Emphasizing the metamaterial behavior of the Mie scattering coefficients and Debye series for negative refractive index spherical particles

When an arbitrary wave impinges a spherical particle, the scattering fields can be completely described once the Mie scattering coefficients are known. Their associated Debye series are extremely useful in identifying the various contributions to these fields owed to the infinite series of reflections and refractions that the wave suffers once it encounters the surface of the scatterer. A closer analysis reveals that the associated reflection coefficients in the De-bye series does not goes to zero when the matched condition is imposed on a negative refractive index (NRI) particle surrounded by a positive refractive index (PRI) host medium. Here, we propose to explore some physical insights into this problem, rewriting both the Mie scattering coefficients and the Debye series for a lossless NRI spherical particle impinged by a plane wave, emphasizing the metamaterial behaviour of the scattered fields by writing them as a sum of two terms, one corresponding to the PRI analogous and another one that solely appears for a metamaterial particle. This may help in clarifying some previous results reported by the authors concerning the application of such particles in biomedical optics, especially in optical trapping.