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

TL;DR

This paper demonstrates how a chaotic system, specifically a semiconductor laser, can be driven to produce a long-scale periodic train that still retains a chaotic signature, by injecting a periodic signal to lock the system.

Contribution

It introduces a novel method of embedding chaotic signatures within periodic signals using phase and amplitude modulation in laser systems.

Findings

Chaotic signatures can be embedded in periodic waveforms.

Periodic injection can lock chaotic lasers to produce long-scale periodic trains.

The method demonstrates control over chaos in laser systems.

Abstract

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.