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

Autor(en): Schmidt, Heinz-Juergen
Imlau, Mirco 
Voit, Kay-Michael
Stichwörter: DIFFRACTION; ELECTROOPTIC CRYSTALS; Optics; PHASE; STORAGE; THICK HOLOGRAM GRATINGS
Erscheinungsdatum: 2014
Herausgeber: OPTICAL SOC AMER
Journal: JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION
Volumen: 31
Ausgabe: 6
Startseite: 1158
Seitenende: 1166
Zusammenfassung: 
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. (C) 2014 Optical Society of America
ISSN: 10847529
DOI: 10.1364/JOSAA.31.001158

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