials,” Phys. Rev. B 57, 8819–8822 (1998).
[Crossref]
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
A. Edelman, T. A. Arias, and S. T. Smith, “The geometry of algorithms with orthogonality constraints,” SIAM J. Matrix Anal. Appl. 20, 303–353 (1998).
[Crossref]
J. Chongjun, Q. Bai, Y. Miao, and Q. Ruhu, “Two-dimensional photonic band structure in the chiral medium—transfer matrix method,” Opt. Commun. 142, 179–183 (1997).
[Crossref]
K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[Crossref]
See, e.g., 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]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallo-dielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[Crossref]
J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
[Crossref]
See, e.g., A. Edelman and S. T. Smith, “On conjugate gradient-like methods for eigen-like problems,” BIT 36, 494–509 (1996).
[Crossref]
G. L. G. Sleijpen and H. A. van der Vorst, “A Jacobi-Davidson iteration method for linear eigenvalue problems,” SIAM J. Matrix Anal. Appl. 17, 401–425 (1996).
[Crossref]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[Crossref]
P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Comm. 85, 306–322 (1995).
[Crossref]
J. M. Elson and P. Tran, “Dispersion in photonic media and diffraction from gratings: a different modal expansion for the R-matrix propagation technique,” J. Opt. Soc. Am. A 12, 1765–1771 (1995).
[Crossref]
C. T. Chan, Q. L. Lu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
M. Crouzeix, B. Philippe, and M. Sadkane, “The Davidson Method,” SIAM J. Sci. Comput. 15, 62–76 (1994).
[Crossref]
L.-W. Wang and A. Zunger, “Solving Schrödinger’s equation around a desired energy: application to Silicon quantum dots,” J. Chem. Phys. 100, 2394–2397 (1994).
[Crossref]
J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Software 20, 286–307 (1994).
[Crossref]
H. S. Sozüer and J. W. Haus, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[Crossref]
[PubMed]
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, “A set of Level 3 Basic Linear Algebra Subprograms,” ACM Trans. Math. Soft. 16, 1–17 (1990).
[Crossref]
K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]
[PubMed]
B. Philippe, “An algorithm to improve nearly orthonormal sets of vectors on a vector processor,” SIAM J. Alg. Disc. Meth. 8, 396–403 (1987).
[Crossref]
A. H. Sameh and J. A. Wisniewski, “A trace minimization algorithm for the generalized eigenvalue problem,” SIAM J. Numer. Anal. 19, 1243–1259 (1982).
[Crossref]
E. R. Davidson, “The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices,” Comput. Phys. 17, 87–94 (1975).
[Crossref]
J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
S. Ismail-Beigi and T. A. Arias, “New algebraic formulation of density functional calculation,” Comp. Phys. Commun. 128, 1–45 (2000).
[Crossref]
A. Edelman, T. A. Arias, and S. T. Smith, “The geometry of algorithms with orthogonality constraints,” SIAM J. Matrix Anal. Appl. 20, 303–353 (1998).
[Crossref]
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
J. Arriaga, A. J. Ward, and J. B. Pendry, “Order N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[Crossref]
N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comput. Phys. 150, 468–481 (1999).
[Crossref]
J. Chongjun, Q. Bai, Y. Miao, and Q. Ruhu, “Two-dimensional photonic band structure in the chiral medium—transfer matrix method,” Opt. Commun. 142, 179–183 (1997).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Comm. 85, 306–322 (1995).
[Crossref]
J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]
D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2D photonic crystals,” J. Lightwave Tech. 17, 2078–2081 (1999).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[Crossref]
J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]
C. T. Chan, Q. L. Lu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]
[PubMed]
J. Chongjun, Q. Bai, Y. Miao, and Q. Ruhu, “Two-dimensional photonic band structure in the chiral medium—transfer matrix method,” Opt. Commun. 142, 179–183 (1997).
[Crossref]
S. J. Cooke and B. Levush, “Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm,” J. Comput. Phys. 157, 350–370 (2000).
[Crossref]
M. Crouzeix, B. Philippe, and M. Sadkane, “The Davidson Method,” SIAM J. Sci. Comput. 15, 62–76 (1994).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
E. R. Davidson, “The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices,” Comput. Phys. 17, 87–94 (1975).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, “A set of Level 3 Basic Linear Algebra Subprograms,” ACM Trans. Math. Soft. 16, 1–17 (1990).
[Crossref]
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, “A set of Level 3 Basic Linear Algebra Subprograms,” ACM Trans. Math. Soft. 16, 1–17 (1990).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, “A set of Level 3 Basic Linear Algebra Subprograms,” ACM Trans. Math. Soft. 16, 1–17 (1990).
[Crossref]
E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band-gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]
A. Edelman, T. A. Arias, and S. T. Smith, “The geometry of algorithms with orthogonality constraints,” SIAM J. Matrix Anal. Appl. 20, 303–353 (1998).
[Crossref]
See, e.g., A. Edelman and S. T. Smith, “On conjugate gradient-like methods for eigen-like problems,” BIT 36, 494–509 (1996).
[Crossref]
See, e.g., J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[Crossref]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallo-dielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[Crossref]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[Crossref]
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[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. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. 1998 IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1998), 1381–1384.
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).
A. Figotin and Y. A. Godin, “The computation of spectra of some 2D photonic crystals,” J. Comput. Phys. 136, 585–598 (1997).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, “A set of Level 3 Basic Linear Algebra Subprograms,” ACM Trans. Math. Soft. 16, 1–17 (1990).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
H. S. Sozüer and J. W. Haus, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]
C. T. Chan, Q. L. Lu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]
[PubMed]
S. Ismail-Beigi and T. A. Arias, “New algebraic formulation of density functional calculation,” Comp. Phys. Commun. 128, 1–45 (2000).
[Crossref]
S. Ismail-Beiji, private communications.
J. Jin, The Finite-Element Method in Electromagnetics (Wiley, New York, 1993), Chap. 5.7.
See, e.g., J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[Crossref]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallo-dielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[Crossref]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[Crossref]
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
S. G. Johnson and J. D. Joannopoulos, The MIT Photonic-Bands Package home page http://ab-initio.mit.edu/mpb/.
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[Crossref]
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
S. G. Johnson and J. D. Joannopoulos, The MIT Photonic-Bands Package home page http://ab-initio.mit.edu/mpb/.
M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. 1998 IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1998), 1381–1384.
J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]
W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comput. Phys. 150, 468–481 (1999).
[Crossref]
See, e.g., K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Methods (CRC, Boca Raton, Fla., 1993).
S. J. Cooke and B. Levush, “Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm,” J. Comput. Phys. 157, 350–370 (2000).
[Crossref]
E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band-gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]
C. T. Chan, Q. L. Lu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[Crossref]
See, e.g., K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Methods (CRC, Boca Raton, Fla., 1993).
J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[Crossref]
[PubMed]
V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997). Erratum: ibid, 109, 4128 (1998).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
R. D. Meade, private communications.
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
J. Chongjun, Q. Bai, Y. Miao, and Q. Ruhu, “Two-dimensional photonic band structure in the chiral medium—transfer matrix method,” Opt. Commun. 142, 179–183 (1997).
[Crossref]
D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2D photonic crystals,” J. Lightwave Tech. 17, 2078–2081 (1999).
[Crossref]
J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Software 20, 286–307 (1994).
[Crossref]
P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Comm. 85, 306–322 (1995).
[Crossref]
W. C. Sailor, F. M. Mueller, and P. R. Villeneuve, “Augmented-plane-wave method for photonic band-gap materials,” Phys. Rev. B 57, 8819–8822 (1998).
[Crossref]
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
B. N. Parlett, The Symmetric Eigenvalue Problem (Prentice-Hall, Englewood Cliffs, NJ, 1980).
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method,” Comput. Phys. Comm. 128, 590–621 (2000).
[Crossref]
J. Arriaga, A. J. Ward, and J. B. Pendry, “Order N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[Crossref]
P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Comm. 85, 306–322 (1995).
[Crossref]
J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[Crossref]
[PubMed]
M. Crouzeix, B. Philippe, and M. Sadkane, “The Davidson Method,” SIAM J. Sci. Comput. 15, 62–76 (1994).
[Crossref]
B. Philippe, “An algorithm to improve nearly orthonormal sets of vectors on a vector processor,” SIAM J. Alg. Disc. Meth. 8, 396–403 (1987).
[Crossref]
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
J. Chongjun, Q. Bai, Y. Miao, and Q. Ruhu, “Two-dimensional photonic band structure in the chiral medium—transfer matrix method,” Opt. Commun. 142, 179–183 (1997).
[Crossref]
D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2D photonic crystals,” J. Lightwave Tech. 17, 2078–2081 (1999).
[Crossref]
M. Crouzeix, B. Philippe, and M. Sadkane, “The Davidson Method,” SIAM J. Sci. Comput. 15, 62–76 (1994).
[Crossref]
W. C. Sailor, F. M. Mueller, and P. R. Villeneuve, “Augmented-plane-wave method for photonic band-gap materials,” Phys. Rev. B 57, 8819–8822 (1998).
[Crossref]
K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[Crossref]
A. H. Sameh and J. A. Wisniewski, “A trace minimization algorithm for the generalized eigenvalue problem,” SIAM J. Numer. Anal. 19, 1243–1259 (1982).
[Crossref]
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band-gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]
G. L. G. Sleijpen and H. A. van der Vorst, “A Jacobi-Davidson iteration method for linear eigenvalue problems,” SIAM J. Matrix Anal. Appl. 17, 401–425 (1996).
[Crossref]
A. Edelman, T. A. Arias, and S. T. Smith, “The geometry of algorithms with orthogonality constraints,” SIAM J. Matrix Anal. Appl. 20, 303–353 (1998).
[Crossref]
See, e.g., A. Edelman and S. T. Smith, “On conjugate gradient-like methods for eigen-like problems,” BIT 36, 494–509 (1996).
[Crossref]
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band-gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]
[PubMed]
H. S. Sozüer and J. W. Haus, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]
A. H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, NJ, 1971).
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
T. Suzuki and P. K. L. Yu, “Method of projection operators for photonic band structures with perfectly conducting elements,” Phys. Rev. B 57, 2229–2241 (1998).
[Crossref]
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997). Erratum: ibid, 109, 4128 (1998).
[Crossref]
J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Software 20, 286–307 (1994).
[Crossref]
H. A. van der Vorst, “Krylov subspace iteration,” Computing in Sci. and Eng. 2, 32–37 (2000).
[Crossref]
G. L. G. Sleijpen and H. A. van der Vorst, “A Jacobi-Davidson iteration method for linear eigenvalue problems,” SIAM J. Matrix Anal. Appl. 17, 401–425 (1996).
[Crossref]
W. C. Sailor, F. M. Mueller, and P. R. Villeneuve, “Augmented-plane-wave method for photonic band-gap materials,” Phys. Rev. B 57, 8819–8822 (1998).
[Crossref]
See, e.g., J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[Crossref]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallo-dielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[Crossref]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[Crossref]
L.-W. Wang and A. Zunger, “Solving Schrödinger’s equation around a desired energy: application to Silicon quantum dots,” J. Chem. Phys. 100, 2394–2397 (1994).
[Crossref]
A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method,” Comput. Phys. Comm. 128, 590–621 (2000).
[Crossref]
J. Arriaga, A. J. Ward, and J. B. Pendry, “Order N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[Crossref]
P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Comm. 85, 306–322 (1995).
[Crossref]
A. H. Sameh and J. A. Wisniewski, “A trace minimization algorithm for the generalized eigenvalue problem,” SIAM J. Numer. Anal. 19, 1243–1259 (1982).
[Crossref]
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
T. Suzuki and P. K. L. Yu, “Method of projection operators for photonic band structures with perfectly conducting elements,” Phys. Rev. B 57, 2229–2241 (1998).
[Crossref]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
L.-W. Wang and A. Zunger, “Solving Schrödinger’s equation around a desired energy: application to Silicon quantum dots,” J. Chem. Phys. 100, 2394–2397 (1994).
[Crossref]
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, “A set of Level 3 Basic Linear Algebra Subprograms,” ACM Trans. Math. Soft. 16, 1–17 (1990).
[Crossref]
J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Software 20, 286–307 (1994).
[Crossref]
See, e.g., A. Edelman and S. T. Smith, “On conjugate gradient-like methods for eigen-like problems,” BIT 36, 494–509 (1996).
[Crossref]
S. Ismail-Beigi and T. A. Arias, “New algebraic formulation of density functional calculation,” Comp. Phys. Commun. 128, 1–45 (2000).
[Crossref]
E. R. Davidson, “The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices,” Comput. Phys. 17, 87–94 (1975).
[Crossref]
A. J. Ward and J. B. Pendry, “A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method,” Comput. Phys. Comm. 128, 590–621 (2000).
[Crossref]
P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Comm. 85, 306–322 (1995).
[Crossref]
H. A. van der Vorst, “Krylov subspace iteration,” Computing in Sci. and Eng. 2, 32–37 (2000).
[Crossref]
J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix, “A high-resolution interpolation at arbitrary interfaces for the FDTD method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[Crossref]
L.-W. Wang and A. Zunger, “Solving Schrödinger’s equation around a desired energy: application to Silicon quantum dots,” J. Chem. Phys. 100, 2394–2397 (1994).
[Crossref]
A. Figotin and Y. A. Godin, “The computation of spectra of some 2D photonic crystals,” J. Comput. Phys. 136, 585–598 (1997).
[Crossref]
S. J. Cooke and B. Levush, “Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm,” J. Comput. Phys. 157, 350–370 (2000).
[Crossref]
W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comput. Phys. 150, 468–481 (1999).
[Crossref]
D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
[Crossref]
D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2D photonic crystals,” J. Lightwave Tech. 17, 2078–2081 (1999).
[Crossref]
See, e.g., 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. Chongjun, Q. Bai, Y. Miao, and Q. Ruhu, “Two-dimensional photonic band structure in the chiral medium—transfer matrix method,” Opt. Commun. 142, 179–183 (1997).
[Crossref]
J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on truncated photonic crystal,” Phys. Rev. B 54, 1711–1715 (1996).
[Crossref]
C. T. Chan, Q. L. Lu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[Crossref]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallo-dielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[Crossref]
K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[Crossref]
J. Arriaga, A. J. Ward, and J. B. Pendry, “Order N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[Crossref]
H. S. Sozüer and J. W. Haus, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]
W. C. Sailor, F. M. Mueller, and P. R. Villeneuve, “Augmented-plane-wave method for photonic band-gap materials,” Phys. Rev. B 57, 8819–8822 (1998).
[Crossref]
T. Suzuki and P. K. L. Yu, “Method of projection operators for photonic band structures with perfectly conducting elements,” Phys. Rev. B 57, 2229–2241 (1998).
[Crossref]
J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[Crossref]
E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band-gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]
K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]
[PubMed]
K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[Crossref]
J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[Crossref]
[PubMed]
C. T. Chan, S. Datta, Q. L. Yu, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “New structures and algorithms for photonic band gaps,” Physica A 211, 411–419 (1994).
[Crossref]
M. C. Payne, M. P. Tater, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]
B. Philippe, “An algorithm to improve nearly orthonormal sets of vectors on a vector processor,” SIAM J. Alg. Disc. Meth. 8, 396–403 (1987).
[Crossref]
A. Edelman, T. A. Arias, and S. T. Smith, “The geometry of algorithms with orthogonality constraints,” SIAM J. Matrix Anal. Appl. 20, 303–353 (1998).
[Crossref]
G. L. G. Sleijpen and H. A. van der Vorst, “A Jacobi-Davidson iteration method for linear eigenvalue problems,” SIAM J. Matrix Anal. Appl. 17, 401–425 (1996).
[Crossref]
A. H. Sameh and J. A. Wisniewski, “A trace minimization algorithm for the generalized eigenvalue problem,” SIAM J. Numer. Anal. 19, 1243–1259 (1982).
[Crossref]
M. Crouzeix, B. Philippe, and M. Sadkane, “The Davidson Method,” SIAM J. Sci. Comput. 15, 62–76 (1994).
[Crossref]
B. N. Parlett, The Symmetric Eigenvalue Problem (Prentice-Hall, Englewood Cliffs, NJ, 1980).
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide (SIAM, Philadelphia, 1999).
[Crossref]
S. Ismail-Beiji, private communications.
See, e.g., K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Methods (CRC, Boca Raton, Fla., 1993).
J. Jin, The Finite-Element Method in Electromagnetics (Wiley, New York, 1993), Chap. 5.7.
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B48, 8434–8437 (1993). Erratum: S. G. Johnson, ibid55, 15942 (1997).
[Crossref]
S. G. Johnson and J. D. Joannopoulos, The MIT Photonic-Bands Package home page http://ab-initio.mit.edu/mpb/.
R. D. Meade, private communications.
V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997). Erratum: ibid, 109, 4128 (1998).
[Crossref]
N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. 1998 IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1998), 1381–1384.
A. H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, NJ, 1971).
P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).