Embedding a chaotic signature in a periodic train: can periodic signals be chaotic?

We show how a chaotic system can be locked to emit a periodic waveform belonging to its chaotic attractor. We numerically demonstrate our idea in a system composed of a semiconductor laser driven to chaos by optical feedback from a short external cavity. The clue is the injection of an appropriate periodic signal that modulates the phase and amplitude of the intra-cavity radiation, a chaotic analogy of conventional mode-locking. The result is a time process that manifests a chaotic signature embedded in a long-scale periodic train.