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

Abstract

Contributions to the fifth-order nonlinear optical susceptibility {chi}{sup (5)} of a collection of homogeneously broadened two-level atoms that scale as N{sup 2}({gamma}{sub at}{sup (3)}){sup 2} and N{sup 2}|{gamma}{sub at}{sup (3)}|{sup 2}, where {gamma}{sub at}{sup (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>10{sup 15} cm{sup -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.