We study theoretically the non-phase-matched degenerate four-wave mixing of type ωs = 2ω1 ωω2 , involving beams
carrying two-dimensional spatial phase dislocations in the form of singly-charged optical vortices (OVs).
Accompanying third-order nonlinear processes in the non-resonant nonlinear medium (NLM), which are accounted
for, are self- and cross-phase modulation. In the case of pump OV beams with identical topological charges the
model predicts the generation of signal beams carrying OVs of the same charge. If the pump beams carry OVs with
opposite charges, the generated signals are predicted to carry triply charged vortices which, in the case of a nonnegligible
initial free-space propagation from the plane of vortex generation to the NLM, decay inside the NLM into
three singly-charged vortices with highly overlapping cores.
Interaction of two coaxial Gaussian pulses of different frequencies simultaneously propagating in the media with cubic nonlinearity and anomalous group velocity dispersion is considered in the case of two spatial dimensions: one transverse spatial dimension and one longitudinal dimension for the propagation axis. Variational approach (the so-called average Lagrangian method) is applied to the set of two coupled nonlinear Srodinger equations with the ansatz in the form of two Gaussian pulses the same center. Different possible modes of propagation are investigated and key parameters defining their limits are found. It is shown that nonlinear interaction results in the complicated non-trivial effects in the interaction of the simultaneously propagating pulses.
Light bullets i.e. ultra short spatial-temporal solitons propagating in the Kerr nonlinear media are investigated in the framework of the paraxial approximation by means of both aberrationless approximation and variational approach. It is shown that oscillatory light bullets of picosecond and femtosecond ranges may be stable for significant distances in the Kerr media. Different possible modes of propagation are investigated, critical threshold values of the energy of the pulse defining the limits of these modes are found. Exact expression for the focal distance of the collapse is found in the (1 + 2)-dimensional case.
Gaussian's functions are used to investigate properties of light bullets in Kerr non linearities media. It is shown that the light bullets oscillate in space and time. The type of the nonlinearity and the collapse problem is discussed.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.