Theory of quasi-phase matching parametric interaction of optical waves in chiral structures considering pump...

We present a theoretical study of three-wave parametric interaction in a chiral medium formed by a periodic sequence of alternating enantiomers with opposite signs of quadratic susceptibility. Both co-propagating and counter-propagating wave configurations are considered within the quasi-phase-matching framework, with explicit inclusion of pump depletion. Analytical expressions describing the interaction are derived and analyzed numerically. Threshold pump amplitudes are obtained for parametric amplification of both the forward signal wave and the backward idler wave. A representative numerical evaluation is carried out for a chiral helicenebisquinone-based film. The dependence of the signal intensities (Is±) on the length of the nonlinear medium is examined to illustrate simultaneous frequency conversion of left- and right-circularly polarized components. The evolution of the signal intensity (Is+) is compared for co-and counter-propagating regimes. The results show that counter-propagating interaction provides higher efficiency. In this case, losses of the backward wave can be partially compensated by those of the forward waves. Furthermore, counter-propagation leads to increased electric-dipole phase mismatch and a corresponding reduction of the coherence length. This effect is important for the design of chiral nonlinear structures. The results obtained provide guidance for engineering periodically structured chiral media enabling efficient quasi-phase-matched frequency conversion and parametric amplification.