We report the discovery of infinite cascades of periodicity hubs and spirals in a semiconductor laser with optoelectronic feedback for which sequences of chaotic spikings were recently linked to incomplete homoclinic scenarios. We obtain the stability curve passing simultaneously through the main laser hub and an infinite alternation of parameter windows corresponding to stable laser oscillations, periodic or not. Our findings open the possibility of measuring the complicated and regular distribution of non-Shilnikov laser oscillations.

© 2010 Optical Society of America

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