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Optics Letters

Optics Letters


  • Vol. 17, Iss. 1 — Jan. 1, 1992
  • pp: 10–12

Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain

R. P. Ratowsky, J. A. Fleck, Jr., and M. D. Feit  »View Author Affiliations

Optics Letters, Vol. 17, Issue 1, pp. 10-12 (1992)

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The numerical scheme for solving the Helmholtz equation, based on the Lanczos orthogonalization scheme, is generalized so that it can be applied to media with space-dependent absorption or gain profiles.

© 1992 Optical Society of America

Original Manuscript: September 4, 1991
Published: January 1, 1992

R. P. Ratowsky, J. A. Fleck, and M. D. Feit, "Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain," Opt. Lett. 17, 10-12 (1992)

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  1. J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976). [CrossRef]
  2. R. P. Ratowsky, J. A. Fleck, M. D. Feit, “Helmholtz beam propagation in rib waveguides and couplers by iterative Lanczos reduction,”J. Opt. Soc. Am. A (to be published).
  3. R. P. Ratowsky, J. A. Fleck, Opt. Lett. 16, 787 (1991). [CrossRef] [PubMed]
  4. T. J. Park, J. C. Light, J. Chem. Phys. 85, 5870 (1986). [CrossRef]
  5. C. LeForestier, R. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H. D. Meyer, N. Lipkin, O. Roncero, R. Kosloff, J. Comput. Phys. 94, 59 (1991). [CrossRef]
  6. See, for example, W. F. Ames, D. Lee, Appl. Num. Math. 3, 25 (1987). [CrossRef]
  7. N. S. Sehmi, Large Order Structural Eigenanalysis for Finite Element Systems (Halsted, New York, 1989), pp. 48–69.
  8. By factoring out the carrier exp(ikz) rather than exp(−ikz), we make it easier to select the exponentially decaying modes that correspond to propagation angles greater than 90 deg (see Ref. 2).
  9. A generalization for real nonsymmetric matrices appears in Lanczos’ original paper, C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).

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