激光光路追踪Wigner分布函数方法

提出了一种考虑衍射效应的激光几何光路追踪方法。引入由激光标量场定义的Wigner激光能量相空间分布函数，并给出该函数满足的刘维尔运动方程。Wigner分布函数用来描述经过空间任一点沿任一方向传输的激光光线上的能量分配。激光能量沿由波包色散关系定义的光线轨迹保持不变（真空中）或者衰减（等离子体中）。与传统几何光路追踪方法相比，该方法从理论上给出了激光光线初始携带能量份额的计算方法，并且将激光标量场的相位信息自然地包含在Wigner分布函数的定义里。算例表明，该方法与解析模型及广泛使用的菲涅耳衍射积分方法结果一致。

Wigner distribution function method for laser-beam ray tracing

A laser ray-tracing method with consideration of diffractive effect is developed. The Wigner distribution function defined by laser scalar wave field is introduced along with the Liouville kinetic equation it satisfies. This function can describe the laser energy of any ray along arbitrary direction at any spatial position. The laser energy retains fixed in vacuum or attenuates in plasmas along ray trace. Compared with the conventional ray-tracing method, the Wigner distribution function method can give laser energy attached to ray theoretically and the phase information at boundary can be included in the definition of Wigner distribution function. Also, this method can describe the propagation of laser beams as well as the analytical model and the Fresnel diffraction method.