Technical memorandum. Cutoff frequencies of waveguides of arbitrary cross-section: optimisation of kohn-kato bounds

Abstract

It is shown that the results obtained by the Kohn-Kato enclosure theorem in the case of hollow-piped waveguides of complicated boundary shape can be optimised if an exponential unknown parameter is included in the co-ordinate functions which satisfy identically the governing boundary conditions, once the given domain is transformed into a unit circle.