Research On The Efficacious Propagation Distance Based On The Main Lobe Of The Finite Energy Diffraction-free Beams

Since the diffraction-free beams have the property of smaller central spot diameter, highly light intensity concentrated and self-healing features in free space, it will be applied widely in optical communication technique, optical micromanipulation and accurate measurement field in future. Although the diffraction-free beams can not be achieved due to their infinite energy, the near diffraction-free beams, which is named the finite energy diffraction-free beams, have been obtained by the finite aperture in experiment. The limited aperture makes the finite energy diffraction-free beams can not propagate long distance with diffraction-free feature, which restrict the use of the beam in light beam pointing technology, the optical distance measurement, and the laser collimation technology. Therefore, to get the finite energy diffraction-free beams with small spot center and remain the size unchanged is the researchers’lifelong pursuit. The specific work which have been done is as follows:Firstly, the transportation features and generation methods of the finite energy diffraction-free beams is summarized and analyzed. The parabolic-like trajectory of the self-accelerating feature, the diffraction-free and the mechanisms of the self-healing characteristics of the finite energy Airy beam in free space are introduced in details. Then a theoretical derivation of the finite beam width Bessel beam and its common generation methods are described. The maximal diffraction-free range of the finite width Bessel beam is obtained by the geometric-optical method.Secondly, according to the transportation characteristics of the Gaussian beam, the Rayleigh Range based on the width of the finite energy Airy beam’s main lobe is defined, for scaling the propagation characteristic of the Airy beam. The results show that the similar diffraction-free distance of finite energy Airy beam can be scaled by Rayleigh range, but it is from infinite (Pure non-diffraction beam) to one Rayleigh range (the same with Gaussian beam) when decay factor is from0to1. Meanwhile, when the decay factor of the finite energy Airy beam is from0to0.4, the expansion of the beam is much less than the fitting Gaussian beam, and the efficacious propagation distance is long. By contrast the efficacious energy in the main lobe is less by studying the power in the bucket (PIB). With increasing the decay factor, the expansion trend of the finite energy Airy is becoming more accessible to the fitting Gaussian beam. And the beam propagation factor of the Airy beam can achieve the minimum1.17when the decay factor is0.756. However, the finite energy Airy beam looks like the Gaussian beam which can propagate about one Rayleigh range. Lastly, the diffraction-free transportation characteristics of the finite width Bessel beams is analyzes based on the Rayleigh range of the main lobe. The influence of the aperture radius and the relative coefficient of radial vector to the transportation characteristic of the beam is validated and separate analyses were carried out with the two parameters on the effects to the transverse characteristics and the longitudinal characteristics of the finite width Bessel beam. The results show that the maximal diffraction-free range increase with increasing the aperture radius, but it decrease with raising the relative coefficient of radial vector. Moreover, According to the Rayleigh range of the main lobe, the efficacious transportation distance of the finite width Bessel beams is analyzed. And it rise with increasing the relative coefficient of radial vector. At last the finite width Bessel beam’s main lobe with different relative coefficient of radial vector and the fitting Gaussian beam’s main lobe with the change of the transportation distance is illustrated.