Azimuthal eigenmodes at strongly non-degenerate parametric down-conversion

Quantum-optical technologies based on parametric light down-conversion are not yet applied in the terahertz frequency range. This is owing to the complexity of detecting single photons in the terahertz frequency range and the strong entanglement of modes of optical-terahertz biphotons. This study investigates the angular structure of scattered radiation generated by strongly non-degenerate parametric down-conversion when the frequency of the idler radiation does not exceed several terahertz. We demonstrate that under certain approximations, it is possible to obtain azimuthal eigenmodes for the nonlinear-interaction operator. The solution of the evolution equations for the field operators in these eigenmodes has the form of the Bogolyubov transformation, which allows a scattering matrix to be obtained for arbitrary values of the parametric gain. This scattering matrix describes both the production of biphoton pairs and the generation of intense fluxes of correlated optical-terahertz fields that form a macroscopic quantum state of radiation in two spectral ranges.