Coherence and dimensionality of intense spatio-spectral twin beams

Spatio-spectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using the decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is practically independent on the pump intensity owing to the mode structure in this plane. The corresponding auto- and cross-correlation functions approach each other for larger pump intensities. Entanglement dimensionality of a twin beam is determined comparing several approaches.