Optical Third Harmonic Generation in Gases by a Focused Laser Beam

TLDR

Third‑harmonic generation at 2314 Å has been observed in various gases using a focused ruby laser beam at 6943 Å. The study presents a theory of third‑harmonic generation by focused beams to derive atomic or molecular third‑harmonic coefficients from experimental data. The theory incorporates a sign ambiguity that yields two coefficient sets, with one chosen for consistency with literature values, Kerr effect measurements, and theoretical hyperpolarizabilities. Measured third‑harmonic coefficients are 7.3 × 10⁻³⁹ esu/atom for helium, and 8.9, 126, 386, 979, 80, 156, 107 × 10⁻³⁹ esu/atom for Ne, Ar, Kr, Xe, H₂, CO₂, N₂ respectively, with additional data reported for other species.

Abstract

Optical third-harmonic generation at 2314 \AA{} using a focused ruby laser beam (6943 \AA{}) has been observed in a number of gases. A theory of third-harmonic generation by focused beams is presented which is used to derive atomic (or molecular) third-harmonic coefficients from the experimental data. An ambiguity in choice of a sign leads to two alternative sets of coefficients. One set is preferred on the basis of general agreement with data given in or derived from the literature: Theoretical calculations of the third-harmonic coefficients, measurements of the Kerr effect and theoretical dc hyperpolariabilities. For helium the measured absolute value is ${\ensuremath{\chi}}_{\mathrm{He}}=(7\ifmmode\times\else\texttimes\fi{}{3}^{\ifmmode\pm\else\textpm\fi{}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}39}$ esu/atom. For other gases the experimental values of $\ensuremath{\chi}$ in units of ${10}^{\ensuremath{-}39}$ esu/atom and scaled to ${\ensuremath{\chi}}_{\mathrm{He}}=4.0$ (a theoretical value due to Sitz and Yaris which is thought to be reliable to about 1%) are: Ne 8.9 \ifmmode\pm\else\textpm\fi{} 1.5; Ar 126 \ifmmode\pm\else\textpm\fi{} 20; Kr 386 \ifmmode\pm\else\textpm\fi{} 75; Xe 979 \ifmmode\pm\else\textpm\fi{} 150; ${\mathrm{H}}_{2}$ 80 \ifmmode\pm\else\textpm\fi{} 12; C${\mathrm{O}}_{2}$ 156 \ifmmode\pm\else\textpm\fi{} 23; ${\mathrm{N}}_{2}$ 107 \ifmmode\pm\else\textpm\fi{} 11. Some data for ${(\mathrm{C}{\mathrm{H}}_{2})}_{2}$, ${\mathrm{Cl}}_{2}$, ${\mathrm{O}}_{2}$, air, and glass are also presented.