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

[CrossRef]

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).

[CrossRef]

D. Song, L. Yuan, and Y. Y. Lu, “Fourier-matching pseudospectral modal method for diffraction gratings,” J. Opt. Soc. Am. A 28, 613–620 (2011).

[CrossRef]

Y. Wu and Y. Y. Lu, “Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction,” J. Opt. Soc. Am. A 28, 1191–1196 (2011).

[CrossRef]

K. Edee, “Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings,” J. Opt. Soc. Am. A 28, 2006–2013 (2011).

[CrossRef]

L. I. Goray and G. Schmidt, “Solving conical diffraction with integral equations,” J. Opt. Soc. Am. A 27, 585–597 (2010).

[CrossRef]

G. Granet, L. B. Andriamanampisoa, K. Raniriharinosy, A. M. Armeanu, and K. Edee, “Modal analysis of lamellar gratings using the moment method with subsectional basis and adaptive spatial resolution,” J. Opt. Soc. Am. A 27, 1303–1310 (2010).

[CrossRef]

I. Gushchin and A. V. Tishchenko, “Fourier modal method for relief gratings with oblique boundary conditions,” J. Opt. Soc. Am. A 27, 1575–1583 (2010).

[CrossRef]

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the decisive role of hidden modes,” J. Opt. Soc. Am. A 23, 2501–2509 (2006).

[CrossRef]

A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Commun. Comput. Phys. 1, 984–1009 (2006).

D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).

[CrossRef]

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).

[CrossRef]

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).

[CrossRef]

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876(1996).

[CrossRef]

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, “Integral equation method with parametrization of grating profile—theory and experiments,” J. Mod. Opt. 43, 1323–1349 (1996).

[CrossRef]

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).

[CrossRef]

A. Pomp, “The integral method for coated gratings—computational cost,” J. Mod. Opt. 38, 109–120 (1991).

[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

S. Campbell, L. C. Botten, R. C. McPhedran, and C. M. de Sterke, “Modal method for classical diffraction by slanted lamellar gratings,” J. Opt. Soc. Am. A 25, 2415–2426 (2008).

[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

K. Edee, “Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings,” J. Opt. Soc. Am. A 28, 2006–2013 (2011).

[CrossRef]

G. Granet, L. B. Andriamanampisoa, K. Raniriharinosy, A. M. Armeanu, and K. Edee, “Modal analysis of lamellar gratings using the moment method with subsectional basis and adaptive spatial resolution,” J. Opt. Soc. Am. A 27, 1303–1310 (2010).

[CrossRef]

G. Granet, L. B. Andriamanampisoa, K. Raniriharinosy, A. M. Armeanu, and K. Edee, “Modal analysis of lamellar gratings using the moment method with subsectional basis and adaptive spatial resolution,” J. Opt. Soc. Am. A 27, 1303–1310 (2010).

[CrossRef]

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).

[CrossRef]

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).

[CrossRef]

A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Commun. Comput. Phys. 1, 984–1009 (2006).

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, “Integral equation method with parametrization of grating profile—theory and experiments,” J. Mod. Opt. 43, 1323–1349 (1996).

[CrossRef]

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).

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

[CrossRef]

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

[CrossRef]

D. Song, L. Yuan, and Y. Y. Lu, “Fourier-matching pseudospectral modal method for diffraction gratings,” J. Opt. Soc. Am. A 28, 613–620 (2011).

[CrossRef]

Y. Wu and Y. Y. Lu, “Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction,” J. Opt. Soc. Am. A 28, 1191–1196 (2011).

[CrossRef]

Y. Wu and Y. Y. Lu, “Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method,” J. Opt. Soc. Am. A 26, 2444–2451(2009).

[CrossRef]

D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).

[CrossRef]

E. Popov, B. Bozhkov, D. Maystre, and J. Hoose, “Integral method for echelles covered with lossless or absorbing thin dielectric layers,” Appl. Opt. 38, 47–55 (1999).

[CrossRef]

D. Maystre, “Sur la diffraction et l’absorption par les réseaux utilisés dans l’infrarouge, le visible et l’ultraviolet,” Ph.D. dissertation (Université d’Aix-Marseille III, 1974).

D. Maystre, “Integral methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, 1980), Chap. 3.

S. Campbell, L. C. Botten, R. C. McPhedran, and C. M. de Sterke, “Modal method for classical diffraction by slanted lamellar gratings,” J. Opt. Soc. Am. A 25, 2415–2426 (2008).

[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).

[CrossRef]

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, “Integral equation method with parametrization of grating profile—theory and experiments,” J. Mod. Opt. 43, 1323–1349 (1996).

[CrossRef]

A. Pomp, “The integral method for coated gratings—computational cost,” J. Mod. Opt. 38, 109–120 (1991).

[CrossRef]

E. Popov, M. Neviére, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A 19, 33–42 (2002).

[CrossRef]

E. Popov, B. Bozhkov, D. Maystre, and J. Hoose, “Integral method for echelles covered with lossless or absorbing thin dielectric layers,” Appl. Opt. 38, 47–55 (1999).

[CrossRef]

D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).

[CrossRef]

A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Commun. Comput. Phys. 1, 984–1009 (2006).

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).

[CrossRef]

L. I. Goray and G. Schmidt, “Solving conical diffraction with integral equations,” J. Opt. Soc. Am. A 27, 585–597 (2010).

[CrossRef]

A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Commun. Comput. Phys. 1, 984–1009 (2006).

I. Gushchin and A. V. Tishchenko, “Fourier modal method for relief gratings with oblique boundary conditions,” J. Opt. Soc. Am. A 27, 1575–1583 (2010).

[CrossRef]

N. M. Lyndin, O. Parriaux, and A. V. Tishchenko, “Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings,” J. Opt. Soc. Am. A 24, 3781–3788 (2007).

[CrossRef]

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the decisive role of hidden modes,” J. Opt. Soc. Am. A 23, 2501–2509 (2006).

[CrossRef]

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, “Integral equation method with parametrization of grating profile—theory and experiments,” J. Mod. Opt. 43, 1323–1349 (1996).

[CrossRef]

A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Commun. Comput. Phys. 1, 984–1009 (2006).

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

[CrossRef]

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).

[CrossRef]

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).

[CrossRef]

A. Pomp, “The integral method for coated gratings—computational cost,” J. Mod. Opt. 38, 109–120 (1991).

[CrossRef]

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, “Integral equation method with parametrization of grating profile—theory and experiments,” J. Mod. Opt. 43, 1323–1349 (1996).

[CrossRef]

G. Bao, Z. M. Chen, and H. J. Wu, “Adaptive finite-element method for diffraction gratings,” J. Opt. Soc. Am. A 22, 1106–1114 (2005).

[CrossRef]

T. Magath and A. E. Serebryannikov, “Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs,” J. Opt. Soc. Am. A 22, 2405–2418 (2005).

[CrossRef]

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the decisive role of hidden modes,” J. Opt. Soc. Am. A 23, 2501–2509 (2006).

[CrossRef]

N. M. Lyndin, O. Parriaux, and A. V. Tishchenko, “Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings,” J. Opt. Soc. Am. A 24, 3781–3788 (2007).

[CrossRef]

S. Campbell, L. C. Botten, R. C. McPhedran, and C. M. de Sterke, “Modal method for classical diffraction by slanted lamellar gratings,” J. Opt. Soc. Am. A 25, 2415–2426 (2008).

[CrossRef]

Y. Wu and Y. Y. Lu, “Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method,” J. Opt. Soc. Am. A 26, 2444–2451(2009).

[CrossRef]

P. Lalanne and J. P. Hugonin, “Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings,” J. Opt. Soc. Am. A 17, 1033–1042 (2000).

[CrossRef]

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).

[CrossRef]

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).

[CrossRef]

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876(1996).

[CrossRef]

R. H. Morf, “Exponentially convergent and numerically efficient solution of Maxwell’s equations for lamellar gratings,” J. Opt. Soc. Am. A 12, 1043–1056 (1995).

[CrossRef]

L. I. Goray and G. Schmidt, “Solving conical diffraction with integral equations,” J. Opt. Soc. Am. A 27, 585–597 (2010).

[CrossRef]

G. Granet, L. B. Andriamanampisoa, K. Raniriharinosy, A. M. Armeanu, and K. Edee, “Modal analysis of lamellar gratings using the moment method with subsectional basis and adaptive spatial resolution,” J. Opt. Soc. Am. A 27, 1303–1310 (2010).

[CrossRef]

I. Gushchin and A. V. Tishchenko, “Fourier modal method for relief gratings with oblique boundary conditions,” J. Opt. Soc. Am. A 27, 1575–1583 (2010).

[CrossRef]

D. Song, L. Yuan, and Y. Y. Lu, “Fourier-matching pseudospectral modal method for diffraction gratings,” J. Opt. Soc. Am. A 28, 613–620 (2011).

[CrossRef]

Y. Wu and Y. Y. Lu, “Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction,” J. Opt. Soc. Am. A 28, 1191–1196 (2011).

[CrossRef]

K. Edee, “Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings,” J. Opt. Soc. Am. A 28, 2006–2013 (2011).

[CrossRef]

E. Popov, M. Neviére, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A 19, 33–42 (2002).

[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).

[CrossRef]

D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).

[CrossRef]

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).

G. Bao, L. Cowsar, and W. Masters, Mathematical Modeling in Optical Sciences (Society for Industrial and Applied Mathematics, 2001).

D. Maystre, “Sur la diffraction et l’absorption par les réseaux utilisés dans l’infrarouge, le visible et l’ultraviolet,” Ph.D. dissertation (Université d’Aix-Marseille III, 1974).

D. Maystre, “Integral methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, 1980), Chap. 3.

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).