Second-Order Sum- and Difference-Frequency Generation via Quadrupole Transitions in Atomic Vapors

Abstract

Atomic vapors have played an important role in recent work on optical mixing. They have been used to generate tunable IR radiation, tunable vacuum UV, and coherent radiation with wavelengths as short as 380 Å. Until recently, the schemes used all involved susceptibilities derived by keeping only the dipole interaction of light with the medium. Recently we reported second order sum-frequency generation in Na vapor.[1] The dipole susceptibility for second order mixing vanishes for a vapor, and a more general type of susceptibility must be considered to describe this process.[2] For example, our Na sum-frequency generation can be described as phase matched emission from oscillating atomic quadrupole moments driven at frequency ω₃ = ω_l + ω₂ by two applied fields, as shown schematically in Fig. 1. The quadrupole moment density is given by:

$$\begin{gathered} \underline{\underline Q} = {\underline{\underline X} ^{(Q)}}:{\underline E _1}{\underline E _2} \hfill \\ {\text{ = }}{{\text{X}}^{(Q)}}{\text{ }}[{\underline E _1}{\underline E _2} + {\underline E _2}{\underline E _1} - \frac{2}{3}\underline{\underline I} ({\underline E _1} \cdot {\underline E _2})]. \hfill \\ \end{gathered} $$

(1)

This work was done with support from the U.S. Energy Research and Development Administration.