Analysis of mode conversion in waveguide transition sections with surface impedance boundaries applied to VLF radio propagation

First- and second-order correction terms are derived for the reflection and transmission scattering coefficients for a step-type transition between two uniform waveguides with surface impedance boundaries. This analysis yields rigorous expressions for the differential transmission and reflection coefficients defined for an infinitesimal step transition. These coefficients are essential in the derivation of the coupled differential equations for the wave amplitudes in a transition section of gradually varying height.