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Correlated pairs of optical and terahertz-frequency photons can be generated via the spontaneous parametric down-conversion (SPDC) process in the strongly frequency non-degenerate regime. We report results of theoretical study of the frequency-angular distributions of specifically terahertzfrequency idler photons and of the correlation characteristics of optical signal and terahertz idler fields emitted under non-collinear SPDC by a nonlinear crystal. Effects induced by classical thermal field fluctuations and the moderate level of inherent crystal absorption at idler frequencies are considered using the set of generalized Kirchhoff law (GKL) relations for parametric scattering by polaritons first obtained by D. N. Klyshko. We have obtained the scattering matrix coefficients for SPDC in general case without paraxial approximation, accounting the transverse limited spatial profile of the Gaussian pump beam.