Abstract

Splitting scalar fields into a sum of counterpropagating waves leads to formulation of the Helmholtz equation as two coupled parabolic partial differential equations. This rigorous formalism naturally leads to the beam-propagation method (BPM) equation when the backward-propagating field is neglected, but it also permits discussion of various corrections. Two problems specifically are analyzed: wide-angle propagation in near-uniform systems and propagation through lenslike systems, with a strongly discontinuous refractive index. Finally, a BPM modeling is proposed for fiber microlens operation.

© 1993 Optical Society of America

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  1. J. Van Roey, J. van der Donk, P. E. Lagasse, “Beam-propagation method: analysis and assessment,”J. Opt. Soc. Am. 71, 803–810 (1981).
    [CrossRef]
  2. M. D. Feit, J. A. Fleck, “Analysis of rib waveguides and couplers by the propagating beam method,” J. Opt. Soc. Am. A 7, 73–79 (1990).
    [CrossRef]
  3. D. Yevick, M. Glasner, “Analysis of forward wide-angle light propagation in semi-conductor rib waveguides and integrated-optic structures,” Electron. Lett. 25, 1611–1613 (1989).
    [CrossRef]
  4. H. H. Lin, A. Korpel, “Heuristic scalar paraxial beam-propagation method taking into account continuous reflections,” J. Opt. Soc. Am. B 8, 849–857 (1991).
    [CrossRef]
  5. P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 26, 675–676 (1988).
    [CrossRef]
  6. D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
    [CrossRef]
  7. C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).
  8. C. Vassallo, “Pseudo-modes et guides optiques,” Ann. Télécom. 43, 48–65 (1988).
  9. D. Yevick, C. Rolland, B. Hermansson, “Fresnel equation studies of longitudinally varying semiconductor waveguides: reference wavevector dependence,” Electron. Lett. 25, 1254–1256 (1989).
    [CrossRef]
  10. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes—the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).
  11. H. M. Presby, “Near 100% efficient fiber microlenses,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 408–411.
  12. D. Yevick, B. Hermansson, M. Glasner, “Fresnel and wide-angle equation analyses of microlenses,”IEEE Photon. Technol. Lett. 2, 412–414 (1990).
    [CrossRef]
  13. C. Vassallo, M. J. van der Keur, “Ultimate coupling performances for microlensed fibres,” Electron. Lett. 28, 1913–1915 (1992).
    [CrossRef]
  14. P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

1992 (1)

C. Vassallo, M. J. van der Keur, “Ultimate coupling performances for microlensed fibres,” Electron. Lett. 28, 1913–1915 (1992).
[CrossRef]

1991 (2)

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
[CrossRef]

H. H. Lin, A. Korpel, “Heuristic scalar paraxial beam-propagation method taking into account continuous reflections,” J. Opt. Soc. Am. B 8, 849–857 (1991).
[CrossRef]

1990 (2)

M. D. Feit, J. A. Fleck, “Analysis of rib waveguides and couplers by the propagating beam method,” J. Opt. Soc. Am. A 7, 73–79 (1990).
[CrossRef]

D. Yevick, B. Hermansson, M. Glasner, “Fresnel and wide-angle equation analyses of microlenses,”IEEE Photon. Technol. Lett. 2, 412–414 (1990).
[CrossRef]

1989 (2)

D. Yevick, C. Rolland, B. Hermansson, “Fresnel equation studies of longitudinally varying semiconductor waveguides: reference wavevector dependence,” Electron. Lett. 25, 1254–1256 (1989).
[CrossRef]

D. Yevick, M. Glasner, “Analysis of forward wide-angle light propagation in semi-conductor rib waveguides and integrated-optic structures,” Electron. Lett. 25, 1611–1613 (1989).
[CrossRef]

1988 (2)

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 26, 675–676 (1988).
[CrossRef]

C. Vassallo, “Pseudo-modes et guides optiques,” Ann. Télécom. 43, 48–65 (1988).

1981 (1)

Bardyszewski, W.

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
[CrossRef]

Colson, V.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Doussière, P.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Feit, M. D.

Fernier, B.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes—the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).

Fleck, J. A.

Garabedian, P.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Glasner, M.

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
[CrossRef]

D. Yevick, B. Hermansson, M. Glasner, “Fresnel and wide-angle equation analyses of microlenses,”IEEE Photon. Technol. Lett. 2, 412–414 (1990).
[CrossRef]

D. Yevick, M. Glasner, “Analysis of forward wide-angle light propagation in semi-conductor rib waveguides and integrated-optic structures,” Electron. Lett. 25, 1611–1613 (1989).
[CrossRef]

Hermansson, B.

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
[CrossRef]

D. Yevick, B. Hermansson, M. Glasner, “Fresnel and wide-angle equation analyses of microlenses,”IEEE Photon. Technol. Lett. 2, 412–414 (1990).
[CrossRef]

D. Yevick, C. Rolland, B. Hermansson, “Fresnel equation studies of longitudinally varying semiconductor waveguides: reference wavevector dependence,” Electron. Lett. 25, 1254–1256 (1989).
[CrossRef]

Kaczmarski, P.

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 26, 675–676 (1988).
[CrossRef]

Korpel, A.

Lafragette, J. L.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Lagasse, P. E.

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 26, 675–676 (1988).
[CrossRef]

J. Van Roey, J. van der Donk, P. E. Lagasse, “Beam-propagation method: analysis and assessment,”J. Opt. Soc. Am. 71, 803–810 (1981).
[CrossRef]

Leblond, F.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Legouezigou, O.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Lin, H. H.

Monnot, M.

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

Presby, H. M.

H. M. Presby, “Near 100% efficient fiber microlenses,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 408–411.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes—the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).

Rolland, C.

D. Yevick, C. Rolland, B. Hermansson, “Fresnel equation studies of longitudinally varying semiconductor waveguides: reference wavevector dependence,” Electron. Lett. 25, 1254–1256 (1989).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes—the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).

van der Donk, J.

van der Keur, M. J.

C. Vassallo, M. J. van der Keur, “Ultimate coupling performances for microlensed fibres,” Electron. Lett. 28, 1913–1915 (1992).
[CrossRef]

Van Roey, J.

Vassallo, C.

C. Vassallo, M. J. van der Keur, “Ultimate coupling performances for microlensed fibres,” Electron. Lett. 28, 1913–1915 (1992).
[CrossRef]

C. Vassallo, “Pseudo-modes et guides optiques,” Ann. Télécom. 43, 48–65 (1988).

C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes—the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).

Yevick, D.

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
[CrossRef]

D. Yevick, B. Hermansson, M. Glasner, “Fresnel and wide-angle equation analyses of microlenses,”IEEE Photon. Technol. Lett. 2, 412–414 (1990).
[CrossRef]

D. Yevick, M. Glasner, “Analysis of forward wide-angle light propagation in semi-conductor rib waveguides and integrated-optic structures,” Electron. Lett. 25, 1611–1613 (1989).
[CrossRef]

D. Yevick, C. Rolland, B. Hermansson, “Fresnel equation studies of longitudinally varying semiconductor waveguides: reference wavevector dependence,” Electron. Lett. 25, 1254–1256 (1989).
[CrossRef]

Ann. Télécom. (1)

C. Vassallo, “Pseudo-modes et guides optiques,” Ann. Télécom. 43, 48–65 (1988).

Electron. Lett. (4)

D. Yevick, C. Rolland, B. Hermansson, “Fresnel equation studies of longitudinally varying semiconductor waveguides: reference wavevector dependence,” Electron. Lett. 25, 1254–1256 (1989).
[CrossRef]

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 26, 675–676 (1988).
[CrossRef]

C. Vassallo, M. J. van der Keur, “Ultimate coupling performances for microlensed fibres,” Electron. Lett. 28, 1913–1915 (1992).
[CrossRef]

D. Yevick, M. Glasner, “Analysis of forward wide-angle light propagation in semi-conductor rib waveguides and integrated-optic structures,” Electron. Lett. 25, 1611–1613 (1989).
[CrossRef]

IEEE Photon. Lett. (1)

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,”IEEE Photon. Lett. 3, 527–529 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. Yevick, B. Hermansson, M. Glasner, “Fresnel and wide-angle equation analyses of microlenses,”IEEE Photon. Technol. Lett. 2, 412–414 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Other (4)

C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).

P. Doussière, P. Garabedian, V. Colson, O. Legouezigou, F. Leblond, J. L. Lafragette, M. Monnot, B. Fernier, “Polarization-insensitive semiconductor optical amplifier with buried laterally tapered active waveguide,” in Optical Amplifiers and Their Applications, Vol. 17 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 140–143.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes—the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).

H. M. Presby, “Near 100% efficient fiber microlenses,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 408–411.

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