物理学报2016，Vol.65Issue(14)：144201-1-144201-5,5.DOI:10.7498/aps.65.144201
一种含时贝塞尔光束的理论性质研究∗
Theoretical investigation on a kind of time-dep endent Bessel b eam
摘要
Abstract
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 the-oretically. 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.关键词
含时贝塞尔光束/无衍射/时空特性/临界条件Key words
time-dependent Bessel beams/non-diffraction/space-time characters/critical condition引用本文复制引用
乐阳阳,张兴宇,杨波,陆蓉儿,洪煦昊,张超,秦亦强,朱永元..一种含时贝塞尔光束的理论性质研究∗[J].物理学报,2016,65(14):144201-1-144201-5,5.基金项目
国家自然科学基金(批准号:11274163,11274164,11374150,11504166)资助的课题.* Project supported by the National Natural Science Foundation of China (Grant Nos.11274163,11274164,11374150,11504166) （批准号:11274163,11274164,11374150,11504166）
