The University of Southampton
University of Southampton Institutional Repository

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
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.
0740-3224
2391-2399
Hesketh, Graham D.
70c7a4fe-99b5-4ea0-a524-39b632db5a79
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), 2391-2399. (doi:10.1364/JOSAB.32.002391).

Record type: Article

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.

Full text not available from this repository.

More information

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: https://eprints.soton.ac.uk/id/eprint/385218
ISSN: 0740-3224
PURE UUID: 9725cb29-941a-45b8-a30f-7722f77e5ab2

Catalogue record

Date deposited: 18 Dec 2015 12:01
Last modified: 14 Nov 2018 17:30

Export record

Altmetrics

Contributors

Author: Graham D. Hesketh

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×