Optical parametric amplification and oscillation in nonlinear chiral media

We discuss the nonlinear process of optical parametric amplification inside a chiral crystal. We show that circular birefringence, induced by chirality, leads to two different nonlinear processes with different phase-matching conditions that are associated with the opposite states of circular polarizations. A single nonlinear process occurs only when the states of polarization of the incident pump and signal beams are both circular and orthogonal. When these beams are linearly polarized initially, their state of polarization evolves in an elliptical fashion because of the two competing nonlinear processes taking place in parallel. We also discuss the properties of singly and doubly resonant optical parametric oscillators made by placing a chiral nonlinear crystal inside an optical cavity.