  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.
