Two-colour helmholtz solitons with a defocusing Kerr nonlinearity
Bostock, C 2011, Two-colour helmholtz solitons with a defocusing Kerr nonlinearity , PhD thesis, Salford : University of Salford.
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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
|Item Type:||Thesis (PhD)|
|Schools:||Colleges and Schools > College of Science & Technology|
Colleges and Schools > College of Science & Technology > School of Computing, Science and Engineering
|Depositing User:||Institutional Repository|
|Date Deposited:||03 Oct 2012 14:34|
|Last Modified:||20 Aug 2013 18:32|
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