Contributions to the fifth-order nonlinear optical susceptibility ${\chi }^{\left(5\right)}$ of a collection of homogeneously broadened two-level atoms that scale as $N^2{\left({\gamma }_{\mathrm{at}}^{\left(3\right)}\right)}^2$ and $N^2{\mid {\gamma }_{\mathrm{at}}^{\left(3\right)}\mid }^2$, where ${\gamma }_{\mathrm{at}}^{\left(3\right)}$ is the lower-order atomic hyperpolarizability and $N$ is the atomic number density, are predicted theoretically. These “cascaded” contributions are a consequence of local-field effects. We determine them from a fifth-order solution of the Lorentz-Maxwell-Bloch equations. They are missing from a straightforward generalization of Bloembergen’s result for the local field correction to the second order nonlinearity, but are recovered by a careful application of his general approach. We find that at high atomic densities $(N>{10}^{15}{\mathrm{cm}}^{-3})$ the value of the cascaded third-order contribution can be as large as the “direct” fifth-order term in the expression for the fifth-order susceptibility.

• Received 8 August 2007

DOI:https://doi.org/10.1103/PhysRevA.76.063806