S. Benerjee, J. B. Cole, and T. Yatagai, “Calculation of diffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method,” Opt. Rev. 12, 274–280 (2005).

[CrossRef]

N. Nakashima and M. Tateiba, “Computational and memory complexities of Greengard–Rokhlin’s fast multipole algorithm,” IEICE Trans. Electron. E88-C, 1516–1520 (2005).

[CrossRef]

D. W. Peters, S. A. Kemme, and G. R. Hadley, “Effect of finite grating, waveguide width, and end-facet geometry on resonant subwavelength grating reflectivity,” J. Opt. Soc. Am. A 21, 981–987 (2004).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).

[CrossRef]

N. Nakashima and M. Tateiba, “Greengard–Rokhlin’s fast multipole algorithm for numerical calculation of scattering by N conducting circular cylinders,” IEICE Trans. Electron. E86-C, 2158–2166 (2003).

O. M. Mendez and J. Sumaya-Martinez, “Diffraction by Gaussian and Hermite–Gaussian beams by finite gratings,” J. Opt. Soc. Am. A 18, 537–545 (2001).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and A. F. Peterson, “Modeling considerations for rigorous boundary element method analysis of diffractive optical elements,” J. Opt. Soc. Am. A 18, 1495–1506 (2001).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, “Guided-mode resonance subwavelength gratings: effect of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).

[CrossRef]

G. Pelosi, G. Manara, and G. Toso, “Heuristic diffraction coefficient for plane-wave scattering form edges in periodic planar surface,” J. Opt. Soc. Am. A 13, 1689–1697 (1996).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).

[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, and M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).

[CrossRef]

N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

[CrossRef]

T. Kojima and J. Ido, “Boundary-element method analysis of light-beam,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).

[CrossRef]

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414–439 (1990).

[CrossRef]

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325–348 (1987).

[CrossRef]

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).

[CrossRef]

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).

[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).

[CrossRef]

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964), p. 1046.

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and A. F. Peterson, “Modeling considerations for rigorous boundary element method analysis of diffractive optical elements,” J. Opt. Soc. Am. A 18, 1495–1506 (2001).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, “Guided-mode resonance subwavelength gratings: effect of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).

[CrossRef]

S. Benerjee, J. B. Cole, and T. Yatagai, “Calculation of diffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method,” Opt. Rev. 12, 274–280 (2005).

[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

[CrossRef]

D. Poljak and C. A. Brebbia, Boundary Element Methods For Electrical Engineers (WIT, 2005).

C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral-equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 466–470 (1994).

[CrossRef]

S. Benerjee, J. B. Cole, and T. Yatagai, “Calculation of diffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method,” Opt. Rev. 12, 274–280 (2005).

[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).

[CrossRef]

N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

[CrossRef]

P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 3rd ed. (Cambridge Univ. Press, 1996).

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, “Guided-mode resonance subwavelength gratings: effect of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and A. F. Peterson, “Modeling considerations for rigorous boundary element method analysis of diffractive optical elements,” J. Opt. Soc. Am. A 18, 1495–1506 (2001).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).

[CrossRef]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).

[CrossRef]

A. D. Papadopoulos and E. N. Glytsis, “Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings,” Appl. Opt. 47, 1981–1994 (2008).

[CrossRef]

S. D. Wu and E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19, 2018–2029 (2002).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, “Guided-mode resonance subwavelength gratings: effect of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and A. F. Peterson, “Modeling considerations for rigorous boundary element method analysis of diffractive optical elements,” J. Opt. Soc. Am. A 18, 1495–1506 (2001).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).

[CrossRef]

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325–348 (1987).

[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).

[CrossRef]

K. Hirayama, K. Igarashi, and Y. Hayashi, “Finite-substrate-thickness cylindrical diffractive lenses,” J. Opt. Soc. Am. A 16, 1294–1302 (1999).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).

[CrossRef]

T. Kojima and J. Ido, “Boundary-element method analysis of light-beam,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Systematic design process for slanted grating couplers,” Appl. Opt. 45, 6223–6226 (2006).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).

[CrossRef]

D. R. Kincaid, Iterative Methods for Large Linear Systems (Academic, 1989).

T. Kojima and J. Ido, “Boundary-element method analysis of light-beam,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).

[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).

[CrossRef]

C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral-equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 466–470 (1994).

[CrossRef]

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).

[CrossRef]

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).

N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

[CrossRef]

N. Nakashima and M. Tateiba, “Computational and memory complexities of Greengard–Rokhlin’s fast multipole algorithm,” IEICE Trans. Electron. E88-C, 1516–1520 (2005).

[CrossRef]

N. Nakashima and M. Tateiba, “Greengard–Rokhlin’s fast multipole algorithm for numerical calculation of scattering by N conducting circular cylinders,” IEICE Trans. Electron. E86-C, 2158–2166 (2003).

M. Nevier, “The homogenous problem,” in Electromagnetic Theory of Gratings, R.Petit, ed. (Springer-Verlag, 1980), Chap. 5.

B. Wang, J. Jiang, and G. P. Nordin, “Systematic design process for slanted grating couplers,” Appl. Opt. 45, 6223–6226 (2006).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).

[CrossRef]

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).

[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

[CrossRef]

D. Poljak and C. A. Brebbia, Boundary Element Methods For Electrical Engineers (WIT, 2005).

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).

[CrossRef]

N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

[CrossRef]

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414–439 (1990).

[CrossRef]

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325–348 (1987).

[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).

[CrossRef]

P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 3rd ed. (Cambridge Univ. Press, 1996).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964), p. 1046.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).

[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

[CrossRef]

N. Nakashima and M. Tateiba, “Computational and memory complexities of Greengard–Rokhlin’s fast multipole algorithm,” IEICE Trans. Electron. E88-C, 1516–1520 (2005).

[CrossRef]

N. Nakashima and M. Tateiba, “Greengard–Rokhlin’s fast multipole algorithm for numerical calculation of scattering by N conducting circular cylinders,” IEICE Trans. Electron. E86-C, 2158–2166 (2003).

N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Systematic design process for slanted grating couplers,” Appl. Opt. 45, 6223–6226 (2006).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).

[CrossRef]

S. Benerjee, J. B. Cole, and T. Yatagai, “Calculation of diffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method,” Opt. Rev. 12, 274–280 (2005).

[CrossRef]

Y. L. Kok, “General solution to the multiple-metallic-grooves scattering problems: the fast-polarization case,” Appl. Opt. 32, 2573–2581 (1993).

[CrossRef]

B. Wang, J. Jiang, and G. P. Nordin, “Systematic design process for slanted grating couplers,” Appl. Opt. 45, 6223–6226 (2006).

[CrossRef]

A. D. Papadopoulos and E. N. Glytsis, “Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings,” Appl. Opt. 47, 1981–1994 (2008).

[CrossRef]

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).

[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).

[CrossRef]

T. Kojima and J. Ido, “Boundary-element method analysis of light-beam,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).

[CrossRef]

N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

[CrossRef]

N. Nakashima and M. Tateiba, “Computational and memory complexities of Greengard–Rokhlin’s fast multipole algorithm,” IEICE Trans. Electron. E88-C, 1516–1520 (2005).

[CrossRef]

N. Nakashima and M. Tateiba, “Greengard–Rokhlin’s fast multipole algorithm for numerical calculation of scattering by N conducting circular cylinders,” IEICE Trans. Electron. E86-C, 2158–2166 (2003).

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325–348 (1987).

[CrossRef]

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414–439 (1990).

[CrossRef]

O. M. Mendez and J. Sumaya-Martinez, “Diffraction by Gaussian and Hermite–Gaussian beams by finite gratings,” J. Opt. Soc. Am. A 18, 537–545 (2001).

[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, and M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and A. F. Peterson, “Modeling considerations for rigorous boundary element method analysis of diffractive optical elements,” J. Opt. Soc. Am. A 18, 1495–1506 (2001).

[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, “Guided-mode resonance subwavelength gratings: effect of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).

[CrossRef]

S. D. Wu and E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19, 2018–2029 (2002).

[CrossRef]

D. W. Peters, S. A. Kemme, and G. R. Hadley, “Effect of finite grating, waveguide width, and end-facet geometry on resonant subwavelength grating reflectivity,” J. Opt. Soc. Am. A 21, 981–987 (2004).

[CrossRef]

E. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, “Diffraction of a Gaussian beam from a periodic planar screen,” J. Opt. Soc. Am. A 11, 630–636 (1994).

[CrossRef]

K. Hirayama, K. Igarashi, and Y. Hayashi, “Finite-substrate-thickness cylindrical diffractive lenses,” J. Opt. Soc. Am. A 16, 1294–1302 (1999).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).

[CrossRef]

O. M. Mendez and J. S. Martinez, “Scattering of TE-polarized waves by a finite-grating: giant resonant enhancement of the electric field within the grooves,” J. Opt. Soc. Am. A 14, 2203–2211 (1997).

[CrossRef]

L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184–1189 (1993).

[CrossRef]

G. Pelosi, G. Manara, and G. Toso, “Heuristic diffraction coefficient for plane-wave scattering form edges in periodic planar surface,” J. Opt. Soc. Am. A 13, 1689–1697 (1996).

[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).

[CrossRef]

C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral-equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 466–470 (1994).

[CrossRef]

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).

[CrossRef]

S. Benerjee, J. B. Cole, and T. Yatagai, “Calculation of diffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method,” Opt. Rev. 12, 274–280 (2005).

[CrossRef]

D. Poljak and C. A. Brebbia, Boundary Element Methods For Electrical Engineers (WIT, 2005).

M. Nevier, “The homogenous problem,” in Electromagnetic Theory of Gratings, R.Petit, ed. (Springer-Verlag, 1980), Chap. 5.

P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 3rd ed. (Cambridge Univ. Press, 1996).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964), p. 1046.

D. R. Kincaid, Iterative Methods for Large Linear Systems (Academic, 1989).