Third-order sum-frequency generation in droplets: model with numerical results for third-harmonic generation

Abstract

A steady-state model of third-order sum-frequency generation (TSFG) in liquid 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 Chew et al. [ Phys. Rev. A19, 396 ( 1976)]. The frequency of the third-order polarization will only rarely be 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 MDR’s. 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 the droplet sizes and is 4–6 orders of magnitude weaker than SRS.