Study On Propagation Properties Of Lorentz Beams

Study on beam quality and propagation properties is an important region in laser optics. It can afford theory basic for optical system design, beam-quality control, beam propagation and transformation. With the development of laser technique and the appearance of double heterojunction lasers, a kind of scalar optical beams called Lorentz beams because the form of their transverse pattern is an independent Lorentz function is given. And the expressions for Lorentz beams and Super-Lorentzian beams passing through free space which can be represented by means of a linear combination of a finite number of elementary constituent fields of a Lorentz beam are only derived. Nowadays, Propagation of Lorentz beams and Super-Lorentzian beams through first-order optical systems and descriptions of their quality parameters are not reported. In this paper, we have studied basic theories about propagation properties and quality parameters of Lorentz beams and Super-Lorentzian beams. The main concerns are as follows:1. Propagation properties of Lorentz beams and Super-Lorentzian beams passing through a first-order optical system with axial symmetry are studied. Based on the generalized Huygens-Fresnel diffraction integral, the analytic propagation expressions for Lorentz beams and Super-Lorentzian beams passing through first-order systems are respectively derived. It is shown that the new beams obtained while Lorentz beams first propagating through a first-order optical system is the open-form beams with the modulations of both amplitude and phase. Then the above new beams passing again through the first-order optical system hold the closed property. Moreover, generalized Super-Lorentzian beams got by Super-Lorentzian beams first through free space are the open-form beams with the modulations of both amplitude and phase. And generalized Super-Lorentzian beams passing through the first-order optical system hold the closed property.2. The transform characteristics of the beam-width, the far-field divergence angle and the radius of curvature of Lorentz beam in free space are studied. Based on the corresponding definitions of intensity monents and beam-quality parameters, the expressions of the beam-width, the Rayleigh distance, the far-field divergence angle and the radius of curvature of Lorentz beam are given, and the transform characteristics in free space are discussed. It is shown that the Rayleigh distance of Lorentz beams is larger than that of Gaussian beam. However, the expansion speed of the beam-width of Lorentz beams is lower than that of Gaussian beams and the far-field divergence angle of Lorentz beams is smaller than that of Gaussian beams. Moreover, the transfrom laws of the above parameters for Lorentz beams are the same as those for Gaussian beams passing through free space.3. Propagation properties of the Wigner distribution functions for Lorentz beams and Super-Lorentzian beams passing through first-order system with axial symmetry are studied. Based on the Wigner distribution and its propagation law, the Wigner distribution functions for Lorentz beams and Super-Lorentzian beams are derived. A matrix of second moments of Lorentz beams and its propagating expression are given by means of second-moments of the Wigner distribution and its propagation law. And the transform laws of the beam-width, the far-field divergence angle of Lorentz beams are also derived in terms of the relation between second moments and beams-quality parameters. It is shown that the expressions of the above parameters for Lorentz beams obtained by second-order moments of the Wigner distribution are the same as those by intensity moments.