Polarization-preserved Optical Feedback Research Articles

Performance Enhancement of a Delay-Based Reservoir Computing System by Using Gradient Boosting Technology

Gradient boosting technology has been proved to be an effective scheme for enhancing the performances of spatially distributed reservoir computing (RC) systems. In this work, a gradient boosting scheme by combining two reservoirs is proposed and numerically investigated in a delayed-based RC system. The original reservoir in the delayed-based RC system is a vertical-cavity surface-emitting laser (VCSEL) under polarization-rotated optical feedback (PR-OF), and it is trained on the desired output. The other VCSEL under PR-OF or polarization-preserved optical feedback (PP-OF) is supplemented to be an extra reservoir, which is trained on the remaining error of the original reservoir. Via Santa-Fe time series prediction task and 10th-order nonlinear autoregressive moving average (NARMA10) task, the performances of the delay-based RC system are evaluated before and after supplementing the extra reservoir, and then the effectiveness of the gradient boosting technology in the delayed RC system can be analyzed. The simulated results demonstrate that adopting gradient boosting technology is effective in a delay-based RC system. Comparatively speaking, the enhanced effect is more obvious under taking a VCSEL with PR-OF as the extra reservoir.

Parallel information processing by a reservoir computing system based on a VCSEL subject to double optical feedback and optical injection.

In this work, we propose a scheme of reservoir computing (RC) for processing a Santa-Fe time series prediction task and a signal classification task in parallel, and the performances of the RC have been numerically investigated. For this scheme, a vertical-cavity surface-emitting laser (VCSEL) simultaneously subject to double optical feedback and optical injection is utilized as a nonlinear node, and the parallel information processing of the RC system is implemented based on the dynamical responses of X polarization component (X-PC) and Y polarization component (Y-PC) in the VCSEL. Considering that two different feedback frames (polarization-preserved optical feedback (PP-OF) or polarization-rotated optical feedback (PR-OF)) may be adopted in two feedback loops, four feedback combination cases are numerically analyzed. The simulated results show that the parallel processing ability of the proposed RC system depends on the feedback frames adopted in two loops. After comprehensively evaluating the parallel processing performances of the two tasks under different feedback combinations, the best parallel processing performance can be achieved by adopting PP-OFs in both two feedback loops. Under some optimized operation parameters, this proposed RC system can realize the lowest prediction error of 0.0289 and the lowest signal classification error of 2.78 × 10-5.

Dual-channel physical random bits generation by a master-slave vertical-cavity surface-emitting lasers chaotic system

Taking the chaotic output from a master-slave framework chaotic system as chaotic entropy resource, we propose a scheme for acquiring dual-channel high-speed physical random bits (PRBs). For such a scheme, a vertical-cavity surface-emitting laser (VCSEL) under polarization-preserved optical feedback from a fiber Bragg grating is utilized as the master VCSEL (M-VCSEL). Under suitable operating parameters, both X and Y polarization components (X-PC and Y-PC) of the M-VCSEL can output chaotic signals with comparable power and weak time-delay signatures. The chaotic outputs from the X-PC and Y-PC of the M-VCSEL are divided into two parts, and then injected into the corresponding polarized component of another VCSEL (named as slave VCSEL, S-VCSEL) after undergoing different flight-time, and such an injection method is named as dual-path polarization-preserved optical injection (DP-PPOI). The X-PC and Y-PC in the S-VCSEL under DP-PPOI can simultaneously output chaotic signals with enhanced bandwidth, which are quantified by 8-bit analog-to-digital converters and taken as the entropy sources for generating dual-channel bit sequence after adopting m least significant bits (m-LSBs) extraction and logical exclusive-OR post-processing. Finally, the randomness of the bit sequences generated under optimized parameters is tested by NIST SP 800-22 statistical test suite. The results demonstrate that dual-channel random bits at rate of 500 Gbit s−1 can be obtained, and the rate of random bits can be further increased to 1 Tbit s−1 through adopting cross-merging method.

Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback.

In this paper, the influence of the rotating polarization-preserved optical feedback on the chaos synchronization of a vertical-cavity surface-emitting laser (VCSEL) is investigated experimentally. Two VCSELs' polarization modes (XP) and (YP) are gradually rotated and re-injected back into the VCSEL. The anti-phase dynamics synchronization of the two polarization modes is evaluated using the cross-correlation function. For a fixed optical feedback, a clear relationship is found between the cross-correlation coefficient and the polarization angle θp. It is shown that high-quality anti-phase polarization-resolved chaos synchronization is achieved at higher values of θp. The maximum value of the cross-correlation coefficient achieved is -0.99 with a zero time delay over a wide range of θp beyond 65° with a poor synchronization dynamic at θp less than 65°. Furthermore, it is observed that the antiphase irregular oscillation of the XP and YP modes changes with θp. VCSEL under the rotating polarization optical feedback can be a good candidate as a chaotic synchronization source for a secure communication system.

Nonlinear dynamics of 1550 nm VCSELs subject to polarization-preserved optical feedback and orthogonal optical injection

Based on spin-flip model (SFM), the nonlinear dynamics of 1550 nm vertical-cavity surface-emitting lasers (VCSELs) subject to polarization-preserved optical feedback (PPOF) and orthogonal optical injection (OOI) are theoretically investigated. The results show that two linear polarization (LP) modes can be simultaneously stimulated and polarization switching (PS) can be observed, which is different from the case that only y LP mode exists in a VCSEL with PPOF. Under the joint action of PPOF and OOI, the two LP modes will exhibit rich dynamical states, such as period one, period two, multiperiod and chaos oscillation. Different evolution routes to chaos can be also observed. Moreover, frequency detuning Δf (Δf = f m − f s, where f m and f s are the center frequencies of free-running master VCSEL and slave VCSEL, respectively) has an obvious influence on the PS. With the increase of the positive frequency detuning PS points shift toward larger injection strengths; meanwhile, a suitable negative frequency detuning value makes the injection strength for PS be the lowest.

Impact of optical feedback on current-induced polarization behavior of 1550 nm vertical-cavity surface-emitting lasers

Polarization switching (PS) between two orthogonal linearly polarized fundamental modes is experimentally observed in commercial free-running 1550 nm vertical-cavity surface-emitting lasers (VCSELs) (Raycan). The characteristics of this PS are strongly modified after introducing a polarization-preserved (PP) or polarization-orthogonal (PO) optical feedback. Under the case that the external cavity is approximately 30 cm, the PP optical feedback results in the PS point shifting toward a lower injection current, and the region within which the two polarization modes coexist is enlarged with the increase of the PP feedback strength. Under too-strong PP feedback levels, the PS disappears. The impact of PO optical feedback on VCSEL polarization behavior is quite similar to that of PP optical feedback, but larger feedback strength is needed to obtain similar results.

Numerical characterization of time delay signature in chaotic vertical-cavity surface-emitting lasers with optical feedback

We have discussed numerically the characterization of time delay (TD) signature in a chaotic vertical-cavity surface-emitting laser (VCSEL) subject to optical feedback, where the results for polarization-preserved optical feedback (PPOF) and polarization-rotated optical feedback (PROF) are presented comparatively. It is found that, when the feedback strength is moderate, TD signature can be retrieved successfully by analyzing the total intensity, intensities of x-linearly polarized (x-LP) mode, and y-LP mode in a VCSEL with PPOF; while for PROF case, the intensity amplitude peaks in autocorrelation function (ACF)/delayed mutual information (DMI) of the two orthogonal LP modes are located at multiple values of TD. Furthermore, the influence of the feedback strength and time delay has been investigated. The results show that, a further increase of the feedback strength (roughly>40ns−1) leads to the successful identification of the TD signature in the two LP mode intensities of VCSELs with PROF. It is also observed that the estimation of TD depends significantly on the value of the spin–flip relaxation rate (γs). For low relaxation rates the TD signature could be much easier to be revealed by the two LP modes than that for large values of relaxation rate in VCSELs with PROF. Finally the influence of injection current and the device linear anisotropies is investigated, and the results of TD estimation are confirmed by calculating permutation entropy (PE).

Nonlinear dynamics of 1550 nm vertical-cavity surface-emitting laser with polarization- preserved optical feedback

Based on the framework of the spin-flip model, the nonlinear dynamics of 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to polarization-preserved optical feedback is theoretically investigated. The results show that for a free-running 1550 nm-VCSEL, the current value for polarization switching (PS) is affected seriously by the internal parameters; with the increase of the gain anisotropy coefficient γa, the corresponding current for PS increases. Due to the introduction of the polarization-preserved optical feedback, the dominant polarized mode (Y polarized mode) will display different dynamical states for different injection currents while the other mode (X polarized mode) may be excited. As a result, the average output powers of the two polarized modes increase with fluctuation with the increase of current. For different feedback times, the dynamic states of 1550 nm-VCSEL with polarization- preserved optical feedback maybe route into chaos via different evolution paths such as period doubling bifurcation, quasi-periodic bifurcation and intermittent chaos.

Quantifying Chaotic Unpredictability of Vertical-Cavity Surface-Emitting Lasers With Polarized Optical Feedback via Permutation Entropy

To quantify the unpredictability of chaotic signals generated by vertical-cavity surface-emitting lasers (VCSELs) subject to polarized optical feedback, we numerically investigate the properties of recently introduced quantifier based on information theory, i.e., permutation entropy (PE) <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> . VCSEL1 subject to polarization-preserved optical feedback and VCSEL2 subject to polarization-rotated optical feedback are considered. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> for X-polarization (XP) mode, Y-polarization (YP) mode, and total output for both VCSELs are discussed and compared in detail. The influences of feedback strengths, feedback delays, and injection currents are focused on. For lower injection current, the 2-D maps illustrate that the trends of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> for the XP mode, YP mode, and total output are different for both VCSELs. While for higher injection current, the values of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> for both VCSELs increase with the feedback strengths, are not sensitive to feedback delays, and are higher than the counterparts for lower injection current. Moreover, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> increases with injection current for both VCSELs with a decreasing slope. These results show that the PE is an effective tool for quantifying the degree of unpredictability of chaotic signals of VCSELs, and provides valuable information for choosing the proper chaotic carrier.

Chaos synchronization and communication of the polarization modes for two unidirectionally coupled vertical-cavity surface-emitting lasers

We theoretically investigate the synchronization performance of the polarization modes of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs), where the master VCSEL subjects to polarization-preserved optical feedback and the slave VCSEL subjects to polarization-preserved optical injection. We demonstrate that high synchronization can be achieved between corresponding polarization components of the master laser and the slave laser. We also analyze the influence of the internal mismatched parameters on the synchronization performance. Furthermore, this system is used to dual-channel communication and the different transmitted digital information is respectively recovered at each polarization branch of the slaver laser successfully with the encryption scheme of chaos masking (CM). The results open an opportunity for multichannel chaotic communication by utilizing different polarization components in single-mode or multi-transverse-mode VCSELs.

Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection

A novel dual-channel chaotic synchronization configuration is proposed. This system is constructed on the basis of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs), where a VCSEL subjected to polarization-rotated optical feedback is used as a transmitter and the other VCSEL subjected to polarization-rotated optical injection is used as a receiver. The synchronization and communication performances of such a system are numerically investigated. The results show that, similar to polarization-preserved coupled system with polarization-preserved optical feedback at the T-VCSEL port and polarization-preserved optical injection at the R-VCSEL port, such polarization-rotated coupled system can also realize complete synchronization between each pair of linear polarization (LP) modes and the total output of T-VCSEL and R-VCSEL. Compared with the polarization-preserved coupled system, this proposed system has higher tolerance to mismatched parameters. Furthermore, the average intensities of two orthogonal LP modes are almost the same so that this framework may be used to realize dual-channel chaos communication. Under the additive chaos modulation (ACM) encryption scheme, the encoded messages can be successfully extracted for both of orthogonal LP modes.

The effects of polarization-resolved optical feedback on the relative intensity noise and polarization stability of vertical-cavity surface-emitting lasers

The relative intensity noise of vertical-cavity surface-emitting lasers (VCSELs) subject to polarization-resolved optical feedback has been investigated experimentally. A comparison is made of the effects of polarization-selective and polarization-preserving optical feedback on the polarization stability of VCSELs. The experiments show that polarization-selective optical feedback has a greater effect on the dynamics of VCSELs than polarization-preserved optical feedback. Polarization-selective optical feedback can be used to control the polarization stability of the VCSEL operating near the polarization-switching current and is easier to affect the dynamics of the VCSEL in the polarization stable regime