OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 2 — Feb. 1, 1999
  • pp: 284–292

Regularized Waterman and Rayleigh methods: extension to two-dimensional gratings

M. Bagieu and D. Maystre  »View Author Affiliations


JOSA A, Vol. 16, Issue 2, pp. 284-292 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000284


View Full Text Article

Acrobat PDF (335 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The origin of the instabilities of the Waterman method was studied previously and an improvement in the method was developed for one-dimensional gratings and s polarization [J. Opt. Soc. Am.15, 1566 (1998)]. Later, the same kind of regularization was used to improve Rayleigh’s expansion method. We show that the same well-adapted regularization process can be generalized to two-dimensional (2D) gratings. Numerical implementations show that the convergence domain of the Waterman method is extended by a factor of ∼40% in the range of groove depth. In the same way, the convergence domain of the Rayleigh expansion method is extended by a factor of ∼35% for 2D sinusoidal gratings. As a consequence, the new versions of Waterman and Rayleigh methods become simple and efficient tools for use in investigating the properties of 2D gratings that have ratios of groove depth to period up to unity.

© 1999 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(290.0290) Scattering : Scattering
(290.5880) Scattering : Scattering, rough surfaces

History
Original Manuscript: May 8, 1998
Revised Manuscript: October 6, 1998
Manuscript Accepted: October 13, 1998
Published: February 1, 1999

Citation
M. Bagieu and D. Maystre, "Regularized Waterman and Rayleigh methods: extension to two-dimensional gratings," J. Opt. Soc. Am. A 16, 284-292 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-2-284

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited