LOCAL GAUGE-INVARIANCE OF THE 2-BEAM COUPLING EQUATIONS

An analytical comparison between the exact model of two-wave mixing in thin nonlinear local response absorbing media and a simplified theory is presented. The approach adopted here consists of studying the dynamical interaction of four waves: the two incident beams and the two main diffracted orders. The simplified model assumes energy conservation in a weakly absorbing medium. It is demonstrated that the two models give exactly the same results for any absorption coefficient. It is shown that the simplified model is correct in weakly or highly absorbing media. This is due to a local gauge invariance of the coupled equations.