Efficiency of using adaptive artificial boundary conditions at computer simulation of contrast spatio-temporal laser-induced structures in a semiconductor

Many problems of modern laser physics are governed by equations or sets of equations in an unbounded domain. For solving these problems using the computer simulation, it is necessary to introduce the bounded domain, which size should be extended significantly to avoid the spurious wave reflection from the domain boundaries. Alternatively, the artificial (non-reflective or transparent) boundary conditions should be stated. This approach is also effective for enhancing computation performance at the numerical solution of the nonlinear partial differential equations (PDEs). In the current paper, we investigate the laser pulse propagation in a semiconductor, governed by the Schrödinger equation, under the appearance of spatio-temporal contrast structures of semiconductor characteristics. Their evolution is described by a set of PDEs. The optical pulse is partly reflected from the boundaries of these structures. Consequently, even a little reflection of the optical pulse from the artificial boundaries can essentially distort the numerical solution. Thus, these artificial boundary conditions must possess a high quality to minimize their reflection coefficients. With this aim, we propose the method for constructing adaptive artificial boundary conditions and discuss their advantages.