Frequency Dependence of the Higher Susceptibilities

Abstract

Expressions for the susceptibilities appropriate to third harmonic generation, second harmonic generation, and the induced Kerr effect are derived using time‐ordered time‐dependent pertubation theory. These expressions are used to calculate the susceptibilities for atomic hydrogen and helium. Using a six‐pole trial function we obtain for He $$\begin{array}{cc}\text{λ\hspace{0.17em}=\hspace{0.17em}6943 Å,}& {\chi }_{\mathrm{zzzz}}\text{(−\hspace{0.17em}3ω; ω, ω, ω)\hspace{0.17em}=\hspace{0.17em}47.7}\mathrm{a.u.};\\ \text{λ\hspace{0.17em}=\hspace{0.17em}6943 Å,}& {\chi }_{\mathrm{zzzz}}\text{(−\hspace{0.17em}2ω; 0, ω, ω)\hspace{0.17em}=\hspace{0.17em}45.2}\mathrm{a.u.};\\ \text{λ\hspace{0.17em}=\hspace{0.17em}6328 Å,}& {\chi }_{\mathrm{zzzz}}\text{(−\hspace{0.17em}ω, 0, 0, ω)\hspace{0.17em}=\hspace{0.17em}43.6}\mathrm{a.u.};\end{array}$$ ${\chi }_{\mathrm{zzzz}}\text{(0; 0, 0, 0)\hspace{0.17em}=\hspace{0.17em}42.6}\mathrm{a.u.}$ The experimental value of ${\chi }_{\mathrm{zzzz}}\text{(−\hspace{0.17em}ω; 0, 0, ω)}$ obtained from Kerr‐effect measurements is 51.6 ± 8.6 a.u. The calculations are checked by the use of a number of sum rules with the largest disagreement being 0.05%.