For example, if an atom absorbs a photon with energy E, the atom's energy increases by ΔE = E, but as a parametric process, the quantum state cannot change and thus the elevated energy state must be a temporary virtual state.
By the Heisenberg Uncertainty Principle we know that ΔEΔt~ħ/2, thus the lifetime of a parametric process is roughly Δt~ħ/2ΔE, which is appreciably small for any non-zero ΔE.
[1] In a linear optical system the dielectric polarization, P, responds linearly to the presence of an electric field, E, and thus we can write where ε0 is the electric constant, χ is the (complex) electric susceptibility, and nr(ni) is the real(imaginary) component of the refractive index of the medium.
Thus in linear optics a parametric process will act as a lossless dielectric with the following effects: Alternatively, non-parametric processes often involve loss (or gain) and give rise to: In a nonlinear media, the dielectric polarization P responds nonlinearly to the electric field E of the light.
As a parametric process is in general coherent, many parametric nonlinear processes will depend on phase matching and will usually be polarization dependent.