Second-Order Bragg Interaction in Thin Film Devices

Second-order grating film devices have important applications in fiber optic communication systems and integrated optics. The characteristics of the second-order Bragg interaction are investigated for the transverse electric (TE) and the transverse magnetic (TM) modes of an active corrugated dielectric film waveguide with different passive dielectrics for the cover and the substrate. Using a singular perturbation technique, four canonical equations describing the behavior of the interaction among two guided waves propagating in opposite directions in the film and two free waves, incident and radiated, one each in the cover and the substrate, are deduced. The coupling coefficients, satisfying all the requirements imposed by symmetry, reciprocity, and the power conservation principle, are obtained in terms of the physical parameters of the corrugated dielectric waveguide. From the solution of the canonical equations subject to the appropriate boundary conditions, the characteristics of the frequency-selective reflector (filter), output coupler, input coupler, and the distributed feedback (DFB) laser are obtained. To overcome the drawbacks of the single grating devices (low efficiencies due to the excessive radiation loss in the substrate), the double grating scheme is proposed. The characteristics of thin film devices are determined as functions of the two important parameters of the double grating structures, namely, the ratio of the relative amplitudes and the lateral phase shift of the two gratings. For proper choices of the parameters of the double grating film waveguide, highly efficient thin film devices with controllable characteristics are obtained. The characteristics of the second-order double grating passive and active devices supporting the fundamental TM mode are obtained and compared correspondingly with those for the TE mode. It is shown that due to a weaker interaction of the guided and the radiated free waves in the second-order Bragg interaction for the TM mode, the distributed couplers supporting the fundamental TE mode have more desirable features. Selected numerical results are presented to illustrate the important characteristics of the various thin film devices whose operations are based on the second-order Bragg interaction.