Transformation of radiation by the generalized parabolic (aspherical) lens

An action survey of the optical elements class named by generalized parabolic lens is cited in this paper. The approximately-analytical and numerical analysis of radiation transformation realized by the generalized parabolic lens is described within the limits of different theories: geometrical-optics and wave (paraxial and nonparaxial). The types of refracting aspherical surfaces described with power function are defined on base of the geometrical-optics analysis. The surfaces allow to form characteristic intensity distributions on an optical axis. A paraxial propagation of laser beam with an initial arbitrary power phase function is described with approximate analytical expressions which are agreed qualitatively with the geometrical-optics analysis. The obtained expressions are precision for exponents 1 and 4. A nonparaxial analysis is implemented on base of calculation of the Rayleigh-Sommerfeld integral with qualifying corrections. It is shown that essential growth of intensity in the focus happens at the exponent value from 1 to 2, at that the maximal intensity is achieved in a middle of the range.