Nonlinear generation of multipolar radiation in Mie-resonant nanoparticles

We study multipolar composition of the second harmonic generation from Mie-resonant dielectric nanoparticles made of noncentrosymmetric materials. With the use of the Lorentz lemma, we analytically derive excitation coefficients of the nonlinearly generated multipoles in spherical nanoparticles optically driven by the magnetic dipole mode. Multipolar radiation properties are then validated in the direct full-wave numerical calculations. The developed description can be useful for design of nonlinear optical nanoantennas.