装有多瓣反射镜的laser中光的“漫射”和角分布
The `diffusion' of light and angular distribution in the laser equipped with a multilobe mirror
摘要：
本文研究了具有多瓣反射镜的无模激光器的辐射分布，该反射镜的瓣（面）与光轴成小角度倾斜。它表明，由光线通过包括一个多瓣反射镜的光学系统的许多通道所产生的方向的变化可以被描述为沿平面的一个点的布朗行走或等效为二维扩散方程的解。扩散方程的边界条件可以近似地用公式表示为某个角度处的零条件，如果在行走期间达到该零条件，则保证光线从光学系统逸出。在这个近似的框架下，导出了不同角度的出射光线分布的显式公式。在多次通过光学系统之后，角分布趋于某种普适函数。在圆镜的情况下，它可以由零阶贝塞尔函数表示。
英文摘要：
The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray through the optical system including a multilobe mirror may be described as Brownian walk of a point along the plane or equivalently as a solution of the two-dimensional diffusion equation. Boundary conditions for the diffusion equation may be approximately formulated as null conditions at some angle which, if being reached during the walk, guarantees that the ray escape from the optical system. In the framework of this approximation an explicit formula for the distribution of the outgoing ray in different angles is derived. After many passages through the optical system the angular distribution tends to some universal function. In the case of the round mirror it may be presented by the Bessel function of order zero.
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