Abstract

Rigorous coupled-wave analysis (also called the Fourier-modal method) is an efficient tool for the numerical analysis of grating diffraction problems. We show that, with only a few modifications, this method can be used efficiently for the numerical analysis of aperiodic diffraction problems, including photonic crystal waveguides, Bragg mirrors, and grating couplers. We thus extend the domain of applications of grating theories.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  12. P. Vahihama and J. Turunen, in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 69.

1999 (1)

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

1998 (1)

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

1996 (3)

1995 (1)

1993 (1)

E. Popov, Prog. Opt. 31, 141 (1993).

1992 (1)

J. Gerdes, B. Lunitz, D. Benish, and R. Pregla, Electron. Lett. 28, 1013 (1992).
[CrossRef]

1989 (1)

C. H. Henry and B. H. Verbeek, J. Lightwave Technol. 7, 308 (1989).
[CrossRef]

1980 (1)

Benish, D.

J. Gerdes, B. Lunitz, D. Benish, and R. Pregla, Electron. Lett. 28, 1013 (1992).
[CrossRef]

Carrasco, S.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Chang, K. C.

Crespo, R. D.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

De La Rue, R. M.

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

Fernandez, S.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Gaylord, T. K.

Gerdes, J.

J. Gerdes, B. Lunitz, D. Benish, and R. Pregla, Electron. Lett. 28, 1013 (1992).
[CrossRef]

Grann, E. B.

Helfert, S. F.

S. F. Helfert and R. Pregla, J. Lightwave Technol. 14, 2414 (1996).
[CrossRef]

Henry, C. H.

C. H. Henry and B. H. Verbeek, J. Lightwave Technol. 7, 308 (1989).
[CrossRef]

Ibanez, I.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Krauss, T. F.

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

Lalanne, Ph.

Li, L.

Lunitz, B.

J. Gerdes, B. Lunitz, D. Benish, and R. Pregla, Electron. Lett. 28, 1013 (1992).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Olivares, J.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Painter, O.

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

Pandavenes, J.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Pommet, D. A.

Popov, E.

E. Popov, Prog. Opt. 31, 141 (1993).

Pregla, R.

S. F. Helfert and R. Pregla, J. Lightwave Technol. 14, 2414 (1996).
[CrossRef]

J. Gerdes, B. Lunitz, D. Benish, and R. Pregla, Electron. Lett. 28, 1013 (1992).
[CrossRef]

Roberts, J. S.

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

Rodriguez, J.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Scherer, A.

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

Shah, V.

Tamir, T.

Turunen, J.

P. Vahihama and J. Turunen, in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 69.

Vahihama, P.

P. Vahihama and J. Turunen, in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 69.

Verbeek, B. H.

C. H. Henry and B. H. Verbeek, J. Lightwave Technol. 7, 308 (1989).
[CrossRef]

Virgos, J. M.

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

Electron. Lett. (1)

J. Gerdes, B. Lunitz, D. Benish, and R. Pregla, Electron. Lett. 28, 1013 (1992).
[CrossRef]

J. Lightwave Technol. (2)

S. F. Helfert and R. Pregla, J. Lightwave Technol. 14, 2414 (1996).
[CrossRef]

C. H. Henry and B. H. Verbeek, J. Lightwave Technol. 7, 308 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (2)

J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, and J. M. Virgos, Opt. Eng. 38, 1896 (1999).
[CrossRef]

T. F. Krauss, O. Painter, A. Scherer, J. S. Roberts, and R. M. De La Rue, Opt. Eng. 37, 1143 (1998).
[CrossRef]

Prog. Opt. (1)

E. Popov, Prog. Opt. 31, 141 (1993).

Other (2)

Session C09 of the 1998 Progress in Electromagnetics Research Symposium, Nantes, France, July 13–17, 1998.

P. Vahihama and J. Turunen, in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 69.

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Figures (3)

Fig. 1
Fig. 1

Waveguide geometry: The GaAs (refractive index, 3.5) cap, the GaAlAs (refractive index, 2.9) undercap, and the GaAs core are 100, 300, and 240 nm thick, respectively. The groove width is 80 nm, and the Bragg grating period is 500 nm. Lc and Ls are the absorber thicknesses, and d is the groove depth.

Fig. 2
Fig. 2

Reflected and transmitted intensities for the mirror problem of Fig. 1 for TE polarization and for λ=975 nm. Solid curves, RCWA results with N=301 retained Fourier harmonics (Lc=Ls=0.5λ and w=3λ). Pluses, MOL results with 300 discretization points and a 3λ computational-window size.

Fig. 3
Fig. 3

Convergence performance for d=1000 nm. (a) Reflected intensity for TE polarization. (b) Transmitted intensity for TM polarization. Solid curves, RCWA results for w=3λ, 6λ. Pluses, MOL results for a 3λ computational-window size.

Tables (1)

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Table 1 neff Values Obtained with Lc=Ls=1λa

Equations (2)

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bift=S0fi,
b2f2=Tb1f1,

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