Filter Response of Nonuniform Almost-Periodic Structures

Recent papers 1,2 have reported the fabrication of wavelength-selective filters in the form of corrugated, thin-film, optical waveguides and have described the evaluation of the filter characteristics by means of tunable dye lasers. These papers include a numerical comparison of experimental and theoretical results on the nature of the filter response caused by a gradual tapering in the corrugation or grating strength (which we call "tapers"), or by a gradual variation of the effective grating period (called "chirping"). The present paper describes in some detail the theory by which these numerical results were obtained; it offers a discussion of the general characteristics of nonuniform grating filters, such as their scaling properties and the symmetry of the filter response; and it provides a more complete collection of plots representing numerical results for linear and quadratic tapers in the coupling strengths as well as linear and quadratic chirps in the effective grating period. Periodic waveguides serve as band-rejection filters with a center frequencj' determined by the Bragg condition K = 20(«), 109 (1)