Analytical formulas for the synthesis of optical-waveguide filters having arbitrary spectral-response characteristics are derived from coupled-mode formalism. Use of these general formulas is illustrated by design of several filters, one of which is a linear power discriminator. The synthesis yields the functional dependence of spatial-perturbation period on the distance along the direction of wave propagation in the waveguide filter. The coupled-mode equations for the functional perturbation forms as determined by the synthesis process were solved numerically to find the actual response characteristics of the filter designs. Excellent agreement was found between the desired characteristics and those of the synthesized filters.
Masanori Matsuhara, K. O. Hill, and A. Watanabe, "Optical-waveguide filters: Synthesis," J. Opt. Soc. Am. 65, 804-809 (1975)