L. Zschiedrich, R. Klose, A. Schädle, and F. Schmidt, “A new finite element realization of the perfectly matched
layer method for helmholtz scattering problems on polygonal domains in two dimensions,” J. Comput. Appl.
Math. 188, 12–32 (2006).

[CrossRef]

H. Cheng, Advanced Analytic Methods in Applied Mathematics, Science and Engineering (Luban Press, Boston, 2006).

M. Povinelli, S. Johnson, and J. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt.
Express 13, 7145–7159 (2005).

[CrossRef]
[PubMed]

N. Kono and M. Koshiba, “General finite-element modeling of 2-D magnetophotonic crystal waveguides,” IEEE
Photon. Tech. Lett. 17, 1432–1434 (2005).

[CrossRef]

Y. S. Rickard and N. K. Nikolova, “Enhancing the PML absorbing boundary conditions for the wave equation,” IEEE Trans. Antennas Propag. 53, 1242–1246 (2005).

[CrossRef]

Z. Chen and X. Liu, “An adaptive perfectly matched layer technique for time-harmonic scattering problems,” SIAM J. Num. Anal. 43, 645–671 (2005).

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

A. R. Weily, L. Horvath, K. P. Esselle, and B. C. Sanders, “Performance of PML absorbing boundary conditions
in 3d photonic crystal waveguides,” Microwave Opt. Technol.Lett. 40, 1–3 (2004).

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

D. Pissoort and F. Olyslager, “Termination of periodic waveguides by PMLs in time-harmonic integral equationlike
techniques,” IEEE Antennas and Wireless Propagation Lett. 2, 281–284 (2003).

[CrossRef]

E. P. Kosmidou, T. I. Kosmani, and T. D. Tsiboukis, “A comparative FDTD study of various PML configurations
for the termination of nonlinear photonic bandgap waveguide structures,” IEEE Trans. Magn. 39, 1191–1194 (2003).

[CrossRef]

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68 (2003).

Y. Tsuji and M. Koshiba, “Finite element method using port truncation by perfectly matched layer boundary
conditions for optical waveguide discontinuity problems,” J. Lightwave Technol. 20, 463–468 (2002).

[CrossRef]

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

E. Moreno, D. Erni, and C. Hafner, “Modeling of discontinuities in photonic crystal waveguides with the multiple
multipole method,” Phys. Rev. E 66, 036618 (2002).

J. S. Juntunen, N. V. Kantartzis, and T. D. Tsiboukis, “Zero reflection coefficient in discretized PML,” IEEE
Microwave Wirel. Compon. Lett. 11, 155–157 (2001).

[CrossRef]

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

[CrossRef]

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE
Trans. Magn. 35, 1506–1509 (1999).

[CrossRef]

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

[CrossRef]

M. Lassas and E. Somersalo, “On the existence and convergence of the solution of PML equations,” Computing 60, 229–241 (1998).

[CrossRef]

A. Dranov, J. Kellendonk, and R. Seller, “Discrete time adiabatic theorems for quantum mechanical systems,” J.
Math. Phys. 39, 1340–1349 (1998).

[CrossRef]

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves
in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216–2222 (1998).

[CrossRef]

F. L. Teixeira and W. C. Chew, “General close-form PML constitutive tensors to match arbitrary bianisotropic
and dispersive linear media,” IEEE Microwave and Guided Wave Lett. 8, 223–225 (1998).

[CrossRef]

F. Collino and P. B. Monk, “Optimizing the perfectly matched layer,” Comput. Methods Appl. Mech. Engrg. 164, 157–171 (1998).

[CrossRef]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).

[CrossRef]

W. Huang, C. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis
of optical waveguides: leaky mode calculations,” IEEE Photon. Tech. Lett. 8, 652–654 (1996).

[CrossRef]

W. C. Chew and J. M. Jin, “Perfectly matched layers in the discretized space: An analysis and optimization,” Electromagnetics 16, 325–340 (1996).

[CrossRef]

Z. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an
absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).

[CrossRef]

C. M. Rappaport, “Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of
space,” IEEE Microwave and Guided Wave Lett. 5, 90–92 (1995).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with
stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

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

[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd Edition (Academic Press, San Diego, 1991).

J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd Edition (Springer, 1989).

A. Christ and H. L. Hartnagel, “Three-dimensional finite-difference method for the analysis of microwave-device
embedding,” IEEE Trans. Microwave Theory Tech. 35, 688–696 (1987).

[CrossRef]

J. P. Boyd, “The optimization of convergence for Chebyshev polynomial methods in an unbounded domain,” J. Comput. Phys. 45, 43–79 (1982).

[CrossRef]

K. O. Mead and L. M. Delves, “On the convergence rate of generalized fourier expansions,” IMA J. Appl. Math. 12, 247–259 (1973).

[CrossRef]

D. Elliott, “The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function,” Mathematics of Computation 18, 274–284 (1964).

[CrossRef]

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

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd Edition (Springer, 1989).

J. P. Boyd, “The optimization of convergence for Chebyshev polynomial methods in an unbounded domain,” J. Comput. Phys. 45, 43–79 (1982).

[CrossRef]

Z. Chen and X. Liu, “An adaptive perfectly matched layer technique for time-harmonic scattering problems,” SIAM J. Num. Anal. 43, 645–671 (2005).

[CrossRef]

H. Cheng, Advanced Analytic Methods in Applied Mathematics, Science and Engineering (Luban Press, Boston, 2006).

F. L. Teixeira and W. C. Chew, “General close-form PML constitutive tensors to match arbitrary bianisotropic
and dispersive linear media,” IEEE Microwave and Guided Wave Lett. 8, 223–225 (1998).

[CrossRef]

W. C. Chew and J. M. Jin, “Perfectly matched layers in the discretized space: An analysis and optimization,” Electromagnetics 16, 325–340 (1996).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with
stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

A. Christ and H. L. Hartnagel, “Three-dimensional finite-difference method for the analysis of microwave-device
embedding,” IEEE Trans. Microwave Theory Tech. 35, 688–696 (1987).

[CrossRef]

F. Collino and P. B. Monk, “Optimizing the perfectly matched layer,” Comput. Methods Appl. Mech. Engrg. 164, 157–171 (1998).

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

K. O. Mead and L. M. Delves, “On the convergence rate of generalized fourier expansions,” IMA J. Appl. Math. 12, 247–259 (1973).

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

A. Dranov, J. Kellendonk, and R. Seller, “Discrete time adiabatic theorems for quantum mechanical systems,” J.
Math. Phys. 39, 1340–1349 (1998).

[CrossRef]

D. Elliott, “The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function,” Mathematics of Computation 18, 274–284 (1964).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Modeling of discontinuities in photonic crystal waveguides with the multiple
multipole method,” Phys. Rev. E 66, 036618 (2002).

A. R. Weily, L. Horvath, K. P. Esselle, and B. C. Sanders, “Performance of PML absorbing boundary conditions
in 3d photonic crystal waveguides,” Microwave Opt. Technol.Lett. 40, 1–3 (2004).

[CrossRef]

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

[CrossRef]

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves
in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216–2222 (1998).

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Modeling of discontinuities in photonic crystal waveguides with the multiple
multipole method,” Phys. Rev. E 66, 036618 (2002).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

A. Christ and H. L. Hartnagel, “Three-dimensional finite-difference method for the analysis of microwave-device
embedding,” IEEE Trans. Microwave Theory Tech. 35, 688–696 (1987).

[CrossRef]

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68 (2003).

A. R. Weily, L. Horvath, K. P. Esselle, and B. C. Sanders, “Performance of PML absorbing boundary conditions
in 3d photonic crystal waveguides,” Microwave Opt. Technol.Lett. 40, 1–3 (2004).

[CrossRef]

W. Huang, C. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis
of optical waveguides: leaky mode calculations,” IEEE Photon. Tech. Lett. 8, 652–654 (1996).

[CrossRef]

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

W. C. Chew and J. M. Jin, “Perfectly matched layers in the discretized space: An analysis and optimization,” Electromagnetics 16, 325–340 (1996).

[CrossRef]

M. Povinelli, S. Johnson, and J. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt.
Express 13, 7145–7159 (2005).

[CrossRef]
[PubMed]

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

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

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition (Princeton Univ. Press, 2008).

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition (Princeton Univ. Press, 2008).

J. S. Juntunen, N. V. Kantartzis, and T. D. Tsiboukis, “Zero reflection coefficient in discretized PML,” IEEE
Microwave Wirel. Compon. Lett. 11, 155–157 (2001).

[CrossRef]

J. S. Juntunen, N. V. Kantartzis, and T. D. Tsiboukis, “Zero reflection coefficient in discretized PML,” IEEE
Microwave Wirel. Compon. Lett. 11, 155–157 (2001).

[CrossRef]

A. Dranov, J. Kellendonk, and R. Seller, “Discrete time adiabatic theorems for quantum mechanical systems,” J.
Math. Phys. 39, 1340–1349 (1998).

[CrossRef]

Z. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an
absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).

[CrossRef]

L. Zschiedrich, R. Klose, A. Schädle, and F. Schmidt, “A new finite element realization of the perfectly matched
layer method for helmholtz scattering problems on polygonal domains in two dimensions,” J. Comput. Appl.
Math. 188, 12–32 (2006).

[CrossRef]

N. Kono and M. Koshiba, “General finite-element modeling of 2-D magnetophotonic crystal waveguides,” IEEE
Photon. Tech. Lett. 17, 1432–1434 (2005).

[CrossRef]

N. Kono and M. Koshiba, “General finite-element modeling of 2-D magnetophotonic crystal waveguides,” IEEE
Photon. Tech. Lett. 17, 1432–1434 (2005).

[CrossRef]

Y. Tsuji and M. Koshiba, “Finite element method using port truncation by perfectly matched layer boundary
conditions for optical waveguide discontinuity problems,” J. Lightwave Technol. 20, 463–468 (2002).

[CrossRef]

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

[CrossRef]

E. P. Kosmidou, T. I. Kosmani, and T. D. Tsiboukis, “A comparative FDTD study of various PML configurations
for the termination of nonlinear photonic bandgap waveguide structures,” IEEE Trans. Magn. 39, 1191–1194 (2003).

[CrossRef]

E. P. Kosmidou, T. I. Kosmani, and T. D. Tsiboukis, “A comparative FDTD study of various PML configurations
for the termination of nonlinear photonic bandgap waveguide structures,” IEEE Trans. Magn. 39, 1191–1194 (2003).

[CrossRef]

M. Lassas and E. Somersalo, “On the existence and convergence of the solution of PML equations,” Computing 60, 229–241 (1998).

[CrossRef]

Z. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an
absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).

[CrossRef]

Z. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an
absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).

[CrossRef]

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68 (2003).

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

Z. Chen and X. Liu, “An adaptive perfectly matched layer technique for time-harmonic scattering problems,” SIAM J. Num. Anal. 43, 645–671 (2005).

[CrossRef]

W. Huang, C. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis
of optical waveguides: leaky mode calculations,” IEEE Photon. Tech. Lett. 8, 652–654 (1996).

[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd Edition (Academic Press, San Diego, 1991).

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE
Trans. Magn. 35, 1506–1509 (1999).

[CrossRef]

K. O. Mead and L. M. Delves, “On the convergence rate of generalized fourier expansions,” IMA J. Appl. Math. 12, 247–259 (1973).

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition (Princeton Univ. Press, 2008).

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

[CrossRef]

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE
Trans. Magn. 35, 1506–1509 (1999).

[CrossRef]

F. Collino and P. B. Monk, “Optimizing the perfectly matched layer,” Comput. Methods Appl. Mech. Engrg. 164, 157–171 (1998).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Modeling of discontinuities in photonic crystal waveguides with the multiple
multipole method,” Phys. Rev. E 66, 036618 (2002).

Y. S. Rickard and N. K. Nikolova, “Enhancing the PML absorbing boundary conditions for the wave equation,” IEEE Trans. Antennas Propag. 53, 1242–1246 (2005).

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

D. Pissoort and F. Olyslager, “Termination of periodic waveguides by PMLs in time-harmonic integral equationlike
techniques,” IEEE Antennas and Wireless Propagation Lett. 2, 281–284 (2003).

[CrossRef]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

D. Pissoort and F. Olyslager, “Termination of periodic waveguides by PMLs in time-harmonic integral equationlike
techniques,” IEEE Antennas and Wireless Propagation Lett. 2, 281–284 (2003).

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE
Trans. Magn. 35, 1506–1509 (1999).

[CrossRef]

C. M. Rappaport, “Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of
space,” IEEE Microwave and Guided Wave Lett. 5, 90–92 (1995).

[CrossRef]

Y. S. Rickard and N. K. Nikolova, “Enhancing the PML absorbing boundary conditions for the wave equation,” IEEE Trans. Antennas Propag. 53, 1242–1246 (2005).

[CrossRef]

Z. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an
absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).

[CrossRef]

A. R. Weily, L. Horvath, K. P. Esselle, and B. C. Sanders, “Performance of PML absorbing boundary conditions
in 3d photonic crystal waveguides,” Microwave Opt. Technol.Lett. 40, 1–3 (2004).

[CrossRef]

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

[CrossRef]

L. Zschiedrich, R. Klose, A. Schädle, and F. Schmidt, “A new finite element realization of the perfectly matched
layer method for helmholtz scattering problems on polygonal domains in two dimensions,” J. Comput. Appl.
Math. 188, 12–32 (2006).

[CrossRef]

L. Zschiedrich, R. Klose, A. Schädle, and F. Schmidt, “A new finite element realization of the perfectly matched
layer method for helmholtz scattering problems on polygonal domains in two dimensions,” J. Comput. Appl.
Math. 188, 12–32 (2006).

[CrossRef]

A. Dranov, J. Kellendonk, and R. Seller, “Discrete time adiabatic theorems for quantum mechanical systems,” J.
Math. Phys. 39, 1340–1349 (1998).

[CrossRef]

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

M. Lassas and E. Somersalo, “On the existence and convergence of the solution of PML equations,” Computing 60, 229–241 (1998).

[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

F. L. Teixeira and W. C. Chew, “General close-form PML constitutive tensors to match arbitrary bianisotropic
and dispersive linear media,” IEEE Microwave and Guided Wave Lett. 8, 223–225 (1998).

[CrossRef]

E. P. Kosmidou, T. I. Kosmani, and T. D. Tsiboukis, “A comparative FDTD study of various PML configurations
for the termination of nonlinear photonic bandgap waveguide structures,” IEEE Trans. Magn. 39, 1191–1194 (2003).

[CrossRef]

J. S. Juntunen, N. V. Kantartzis, and T. D. Tsiboukis, “Zero reflection coefficient in discretized PML,” IEEE
Microwave Wirel. Compon. Lett. 11, 155–157 (2001).

[CrossRef]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with
stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

A. R. Weily, L. Horvath, K. P. Esselle, and B. C. Sanders, “Performance of PML absorbing boundary conditions
in 3d photonic crystal waveguides,” Microwave Opt. Technol.Lett. 40, 1–3 (2004).

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition (Princeton Univ. Press, 2008).

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves
in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216–2222 (1998).

[CrossRef]

W. Huang, C. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis
of optical waveguides: leaky mode calculations,” IEEE Photon. Tech. Lett. 8, 652–654 (1996).

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

W. Huang, C. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis
of optical waveguides: leaky mode calculations,” IEEE Photon. Tech. Lett. 8, 652–654 (1996).

[CrossRef]

L. Zschiedrich, R. Klose, A. Schädle, and F. Schmidt, “A new finite element realization of the perfectly matched
layer method for helmholtz scattering problems on polygonal domains in two dimensions,” J. Comput. Appl.
Math. 188, 12–32 (2006).

[CrossRef]

F. Collino and P. B. Monk, “Optimizing the perfectly matched layer,” Comput. Methods Appl. Mech. Engrg. 164, 157–171 (1998).

[CrossRef]

M. Lassas and E. Somersalo, “On the existence and convergence of the solution of PML equations,” Computing 60, 229–241 (1998).

[CrossRef]

W. C. Chew and J. M. Jin, “Perfectly matched layers in the discretized space: An analysis and optimization,” Electromagnetics 16, 325–340 (1996).

[CrossRef]

D. Pissoort and F. Olyslager, “Termination of periodic waveguides by PMLs in time-harmonic integral equationlike
techniques,” IEEE Antennas and Wireless Propagation Lett. 2, 281–284 (2003).

[CrossRef]

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

[CrossRef]

C. M. Rappaport, “Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of
space,” IEEE Microwave and Guided Wave Lett. 5, 90–92 (1995).

[CrossRef]

F. L. Teixeira and W. C. Chew, “General close-form PML constitutive tensors to match arbitrary bianisotropic
and dispersive linear media,” IEEE Microwave and Guided Wave Lett. 8, 223–225 (1998).

[CrossRef]

J. S. Juntunen, N. V. Kantartzis, and T. D. Tsiboukis, “Zero reflection coefficient in discretized PML,” IEEE
Microwave Wirel. Compon. Lett. 11, 155–157 (2001).

[CrossRef]

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

[CrossRef]

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly matched layer-absorbing boundary condition
for left-handed materials,” IEEE Microwave Wirel. Compon. Lett. 14, 301–303 (2004).

[CrossRef]

W. Huang, C. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis
of optical waveguides: leaky mode calculations,” IEEE Photon. Tech. Lett. 8, 652–654 (1996).

[CrossRef]

N. Kono and M. Koshiba, “General finite-element modeling of 2-D magnetophotonic crystal waveguides,” IEEE
Photon. Tech. Lett. 17, 1432–1434 (2005).

[CrossRef]

Y. S. Rickard and N. K. Nikolova, “Enhancing the PML absorbing boundary conditions for the wave equation,” IEEE Trans. Antennas Propag. 53, 1242–1246 (2005).

[CrossRef]

Z. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an
absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).

[CrossRef]

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE
Trans. Magn. 35, 1506–1509 (1999).

[CrossRef]

E. P. Kosmidou, T. I. Kosmani, and T. D. Tsiboukis, “A comparative FDTD study of various PML configurations
for the termination of nonlinear photonic bandgap waveguide structures,” IEEE Trans. Magn. 39, 1191–1194 (2003).

[CrossRef]

A. Christ and H. L. Hartnagel, “Three-dimensional finite-difference method for the analysis of microwave-device
embedding,” IEEE Trans. Microwave Theory Tech. 35, 688–696 (1987).

[CrossRef]

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves
in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216–2222 (1998).

[CrossRef]

K. O. Mead and L. M. Delves, “On the convergence rate of generalized fourier expansions,” IMA J. Appl. Math. 12, 247–259 (1973).

[CrossRef]

L. Zschiedrich, R. Klose, A. Schädle, and F. Schmidt, “A new finite element realization of the perfectly matched
layer method for helmholtz scattering problems on polygonal domains in two dimensions,” J. Comput. Appl.
Math. 188, 12–32 (2006).

[CrossRef]

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

[CrossRef]

J. P. Boyd, “The optimization of convergence for Chebyshev polynomial methods in an unbounded domain,” J. Comput. Phys. 45, 43–79 (1982).

[CrossRef]

A. Dranov, J. Kellendonk, and R. Seller, “Discrete time adiabatic theorems for quantum mechanical systems,” J.
Math. Phys. 39, 1340–1349 (1998).

[CrossRef]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).

[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter , “Comparative study of three methods for
the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).

[CrossRef]

D. Elliott, “The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function,” Mathematics of Computation 18, 274–284 (1964).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with
stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

A. R. Weily, L. Horvath, K. P. Esselle, and B. C. Sanders, “Performance of PML absorbing boundary conditions
in 3d photonic crystal waveguides,” Microwave Opt. Technol.Lett. 40, 1–3 (2004).

[CrossRef]

E. Moreno, D. Erni, and C. Hafner, “Modeling of discontinuities in photonic crystal waveguides with the multiple
multipole method,” Phys. Rev. E 66, 036618 (2002).

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68 (2003).

S. G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem
and continuous coupled-mode theory for efficient taper transitions in photonic crystals,”Phys. Rev. E 66, 066608 (2002).

Z. Chen and X. Liu, “An adaptive perfectly matched layer technique for time-harmonic scattering problems,” SIAM J. Num. Anal. 43, 645–671 (2005).

[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition (Princeton Univ. Press, 2008).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd Edition (Academic Press, San Diego, 1991).

J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd Edition (Springer, 1989).

H. Cheng, Advanced Analytic Methods in Applied Mathematics, Science and Engineering (Luban Press, Boston, 2006).