横截面上光强的精确表述

Accurate Expression of Light Intensity at Transverse Plane

在考虑了时间平均能流密度的矢量特性的情况下，对光强的概念进行了推广──定义为单位时间单位面积内所流过的能量的时间平均值，从而使其可适用于任何一个连续的曲面，也能与光强的实际测量值取得一致。这个推广的定义式表明，曲面上任一点处的光强值都不仅与该处的振幅有关，而且还和该处的时间平均能流密度与面元方向的夹角有关。作为一个重要的特例情况，文中还给出了横截面（垂直于光束传输方向）上的光强公式，这个结果可用来对非傍轴光束的强度二阶矩及M2因子等物理量进行研究。

By taking the vectorial property of the time-average enregy flow density into account, a new extensive definition of the light intensity is proposed. It is expressed as the time average of the amount of energy which crosses in a unit time and a unit area, so it can be applied to any point at any curved surface. This definition is directly related to the measurement quantity of the light intensity on a curved surface. The intensity formula shows that the light intensity at any point of a curved surface is not only related to the amplitude at the point, but also related to the included angle between the Poynting vector (time average ) and the direction of the local differential surface element.Especially, as an important consequence, the light intensity on the transverse plane perpendicular to the propagation axis is given. These results can be used to study the second intensity moments and the M2 factors of the non-paraxial beams.