Abstract: This work is focused on generation of quantum-entangled photons through
spontaneous parametric down-conversion in array of nonlinear waveguides.
First we present short description of the process together with its
Hamiltonian. Next we discuss possible methods of calculation of the output
states. We mention first and second order of the perturbation theory and
outline the solution using the Schmidt decomposition (but both methods are
neglecting the time-ordering effects). Finally we calculate the first two
nontrivial terms of Dyson series (this method already contains the
time-ordering effects).