Efficiency of multi-wave mixing in a sphere

We consider nonlinear muti-wave mixing in a sphere. We compare the efficiency of wave mixing in a sphere with the efficiency in a bulk or in the slab where, as well-known, the phase-matching plays an important role. We have found the optimal conditions for nonlinear generation in a sphere. The obtained results can be applied to coherent Raman microscopy and allow us to maximize the signal for arbitrary shpae of nanoparticles.