Non-linear wave mixing in optical microresonators offers new perspectives for the realization of compact optical frequency ‘microcombs’, holding many promising applications. These typically rely on dissipative soliton formation in driven nonlinear passive cavities with anomalous dispersion, yielding a sech pulse shape. Here, we use a genetic algorithm to ‘invert’ the Lugiato-Lefever equation that models these systems, in order to find the optimum arbitrary dispersion profile needed to achieve a microcomb with a targeted spectral shape. We consider several use cases, such as generating near gaussian pulses, or a telecom-optimized microcomb, as well as optimize a dispersive wave position and power.
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