Study On Relevant Propagation Properties Of Lorentz Beams In The Case Of Non-Paraxial And Paraxial

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. The present study is the propagation properties for Lorentz beams passing through free space and first-order axisymmetric ABCD optical systems in the case of spatial space paraxial, for propagation properties of Lorentz beams in the case of non-paraxial, in near-field diffraction, and in the case of frequency domain when through graded-index fiber are not reported. In this paper, we have studied basic theories about Lorentz beams in the three cases, the main concerns are as follows:1. Propagation properties of Lorentz beams in the case of non-paraxial are studied. Based on the angular spectrum of plane waves, the wave field expressions of non-paraxial Lorentz beams through free space are derived. Based on the theory of the second intensity moment, the analytic expressions of the far-field divergence angle, near-field divergence angle, waist width and beam propagation factor of non-paraxial Lorentz beams are derived, and the transform characteristics are discussed. It is shown that, comparing with the non-paraxial Gaussian beams possessing the same beam waist, on the same condition, the divergence angle of the non-paraxial Lorentz beams is smaller than the non-paraxial Gaussian beams', and its propagation factor is greater than the non-paraxial Gaussian beams', the transform laws of the above parameters for non-paraxial Lorentz beams are as similar as those for non-paraxial Gaussian beams. In the case of ratio of the waist width to the wavelength is accord with diode laser, the non-paraxial Lorentz beam is more in accordance with actual situations of diode laser beams.2. Propagation properties of Lorentz beams in near-field diffraction process are studied. Based on the near-field scalar diffraction theory and Fourier transform theory, the diffracted wave field on the observation plane of Lorentz beams which can be represented as plane waves and spherical waves are derived respectively, the relationship of the two different methods for describing Lorentz beams in near-field diffraction and the near-field diffracted properties are analyzed. Based on the general Rayleigh-Sommerfeld diffraction formula, the diffracted wave field of Lorentz beams represented as spherical waves on a plane and on a hemisphere are derived. It is shown that, the diffracted wave field of Lorentz beams represented as superposition plane waves by utilizing transfer function, is equivalent to the diffracted wave field represented as superposition spherical waves by utilizing impulse response; the intensity distribution on the observation plane is diminished gradually versusing the direction far from the axis.3. Propagation properties of Lorentz beams passing through a first-order optical system and graded-index fiber in frequency domain are studied. Based on the frequencied form of generalized Huygens-Fresnel diffraction integral, the analytic propagation expressions in frequency domain for Lorentz beams passing through a first-order optical system and graded-index fiber are derived. Based on the frequencied form of second-moments of Wigner distribution and its propagation law, the expressions of the beam-width, the divergence angle and the radius of curvature of Lorentz beams are given, and the transform characteristics in graded-index fiber are discussed. It is shown that, the expressions of the beam-width, the divergence angle and the radius of curvature of Lorentz beams given in frequency domain are as the same as those in spatial domain, comparing with the Gaussian beams possessing the same beam waist, on the same condition, the Rayleigh distance of Lorentz beams is larger than that of Gaussian beams. However, the expansion speed of the beam-width of Lorentz beams is lower than that of Gaussian beams and the divergence angle of Lorentz beams is smaller than that of Gaussian beams. Moreover, the transfrom laws of the above parameters for Lorentz beams are as the same as those for Gaussian beams passing through graded-index fiber.