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 | Enthalten in: | JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION | Band: | 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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geprüft am 06.06.2024