Generation of optical signal and terahertz idler photons by spontaneous parametric down-conversion

Frequency-angular characteristics of signal and idler photons generated under spontaneous parametric down-conversion are studied in a strongly frequency nondegenerate regime, without paraxial approximation, accounting for possible inherent absorption of idler waves in a nonlinear crystal, classical thermal field fluctuations, and the multimode character of parametric interaction induced by transverse spatial limitation of the pump beam. Spatial limitation is shown to lead to a huge increase in angular divergence of the idler photons generated at terahertz frequencies. General expressions are obtained for the frequency-angular sensitivity function of the nonlinear-optical terahertz wave detector and for power densities of the signal and idler photon fluxes. The absorption-induced difference in the parametric conversion coefficients for the noise and externally incident radiation of the idler frequency is shown to be described by approximately the same loss factor for all active spatial idler modes. Two different parametric contributions of the internal thermal noise to the number of output idler photons were revealed with different dependence on the idler-wave absorption. Expressions for the loss factors, which describe absorption-induced effects in signal and idler channels, are obtained and shown to be turning into one another by changing the sign of the absorption coefficient. Relative contribution of thermal and quantum field fluctuations into the intrinsic radiation of a nonlinear crystal at signal and idler frequencies is analyzed accounting for the crystal absorption properties.