Airy transformation of Lorentz-Gauss beams

By using the first three terms of expansion of the Lorentz function, the approximate description of an incident Lorentz-Gauss beam is analytically obtained. Moreover, this approximation is proved to be effective. Based on this approximate description, analytical outcome of the Airy transformation of a Lorentz-Gauss beam is presented, which is separable in two transversal directions. Analytical formulas of the centroid and the beam half width of a Lorentz-Gauss beam in the output plane of Airy transformation are also derived. Since the optical fields of transformed Lorentz-Gauss beams have the same evolution law in two transversal directions, first only one transversal direction is considered. The effects of the Airy control parameter and the Lorentzian parameter on the intensity, the centroid, the beam half width, the location of the predominant peak, and the intensity of the predominant peak for a transformed Lorentz-Gauss beam are investigated in one transversal direction, respectively. Using the above-mentioned parameters, the Airy transformation of a Lorentz-Gauss and a Gaussian beam is compared in detail. Finally, two-dimensional intensity contours of Lorentz-Gauss beams propagating through different Airy transform optical systems are demonstrated. The characteristics of a Lorentz-Gauss beam in the output plane of Airy transformation are well displayed. Also, this research reveals the difference of the Airy transformation of a Lorentz-Gauss and a Gaussian beam.