Thin film devices based on second order Bragg interaction

Abstract

For an active dielectric film waveguide with different passive dielectrics for the cover and the substrate and with periodic corrugations on the upper surface, the characteristics of the second order Bragg interaction are investigated for the transverse electric mode with reference to such applications as frequency-selective reflector, couplers, and distributed feedback laser. Four canonical equations that are valid for a distributed coupler with two guided waves and two free waves, incident and radiated, one each in the cover and the substrate, are deduced systematically. The coupling coefficients are shown to satisfy all the requirements imposed by symmetry, reciprocity, and power conservation. From the solution of the canonical equations with the appropriate terminal conditions, the characteristics of the devices are obtained. The design parameters leading to the optimum performance of these devices are determined. For the distributed feedback laser, the frequencies of oscillation, the corresponding gain thresholds, and the relative power distributions in the two guided and the two radiated waves are obtained for the first few modes in the neighborhood of the second order Bragg frequency. The modifications of the characteristics introduced by the presence of a phase shifting section on the grating structure are analyzed for symmetrical and asymmetrical grating configurations. The effects of radiation and the phase shifting section on the separation of the gain thresholds of the neighboring lower order laser modes are investigated with a view to increasing the possibility of a single mode oscillation. Selected numerical results are presented to illustrate the important characteristics of the various thin film devices based on the second-order Bragg interaction.