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 Schrödinger
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 Schrödinger 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.
We investigate the phenomena, which are similar to effects of the quantum teleportation and of superluminality, at the
two-wave interaction in a medium with the quadratic and cubic nonlinear responses taking place simultaneously. The
interaction of two femtosecond tosecond pulses occurs under the conditions of a group velocity mismatch. The formation
of sub-pulses at both frequencies, part of which demonstrate soliton properties with a velocity higher or lower than the
velocity of linear pulse propagation in considering condition at the same group velocity dispersion, is revealed. The
reason of an acceleration of the sub-pulse is the induced periodic grating o dielectric permittivity. Consequently, the
acceleration of the light pulse is due to tunneling through these gratings. It is very important that the gratings are absent
before the interaction of laser radiation with the medium.
The second important feature is the following. For each fast sub-pulse there is a pulse whose velocity is smaller than the
velocity of the linear propagation. Hence, the preservation of an impulse of whole pulse takes place.
The interesting property of the formed structures is the sensitivity of each of the anomalously propagating sub-pulses to
perturbation introduced in the other sub-pulse at a chosen cross section. Another sub-pulse changes instantaneously at
the perturbation of the given sub-pulse. This is similar to the effect of the quantum teleportation.
We analyze a stability of optical soliton, which is propagated along the nonlinear layered structure (photonic crystal),
with respect to perturbation of propagation direction. Soliton is located over a number of layers. Profile of soliton is
found as a solution of corresponding eigenfunction problem for nonlinear Schrödinger equation with periodic
coefficients. The stability of optical soliton is investigated for transverse perturbations with respect to propagation
direction on the base of computer simulation. Three different types of soliton evolution depending on the amplitude of
transverse perturbation are discussed.
We report the possibility of energy conversion with 95% (and higher) efficiency under the SHG of femtosecond pulse without increasing of pulse duration on doubling frequency. The main feature of the discussing regime of doubling frequency is the absence of the inverse energy conversion. This regime is realized due to cascading generation in medium with quadratic and cubic nonlinear responses at big phase mismatching and to using of compound medium. It should be emphasized that the input pulse shape on fundamental frequency is close to the soliton one. After definite section of medium, in which SHG takes place under the condition of phase matching, a medium with big phase mismatching is used.
The process of doubling frequency of femtosecond pulse is considered in optical fiber with cubic and quadratic nonlinear response. Our computer simulation had shown a bistable (multistable) dependence of phase mismatching, conversion efficiency, duration of pulses from the total energy of interacting waves. Essentially, for constant total energy of interacting waves the solitons with various maximum intensity and their durations take place but their shapes remain unchanging. As a consequence, one can realize two stable states on phenomenon under consideration. The other application can conclude in encoding of information.
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