Application of radiative renormalization to strong-field resonant nonlinear optical interactions

Abstract

The Liouville equation for the density matrix can be recast so that the external-field terms which couple density-matrix elements are second order in the field. This approach is shown to have a profound effect on the steady-state analysis of strong-field resonant nonlinear optical problems. First, in the case where parity or appropriate field restrictions apply, there is a reduction of the number of coupled equations which must be solved by at least a factor of 2. Second, this reformulation naturally leads to radiative-renormalization terms which are directly related to saturation, Stark shifts, and Rabi splittings. We can use this simple formalism to obtain solutions to a number of resonant nonlinear problems including cases where there are two or more strong fields. The renormalization described here is equivalent to a Dyson-equation analysis.