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

We derive a perturbed parametrically forced nonlinear Schrِdinger 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.