A new regime of anomalous penetration of relativistically strong laser   radiation into an overdense plasma
  It is shown that penetration of relativistically intense laser light into an overdense plasma, accessible by self-induced transparency, occurs over a finite length only. The penetration length depends crucially on the overdense plasma parameter and increases with increasing incident intensity after exceeding the threshold for self-induced transparency. Exact analytical solutions describing the plasma-field distributions are presented. 
A. Kim, F. Cattani, D. Anderson, M. Lisak