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.