## Explaining the success of Kogelnik’s coupled-wave theory by means of perturbation analysis: discussion |

JOSA A, Vol. 31, Issue 6, pp. 1158-1166 (2014)

http://dx.doi.org/10.1364/JOSAA.31.001158

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### Abstract

The problem of diffraction of an electromagnetic wave by a thick hologram grating can be solved by the famous Kogelnik’s coupled-wave theory (CWT) to a very high degree of accuracy. We confirm this finding by comparing the CWT and the exact result for a typical example and propose an explanation in terms of perturbation theory. To this end we formulate the problem of diffraction as a matrix problem following similar well-known approaches, especially rigorous coupled-wave theory (RCWT). We allow for a complex permittivity modulation and a possible phase shift between refractive index and absorption grating and explicitly incorporate appropriate boundary conditions. The problem is solved numerically exact for the specific case of a planar unslanted grating and a set of realistic values of the material’s parameters and experimental conditions. Analogously, the same problem is solved for a two-dimensional truncation of the underlying matrix that would correspond to a CWT approximation but without the usual further approximations. We verify a close coincidence of both results even in the off-Bragg region and explain this result by means of a perturbation analysis of the underlying matrix problem. Moreover, the CWT is found not only to coincide with the perturbational approximation in the in-Bragg and the extreme off-Bragg cases, but also to interpolate between these extremal regimes.

© 2014 Optical Society of America

**OCIS Codes**

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(060.2420) Fiber optics and optical communications : Fibers, polarization-maintaining

(140.3490) Lasers and laser optics : Lasers, distributed-feedback

(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: December 17, 2013

Revised Manuscript: March 9, 2014

Manuscript Accepted: April 1, 2014

Published: May 2, 2014

**Citation**

Heinz-Jürgen Schmidt, Mirco Imlau, and Kay-Michael Voit, "Explaining the success of Kogelnik’s coupled-wave theory by means of perturbation analysis: discussion," J. Opt. Soc. Am. A **31**, 1158-1166 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-6-1158

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