ИСТИНА

For a strongly non-degenerate parametric down-conversion, when the frequency of idler photons lies in the terahertz range, the angular width of phase matching is tens of degrees. In this case, the tensor character of the nonlinear crystal's susceptibility is important, and the parametric gain significantly depends on the scattering angles. In this work, we consider the decomposition of the biphoton field into the Schmidt azimuthal modes, taking this angular dependence into account. It is shown that the operator of nonlinear interaction of the angular modes of signal and idler radiation in the basis of the Fourier modes has a tri-diagonal matrix. The diagonalization of the scattering matrix obtained by solving the equations for field operators allows one to find Schmidt modes for any value of the parametric gain.