W. Lu, Y. Y. Lu, "Waveguide mode solver based on Neumann-to-Dirichlet
operators and boundary integral equations," J.
Comput. Phys. 231, 1360-1371 (2012).

B. Y. Lin, C. H. Teng, H. C. Chang, H. H. Hsiao, J. K. Wang, Y. L. Wang, "Pseudospectral modeling of
nano-optics in Ag sphere arrays," J. Sci. Comput. 45, 429-446 (2010).

S. Zhao, "High-order matched interface
and boundary methods for the Helmholtz equation in media with arbitrarily
curved interfaces," J. Comput. Phys. 229, 3155-3170 (2010).

J. Xiao, X. Sun, "Full-vectorial mode solver for anisotropic
optical waveguides using multidomain spectral collocation method," Opt. Commun. 283, 2835-2840 (2010).

B. Y. Lin, H. C. Hsu, C. H. Teng, H. C. Chang, J. K. Wang, Y. L. Wang, "Unraveling near-field origin
of electromagnetic waves scattered from silver nanorod arrays using pseudo-spectral
time-domain calculation," Opt. Exp. 17, 14211-14228 (2009).

C. H. Teng, B. Y. Lin, H. C. Chang, H. C. Hsu, C. N. Lin, K. A. Feng, "A Legendre pseudospectral penalty
scheme for solving time-domain Maxwell's equations," J.
Sci. Comput. 36, 351-390 (2008).

P.-J. Chiang, C.-L. Wu, C.-H. Teng, C.-S. Yang, H.-C. Chang, "Full-vectorial optical waveguide mode solvers
using multidomain pseudospectral frequency-domain (PSFD) formulations," IEEE J. Quantum Electron. 44, 56-66 (2008).

S. Zhao, "Full-vectorial matched interface
and boundary (MIB) method for the modal analysis of dielectric waveguides," J. Lightw. Technol. 26, 2251-2259 (2008).

N. Thomas, P. Sewell, T. M. Benson, "A new full-vectorial higher
order finite-difference scheme for the modal analysis of rectangular dielectric
waveguides," J. Lightw. Technol. 25, 2563-2570 (2007).

C.-C. Huang, C.-C. Huang, J.-Y. Yang, "A full-vectorial pseudospectral
modal analysis of dielectric optical waveguides with stepped refractive index
profiles," IEEE J. Quantum Electron. 11, 457-465 (2005).

C.-C. Huang, C.-C. Huang, J.-Y. Yang, "An efficient method for computing
optical waveguides with discontinuous refractive index profiles using spectral
collocation method with domain decomposition," J.
Lightw. Technol. 21, 2284-2296 (2003).

G. R. Hadley, "High-accuracy finite-difference
equations for dielectric waveguide analysis: II. Dielectric corners," J. Lightw. Technol. 20, 1219-1231 (2002).

Y. P. Chiou, Y. P. Chiang, H. C. Chang, "Improved three-point formulas
considering the interface conditions in the finite-difference analysis of
step-index optical devices," J. Lightw. Technol. 18, 243-251 (2000).

D. U. Li, H. C. Chang, "An efficient full-vectorial
finite-element modal analysis of dielectric waveguides incorporating inhomogeneous
elements across dielectric discontinuities," IEEE
J. Quantum Electron. 36, 1251-1261 (2000).

M. Koshiba, S. Maruyama, K. Hirayama, "A vector finite element method
with the high-order mixed-interpolation-type triangular elements for optical
waveguiding problems," J. Lightw. Technol. 12, 495-502 (1994).

P. Lüsse, P. Stuwe, J. Schüle, H.-G. Unger, "Analysis of vectorial mode fields in optical
waveguides by a new finite difference method," J.
Lightw. Technol. 12, 487-494 (1994).

C. Vassallo, "Improvement of finite difference
methods for step-index optical waveguides," IEE
Proc. J. Optoelectron. 139, 137-142 (1992).

M. Koshiba, K. Inoue, "Simple and efficient finite-element analysis
of microwave and optical waveguides," IEEE Trans.
Microw. Theory Tech. 40, 371-377 (1992).

J. F. Lee, D. K. Sun, Z. J. Cendes, "Tangential vector finite element
for electromagnetic field computation," IEEE
Trans. Magn. 27, 4032-4035 (1991).

D. Funaro, D. Gottlieb, "A new method of imposing boundary
conditions in pseudospectral approximations of hyperbolic equations," Math. Comput. 51, 599-613 (1988).

M. S. Stern, "Semivectorial polarized finite
difference method for optical waveguides with arbitrary index profiles," IEE Proc. J. Optoelectron. 135, 56-63 (1988).

K. Bierwirth, N. Schulz, F. Arndt, "Finite-difference analysis of rectangular
dielectric waveguide structures," IEEE Trans.
Microw. Theory Tech. 34, 1104-1113 (1986).

W. J. Gordon, C. A. Hall, "Transfinite element methods:
Blending-function interpolation over arbitrary curved element domains," Numer. Math. 21, 109-129 (1973).

C. Vassallo, "Improvement of finite difference
methods for step-index optical waveguides," IEE
Proc. J. Optoelectron. 139, 137-142 (1992).

M. S. Stern, "Semivectorial polarized finite
difference method for optical waveguides with arbitrary index profiles," IEE Proc. J. Optoelectron. 135, 56-63 (1988).

D. U. Li, H. C. Chang, "An efficient full-vectorial
finite-element modal analysis of dielectric waveguides incorporating inhomogeneous
elements across dielectric discontinuities," IEEE
J. Quantum Electron. 36, 1251-1261 (2000).

J. F. Lee, D. K. Sun, Z. J. Cendes, "Tangential vector finite element
for electromagnetic field computation," IEEE
Trans. Magn. 27, 4032-4035 (1991).

P.-J. Chiang, C.-L. Wu, C.-H. Teng, C.-S. Yang, H.-C. Chang, "Full-vectorial optical waveguide mode solvers
using multidomain pseudospectral frequency-domain (PSFD) formulations," IEEE J. Quantum Electron. 44, 56-66 (2008).

C.-C. Huang, C.-C. Huang, J.-Y. Yang, "A full-vectorial pseudospectral
modal analysis of dielectric optical waveguides with stepped refractive index
profiles," IEEE J. Quantum Electron. 11, 457-465 (2005).

K. Bierwirth, N. Schulz, F. Arndt, "Finite-difference analysis of rectangular
dielectric waveguide structures," IEEE Trans.
Microw. Theory Tech. 34, 1104-1113 (1986).

M. Koshiba, K. Inoue, "Simple and efficient finite-element analysis
of microwave and optical waveguides," IEEE Trans.
Microw. Theory Tech. 40, 371-377 (1992).

W. Lu, Y. Y. Lu, "Waveguide mode solver based on Neumann-to-Dirichlet
operators and boundary integral equations," J.
Comput. Phys. 231, 1360-1371 (2012).

P. Lüsse, P. Stuwe, J. Schüle, H.-G. Unger, "Analysis of vectorial mode fields in optical
waveguides by a new finite difference method," J.
Lightw. Technol. 12, 487-494 (1994).

C.-C. Huang, C.-C. Huang, J.-Y. Yang, "An efficient method for computing
optical waveguides with discontinuous refractive index profiles using spectral
collocation method with domain decomposition," J.
Lightw. Technol. 21, 2284-2296 (2003).

C. H. Teng, B. Y. Lin, H. C. Chang, H. C. Hsu, C. N. Lin, K. A. Feng, "A Legendre pseudospectral penalty
scheme for solving time-domain Maxwell's equations," J.
Sci. Comput. 36, 351-390 (2008).

S. Zhao, "High-order matched interface
and boundary methods for the Helmholtz equation in media with arbitrarily
curved interfaces," J. Comput. Phys. 229, 3155-3170 (2010).

G. R. Hadley, "High-accuracy finite-difference
equations for dielectric waveguide analysis: II. Dielectric corners," J. Lightw. Technol. 20, 1219-1231 (2002).

N. Thomas, P. Sewell, T. M. Benson, "A new full-vectorial higher
order finite-difference scheme for the modal analysis of rectangular dielectric
waveguides," J. Lightw. Technol. 25, 2563-2570 (2007).

Y. P. Chiou, Y. P. Chiang, H. C. Chang, "Improved three-point formulas
considering the interface conditions in the finite-difference analysis of
step-index optical devices," J. Lightw. Technol. 18, 243-251 (2000).

S. Zhao, "Full-vectorial matched interface
and boundary (MIB) method for the modal analysis of dielectric waveguides," J. Lightw. Technol. 26, 2251-2259 (2008).

M. Koshiba, S. Maruyama, K. Hirayama, "A vector finite element method
with the high-order mixed-interpolation-type triangular elements for optical
waveguiding problems," J. Lightw. Technol. 12, 495-502 (1994).

B. Y. Lin, C. H. Teng, H. C. Chang, H. H. Hsiao, J. K. Wang, Y. L. Wang, "Pseudospectral modeling of
nano-optics in Ag sphere arrays," J. Sci. Comput. 45, 429-446 (2010).

D. Funaro, D. Gottlieb, "A new method of imposing boundary
conditions in pseudospectral approximations of hyperbolic equations," Math. Comput. 51, 599-613 (1988).

W. J. Gordon, C. A. Hall, "Transfinite element methods:
Blending-function interpolation over arbitrary curved element domains," Numer. Math. 21, 109-129 (1973).

J. Xiao, X. Sun, "Full-vectorial mode solver for anisotropic
optical waveguides using multidomain spectral collocation method," Opt. Commun. 283, 2835-2840 (2010).

B. Y. Lin, H. C. Hsu, C. H. Teng, H. C. Chang, J. K. Wang, Y. L. Wang, "Unraveling near-field origin
of electromagnetic waves scattered from silver nanorod arrays using pseudo-spectral
time-domain calculation," Opt. Exp. 17, 14211-14228 (2009).

J. S. Hesthaven, S. Gottlieb, D. Gottlieb, Spectral Methods for Time-Dependent
Problems (Cambridge Univ. Press, 2007).

R. Collin, Field Theory of Guided Waves (McGraw-Hill, 1960).

S. F. Chiang, B. Y. Lin, C. H. Teng, H. C. Chang, "Improved analysis of rectangular
dielectric waveguides based on a Legendre pseudospectral penalty scheme," presented at the Integr. Photon. Res., Silicon and Nano Photon. WashingtonDC (2010) Paper IWH8.