Fresnel formulae for scattering operators

Abstract

For the scalar problem of mode diffraction onthe abrupt waveguide discontinuity the Fresnel formulae for the reflection and transmission matrix operators are derived using the mode‐marching technique. This generalized form of the matrix model is an immediate corollary of theproposed new statement of the problem. Making use of the energy conservation law in operatorform, the correctness of the obtained Fresnel formulae for the scattering operators is proved analytically. Thus, the developed approach makes it possible to substantiate completely thewidely used mode‐matching technique for the class of diffraction problems under consideration