Conservative finite-difference scheme for the 2D problem of femtosecond laser pulse interaction with kink structure of high absorption in semiconductor

ABSTRACT

The problem of high-intense laser pulse interaction with a semiconductor under the condition of a light energy nonlinear absorption, which results in high absorption domains formation, is considered. Such interaction allows reaching a construction of an element for all-optical data treatment. For its adequate description we propose new mathematical model taking into account the longitudinal and transverse diffraction effects. The longitudinal diffraction induced a reflection of laser radiation from boundaries of the high absorption domains that results in changing of their spatial structure. The conservative finite-difference scheme (FDS) is developed for numerical computation of the complicated nonlinear processes. The property of the FDS conservatism is proved. For the proposed FDS realization the two-stage iteration method is proposed. Computer simulation results are presented. We show the uniform boundedness of the mesh functions at the iterations and the convergence of the iteration process. We show also positiveness and boundedness of the mesh function corresponding to free-charged particles. We discuss some properties of differential problem including the problem invariants, positiveness of the free-charged concentrations.

KEYWORDS:

• Conservative finite-difference scheme
• femtosecond laser pulse
• nonlinear absorption
• diffraction of laser beam
• kink structure

2010 MSC CLASSIFICATIONS:

• 65N06
• 65N12
• 35Q60

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper was made using the support of the Russian Science Foundation [grant number 14-21-00081].