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.