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

Contributions to the fifth-order nonlinear optical susceptibility 5 of a collection of homogeneously broadened two-level atoms that scale as N2 at 3 2 and N2 at 3 2, where at 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-MaxwellBloch 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 1015 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.