7 research outputs found
Higher-order nonlinear modes and bifurcation phenomena due to degenerate parameteric four-wave mixing.
Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing
We demonstrate that weak parametric interaction of a fundamental beam with
its third harmonic field in Kerr media gives rise to a rich variety of families
of non-fundamental (multi-humped) solitary waves. Making a comprehensive
comparison between bifurcation phenomena for these families in bulk media and
planar waveguides, we discover two novel types of soliton bifurcations and
other interesting findings. The later includes (i) multi-humped solitary waves
without even or odd symmetry and (ii) multi-humped solitary waves with large
separation between their humps which, however, may not be viewed as bound
states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.
Standard and Embedded Solitons in Nematic Optical Fibers
A model for a non-Kerr cylindrical nematic fiber is presented. We use the
multiple scales method to show the possibility of constructing different kinds
of wavepackets of transverse magnetic (TM) modes propagating through the fiber.
This procedure allows us to generate different hierarchies of nonlinear partial
differential equations (PDEs) which describe the propagation of optical pulses
along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium
and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order
derivative nonlinearity, governing the dynamics for the amplitude of the
wavepacket. In this derivation the dispersion, self-focussing and diffraction
in the nematic are taken into account. Although the resulting nonlinear
may be reduced to the modified Korteweg de Vries equation (mKdV), it also has
additional complex solutions which include two-parameter families of bright and
dark complex solitons. We show analytically that under certain conditions, the
bright solitons are actually double embedded solitons. We explain why these
solitons do not radiate at all, even though their wavenumbers are contained in
the linear spectrum of the system. Finally, we close the paper by making
comments on the advantages as well as the limitations of our approach, and on
further generalizations of the model and method presented.Comment: "Physical Review E, in press