Factorization of Helmholtz Determinant Operator for Decomposable Bi-Anisotropic Media

Abstract

Conditions for the most general bi-anisotropic media in which the electromagnetic field can be decomposed in two components with respect to two six-vectors were recently derived by these authors. In the present paper it is shown that the fourth-order Helmholtz determinant operator, which appears in the basic scalar Helmholtz equation for electromagnetic fields, can be expressed in factorized form as a product of two second-order operators. These two operators are shown to correspond to the decomposition of the field. Finally, because of the factorization, the scalar Green function corresponding to the Helmholtz determinant is shown to take a numerically tractable form in terms of two finite integrations.