On the transfer matrix method for distributed-feedback waveguide devices

The local normal mode transfer matrix method (TMM) is introduced and developed for the rigorous analysis of distributed feedback (DFB) waveguide devices. This approach is valid for relatively large grating depth and index difference and applicable to both TE and TM modes. Remarkably simple analytical expressions for the coupling coefficients and the power reflectivity are derived and the correspondence between the transfer matrix method and the coupled-mode theory (CMT) is established. Comparisons with the coupled-mode theory have been carried out and some salient features of the DFB structures are discussed. The natural links among the transfer matrix method, the Bloch wave approach, and the coupled-mode theory are also revealed and discussed. The analysis demonstrates unambiguously the power of the transfer matrix method and its overall advantages in terms of not only accuracy and scope of validity but also simplicity and insightfulness