Analysing distributed feedback waveguides

A method for analysing distributed feedback waveguides with arbitrary refractive index profiles is reported. The method considers a waveguide as a number of segments within which the reflection is weak, and thus the relevant transmission loss and multiple reflections can be neglected. By introducing a concept of reflective density formulas are derived for calculating the reflection and transmission coefficients and therefore the transfer matrix of an individual waveguide segment. The global reflection and transmission characteristics of the waveguide are then obtained by multiplying transfer matrices of all the waveguide segments together. The proposed method shows better accuracy than the coupled-mode method and requires less computation time than the effective-index method. The limitation of the coupled-mode method is shown both numerically and analytically for the first time and it is demonstrated that the coupled-mode method is only valid for analysing long Bragg gratings with particular initial phases