Abstract:

Chirped gratings, resulting from natural or intentional variations in the properties and geometries of an otherwise periodic structure, have been extensively treated in the literature. Analyses of chirped gratings are usually based on the coupled-mode (CM) theory, first proposed by Kogelnik. The direct numerical integration of the CM equations along chirped gratings, as suggested by Kogelnik, has been shown to agree well with experimental results of mildly chirped gratings. Hong et al. have developed asymptotic approximations of the CM equations for linearly chirped gratings. Fukuzawa and Nakamura and Livanos et al. have suggested a chirped grating reflectivity calculation method, which is based on the approximate form of the CM theory. In the approximate form, use is made of an "effective" grating length-defined as the distance over which significant reflectance occurs. Their approximation was found to agree reasonably well with the results of the direct CM numerical integration.

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