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 2ω 0 between the penetrated breather like structure and the background plasmas. A qualitative interpretation has been given to describe this mechanism of energy exchange.PACS numbers: 52.38. Kd, 41.75.Jv, 52.35.Mw, The dynamics of the penetration of ultra-intense laser irradiation into classically-forbidden plasmas has attracted wide attention for its distinct prospective applications. The penetration of intense laser radiation into over-dense plasma core would be crucial in the concept of the fast ignition fusion 1 , plasma lens for ultra-intense laser focusing 2 and betatron oscillations for high intense electron acceleration 3,4 . Kaw et al. are the first to predict that relativistically strong laser can reduce the effective plasma frequency below the frequency of the laser radiation, allowing the laser to penetrate through the over-dense plasmas 5 . This problem has been greatly enriched by a series of theoretical and particle-in-cell simulation studies 6-21 . Tushentsov et al. are the first to study the irradiation penetration of the circularly polarized (CP) laser pulse through fluid-Maxwell simulations 23 , but there is a serious shortcoming: the Maxwell equations are solved within the framework of parabolic approximation, which will certainly break down for ultrashort laser pulse. Afterward, Berezhiani et al. abandon the parabolic approximation and solve the full system of relativistic hydrodynamic and Maxwell equations 24 . However in their results, we have not found the intrinsic application to the study of ultra-short laser penetration into over-dense plasmas. In their fluid-Maxwell simulations, the laser duration and solitons formation time are over 100T 0 . Their simulation results just reconfirm that of Tushentsov et al. with parabolic approximation. It a) Electronic mail: wudongphysics@gmail.com b) Electronic mail: zheng chunyang@iapcm.ac.cn c) Electronic mail: xthe@iapcm.ac.cn should be emphasized that their is no theoretical analysis on the penetration into over-dense plasmas with linearly polarized (LP) laser, because the second-harmonic oscillating component of the ponderomotive force could disturb the background plasma density and make the problem even more complicated. The difficulty of th...