Bragg gratings: impact of apodization lobes and design of a dispersionless optical filter

Several Bragg-grating (BG) filters employing an asymmetrical and multilobe apodization curve, obtained by inverse-problem solving techniques, have been described in literature. To our knowledge, the roles played by the asymmetry of the apodization function and by each apodization lobe have never been determined. In this paper, the role of the lobes and asymmetry is mathematically analyzed, and the validity of the given description is numerically demonstrated. The physical insight gained allows to optimize the filters obtained as solution of the inverse problem.