A SYMMETRY ANALYSIS IN THE MIXED GRATING GEOMETRY OF DEGENERATE 4-WAVE-MIXING IN SATURABLE-GAIN MEDIA

The mixed grating degenerate four-wave mixing equations in saturable g ain media are presented in the transient regime. It is shown that they cannot be obtained from the superposition of the single grating equat ions. SO(4) and Sp(2) are respectively identified as the symmetry grou ps acting upon the transmission and reflection grating process, where conserved quantities are shown to arise naturally. No conserved quanti ties were found for the mixed grating case.