Generalized lens: calculation of distribution on the optical axis

We analytically and numerically consider action of the generalized lens – a diffractive optical element with arbitrary degree of dependence of a phase function. Special cases of the generalized lens are axicon and a parabolic lens. On the basis of the modified stationary phase method analytical expressions for the axial distribution formed by the generalized lens in paraxial approach are received. Two types of analytical expressions provide high accuracy of calculation in various ranges of a degree of the generalized lens.