Analysing distributed feedback waveguides

A method for analysing distributed feedback waveguides with arbitrary refra ctive index profiles is reported. The method considers a waveguide as a num ber 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 r eflection and transmission coefficients and therefore the transfer matrix o f an individual waveguide segment. The global reflection and transmission c haracteristics of the waveguide are then obtained by multiplying transfer m atrices of all the waveguide segments together. The proposed method shows b etter accuracy than the coupled-mode method and requires less computation t ime than the effective-index method. The limitation of the coupled-mode met hod 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.