Abundance of invariant equations and properties for wave propagation in a space of arbitrary dimensions

Abstract

This paper continues earlier work on the generalisation of the differential equations governing the propagation of electromagnetic waves in an inhomogeneous ionised plasma in a space of arbitrary (odd) dimensions. Using a convenient definition of curl in such a space, together with appropriate definitions of electric and magnetic field components, Maxwell's first-order equations are defined together with the corresponding second-order wave equation involving the generalised curl curl operator. Various forms of these equations are discussed when a suitable plane of incidence is defined. The property of invariance is introduced, under which various forms of the equations and deductions therefrom are independent of the dimensions of the space in which propagation is defined to occur; both isotropic and anisotropic media are discussed.