  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.
