Constitutive relations in classical optics in terms of geometric algebra

Abstract

To have a closed system, the Maxwell electromagnetic equations should be supplemented by constitutive relations which describe medium properties and connect primary fields (E, B) with secondary ones (D, H). J.W. Gibbs and O. Heaviside introduced the basis vectors {i, j, k} to represent the fields and constitutive relations in the three-dimensional vectorial space. In this paper the constitutive relations are presented in a form of Cl_3,0 algebra which describes the vector space by three basis vectors {σ₁, σ₂, σ₃} that satisfy Pauli commutation relations. It is shown that the classification of electromagnetic wave propagation phenomena with the help of constitutive relations in this case comes from the structure of Cl_3,0 itself. Concrete expressions for classical constitutive relations are presented including electromagnetic wave propagation in a moving dielectric.