Exact Scattering Theory for Objects with Non-Mode MatchingBoundaries.

摘要

The exact theory for scattering of waves by objects with Non-Mode Matching Boundaries (NMMB), is developed. A NMMB is a boundary such that a mode of the field outside the object does not "match" with a mode of the field inside the scattering object. "Matching" means that field modes outside- and inside the object have the same values at the boundary of the scatterer. This property e.g. is valid in the case of scattering by a dielectric slab with constant refractive index. An example of a NMMB object is a halve infinite horizontal stack of N dielectric layers in free space. The theory is based on a new set of modes into which the fields inside and outside the boundary are expanded. Each field mode of this set outside the object couples to only one field mode of this set inside the medium.Exact Scattering and non-standard BoundariesThe analysis of scattering- and boundary value problems is a very important part of physics and has been extensively explored since the 18th century [1-4]. Unfortunately, no simple exact scattering theory exists for scattering by media with so-called Non-Mode Matching boundaries (NMMB). By this we mean the following: The "simple" exactly solvable boundary value problems in mathematical physics all share one property: The modes outside- and inside a scatterer match at its boundary.