Generalized decomposition of electromagnetic fields in bi-anisotropic media

TE/TM decomposition of electromagnetic fields, with respect to one special direction in space, is well known to be valid for fields in isotropic and uniaxially anisotropic media. The theory was recently generalized to bi-anisotropic media by defining the decomposition for linear combinations of electric and magnetic fields with respect to two vectors. In the present paper, the theory is further generalized by defining the decomposition with respect to four vectors (two six-vectors), which restrict the polarizations of the decomposed electromagnetic fields. It is shown that the class of bi-anisotropic media in which electromagnetic fields can be decomposed into two independent electromagnetic fields (a-field and b-field) is more general than in all previous decomposition theories, It is also shown that the decomposed a- and b-fields see the original bi-anisotropic medium as simpler equivalent ones (a- and b-media) for which analytic Green dyadics were previously derived by these authors.