Phase conjugation and adiabatic mode conversion in a driven optical parametric oscillator with orbital angular momentum
We developed a theoretical model for the spatial mode dynamics of an optical parametric oscillator under injection of orbital angular momentum. This process is interpreted in terms of a Poincaré representation of first order spatial modes. The spatial properties of the down-converted fields can be easily understood from their symmetries in this geometric representation. By considering an adiabatic mode conversion of the injected signal, we calculate the evolution of the down-converted beams. A phase conjugation effect is predicted which is a consequence of the symmetry in the Poincaré sphere. We also propose an experiment to measure this effect.