May 1 2014
The Haus Master Equation is used mainly in a physical model for describing the generation of pulse in the resonator of a mode-locked laser.
The fundamental principle of this model is that the evolution of a pulse in the resonator is described as a function of time domain and complex amplitude A (t). This function applies to a single pulse at a particular position within the resonator. The amplitude is normalized, such that the optical intensity of the gain medium is the squared modulus of A(t).
The variations in this function, denoted by ΔA(t), within the resonator are caused by factors such as optical nonlinearities, chromatic dispersion, and laser gain. They are then calculated.
However, the overall time delay, with respect to the resonator round-trip time, is not taken into account during the calculation, such that the pulse remains near t = 0. Amplitudes Aj (t) can be considered, where j denotes the number of resonator round trips. The index, j, is replaced with a second time variable T = j Trt, where Trt is the resonator round trip time, which leads to a function, A (T, t).
In deriving the Master equation, T is considered as a continuous variable, and the combined changes of the amplitude per round trip are taken as ΔA. The resulting Master equation is given by
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