On a General Class of Scattering Problems

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Abstract
This paper considers a class of scattering problems corresponding to a wave of propagation number K1 exciting an object characterized by K2, and giving rise to a scattered field of propagation number K3. In addition, the boundary conditions on the wave functions and their normal derivatives at the object involve three sets of two parameters associated with the three propagation numbers. This generalized class of scattering problems can be treated by conventional analytical procedures (as for the usual problems K1 = K3, etc.) to obtain series solutions for symmetrical shapes and Green's function representations for general shapes. The numerators of the new series coefficients differ from the usual ones, and the Green's function representation has an additional inhomogeneous term, i.e., a volume integral containing the source term in its kernel. These results are applied for special cases to obtain explicit approximations for the ``two‐external‐space'' scattering amplitude g(K3, K1) (e.g., for small spheres with three sets of ε's and μ's, and for large tenuous scatterers).

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