Abstract

Critical modeling issues relating to rigorous boundary element method (BEM) analysis of diffractive optical elements (DOEs) are identified. Electric-field integral equation (EFIE) and combined-field integral equation (CFIE) formulations of the BEM are introduced and implemented. The nonphysical interior resonance phenomenon and thin-shape breakdown are illustrated in the context of a guided-mode resonant subwavelength grating. It is shown that modeling such structures by using an open geometric configuration eliminates these problems that are associated with the EFIE BEM. Necessary precautions in defining the incident fields are also presented for the analysis of multiple-layer DOEs.

© 2001 Optical Society of America

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1999 (2)

1998 (2)

1997 (2)

1996 (2)

1995 (3)

Feature issue on diffractive optics applications, Appl. Opt. 34, 2399–2559 (1995).
[CrossRef]

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
[CrossRef] [PubMed]

T. W. Wu, “A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies,” J. Acoust. Soc. Am. 97, 84–91 (1995).
[CrossRef]

1994 (1)

G. Krishnasamy, F. J. Rizzo, Y. Liu, “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994).
[CrossRef]

1993 (1)

1992 (1)

P. M. Goggans, A. A. Kishk, A. W. Glisson, “A systematic treatment of conducting and dielectric bodies with arbitrarily thick or thin features using the method of moments,” IEEE Trans. Antennas Propag. 40, 555–560 (1992).
[CrossRef]

1991 (2)

R. Martinez, “The thin-shape breakdown (TSB) of the Helmholtz integral equation,” J. Acoust. Soc. Am. 90, 2728–2738 (1991).
[CrossRef]

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

1990 (1)

A. F. Peterson, “The ‘interior resonance’ problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies,” Electromagnetics 10, 293–312 (1990).
[CrossRef]

1985 (1)

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

1979 (1)

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

1975 (1)

C. A. Klein, R. Mittra, “An application of the ‘condition number’ concept to the solution of scattering problems in the presence of the interior resonant frequencies,” IEEE Trans. Antennas Propag. 23, 431–435 (1975).
[CrossRef]

1974 (1)

N. Morita, “Analysis of scattering by a dielectric rectangular cylinder by means of integral equation formulation,” Electron. Commun. Jpn. 57-B, 72–80 (1974).

1973 (1)

J.-C. Bolomey, W. Tabbara, “Numerical aspects on coupling between complementary boundary value problems,” IEEE Trans. Antennas Propag. AP-21, 356–363 (1973).
[CrossRef]

Bendickson, J. M.

Bolomey, J.-C.

J.-C. Bolomey, W. Tabbara, “Numerical aspects on coupling between complementary boundary value problems,” IEEE Trans. Antennas Propag. AP-21, 356–363 (1973).
[CrossRef]

Engel, H.

Friesem, A. A.

Gaylord, T. K.

Glisson, A. W.

P. M. Goggans, A. A. Kishk, A. W. Glisson, “A systematic treatment of conducting and dielectric bodies with arbitrarily thick or thin features using the method of moments,” IEEE Trans. Antennas Propag. 40, 555–560 (1992).
[CrossRef]

Glytsis, E. N.

Goggans, P. M.

P. M. Goggans, A. A. Kishk, A. W. Glisson, “A systematic treatment of conducting and dielectric bodies with arbitrarily thick or thin features using the method of moments,” IEEE Trans. Antennas Propag. 40, 555–560 (1992).
[CrossRef]

Harrigan, M. E.

Harrington, R. F.

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

Hayashi, Y.

Hirayama, K.

Ido, J.

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

Igarashi, K.

Kishk, A. A.

P. M. Goggans, A. A. Kishk, A. W. Glisson, “A systematic treatment of conducting and dielectric bodies with arbitrarily thick or thin features using the method of moments,” IEEE Trans. Antennas Propag. 40, 555–560 (1992).
[CrossRef]

Klein, C. A.

C. A. Klein, R. Mittra, “An application of the ‘condition number’ concept to the solution of scattering problems in the presence of the interior resonant frequencies,” IEEE Trans. Antennas Propag. 23, 431–435 (1975).
[CrossRef]

Kojima, T.

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

Koshiba, M.

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.

Krishnasamy, G.

G. Krishnasamy, F. J. Rizzo, Y. Liu, “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994).
[CrossRef]

Liu, Y.

G. Krishnasamy, F. J. Rizzo, Y. Liu, “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994).
[CrossRef]

Magnusson, R.

Mait, J. N.

Martinez, R.

R. Martinez, “The thin-shape breakdown (TSB) of the Helmholtz integral equation,” J. Acoust. Soc. Am. 90, 2728–2738 (1991).
[CrossRef]

Mautz, J. R.

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

Miller, E. K.

A. J. Poggio, E. K. Miller, “Integral equation solutions of three-dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, Oxford, UK, 1973), Chap. 4.

Mirotznik, M. S.

Mittra, R.

C. A. Klein, R. Mittra, “An application of the ‘condition number’ concept to the solution of scattering problems in the presence of the interior resonant frequencies,” IEEE Trans. Antennas Propag. 23, 431–435 (1975).
[CrossRef]

Morita, N.

N. Morita, “Analysis of scattering by a dielectric rectangular cylinder by means of integral equation formulation,” Electron. Commun. Jpn. 57-B, 72–80 (1974).

Ohkawa, S.

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

Peterson, A. F.

A. F. Peterson, “The ‘interior resonance’ problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies,” Electromagnetics 10, 293–312 (1990).
[CrossRef]

Poggio, A. J.

A. J. Poggio, E. K. Miller, “Integral equation solutions of three-dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, Oxford, UK, 1973), Chap. 4.

Prather, D. W.

Rizzo, F. J.

G. Krishnasamy, F. J. Rizzo, Y. Liu, “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994).
[CrossRef]

Rosenblatt, D.

Sharon, A.

Steingrueber, R.

Tabbara, W.

J.-C. Bolomey, W. Tabbara, “Numerical aspects on coupling between complementary boundary value problems,” IEEE Trans. Antennas Propag. AP-21, 356–363 (1973).
[CrossRef]

Wang, S. S.

Weber, H. G.

Wu, T. W.

T. W. Wu, “A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies,” J. Acoust. Soc. Am. 97, 84–91 (1995).
[CrossRef]

Yashiro, K.

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

Appl. Opt. (4)

Arch. Elektr. Uebertrag. (1)

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

Electromagnetics (1)

A. F. Peterson, “The ‘interior resonance’ problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies,” Electromagnetics 10, 293–312 (1990).
[CrossRef]

Electron. Commun. Jpn. (1)

N. Morita, “Analysis of scattering by a dielectric rectangular cylinder by means of integral equation formulation,” Electron. Commun. Jpn. 57-B, 72–80 (1974).

Electron. Commun. Jpn., Part 2: Electron. (1)

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

J.-C. Bolomey, W. Tabbara, “Numerical aspects on coupling between complementary boundary value problems,” IEEE Trans. Antennas Propag. AP-21, 356–363 (1973).
[CrossRef]

C. A. Klein, R. Mittra, “An application of the ‘condition number’ concept to the solution of scattering problems in the presence of the interior resonant frequencies,” IEEE Trans. Antennas Propag. 23, 431–435 (1975).
[CrossRef]

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

P. M. Goggans, A. A. Kishk, A. W. Glisson, “A systematic treatment of conducting and dielectric bodies with arbitrarily thick or thin features using the method of moments,” IEEE Trans. Antennas Propag. 40, 555–560 (1992).
[CrossRef]

Int. J. Numer. Methods Eng. (1)

G. Krishnasamy, F. J. Rizzo, Y. Liu, “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994).
[CrossRef]

J. Acoust. Soc. Am. (2)

T. W. Wu, “A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies,” J. Acoust. Soc. Am. 97, 84–91 (1995).
[CrossRef]

R. Martinez, “The thin-shape breakdown (TSB) of the Helmholtz integral equation,” J. Acoust. Soc. Am. 90, 2728–2738 (1991).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Lett. (1)

Other (3)

A. J. Poggio, E. K. Miller, “Integral equation solutions of three-dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, Oxford, UK, 1973), Chap. 4.

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings,” J. Opt. Soc. Am. A18 (to be published).

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.

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