非球面系统中高斯光束传输的数值计算

Numerical Computation for Propagation of Gaussian Beam through Aspheric System

高斯光束的理论公式从整体上描述了光束的传输特性,但并没有描述光束内每一光子的传播行为。基于高斯光束的单叶双曲面特性,建立了一个新的高斯光束光子传输模型。该模型将高斯光束视为由无数个共轴单叶双曲面构成的双曲线体,光子传播方向是在过该光子初始发射点的双曲面的两条直母线中等概率选择。基于该模型,通过计算大量光子经光学系统的传播轨迹可获得高斯光束的几何构形、光强分布、光子光程分布及其传播方向。对实际非球面光学系统的计算结果充分验证了该方法可全面、准确地模拟高斯光束的传输特性,且数值计算效率高。

The theoretical formulas of Gaussian beam describe its propagation characteristics on the whole, but they don not give any description of the propagation of photons within the beam. Based on Gaussian beam＇s characteristic of hyperboloid with one sheet, a new photon propagation model for Gaussian beam was built. The model takes the Gaussian beam as a hyperboloid consisting of myriads of co-axis hyperboloids of one sheet, and the propagation direction of a photon is chosen equiprobably between the two generatrices of the hyperboloid that goes through the photon＇s initial emission point. With this model and by use of tracing the propagations of lots of photons through an optical system, the parameters of Gaussian beam were obtained, i.e. geometric configuration, light intensity distribution, photons＇ optical path length distribution and their propagation directions. The computation result for a practical aspheric optical system has fully proved that the method can be used to simulate the propagation characteristics of Gaussian beam allsidedly and accurately with high numerical computation efficiency.