Mode of propagation of optical radiation with self-similar pulse shape in layered medium with nonlinear absorption

Abstract

We investigate the mode of laser pulse propagation as in a homogeneous medium so in layered medium with the twophoton absorption at which the shape of pulse is self-similar along some distance of the propagation. Finding of the laser pulse shape with such property is based on the solution of nonlinear eigenfunction problem for Schrodinger equation with nonlinear absorption. Under certain conditions this eigenfunction gives us the pulse shape with requiring properties. This eigenfunction is considered as a spatial distribution of function for the nonlinear Schrodinger equation which contains the term describing the two-photon absorption. We have found out that the self-similar shape of pulse in a medium with the two-photon absorption is similar to the laser soliton at its propagation in a medium with Kerr nonlinearity. Nevertheless, the duration of self-similar pulse propagating in the homogeneous medium is less in comparison with the soliton duration for Kerr medium. The other difference between self-similar shape of pulse and soliton concludes in existence of mode of the self-similar shape of pulse only on limited distance of the optical pulse propagation. We show the reason of this evolution of the laser pulse. We see some applications of such mode of the laser pulse propagation. First, it is important for the laser pulse propagation in an active medium: obviously, the self-similar mode of laser pulse propagation may take place. Second, at a formation of TW or PW laser pulse with wide aperture on the base of non-linear compression of laser pulse in glass the two-photon (or three-photon) absorption occurs. Hence, the self-similar shape of pulse plays an essential role for practical problems.