  As the rapid development of nonlinear optics, the enhancement of optical
third harmonic generation becomes a pop research realm in the fields of
physics, chemistry, biology, materials science, information science and other
fields. In this letter, theoretical analysis on double resonance situation in
metallic core-shell nanostructure is performed in order to optimize the
efficiency of third harmonic generation. As plenty of cavity modes ranging from
visible area to near infrared can be excited efficiently in core-shell
nanospheres, kinds of double resonant conditions can be formed by matching two
different multipolar cavity modes. Numerical simulations show that the third
harmonic generation (THG) intensity in the far field can be enhanced remarkably
when the THG signal couples well with the high order cavity mode. More
importantly, THG efficiency is optimum from the cavity on double resonant
conditions coupling two modes with the same order. The THG intensity differs up
to 3 magnitudes on this condition. Subsequent theoretical analysis indicates
that changing third-order nonlinear susceptibility of the metal shell while
keeping that of the core fixed has almost no effect on THG efficiency. This
finding about optimal double resonance has an appreciable effect on optimizing
THG in spherical cavity structures.
