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Two-colour helmholtz solitons with a defocusing Kerr nonlinearity

Bostock, C


C Bostock


JM Christian


Multi-colour spatial solitons comprise localised optical waves at distinct temporal
frequencies. These components (which may be bright-like and/or darklike
in nature) tend to overlap in the propagation plane of a waveguide, allowing
the interplay between diffractive broadening and medium non-linearity
(self- and mutual-focusing processes) to result in an electromagnetic structure
with a stationary intensity pattern. Two-colour spatial solitons for a
Kerr-type host medium were first proposed some two decades ago within
the context of an intuitive Schrodinger-type model. Subsequent experiments
using laser light at infra-red and (frequency-doubled to) green wavelengths
demonstrated that such mutually-trapped light beams could be generated
in CS2 planar waveguides. This seminal work opened up the possibility of
designing novel photonic architectures based on multi-colour operation.
Here, a new model is proposed for two-colour continuous-wave optical
fields with similarly distinct temporal frequencies. A key advantage of this
more general Helmholtz approach is that one may capture multi-component
geometries involving propagation at arbitrary angles and orientations with
respect to the reference direction. While such off-axis considerations are central
to a very broad range of configurations (e.g., any arrangement involving
beam multiplexing and interfaces), they cannot be described by current models
based on the paraxial approximation. Particular attention is paid hereto the defocusing Kerr non-linearity [the focusing regime was investigated
in C. Bostock, "Simulations &; analysis of 2-colour Helmholtz solitons," BSc
dissertation, University of Salford (2010)]. Linear analysis is deployed to investigate
the modulational instability (MI) characteristics of plane waves. A
closed-form solution to the MI problem can be found and simulations confirm
theoretical predictions. Like its focusing counterpart, the defocusing
Helmholtz model supports two families of exact analytical two-colour soliton
(dark-bright and dark-dark), each of which has two distinct classes of solution
(co-propagating and counter-propagating). The geometry of these novel
solitons is explored in detail, and extensive computer simulations investigate
their robustness against perturbations to the transverse beam shape


Bostock, C. Two-colour helmholtz solitons with a defocusing Kerr nonlinearity. (Thesis). Salford : University of Salford

Thesis Type Thesis
Deposit Date Oct 3, 2012
Publicly Available Date Sep 23, 2023

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