General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two- and three-mode systems of differential equations coupled via quadratic chi2 type nonlinearity as well as two-mode systems coupled via cubic chi3 type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum- and difference-frequency generation, polarization dynamics, parity-time dynamics, and optical processing applications.
2391-2399
Hesketh, Graham D.
70c7a4fe-99b5-4ea0-a524-39b632db5a79
1 December 2015
Hesketh, Graham D.
70c7a4fe-99b5-4ea0-a524-39b632db5a79
Hesketh, Graham D.
(2015)
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity.
Journal of the Optical Society of America B, 32 (12), .
(doi:10.1364/JOSAB.32.002391).
Abstract
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two- and three-mode systems of differential equations coupled via quadratic chi2 type nonlinearity as well as two-mode systems coupled via cubic chi3 type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum- and difference-frequency generation, polarization dynamics, parity-time dynamics, and optical processing applications.
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Accepted/In Press date: 7 October 2015
e-pub ahead of print date: 3 November 2015
Published date: 1 December 2015
Organisations:
Optoelectronics Research Centre
Identifiers
Local EPrints ID: 385218
URI: http://eprints.soton.ac.uk/id/eprint/385218
ISSN: 0740-3224
PURE UUID: 9725cb29-941a-45b8-a30f-7722f77e5ab2
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Date deposited: 18 Dec 2015 12:01
Last modified: 14 Mar 2024 22:12
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Author:
Graham D. Hesketh
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