一种含时贝塞尔光束的理论性质研究

本文从理论角度提出了一种"含时贝塞尔光束"的概念.在非傍轴和非时谐条件下,直接从麦克斯韦方程出发,借鉴半贝塞尔光束的处理方法,同时引入第四维虚数坐标,由此获得了完整的"含时贝塞尔光束"的解析表达式.并从无衍射性质和时空特性两个方面对其进行了探讨和研究,发现该光束具有如下性质:符合贝塞尔光束类型的无衍射特征;在时空双曲线上强度保持不变;光波时空特性的临界条件类似于相对论中的光锥."含时贝塞尔光束"的概念为无衍射自加速光束的研究开拓了新的思路和方向.

Theoretical investigation on a kind of time-dependent Bessel beam

Non-diffracting beams have been a hot topic since the Airy wave packet was introduced to optics domain from quantum mechanics. Great efforts have been made to study this theme in recent years. The researches have ranged from paraxial regime to non-paraxial regime, and a series of new non-diffracting beams have been discovered. However, most of these beams are obtained under the time harmonic condition. To break this limitation, we propose a concept of time-dependent Bessel beam in this paper, which generalizes the non-diffracting beams to non-time-harmonic regime.We start from Maxwell's equations in vacuum under non-paraxial condition using the method borrowed from the half-Bessel beam. To obtain the non-time-harmonic solution, the fourth dimensional imaginary coordinate is introduced, which refers to the covariance in the theory of special relativity. By solving the wave equation without the time harmonic condition, we obtain the analytical expression for a time-dependent beam in the form of Bessel functions. Thus we call it time-dependent Bessel beam.The diffraction properties and space-time characteristics of the time-dependent Bessel beam are investigated theoretically. The transverse intensity and the intensity distribution of the beam are calculated and discussed in detail. The wave function of the time-dependent Bessel beam is in the same form as the normal Bessel beam so that it can exhibit non-diffraction in the four dimensional space-time. When propagating along a space-time hyperbolic trajectory, the intensity of the time-dependent Bessel beam remains constant and the width of the beam decreases with propagating distance and time increasing. Besides, we deduce the critical condition of the spatiotemporal characteristics of the beam, and the result agrees well with the concept of the light cone in the theory of special relativity.The method to deduce the time-dependent Bessel beam used in this paper is universal, and it will provide a valuable access to other solutions for the wave equations under different conditions. We extend the study of non-diffracting beams from time harmonic regime to non-time-harmonic regime. Furthermore, our work demonstrates the relation between the non-diffracting accelerating beams and the theory of special relativity. We believe this work will open up a new vista and give a new insight into the research of non-diffracting accelerating beams or other relevant research fields.