OSA's Digital Library

Optics Letters

Optics Letters


  • Vol. 19, Iss. 2 — Jan. 15, 1994
  • pp: 84–86

Numerical simulation of reflecting structures by solution of the two-dimensional Helmholtz equation

G. Ronald Hadley  »View Author Affiliations

Optics Letters, Vol. 19, Issue 2, pp. 84-86 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (482 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A method is described for modeling two-dimensional reflecting structures based on a solution of the scalar Helmholtz equation. The equation is solved by use of an alternating-direction-implicit iterative method together with a semioptimum sequence of acceleration parameters similar to those introduced decades ago for the solution of elliptic equations with positive-definite operators. The resulting technique is efficient and simple to program, permits the simulation of complex structures with modest storage requirements, and is of very general applicability.

© 1994 Optical Society of America

Original Manuscript: July 28, 1993
Published: January 15, 1994

G. Ronald Hadley, "Numerical simulation of reflecting structures by solution of the two-dimensional Helmholtz equation," Opt. Lett. 19, 84-86 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. Kaczmarski, P. Lagasse, Electron. Lett. 24, 675 (1988). [CrossRef]
  2. C. H. Henry, IEEE J. Quantum Electron. 27, 523 (1991). [CrossRef]
  3. D. Marcuse, Bell Syst. Tech. J. 55, 1295 (1976).
  4. A. Hardy, D. F. Welch, W. Streifer, IEEE J. Quantum Electron. 25, 2096 (1989). [CrossRef]
  5. E. I. Wachspress, J. Soc. Ind. Appl. Math. 10, 339 (1962). [CrossRef]
  6. A. Bayliss, C. I. Goldstein, E. Turkel, J. Comp. Phys. 49, 443 (1983). [CrossRef]
  7. R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1963), Chap. 7 (especially p. 212).
  8. E. L. Wachspress, Iterative Methods for Large Linear Systems (Academic, San Diego, Calif., 1990), Chap. 15.
  9. W. P. Huang, S. T. Chu, A. Goss, S. K. Chaudhuri, IEEE Photon. Technol. Lett. 3, 524 (1991). [CrossRef]
  10. D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, IEEE Photon. Technol. Lett. 3, 342 (1991). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited