[en] It is demonstrated that in the framework of the perturbation theory on laser field strength and the Fermi equivalent photon method expressions for photon transition, probabilities can be obtained that permit the derivation of scaling laws in terms of atomic state quantum numbers and pulse duration. A unified approach is developed that identifies universal scaling parameters for energy and pulse duration that allow analytical investigation of the interrelation of scaling laws for the two important regimes of above and below-threshold ionization. Numerical studies are presented that illuminate the conditions for linear and nonlinear regimes of photoionization, as dependent on the cycle number and carrier frequencies. We also discuss analytical asymptotic forms of the different regimes of photoionization. Finally, we develop a generalized unified approach that permits studies in terms of principal and orbital quantum numbers as well as in pulse duration for any regime of carrier frequencies. (paper)