M. Ehrhardt, J. G. Sun, and C. Zheng, “Evaluation of scattering operators for semi-infinite periodic arrays,” Commun. Math. Sci. 7, 347–364 (2009).

Z. Hu and Y. Y. Lu, “Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps,” Opt. Express 16, 17383–17399 (2008).

Z. Hu and Y. Y. Lu, “Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices,” Opt. Quantum Electron. 40, 921–932 (2008).

[CrossRef]

J. Yuan, Y. Y. Lu, and X. Antoine, “Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps,” J. Comput. Phys. 227, 4617–4629 (2008).

[CrossRef]

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).

[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

J. Yuan, Y. Y. Lu, and X. Antoine, “Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps,” J. Comput. Phys. 227, 4617–4629 (2008).

[CrossRef]

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

[CrossRef]

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).

[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

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

[CrossRef]

M. Ehrhardt, J. G. Sun, and C. Zheng, “Evaluation of scattering operators for semi-infinite periodic arrays,” Commun. Math. Sci. 7, 347–364 (2009).

S. H. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).

[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

P. Joly, J.-R. Li, and S. Fliss, “Exact boundary conditions for periodic waveguides containing a local perturbation,” Commun. Comput. Phys. 1, 945–973 (2006).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002).

S. H. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).

[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

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

S. H. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).

[CrossRef]

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

P. Joly, J.-R. Li, and S. Fliss, “Exact boundary conditions for periodic waveguides containing a local perturbation,” Commun. Comput. Phys. 1, 945–973 (2006).

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

P. Joly, J.-R. Li, and S. Fliss, “Exact boundary conditions for periodic waveguides containing a local perturbation,” Commun. Comput. Phys. 1, 945–973 (2006).

L. Yuan and Y. Y. Lu, “An efficient numerical method for analyzing photonic crystal slab waveguides,” J. Opt. Soc. Am. B 28, 2265–2270 (2011).

[CrossRef]

L. Yuan and Y. Y. Lu, “Dirichlet-to-Neumann map method for analyzing hole arrays in a slab,” J. Opt. Soc. Am. B 27, 2568–2579 (2010).

[CrossRef]

S. Li and Y. Y. Lu, “Efficient method for computing leaky modes in two-dimensional photonic crystal waveguides,” J. Lightwave Technol. 28, 978–983 (2010).

[CrossRef]

Z. Hu and Y. Y. Lu, “Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps,” Opt. Express 16, 17383–17399 (2008).

J. Yuan, Y. Y. Lu, and X. Antoine, “Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps,” J. Comput. Phys. 227, 4617–4629 (2008).

[CrossRef]

Z. Hu and Y. Y. Lu, “Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices,” Opt. Quantum Electron. 40, 921–932 (2008).

[CrossRef]

Y. Huang, Y. Y. Lu, and S. Li, “Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. B 24, 2860–2867 (2007).

[CrossRef]

Y. Huang and Y. Y. Lu, “Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps,” J. Lightwave Technol. 24, 3448–3453 (2006).

[CrossRef]

P. A. Martin, Multiple Scattering (Cambridge University, 2006).

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

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer-Verlag, 2006).

D. W. Prather, S. Shi, A. Sharkawy, and G. J. Schneider, Photonic Crystals: Theory, Applications, and Fabrication (Wiley, 2009).

D. W. Prather, S. Shi, A. Sharkawy, and G. J. Schneider, Photonic Crystals: Theory, Applications, and Fabrication (Wiley, 2009).

D. W. Prather, S. Shi, A. Sharkawy, and G. J. Schneider, Photonic Crystals: Theory, Applications, and Fabrication (Wiley, 2009).

D. W. Prather, S. Shi, A. Sharkawy, and G. J. Schneider, Photonic Crystals: Theory, Applications, and Fabrication (Wiley, 2009).

M. Ehrhardt, J. G. Sun, and C. Zheng, “Evaluation of scattering operators for semi-infinite periodic arrays,” Commun. Math. Sci. 7, 347–364 (2009).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

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

[CrossRef]

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

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer-Verlag, 2006).

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).

[CrossRef]

J. Yuan, Y. Y. Lu, and X. Antoine, “Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps,” J. Comput. Phys. 227, 4617–4629 (2008).

[CrossRef]

M. Ehrhardt, J. G. Sun, and C. Zheng, “Evaluation of scattering operators for semi-infinite periodic arrays,” Commun. Math. Sci. 7, 347–364 (2009).

P. Joly, J.-R. Li, and S. Fliss, “Exact boundary conditions for periodic waveguides containing a local perturbation,” Commun. Comput. Phys. 1, 945–973 (2006).

M. Ehrhardt, J. G. Sun, and C. Zheng, “Evaluation of scattering operators for semi-infinite periodic arrays,” Commun. Math. Sci. 7, 347–364 (2009).

J. Yuan, Y. Y. Lu, and X. Antoine, “Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps,” J. Comput. Phys. 227, 4617–4629 (2008).

[CrossRef]

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

[CrossRef]

Y. Huang and Y. Y. Lu, “Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps,” J. Lightwave Technol. 24, 3448–3453 (2006).

[CrossRef]

J. Yonekura, M. Ikeda, and T. Baba, “Analysis of finite 2-D photonic crystals of columns and lightwave devices using the scattering matrix method,” J. Lightwave Technol. 17, 1500–1508 (1999).

[CrossRef]

S. Li and Y. Y. Lu, “Efficient method for computing leaky modes in two-dimensional photonic crystal waveguides,” J. Lightwave Technol. 28, 978–983 (2010).

[CrossRef]

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

[CrossRef]

Y. Huang, Y. Y. Lu, and S. Li, “Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. B 24, 2860–2867 (2007).

[CrossRef]

L. Yuan and Y. Y. Lu, “An efficient numerical method for analyzing photonic crystal slab waveguides,” J. Opt. Soc. Am. B 28, 2265–2270 (2011).

[CrossRef]

S. H. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).

[CrossRef]

L. Yuan and Y. Y. Lu, “Dirichlet-to-Neumann map method for analyzing hole arrays in a slab,” J. Opt. Soc. Am. B 27, 2568–2579 (2010).

[CrossRef]

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

[CrossRef]

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).

[CrossRef]

Z. Hu and Y. Y. Lu, “Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices,” Opt. Quantum Electron. 40, 921–932 (2008).

[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

[CrossRef]

M. Ehrhardt, ed., Wave Propagation in Periodic Media—Analysis, Numerical Techniques and Practical Applications, Progress in Computational Physics, Vol. 1 (Bentham Science, 2010).

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer-Verlag, 2006).

P. A. Martin, Multiple Scattering (Cambridge University, 2006).

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

D. W. Prather, S. Shi, A. Sharkawy, and G. J. Schneider, Photonic Crystals: Theory, Applications, and Fabrication (Wiley, 2009).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002).