A variational expression for the terminal admittance of a semi-infinite dielectric rod

The reflection that the abrupt termination of a semi-infinite circular dielectric rod produces on the
TM_{0.1}
surface wave is determined here by calculating the terminal admittance of the surface wave at the end of the rod. The semi-infinite dielectric rod is regarded as an open waveguide partially filled with dielectric. The half space at the end of the rod is analyzed as a homogeneous open waveguide. The complete sets of proper and improper eigenfunctions are found for both waveguides and used to represent the transversal fields. Finally, a variational expression is set up for the admittance and an approximate value is obtained using as trial field the pure
TM_{0.1}
surface wave.