Accumulation horizons and period adding in optically injected semiconductor lasers

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as, e.g., secure communications.