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 extended Mie theory, we analytically derive equivalent permittivity of polar dielectric nanospheres. Then, establish conditions surface phonon amplification by stimulated emission radiation core-gain shell nanoparticle laser based polaritons. The results show that nonlocality dramatically affects selection gain medium lasing condition, which also new degree freedom in modulation medium. validity derived is demonstrated comparing obtained extinction spectra choice threshold with those under theory. Our research may provide practical tool designing polariton lasers.