Cascaded nonlinearity caused by local-field effects in the two-level atom

Contributions to the fifth-order nonlinear optical susceptibility χ⁽⁵⁾ of a collection of homogeneously broadened two-level atoms that scale as N²(γₐₜ⁽³⁾)² and N²γₐₜ⁽³⁾², where γₐₜ⁽³⁾ 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>10¹⁵0.3em0excm^-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.