Abstract

A boundary variation method for the forward modeling of multilayered diffraction optics is presented. The approach permits fast and high-order accurate modeling of periodic transmission optics consisting of an arbitrary number of materials and interfaces of general shape subject to plane-wave illumination or, by solving a sequence of problems, illumination by beams. The key elements of the algorithm are discussed, as are details of an efficient implementation. Numerous comparisons with exact solutions and highly accurate direct solutions confirm the accuracy, the versatility, and the efficiency of the proposed method.

© 2004 Optical Society of America

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  1. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  2. B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 1592–1598 (1994).
    [CrossRef]
  3. K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
    [CrossRef]
  4. D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1141 (1999).
    [CrossRef]
  5. P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, L. Lading, “Pseudospectral method for the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 16, 1124–1130 (1999).
    [CrossRef]
  6. J. S. Hesthaven, P. G. Dinesen, J. P. Lynov, “Spectral collocation time-domain modeling of diffractive optical elements,” J. Comput. Phys. 155, 287–306 (1999).
    [CrossRef]
  7. J. S. Hesthaven, “High-order accurate methods in time-domain computational electromagnetics: a review,” Adv. Electron. Electron Phys. 127, 59–123 (2003).
  8. O. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A 10, 1168–1175 (1993).
    [CrossRef]
  9. O. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A 10, 2307–2316 (1993).
    [CrossRef]
  10. O. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A 10, 2551–2562 (1993).
    [CrossRef]
  11. P. G. Dinesen, J. S. Hesthaven, “A fast and accurate boundary variation method for diffractive gratings,” J. Opt. Soc. Am. A 17, 1565–1572 (2000).
    [CrossRef]
  12. P. G. Dinesen, J. S. Hesthaven, “A fast and accurate boundary variation method for diffractive gratings. II.The three-dimensional vectorial case,” J. Opt. Soc. Am. A 18, 2876–2885 (2001).
    [CrossRef]
  13. R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–52.
  14. O. Bruno, F. Reitich, “Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh, Sect. A 122, 317–340 (1992).
    [CrossRef]
  15. G. A. Baker, P. Graves-Morris, Padé Approximants, 2nd ed., Vol. 59 of Encyclopedia of Mathematics and Its Applications (Cambridge U. Press, Cambridge, UK.1996).
  16. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

2003 (1)

J. S. Hesthaven, “High-order accurate methods in time-domain computational electromagnetics: a review,” Adv. Electron. Electron Phys. 127, 59–123 (2003).

2001 (1)

2000 (1)

1999 (3)

1996 (1)

1994 (1)

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 1592–1598 (1994).
[CrossRef]

1993 (3)

1992 (1)

O. Bruno, F. Reitich, “Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh, Sect. A 122, 317–340 (1992).
[CrossRef]

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Baker, G. A.

G. A. Baker, P. Graves-Morris, Padé Approximants, 2nd ed., Vol. 59 of Encyclopedia of Mathematics and Its Applications (Cambridge U. Press, Cambridge, UK.1996).

Bruno, O.

Dinesen, P. G.

Gallagher, N. C.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 1592–1598 (1994).
[CrossRef]

Gaylord, T. K.

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

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Glytsis, E. N.

Graves-Morris, P.

G. A. Baker, P. Graves-Morris, Padé Approximants, 2nd ed., Vol. 59 of Encyclopedia of Mathematics and Its Applications (Cambridge U. Press, Cambridge, UK.1996).

Hesthaven, J. S.

Hirayama, K.

Lading, L.

Lichtenberg, B.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 1592–1598 (1994).
[CrossRef]

Lynov, J. P.

J. S. Hesthaven, P. G. Dinesen, J. P. Lynov, “Spectral collocation time-domain modeling of diffractive optical elements,” J. Comput. Phys. 155, 287–306 (1999).
[CrossRef]

P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, L. Lading, “Pseudospectral method for the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 16, 1124–1130 (1999).
[CrossRef]

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Petit, R.

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–52.

Prather, D. W.

Reitich, F.

Shi, S.

Wilson, D. W.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Adv. Electron. Electron Phys. (1)

J. S. Hesthaven, “High-order accurate methods in time-domain computational electromagnetics: a review,” Adv. Electron. Electron Phys. 127, 59–123 (2003).

J. Comput. Phys. (1)

J. S. Hesthaven, P. G. Dinesen, J. P. Lynov, “Spectral collocation time-domain modeling of diffractive optical elements,” J. Comput. Phys. 155, 287–306 (1999).
[CrossRef]

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

P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, L. Lading, “Pseudospectral method for the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 16, 1124–1130 (1999).
[CrossRef]

D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1141 (1999).
[CrossRef]

O. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A 10, 1168–1175 (1993).
[CrossRef]

O. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A 10, 2307–2316 (1993).
[CrossRef]

O. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A 10, 2551–2562 (1993).
[CrossRef]

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

P. G. Dinesen, J. S. Hesthaven, “A fast and accurate boundary variation method for diffractive gratings,” J. Opt. Soc. Am. A 17, 1565–1572 (2000).
[CrossRef]

P. G. Dinesen, J. S. Hesthaven, “A fast and accurate boundary variation method for diffractive gratings. II.The three-dimensional vectorial case,” J. Opt. Soc. Am. A 18, 2876–2885 (2001).
[CrossRef]

Opt. Eng. (1)

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 1592–1598 (1994).
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Proc. R. Soc. Edinburgh, Sect. A (1)

O. Bruno, F. Reitich, “Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh, Sect. A 122, 317–340 (1992).
[CrossRef]

Other (3)

G. A. Baker, P. Graves-Morris, Padé Approximants, 2nd ed., Vol. 59 of Encyclopedia of Mathematics and Its Applications (Cambridge U. Press, Cambridge, UK.1996).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–52.

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