Analysis of temporal structure of laser chaos by Allan variance

TL;DR

This paper demonstrates that Allan variance effectively analyzes the multi-scale chaotic dynamics of semiconductor lasers with delayed feedback, capturing low-frequency fluctuations that are difficult to detect with traditional spectral methods.

Contribution

The study introduces Allan variance as a novel tool for characterizing complex laser chaos, especially low-frequency fluctuations, across multiple time scales.

Findings

Allan variance captures multi-scale laser dynamics.

It detects low-frequency fluctuations not seen in power spectrum.

The method enhances understanding of laser chaos complexity.

Abstract

Allan variance has been widely utilized in evaluating the stability of the time series generated by atomic clocks and lasers, in time regimes ranging from short to extremely long. This multi-scale examination capability of the Allan variance may also be beneficial in evaluating the chaotic oscillating dynamics of semiconductor lasers, not just for conventional phase stability analysis purposes. Here we demonstrate Allan variance analysis of the complex time series generated by a semiconductor laser with delayed feedback, including low-frequency fluctuations (LFFs), which exhibit both fast and slow dynamics. Whereas the detection of LFFs is not easy with the conventional power spectrum analysis method in the low-frequency regime, we show that the Allan variance approach clearly captured the appearance of multiple time-scale dynamics, like LFFs. This study demonstrates that Allan variance can help in understanding and characterizing versatile laser dynamics, including LFFs, which involve dynamics spanning a wide range of time scales.