Particle on or near an Arbitrary Surface

In the precedent analysis, we considered scattering by a particle situated near a plane surface. The scattering problem of a particle situated in the 

We briefly recall the definitions and the basic properties of scalar and vector plane waves [14]. The scalar plane wave is defined by 

Alternative expressions for the vector plane waves are M (r, K ) = -jCaX (r, Kj,),  

The incident field is a prescribed field, whose sources are assumed to be situated in Dg. This means that in any case, the sources are below the fictitious plane z = and we can represent the external excitation as an integral over up-going vector plane waves 

For r D and 2 2 , we use the plane wave expansion of the Green dyad and the orthogonality properties of the vector plane waves to obtain 

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