Mie theory-based calculation of pumping enhancing and nano-lasing abilities for a single dielectric sphere

To conquer ohmic losses and enhance pump absorption efficiency of a nanolaser, we theoretically calculate Mie coefficients of a single dielectric sphere and obtain negative effective permittivity and permeability simultaneously at frequencies around 153 THz under a plane wave excitation with the expected negative Goos-Hänchen effect, thus promoting the pump absorption efficiency in a laser system. Meanwhile, a magnetic lasing mode is demonstrated in the dielectric sphere with an energy vortex loop, providing a possible stopped light feedback mechanism and validating the lasing ability of a single dielectric nanoparticle. Finally, according to Mie resonance, we make an analogue between the lasing modes of the dielectric and metallic nanoparticles.