Four-photon mixing and squeezed states in a resonator

The problems of eigenfunctions and eigenvalues of the modes in a confocal resonator, where counterpropagating four-photon mixing takes place as a result of planar pumping, is solved at the quantum level. It is shown that the quadrature components of the waves generated in such a resonator have different losses and an analytical solution is obtained for these waves. This provides an opportunity to describe correctly the process of formation of squeezed states allowing for the spatial configuration of the waves interacting in such a resonator.