Abstract
Polarization-resolved chaotic emission intensities from a vertical-cavity surface-emitting laser (VCSEL) subject to feedback from a fiber Bragg grating (FBG) are numerically investigated. Time-delay (TD) signatures of the feedback are examined through various means including self-correlations of intensity time-series of individual polarizations, cross-correlation of intensities time-series between both polarizations, and permutation entropies calculated for the individual polarizations. The results show that the TD signatures can be clearly suppressed by selecting suitable operation parameters such as the feedback strength, FBG bandwidth, and Bragg frequency. Also, in the operational parameter space, numerical maps of TD signatures and effective bandwidths are obtained, which show regions of chaotic signals with both wide bandwidths and weak TD signatures. Finally, by comparing with a VCSEL subject to feedback from a mirror, the VCSEL subject to feedback from the FBG generally shows better concealment of the TD signatures with similar, or even wider, bandwidths.
Highlights
External cavity feedback (ECF) is the most commonly used technique to drive a semiconductor laser (SL) into chaotic states [1,2,3,4,5,6,7,8,9]
Based on the spin-flip model (SFM) formulism, the intensity time-series for both x-polarization components (PCs) and y-PC are calculated, where self-correlations, cross-correlations, and permutation entropies are used to quantitatively evaluate the TD signatures
The results show that, under suitable operational parameters, the TD signatures of chaos in both polarizations can be suppressed efficiently by the fiber Bragg grating (FBG) instead of the mirror for feedbacks
Summary
External cavity feedback (ECF) is the most commonly used technique to drive a semiconductor laser (SL) into chaotic states [1,2,3,4,5,6,7,8,9]. The chaotic output from an ECF-SL typically contains obvious signatures of the time-delay (TD) originating from the optical round trip between the laser and the external feedback mirror [5, 6]. Such TD signatures of chaos can potentially compromise the security in optical chaos encryption systems [7,8,9]. We investigated the TD features of a chaotic VCSEL under variable-polarization feedback from a grating [28], but only the total output intensity was considered without resolving the two polarization components (PCs) This was due to the challenge of operating the VCSEL with two co-existing PCs in chaos. When compared to the conventional ECF-VCSEL using a mirror, the feedback from the FBG is found to generally show better concealment of the TD signatures, illustrating the benefits of using FBG feedback on the VCSEL
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