Formulation of differential transfer matrix method in cylindrical geometry

Abstract

Transfer and scattering matrix methods are widely in use for description of the propagation of waves in multilayered media. When the profile of refractive index is continuous, however, a modified formulation of transfer matrices does exist, which provides a complete analytical solution of the wave phenomena in such structures. Previously reported variations of the so-called Differential Transfer Matrix Method (DTMM) had been limited to Cartesian geometry where layered media form one-dimensional structures and plane waves are used as basis functions. In this work, we extend the formalism to cylindrical geometry with radial symmetry, in which Bessel functions need to be employed as basis functions. Hence, complete analytical formulation of the DTMM under radial and axial symmetry is described and derived. This work could have applications in the analysis of propagation in optical fibers and motion of electrons in nanowires and nanotubes.