Frequency Mixing in the Scattering of Light by Harmonically Bound Electrons

Abstract

CLASSICAL electrodynamics predicts harmonic generation^1–3 and frequency mixing⁴ in the scattering of light by free electrons. Quantum theory confirms these results^3–7. Several authors (for example, refs. 8 and 9) have used the classical anharmonic oscillator model to give a qualitative account of non-linear phenomena in dielectrics. In the absence of an anharmonic restoring force, non-linear effects, up to the lowest order in external electric field, are in general quite small¹⁰. Calculations¹¹ stress this point in the case of second harmonic generation in the scattering of light. Here we extend these calculations to study the scattering of light when the incident beam contains two frequencies. As expected, we find that the combination frequencies also exist in the scattered radiation besides the fundamentals and their harmonics, and that the non-linear cross-sections become large for resonant denominators. Further, a proper choice of the two incident frequencies can yield an appreciable increase in the non-linear scattering cross-sections even without any precise resonance.