The breather like penetration of the ultra-short linearly polarized laser into over-dense plasmas

Relativistic electromagnetic penetration behavior is reexamined in the relativistic transparency region. The interaction is modeled by the relativistic hydrodynamic equations coupled with the full system of Maxwell equations, which are solved by a fully implicit energy-conserving numerical scheme. For the first time, we have studied the penetration behavior through ultra-short circularly polarized and linearly polarized laser pulses interaction with over-dense plasmas. It is shown that for the ultra-short circularly polarized laser penetration occurs through a soliton like behavior, which is quite consistent with the existing studies. However, we have found that the ultra-short linearly polarized laser penetrates through a breather like behavior, and there is an energy transition mechanism with a frequency $2\omega_0$ between the penetrated breather like structure and the background plasmas. A qualitative interpretation has been given to describe this mechanism of energy exchange.