Electromagnetic energy penetration in the self-induced transparency   regime of relativistic laser-plasma interactions
  Two scenarios for the penetration of relativistically intense laser radiation into an overdense plasma, accessible by self-induced transparency, are presented. For supercritical densities less than 1.5 times the critical one, penetration of laser energy occurs by soliton-like structures moving into the plasma. At higher background densities laser light penetrates over a finite length only, that increases with the incident intensity. In this regime plasma-field structures represent alternating electron layers separated by about half a wavelength by depleted regions. 
M. Tushentsov, F. Cattani, A. Kim, D. Anderson, M. Lisak