Theory of symmetry in optical filter responses

Abstract

The symmetry characteristics in various optical waveguide filters that employ the Bragg-scattering mechanism are generalized in terms of scattering coefficients and the coupling potential. A formalism known as the Zakharov–Shabat system of coupled-mode equations is employed, along with the associate Gel’fand–Levitan–Marchenko inverse-scattering formalism. The resulting symmetry characteristics between the coupling potential and the filter spectral response resemble the Fourier relationship. It is found, however, that complications exist because there are two scattering coefficients involved. Common variations of perturbation are then associated with special symmetry characteristics in the two scattering coefficients. The misinterpretation of physical inversion in the literature is also corrected.