Path integral formulation of light propagation in a static collisionless plasma, and its application to dynamic plasma

In many studies on the laser impinging on a plasma surface, an assumption is made that the reflection of a laser pulse propagating to a plasma surface takes place only at the turning point, at which the plasma density exceeds the critical one. A general reflection amplitude of light R from an arbitrary inhomogeneous medium can be obtained by solving a Riccati-type integral equation, which can be solved analytically in low-reflection conditions, i.e., |R| 2  ≪ 1. In this work, we derive an intuitive analytic solution for the reflection amplitude of light R from a plasma surface by integrating all possible reflection paths given by the Fresnel equation. In the low-reflection condition, reflection paths having only one reflection event can be used. By considering the higher-order reflection paths, our analytic expression can describe reflection in the high-reflection condition. We show the results of a one-dimensional particle-in-cell simulation to support our discussions. Since our model derived for static plasmas is well corroborated by the simulation results, it can be a useful tool for analyzing light reflection from dynamically varying plasmas.