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
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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 -