Design Method for Optical Waveguide Filters Having Corrugation Structures by Corrugation Width Modulation

A method to design a corrugated optical waveguide filter by modulating the corrugation width profile is proposed. This method is based on combined applications of the Fourier transformation and the F-matrix formalism. The method achieves the spatial profile of the corrugation width required to design a filter with any specified spectral profile of the reflection coefficient. The idea of the technique is that the spatial variation of the effective refractive index can be transformed, with the help of the F-matrix formalism, to variation of the corrugation width while maintaining a constant amplitude of the refractive index variation. Two examples are given applying the technique to the design of optical waveguide filters with reflectivity profiles of two- and four-rejection bands.