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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 4 — Apr. 1, 1994
  • pp: 1307–1320

Propagation through nonuniform grating structures

J. E. Sipe, L. Poladian, and C. Martijn de Sterke  »View Author Affiliations


JOSA A, Vol. 11, Issue 4, pp. 1307-1320 (1994)
http://dx.doi.org/10.1364/JOSAA.11.001307


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Abstract

We consider linear propagation through shallow, nonuniform gratings, such as those written in the core of photosensitive optical fibers. Though, of course, the coupled-mode equations for such gratings are well known, they are often derived heuristically. Here we present a rigorous derivation and include effects that are second order in the grating parameters. While the resulting coupled-mode equations can easily be solved numerically, such a calculation often does not give direct insight into the qualitative nature of the response. Here we present a new way of looking at nonuniform gratings that immediately does yield such insight and, as well, provides a convenient starting point for approximate treatments such as WKB analysis. Our approach, which is completely within the context of coupled-mode theory, makes use of an effective-medium description, in which one replaces the (in general, nonuniform) grating by a medium with a frequency-dependent refractive index distribution but without a grating.

© 1994 Optical Society of America

History
Original Manuscript: April 26, 1993
Revised Manuscript: August 30, 1993
Manuscript Accepted: September 2, 1993
Published: April 1, 1994

Citation
J. E. Sipe, L. Poladian, and C. Martijn de Sterke, "Propagation through nonuniform grating structures," J. Opt. Soc. Am. A 11, 1307-1320 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-4-1307

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