Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators

Richard O. Moore; Keith Promislow

doi:10.1016/j.physd.2005.04.015

Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators

Richard O. Moore, Keith Promislow

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We derive a perturbed parametrically forced nonlinear Schrödinger equation to model pulse evolution in an optical parametric oscillator with absorption-induced heating. We apply both a rigorous renormalization group (RG) technique and the formal Wilsonian renormalization group to obtain a low-dimensional system of equations which captures the mutual interaction of pulses as well as their response to the thermally induced potential. We compare the methodologies of the two approaches and find that the two reduced systems agree to leading order, and compare well to simulations of the full equation, predicting the formation of stably bound pulse pairs.

Original language	English (US)
Pages (from-to)	62-81
Number of pages	20
Journal	Physica D: Nonlinear Phenomena
Volume	206
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physd.2005.04.015
State	Published - Jun 15 2005

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Nonlinear Schrödinger equation
Optical parametric oscillator
Renormalization group

Access to Document

10.1016/j.physd.2005.04.015

Cite this

@article{2cb41570e44247009b9607b056bf9bce,

title = "Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators",

abstract = "We derive a perturbed parametrically forced nonlinear Schr{\"o}dinger equation to model pulse evolution in an optical parametric oscillator with absorption-induced heating. We apply both a rigorous renormalization group (RG) technique and the formal Wilsonian renormalization group to obtain a low-dimensional system of equations which captures the mutual interaction of pulses as well as their response to the thermally induced potential. We compare the methodologies of the two approaches and find that the two reduced systems agree to leading order, and compare well to simulations of the full equation, predicting the formation of stably bound pulse pairs.",

keywords = "Nonlinear Schr{\"o}dinger equation, Optical parametric oscillator, Renormalization group",

author = "Moore, {Richard O.} and Keith Promislow",

note = "Funding Information: The first author acknowledges support from the Natural Sciences and Engineering Research Council of Canada. The second author acknowledges support from the National Science Foundation under grant DMS 0345705. Both authors thank Bj{\"o}rn Sandstede and Arnd Scheel for helpful discussions concerning ref. [23] .",

year = "2005",

month = jun,

day = "15",

doi = "10.1016/j.physd.2005.04.015",

language = "English (US)",

volume = "206",

pages = "62--81",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier B.V.",

number = "1-2",

}

TY - JOUR

T1 - Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators

AU - Moore, Richard O.

AU - Promislow, Keith

N1 - Funding Information: The first author acknowledges support from the Natural Sciences and Engineering Research Council of Canada. The second author acknowledges support from the National Science Foundation under grant DMS 0345705. Both authors thank Björn Sandstede and Arnd Scheel for helpful discussions concerning ref. [23] .

PY - 2005/6/15

Y1 - 2005/6/15

N2 - We derive a perturbed parametrically forced nonlinear Schrödinger equation to model pulse evolution in an optical parametric oscillator with absorption-induced heating. We apply both a rigorous renormalization group (RG) technique and the formal Wilsonian renormalization group to obtain a low-dimensional system of equations which captures the mutual interaction of pulses as well as their response to the thermally induced potential. We compare the methodologies of the two approaches and find that the two reduced systems agree to leading order, and compare well to simulations of the full equation, predicting the formation of stably bound pulse pairs.

AB - We derive a perturbed parametrically forced nonlinear Schrödinger equation to model pulse evolution in an optical parametric oscillator with absorption-induced heating. We apply both a rigorous renormalization group (RG) technique and the formal Wilsonian renormalization group to obtain a low-dimensional system of equations which captures the mutual interaction of pulses as well as their response to the thermally induced potential. We compare the methodologies of the two approaches and find that the two reduced systems agree to leading order, and compare well to simulations of the full equation, predicting the formation of stably bound pulse pairs.

KW - Nonlinear Schrödinger equation

KW - Optical parametric oscillator

KW - Renormalization group

UR - http://www.scopus.com/inward/record.url?scp=19944370883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=19944370883&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2005.04.015

DO - 10.1016/j.physd.2005.04.015

M3 - Article

AN - SCOPUS:19944370883

SN - 0167-2789

VL - 206

SP - 62

EP - 81

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-2

ER -

Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this