2.4.1 Introduction

Curvilinear boundaries of acoustic or electromagnetic objects carry specific waves. On convex surfaces these are creeping waves and on concave surfaces these are whispering gallery waves. Penetrable surfaces in some cases can be described with the Leontovich impedance boundary condition. Here we examine creeping and whispering gallery waves running along curvilinear interfaces of acoustic and electromagnetic media. Depending on the parameters of that media and depending on the type of considered waves one can or cannot use the Leontovich impedance boundary condition.

We discover that if the contrast of parameters in the two media is sufficiently large, then waves of creeping and of whispering gallery types are possible. Both can be simulated by an impedance boundary condition. If the contrast is small, then waves appear of mixed type. Such waves do not satisfy an impedance boundary condition, their attenuation parameters are subject to a more complicated dispersion equation.

We examine the excitation of interface waves both for large and small contrast and found that waves of creeping type are well excited while excitation coefficients for whispering gallery waves are exponentially small. Original papers are [18,19].

2.4.2 Scalar waves

2.4.2.1 The problem formulation and the Ansatz

Let ? denote the transparent body. The creeping waves on its surface satisfy the Helmholtz equation

(2.123)

The index is N=1 outside ?. Inside ? it is a function of coordinates. We consider N depending only on the external normal