Abstract

Convergence problems in modal methods for TM polarized fields are often attributed to the inaccuracies in computing the modes of a grating. We report that even in the absence of these inaccuracies convergence problems persist. These arise because of the truncation of the infinite set of linear equations resulting from matching the fields at the grating–substrate and grating–superstrate interfaces with a square matrix. We show that dramatic improvement in convergence can be achieved if the infinite set of linear equations is truncated with a rectangular matrix and by seeking a solution with minimum least squared error.

© 2010 Optical Society of America

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2008 (1)

2007 (1)

2006 (2)

2004 (1)

2001 (1)

P. Bienstman, “Rigorous and efficient modelling of wavelength scale photonic components,” doctoral thesis (Universiteit Gent, 2001).

1996 (3)

1995 (1)

1993 (1)

1983 (1)

J. Suratteau, M. Cadilhac, and R. Petit, “Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds,” J. Opt. 14, 273–288 (1983).
[CrossRef]

1981 (1)

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Adams, J.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

Andrewartha, J.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

Bienstman, P.

P. Bienstman, “Rigorous and efficient modelling of wavelength scale photonic components,” doctoral thesis (Universiteit Gent, 2001).

Bonod, N.

Botten, L.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

Cadilhac, M.

J. Suratteau, M. Cadilhac, and R. Petit, “Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds,” J. Opt. 14, 273–288 (1983).
[CrossRef]

Chernov, B.

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Craig, M.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

Foresti, M.

Gaylord, T.

Granet, G.

Grann, E.

Guizal, B.

Haggans, C.

Jazayeri, A.

Johnson, P.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Khavasi, A.

Lalanne, P.

Li, L.

Lyndin, N.

Mansuripur, M.

McPhedran, R.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

Mehrany, K.

Menez, L.

Moharam, M.

Moloney, J.

Morris, G.

Nevière, M.

Parriaux, O.

Petit, R.

J. Suratteau, M. Cadilhac, and R. Petit, “Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds,” J. Opt. 14, 273–288 (1983).
[CrossRef]

Pommet, D.

Popov, E.

Suratteau, J.

J. Suratteau, M. Cadilhac, and R. Petit, “Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds,” J. Opt. 14, 273–288 (1983).
[CrossRef]

Tishchenko, A.

Xie, Y.

Zakharian, A.

J. Opt. (1)

J. Suratteau, M. Cadilhac, and R. Petit, “Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds,” J. Opt. 14, 273–288 (1983).
[CrossRef]

J. Opt. Soc. Am. A (8)

Opt. Acta (1)

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “Dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Other (1)

P. Bienstman, “Rigorous and efficient modelling of wavelength scale photonic components,” doctoral thesis (Universiteit Gent, 2001).

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