Green´s function for a biaxial medium using a four-vector formalism

The rapid prototyping of antennas and complex media propagation environments has been aided by recent advances in material fabrication capabilities; such as, conductive-inkjet and 3D printing. These advances have prompted the need for alternative mathematical methods of analysis, which more easily accommodate anisotropic and bianisotropic media while providing greater physical insight. For example, casting Maxwell´s equations into a compact six-vector formalism aides in the mathematical manipulation, and subsequent solution, of problems involving complex media (I.V. Lindell, A.H. Sihvola, and K. Suchy, J. of Electrom. Waves and Appl., 9, 7/8, 887–903, 1955). This formulation accommodates fully-populated material tensors (i.e., material tensors where all elements are non-zero); however, the analysis does lead to a block 3×3 matrix that requires inversion.