By starting with the Maxwell theory of x-ray laser propagation in collisionless plasmas, we study the phase difference of the probe and reference beams of x-ray laser interferometry in measuring the plasma electron density. The basic idea is to reduce the Maxwell equation to a Schrodinger-like equation. By using the quantum mechanical technique and introducing a novel picture, we obtain a modified relation between the phase and the electron density, where the phase corresponds to the interference of probe and reference light and the contribution of gradient of the electron density has been taken into account.
The fundamental algorithm of light beam propagation in high powerlaser system is investigated and the corresponding computational codes are given. It is shown that the number of modulation ring due to the diffraction is related to the size of the pinhole in spatial filter (in terms of the times of diffraction limitation, i.e. TDL) and the Fresnel number of the laser system; for the complex laser system with multi-spatial filters and free space, the system can be investigated by the reciprocal rule of operators.
