TWO DIMENSIONAL GREEN'S FUNCTION FOR A HALF SPACE GEOMETRY DUE TO TWO DIFFERENT NON-INTEGER DIMENSIONAL SPACES

A two-dimensional Green’s function for a half space geometry, comprising planar interface only due to two different non-integer dimensional spaces, has been derived. Medium hosting the time harmonic electric line source and planar interface is homogeneous and isotropic. Radiated field is written in terms of unknown spectrum of plane waves. Unknown spectrum functions are determined using the related boundary conditions. It has been shown that although wavenumbers of two half spaces are same, due to difference of dimensions of the two half spaces, reflection and transmission occur. When dimensions of both half spaces are taken equal to two, derived expressions yield field radiated by a line source in an unbounded homogeneous medium with integer dimensional space.