文档介绍：This is page 247
Printer: Opaque this
12
Solitons in Optical Media with
Quadratic Nonlinearity
Boris A. Malomed
ABSTRACT A brief review of basic models describing second harmonic
generation (SHG) in dispersive and diffractive optical systems,and of fun-
damental soliton solutions to these models is given. Included are two- and
three-wave models,gap solitons,linearly coupled waveguides with an in-
trinsic quadratic nonlinearity,multidimensional “light bullets”,two-soliton
bound states (which are always unstable in the usual SHG models,but may
be stable in the SHG models that give rise to gap solitons),and modula-
tional instability of cw states. Both analytical results,obtained by means of
the variational approximation (VA),and numerical results are presented.
In practically all the cases,VA demonstrates a fairly good agreement with
direct simulations.
1 Introduction
Nowadays, optical solitons constitute a huge research area that has been
attracting a great deal of interest. Several fundamental monographs have
summarized the results of theoretical and experimental studies obtained,
chiefly, for the solitons propagating in glass fibers [1]. This type of solitons
is referred to as being in the temporal domain.
In generating optical solitons, the crucial role belongs to nonlinear prop-
erties of the medium. Usually, the optical nonlinearity (the Kerr effect)
is quite weak. In optical fibers, this can pensated by choosing the
carrier wavelength of light close to the zero-dispersion point, where even a
weak nonlinearity pete with the dispersion. However, the search for
physical mechanisms that are able to induce a stronger optical nonlinearity
is a very relevant problem.
An important result in this direction was obtained when it was experi-
mentally demonstrated that a classical nonlinear optical effect in the form
of the second harmonic generation (SHG) induced by a quadratic (χ(2)),
rather than cubic (χ(3)), nonlinearity of the m