Combination of characteristic Green´s function technique and rational function fitting method for computation of modal reflectivity at the optical waveguide end-facet

A novel method for computation of modal reflectivity at optical waveguide end-facet is presented. The method is based on the characteristic Green´s function (CGF) technique. Using separability assumption of the structure and rational function fitting method (RFFM), a closed-form field expression is derived for optical planar waveguide. The uniform derived expression consists of discrete and continuous spectrum contributions which denotes guided and radiation modes effects respectively. An optimization problem is then defined to calculate the exact reflection coefficients at the end-facet for all extracted poles obtained from rational function fitting step. The proposed CGF-RFFM-optimization offers superior exactness in comparison with the previous reported CGF-complex images (CI) technique due to contribution of all components of field in the optimization problem. The main advantage of the proposed method lies in its simple implementation as well as precision for any refractive index contrast. Excellent numerical agreements with rigorous methods are shown in several examples.