Equivalent permittivity and design of nanoparticle lasers for nonlocal polar dielectrics

Polar dielectrics are being actively investigated as a promising platform for mid-infrared nanophotonics, and it indicates dramatic nonlocal phenomena at the nanoscale. Based on full-wave nonlocal extended Mie theory, we analytically derive the equivalent permittivity of nonlocal polar dielectric nanospheres. Then, we establish the conditions for surface phonon amplification by stimulated emission of radiation of the nonlocal polar dielectric core-gain shell nanoparticle laser based on phonon polaritons. The results show that the nonlocality dramatically affects the selection of the gain medium for lasing condition, which also indicates a new degree of freedom in the modulation of the gain medium. The validity of the derived equivalent permittivity is demonstrated by comparing the obtained extinction spectra and the choice of the threshold gain with those under nonlocal extended Mie theory. Our research may provide a practical tool for designing phonon polariton nanoparticle lasers.