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. 21, Iss. 2 — Feb. 1, 2004
  • pp: 199–206

Differential theory: application to highly conducting gratings

Evgeny Popov, Boris Chernov, Michel Nevière, and Nicolas Bonod  »View Author Affiliations


JOSA A, Vol. 21, Issue 2, pp. 199-206 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000199


View Full Text Article

Enhanced HTML    Acrobat PDF (352 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The recently developed fast Fourier factorization method, which has greatly improved the application range of the differential theory of gratings, suffers from numerical instability when applied to metallic gratings with very low losses. This occurs when the real part of the refractive index is small, in particular, smaller than 0.1–0.2, for example, when silver and gold gratings are analyzed in the infrared region. This failure can be attributed to Li’s “inverse rule” [LiL., J. Opt. Soc. Am. A 13, 1870 (1996)] as shown by studying the condition number of matrices that have to be inverted. Two ways of overcoming the difficulty are explored: first, an additional truncation of the matrices containing the coefficients of the differential system, which reduces the numerical problems in some cases, and second, an introduction of lossier material inside the bulk, thus leaving only a thin layer of the highly conducting metal. If the layer is sufficiently thick, this does not change the optical properties of the system but significantly improves the convergence of the differential theory, including the rigorous coupled-wave method, for various types of grating profiles.

© 2004 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1940) Diffraction and gratings : Diffraction
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: June 23, 2003
Revised Manuscript: September 12, 2003
Manuscript Accepted: September 24, 2003
Published: February 1, 2004

Citation
Evgeny Popov, Boris Chernov, Michel Nevière, and Nicolas Bonod, "Differential theory: application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-2-199

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. Figure files 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