  In this review, we compare different descriptions of photon-number statistics
in harmonic generation processes within quantum, classical and semiclassical
approaches. First, we study the exact quantum evolution of the harmonic
generation by applying numerical methods including those of Hamiltonian
diagonalization and global characteristics. We show explicitly that the
harmonic generations can indeed serve as a source of nonclassical light. Then,
we demonstrate that the quasi-stationary sub-Poissonian light can be generated
in these quantum processes under conditions corresponding to the so-called
no-energy-transfer regime known in classical nonlinear optics. By applying
method of classical trajectories, we demonstrate that the analytical
predictions of the Fano factors are in good agreement with the quantum results.
On comparing second and higher harmonic generations in the no-energy-transfer
regime, we show that the highest noise reduction is achieved in third-harmonic
generation with the Fano-factor of the third harmonic equal to 13/16.
