Theory of multidimensional parametric band-gap simultons

He, H and Drummond, PD (1998) Theory of multidimensional parametric band-gap simultons. Physical Review E, 58 4: 5025-5046. doi:10.1103/PhysRevE.58.5025

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Author He, H
Drummond, PD
Title Theory of multidimensional parametric band-gap simultons
Journal name Physical Review E   Check publisher's open access policy
ISSN 1063-651X
Publication date 1998
Sub-type Article (original research)
DOI 10.1103/PhysRevE.58.5025
Open Access Status File (Publisher version)
Volume 58
Issue 4
Start page 5025
End page 5046
Total pages 22
Language eng
Abstract Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].
Keyword Physics, Fluids & Plasmas
Physics, Mathematical
Quadratic Nonlinearity
Solitary Waves
2nd-harmonic Generation
Dark Solitons
Light-beams
Media
Quantization
Dispersion
Amplifier
Guide
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Physical Sciences Publications
 
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Created: Mon, 13 Aug 2007, 10:44:11 EST