Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser

Abstract

Phase-modulated dual-path feedback (PM-DPF) is proposed to conceal time delay (TD) signatures from both intensity chaos and phase chaos in semiconductor lasers (SLs). The TD signatures are evaluated via both auto-correlation function and permutation entropy function. For the purpose of comparison, we also consider three other feedback configurations: SL with single-path feedback (SPF), SL with phase-modulated single-path feedback (PM-SPF), and SL with dual-path feedback (DPF). It is found that, for four feedback configurations, under the condition of strong feedback, successful TD concealment from both intensity and phase chaos can only be realized in SL with PM-DPF, due to the joint contribution of dual path feedback structure and phase modulation. Furthermore, to check the key factor contributing to TD concealment in SL with PM-DPF, the effects of feedback strength, feedback delay, modulation depth and modulation frequency are examined carefully. It is shown that, to obtain successful TD concealment from both intensity and phase chaos under the condition of strong feedback, the modulation frequency close to or greater than the relaxation oscillation frequency is suggested, while the modulation depth is the most important factor contributing to TD concealment, and higher modulation depth is desired. Besides, similar feedback strengths for two feedback paths are suggested. The TD signatures of intensity chaos for SLs with different feedback configurations are also verified experimentally. The SL with PM-DPF is an excellent chaotic source for security-enhanced chaotic communication systems as well as random number of generators based on chaotic SLs.