Schmidt modes in the angular spectrum of bright squeezed vacuum
  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. 
Polina R. Sharapova, Angela M. Perez, Olga V. Tikhonova, and Maria V.   Chekhova
quant-ph