RAY OPTICS DETERMINATION OF THE DFB COUPLING COEFFICIENT FOR TRAPEZOIDAL GRATINGS

A ray optics technique is used to derive a closed-form expression for the first-order coupling coefficient of trapezoidal gratings in a gene ric five-layer separate confinement heterostructure distributed feedba ck (DFB) laser configuration for transverse electric (TE) mode. Expres sions for a rectangular grating with the duty cycle of 0.5 and a symme tric triangular grating are also obtained as special cases of our gene ral expressions. Based on the comparison of the coupling coefficient c alculated by the ray optics technique with those calculated by the ext ended additional layer method, we show that the ray optics technique i s very useful to calculate the coupling coefficient for most cases of realistic grating depths and profiles used in multilayer DFB devices w ithout using any numerical techniques.