CAJ | 학술논문

为了求解柱坐标系下非傍轴矢量波动方程，得到光束的电场解析表达式，基于轴对称情况下沿角向偏振的电场，将非傍轴近似情况下的矢量波动方程进行了抛物线坐标的转化，利用分离变量法进行了相应求解，并给出了相应的数值计算。结果表明，非傍轴近似情况下，矢量波动方程的解能描述一种光束的电场，该场的解析表达式与合流超几何函数以及梅杰函数的解有关；光束的光强分布与第1类零阶贝塞尔模式光束类似；光束在近光轴处的光强表现为无限大并且沿边缘方向急剧衰减；在焦平面上沿着径向方向光强急剧减小。所得结果对于探究非傍轴近似情况下矢量光束的传输特性有一定的意义。
위료구해주좌표계하비방축시량파동방정，득도광속적전장해석표체식，기우축대칭정황하연각향편진적전장，장비방축근사정황하적시량파동방정진행료포물선좌표적전화，이용분리변량법진행료상응구해，병급출료상응적수치계산。결과표명，비방축근사정황하，시량파동방정적해능묘술일충광속적전장，해장적해석표체식여합류초궤하함수이급매걸함수적해유관；광속적광강분포여제1류령계패새이모식광속유사；광속재근광축처적광강표현위무한대병차연변연방향급극쇠감；재초평면상연착경향방향광강급극감소。소득결과대우탐구비방축근사정황하시량광속적전수특성유일정적의의。
In order to solve the nonparaxial vector wave equation in the cylindrical coordinates and obtain electric field expression of the beams , based on the electric field along the azimuthal polarization under the axisymmetric circumstance , the vector wave equation under the nonparaxiality similar circumstances was transformed to the parabolic coordinates and was solved appropriately with the separation variables method .The corresponding numerical calculation was made .The results show that the new analytical solution of the nonparaxial vector wave equation is discussed to describe the propagation of a laser beam.The electric field of such a beam is found to be based on the solutions of the confluent hypergeometric function and the Meijer functions .The intensity distribution of beam is similar to the first-class zero-order Bessel beam mode.The intensity of the light beam near the optical axis is nearly infinite , and decays rapidly along the peripheral direction and decreases sharply along the radial direction in the focal plane .The acquired results are of certain significance for exploring the propagation properties of vector beams in case of nonparaxial approximation .