Application of a two-temperature model for the investigation of the   periodic structure formation on Si surface in femtosecond laser interaction
  We consider the case of surface irradiation by a small number of femtosecond laser shots leading to the formation of surface ripples. To explain this effect, we propose a numerical model that accounts for the following processes: (i) interference of the laser irradiation with an electromagnetic surface wave propagating on a silicon sample; (ii) free carrier formation and laser energy absorption; (iii) energy relaxation and electron-phonon coupling. We perform numerical calculations taking into account the interference of a surface wave with laser; and present the obtained simulation results in order to explain formation mechanisms of the experimentally observed patterns. 
Thibault J.Y. Derrien and Thierry Sarnet and Marc Sentis and Tatiana   E. Itina
physics.plasm-ph cond-mat.mtrl-sci physics.optics