We study the spatial properties of high-gain parametric down-conversion (PDC). From the Hamiltonian we find the Schmidt modes, apply the Bloch-Messiah reduction, and calculate analytically the measurable quantities, such as the angular distributions of photon numbers and photon-number correlations. Our approach shows that the Schmidt modes of PDC radiation can be considered the same as for the low-gain (biphoton) case while the Schmidt eigenvalues strongly depend on the parametric gain. Its validity is confirmed by comparison with several experimental results, obtained by us and by other groups.
@article{arxiv.1410.6658,
title = {Schmidt modes in the angular spectrum of bright squeezed vacuum},
author = {Polina R. Sharapova and Angela M. Perez and Olga V. Tikhonova and Maria V. Chekhova},
journal= {arXiv preprint arXiv:1410.6658},
year = {2016}
}