Abstract

A model with two roughness levels for the diffraction of a plane wave by a metallic grating with periodic imperfections is presented. The grating surface is the sum of a reference profile and a perturbation profile. First, the diffraction by the reference grating is treated. At this stage the Chandezon method is used. This method leads to the resolution of eigenvalue systems. Each eigensolution defines an elementary wave function that characterizes a propagating or an evanescent wave. Second, the periodic errors are taken into account and a Rayleigh hypothesis is expressed: Everywhere in space the diffracted fields can be written as a linear combination of reference wave functions. The boundary conditions on the perturbed grating allow the diffraction amplitudes to be determined and therefore lead to the energetic magnitudes (efficiencies). The domain of analytical validity of this hypothesis is not defined. In fact, this method is considered to be an approximation. The proposed numerical study leads to some utilization rules. With a plane as the reference surface, the electromagnetic fields are given by classical Rayleigh expansions. Here the reference profile is a grating, hence the term generalized Rayleigh expansion.

© 1998 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings

Song Peng and G. Michael Morris
J. Opt. Soc. Am. A 12(5) 1087-1096 (1995)

Rigorous and efficient grating-analysis method made easy for optical engineers

Lifeng Li, Jean Chandezon, Gérard Granet, and Jean-Pierre Plumey
Appl. Opt. 38(2) 304-313 (1999)

Reflection by a grating: Rayleigh methods

P. M. van den Berg
J. Opt. Soc. Am. 71(10) 1224-1229 (1981)

References

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
Login to access OSA Member Subscription

Cited By

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
Login to access OSA Member Subscription

Figures (14)

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
Login to access OSA Member Subscription

Tables (5)

You do not have subscription access to this journal. Article tables 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
Login to access OSA Member Subscription

Equations (78)

You do not have subscription access to this journal. Equations 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
Login to access OSA Member Subscription

Metrics

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
Login to access OSA Member Subscription