Diffracted and Head Waves Associated With Waves on Nonseparable Surfaces

A theory is presented for computing waves radiated from waves on a smooth surface. With the assumption that attenuation of the surface wave is due only to radiation and not to dissipation in the surface material, the radiation coe cient is derived in terms of the attenuation factor. The excitation coe cient is determined by the reciprocity condition. Formulas for the shape and the spreading of the radiated wave are derived, and some sample calculations are presented. An investigation of resonant phase matching for nonseparable surfaces is presented with a sample calculation. A discussion of how such calculations might be related to resonant frequencies of nonseparable thin shell structures is included. A description is given of nonseparable surfaces that can be modeled in the vector form that facilitates use of the appropriate formulas of di erential geometry.