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

Contributions to the fifth-order nonlinear optical susceptibility chi((5)) of a collection of homogeneously broadened two-level atoms that scale as N-2(gamma((3))(at))(2) and N-2 vertical bar gamma((3))(at)vertical bar(2), where gamma((3))(at) 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) 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.