Third-order sum-frequency generation in droplets

Abstract

A steady-state model of third-order sum-frequency generation (TSFG) in droplets is presented. A third-order polarization is generated in a droplet by stimulated Raman scattering (SRS) or by SRS in combination with fields at the incident laser frequency. This third-order polarization radiates inside the sphere as described in the general model of H. Chew et all1 The frequency of the third-order polarization is only rarely within a few linewidths of a high-Q output morphology-dependent resonance (MDR). The TSFG intensity is proportional to the spatial and frequency overlap between the generating polarization and the fields of the output modes. For a distribution of particle sizes, the probability of detecting TSFG increases with the density of output MDRs. Numerical results are presented for the specific case of the generation of the third harmonic of the first-order SRS. Although the comparison with experiment is only qualitative, the theory is consistent with experimental observations that TSFG in droplets is detectable at only a small fraction of droplet sizes and is 4 to 6 orders of magnitude weaker than SRS. New high-and low-resolution experimental observations are discussed.