Symmetry relations in the generalized Lorenz-Mie theory for lossless negative refractive index media

•A theoretical analysis of the GLMT for NRI media and scatterers is proposed.•It relies on all four combinations of refractive indices between particle and medium.•Symmetry relations are established from the usual problem with positive indices only.•Symmetry relations are given for a few physical parameters.

In this paper we present a theoretical analysis of the generalized Lorenz-Mie theory for negative refractive index (NRI) media and spherical scatterers, extending the well-known concepts and definitions found in the literature involving dielectric or positive refractive index (PRI) particles. The consequences of a negative phase velocity and an anti-parallelism of the wave vector with respect to the Poynting vector are investigated and interpreted in this framework and, together with the symmetries found for the beam-shape coefficients when compared to the conventional PRI case, it is shown that the description of plane waves, Gaussian beams and, more generally, on-axis azimuthally symmetric waves along a NRI medium, their fields and all physical properties can be conveniently correlated with that of dielectric media once the electromagnetic response functions are replaced by their corresponding dielectric counterparts.