Double Optical Feedback Research Articles

Dynamics of Semiconductor Laser Coupled with Two External Cavities

An investigation into the dynamic states and relative intensity noise of laser diodes subjected to double optical feedback has been conducted. We employed modified and improved time-delay rate equations to account for double external optical feedback. The dynamic states and noise of lasers will be investigated using bifurcation diagrams of the output photon number, its temporal variations, and the intensity noise of the laser. This analysis considers feedback strengths due to the double external cavity and their spacing from the front facet of the laser with and without phase due to feedback. The results reveal that considering phase causes significant variations in laser intensity and a phase shift in the temporal variations of the laser output. This results in relative intensity noise suppression and a frequency shift in the intensity noise spectrum. These findings represent new contributions to our understanding of the reliance of lasing frequency shift on the phase due to feedback, regardless of whether feedback originates from a single or double external cavity. We investigated the optimal conditions corresponding to stable dynamic states of the laser with the lowest noise level. Additionally, we identified conditions that result in chaotic dynamics, where the spectrum does not convey information about the laser system. These insights have potential applications in chaotic and secure optical data encryption.

Privacy protection for 3D point cloud classification based on an optical chaotic encryption scheme.

In allusion to the privacy and security problems in 3D point cloud classification, a novel privacy protection method for 3D point cloud classification based on optical chaotic encryption scheme is proposed and implemented in this paper for the first time. The mutually coupled spin-polarized vertical-cavity surface-emitting lasers (MC-SPVCSELs) subject to double optical feedback (DOF) are studied to generate optical chaos for permutation and diffusion encryption process of 3D point cloud. The nonlinear dynamics and complexity results demonstrate that the MC-SPVCSELs with DOF have high chaotic complexity and can provide tremendously large key space. All the test-sets of ModelNet40 dataset containing 40 object categories are encrypted and decrypted by the proposed scheme, and then the classification results of 40 object categories for original, encrypted, and decrypted 3D point cloud are entirely enumerated through the PointNet++. Intriguingly, the class accuracies of the encrypted point cloud are nearly all equal to 0.0000% except for the plant class with 100.0000%, indicating the encrypted point cloud cannot be classified and identified. The decryption class accuracies are very close to the original class accuracies. Therefore, the classification results verify that the proposed privacy protection scheme is practically feasible and remarkably effective. Additionally, the encryption and decryption results show that the encrypted point cloud images are ambiguous and unrecognizable, while the decrypted point cloud images are identical to original images. Moreover, this paper improves the security analysis via analyzing 3D point cloud geometric features. Eventually, various security analysis results validate that the proposed privacy protection scheme has high security level and good privacy protection effect for 3D point cloud classification.

Chaotic characteristics of output light from semiconductor laser with self-chaotic phase modulation and optical feedback

<sec>Distributed feedback semiconductor lasers (DFB-SLs) are the class B lasers, and would output chaotic laser under the external disturbances, such as external optical feedback and optical injection. Chaotic laser are widely used in many fields, including optical fiber sensing, chaotic laser secure communication, and better entropy sources for generating high-speed random number. However, the chaotic laser outputted from the semiconductor lasers with external cavity optical feedback produces a time delay signature (TDS) , which limits the applications of chaotic laser. On the other hand, the bandwidth (BW) of chaotic carrier signal plays the important role in determining the transmission rate of information signal. Therefore, the TDS and BW are two important parameters that will affect chaotic laser’s applications, and they are usually used to describe the chaos characteristics of chaotic laser.</sec><sec>In this paper, we present a new scheme used to describe the TDS and investigate the BW of chaotic laser from semiconductor laser. For this scheme, the output laser from a DFB-SL with external single optical feedback is injected in double ways into another DFB-SL with phase modulation optical feedback by self chaos light. Thus they form a semiconductor laser system with external double optical injection and phase modulation optical feedback by self chaos light (SL-EDOI-PMOFBSCL). We investigate numerically the influences of the system parameters on TDS, such as the injection coefficient and feedback coefficient. Then the suppression effects on TDS are contrasted and analyzed with two other systems, that is to say, the semiconductor laser with external double optical injection and optical feedback (SL-EDOI-OF) and the semiconductor laser with external single optical injection and phase modulation optical feedback by self chaos light (SL-ESOI-PMOFBSCL). The results indicate that the proposed scheme in this work has the better suppression effect on TDS. Then the BW of the chaotic laser is investigated under the parameters conditions of effectively suppressing TDS. The simulation results show that the scheme proposed in this work can enhance the BW of chaotic laser by appropriately selecting the parametric values, and the maximum BW value of the obtained chaotic laser reaches about 16 GHz.</sec>

Bidirectional digital image secure transmission and recognition based on a long-distance chaos synchronization system with machine learning capability

Based on chaos synchronization of two response lasers (RLs) injected by the common chaos signals from a driving laser (DL) with double optical feedback (DOF) and an additional neural network (NN), a bidirectional chaotic secure communication system with machine learning capability is proposed and the long-distance digital image transmission and recognition performances are numerically investigated. The simulated results show that the time delay signature (TDS) of the driving chaotic signals from DL with DOF is greatly weakened under suitable operation conditions. Two RLs can generate chaos signals with low TDS and broad bandwidth, and the high-quality chaos synchronization between two RLs can be achieved while the synchronization quality between DL and any one of RLs is extremely bad, which is helpful to realize the secure communication. Using the synchronized chaos output signals from two RLs as chaos carriers and chaos masking (CM) encoding method, the bidirectional 10 Gb/s secure communication over 140 km fiber channel can be realized and the effects of the fiber parameters on the communication performances are discussed. After adopting an additional NN, a long-distance digital image transmission and recognition based on this proposed secure communication system can be realized and the communication distance can be extended to 220 km.

Time delay signature and bandwidth of chaotic laser output from semiconductor laser

<sec> Semiconductor laser (SL) can output chaotic lasers under external disturbances such as optical injection or optical feedback, and the bandwidth can reach up to GHz magnitude. External-cavity feedback semiconductor lasers can output high-dimensional chaotic lasers and are considered to be better sources of chaotic entropy. However, due to external cavity feedback and other effects, it will give rise to obvious external cavity time delay signature (TDS) in the output chaotic laser, which restricts the application of chaotic lasers. On the other hand, the bandwidth of chaotic laser determines the transmission rate of confidential communication, and therefore TDS and bandwidth are two important parameters that will affect chaotic laser’s applications. Therefore, it is significant to take appropriate measures to suppress the TDS and increase the bandwidth of chaotic laser output by semiconductor laser. </sec><sec> In this paper the output laser from a semiconductor laser with single optical feedback is partially injected to another semiconductor laser with double filtered optical feedback. Thus they form a semiconductor laser system with external optical injection and double filtered optical feedback, i.e. a master-slave laser system which is used to suppress the TDS of chaotic laser and investigate its bandwidth. We numerically investigate the influences of external light injection coefficient, feedback intensity, pumping factor, and filter bandwidth on TDS. Then the suppression effects of this system on TDS are analyzed and compared with those of semiconductor laser system with external optical injection and single optical feedback, those of semiconductor laser system with external optical injection and double optical feedback, those of semiconductor laser system with external optical injection and single filtered optical feedback, and those of semiconductor laser system with double filtered optical feedback. The results show that the proposed scheme in this paper has the best suppression effect on TDS. Then the bandwidth of the chaotic laser output from the system is investigated under the condition of parameters of effectively suppressing TDS. The results show that the system proposed in this paper can increase the bandwidth of the system output chaotic laser by properly selecting the parametric values, and the maximum bandwidth value of the obtained chaotic laser is about 8.8 GHz. The above investigations indicate the effectiveness of the proposed scheme. The results of this investigation are significant for the application of chaotic lasers. </sec>

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.

Statistics of chaos in a bursting laser

We demonstrate experimentally how semiconductor lasers subjected to double optical feedback change the statistics of their chaotic spiking dynamics from Gaussian to long-tail Power Law distributions associated to the emergency of bursting. These chaotic regimes, which are features of excitable complex systems, are quantified by the tail exponent $\alpha$ and appear by changing the ratio between the feedback times. Transitions to bursting occur in the neighbourhood of low order Farey fractions. The physics behind these transitions is related to the variation of threshold pump current in the compound system as obtained from a deterministic set of rate equations. Numerical integration also verifies the observed chaos transitions indicating the possibility of controlling the bursting chaotic statistics.

Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection.

A reservoir computing (RC) system based on a semiconductor laser (SL) with double optical feedback and optical injection is proposed, and the prediction performance of such a system is numerically investigated via Santa Fe Time-Series Prediction task. The simulation results indicate that the RC system can yield a good prediction performance. Through optimizing some relevant operating parameters, ultra-fast information processing rates up to Gb/s level can be realized for the prediction error is below 3%.

Time delay characteristics and bandwidth of chaotic laser from semiconductor laser

The center wavelength of the distribution feedback semiconductor laser is about 1550 nm, and it is in the lowest loss window of the optical fiber communication. A distribution feedback semiconductor laser (DFB-SL) can generate wideband chaotic signals under external disturbances such as optical feedback, optical injection, etc. Thus, due to the simple structure, DFB-SLs with the optical feedback are widely applied to many fields, including information security, lasers radar, and physical entropy sources for generating physical random numbers. However, optical feedback can cause weak periodicity in chaotic signals from the semiconductor laser, and increase the time delay characteristics of chaotic laser, moreover reduce the quality of random numbers generated by using chaotic signals. Meanwhile, to meet the needs of the current high speed and large capacity communication, the DFB-SL, which can generate wideband chaotic laser with low time delay characteristics, has received wide attention and become a hot research subject.In this paper, we present a new scheme for suppressing the time delay characteristics and investigating the bandwidth (BW) of chaotic signals from the semiconductor laser. In this scheme, we build a system that is a distribution feedback semiconductor laser with double phase modulated optical feedback (DFB-SL-DPMOF). In this system, two phase modulators driven by the pseudorandom signals are respectively added to the two optical feedback cavities to eliminate the weak periodicity of the generated chaotic signals. For this system, we numerically investigate the influence of the system parameter, such as the delay time, feedback coefficient, etc., on the time delay characteristic of the chaotic laser. In this paper, the time delay characteristic of chaotic signal is expressed by the maximum value of the time delay signature (TDS) peak of the autocorrelation function curve. Then, to illuminate the effectiveness of this system, other two systems, i.e., DFB-SL with double optical feedback (DFB-SL-DOF) and DFB-SL with single phase modulated optical feedback (DFB-SL-SPMOF) are considered. We study the suppression effect of the system on the TDS among DFB-SL-DPMOF, DFB-SL-DOF and DFB-SL-SPMOF. For these three systems, we give and analyze the simulation curves of the time delay characteristic values with the feedback coefficient and the pumping factor respectively. The results indicate that our proposed scheme has the best suppression effect. Moreover, we numerically investigate the BW of chaotic signals from DFB-SL-DPMOF based on the parameter conditions suppressing TDS effectively. The results show that BW becomes large with the pumping factor and feedback coefficient increasing, and the maximum BW value of the obtained chaotic laser is about 7.2 GHz. Therefore the effectiveness of the presented scheme is numerically clarified. And the conclusions of this paper are useful for applying the chaotic laser to the secure communication field.

Concealment of time delay signature of chaotic output in a slave semiconductor laser with chaos laser injection

An improved chaotic laser system, which has a slave semiconductor laser (SL) injected by a master SL with double optical feedback (DOF), is proposed, so that the time delay (TD) signature can be successfully concealed from both intensity and phase chaos via choosing appropriate parameters. The TD signature is investigated by employing autocorrelation function (ACF) and mutual information (MI) function. Through analyzing the influence on TD signature in the region of injection current and injection strength for the slave SL, we find that, for both intensity chaos and phase chaos, the TD signature can be easily concealed under weak injection strength. When the injection strength is strong, we can not only successfully conceal TD signature, but also improve the bandwidth of chaotic laser output by choosing the optimal detuning frequency.

双光反馈双光注入混沌半导体激光器延时特征峰抑制

双光反馈双光注入混沌半导体激光器延时特征峰抑制

Theoretical and experimental investigation on the narrow-linewidth photonic microwave generation based on parallel polarized optically injected 1550 nm vertical-cavity surface-emitting laser

Photonic microwave generation has attracted much attention in recent years due to its potential applications in various fields such as radio-over-fiber communication, signal processing and radar systems. So far, different photonic microwave generation schemes have been proposed and investigated, such as the optical heterodyne method based on the beat of two independent lasers with a certain wavelength difference, the external modulation method based on electro-optical modulator, the dual-mode beat method based on the monolithic dual-mode semiconductor lasers, and the optoelectronic microwave oscillator method based on optoelectronic feedback loops. These schemes have their own advantages and deficiencies. Unlike the above schemes, in this paper we propose an all optical scheme for generating high-quality microwave based on a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL). For such a scheme, high frequency microwave can be obtained based on a 1550 nm-VCSEL subjected to external optical injection, where the polarization of the injected light is the same as that of the dominant mode of the free-running 1550 nm-VCSEL (named parallel-polarized optical injection) and its wavelength is adjusted to being close to the wavelength of the suppressed polarization mode of the free-running 1550 nm-VCSEL. With the aid of double optical feedback, the linewidth of the obtained microwave can be narrowed. In this work, firstly, the feasibility of microwave generation based on parallel-polarized optically injected 1550 nm-VCSEL is analyzed theoretically by using the spin-flip model. Next, a corresponding experimental system is constructed, and the performance of microwave generation is preliminarily investigated experimentally. The experimental results show that 30 GHz microwave signals could be obtained based on a parallel-polarized, optically injected 1550 nm-VCSEL under suitable injection parameters, but the linewidth of microwave signal is relatively wide (hundreds of MHz). Finally, after introducing double optical feedback, the linewidth of microwave signal can be reduced by more than two orders of magnitude and narrowed to less than 1 MHz, meanwhile the signal-noise ratio is larger than 40 dB. This work is helpful to develop relevant techniques to acquire high-performance narrow linewidth photonic microwave.

Dual-channel chaos synchronization and communication based on a vertical-cavity surface emitting laser with double optical feedback

Using two orthogonal polarization mode outputs from a vertical-cavity surface emitting lasers (VCSEL) with double optical feedback as two chaotic carriers, a dual-channel chaos secure communication system is established, and the synchronization and communication performances of such a system are numerically investigated. The results show that under suitable operated condition, the time-delay signatures of two chaotic carriers originating from two linear polarization modes in the T-VCSLE with double optical feedback can be suppressed efficiently. Under the strong injection locking case, high-quality chaos synchronization between two corresponding modes of T-VCSEL and R-VCSEL can be realized by polarization-preserved optical injection from T-VCSEL to R-VCSEL. Moreover, the tolerance of the synchronization quality on the frequency detuning between T-VCSEL and R-VCSEL is enhanced with the increase of the injection strength. Adopting additive chaos modulation encryption scheme, two pieces of 500 Mbit/s encoded message can be hidden efficiently in the two chaotic carriers in the propagation process and can be successfully extracted at the receiver. Although Q factor decreases with the increase of message transmission rate, the values of Q factor for two channels are still larger than 6 for 6 Gbit/s message.

Can Fixed Time Delay Signature be Concealed in Chaotic Semiconductor Laser With Optical Feedback?

External-cavity lasers are usually used for chaos encryption in optical chaos-based communication systems. The external-cavity round-trip time (the time delay in the laser dynamics) is often regarded as an additional key to encode messages, which is a critical security parameter. The feasibility of identifying the time delay has been a crucial issue in chaotic optical communication. Some researchers propose that the time delay can be hidden by modulating the value of feedback strength or increasing the number of feedback cavities. In this paper, we experimentally and numerically demonstrate that the time delay signatures cannot be concealed in optical feedback semiconductor lasers. Whether single or double optical feedback, the time delay signatures can all be identified by the power spectrum analysis method. Furthermore, adjusting the feedback strength, the pumping current and the time-delay value, we find that the extraction of the time delay signatures still cannot be influenced.

Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback

In order to obtain a chaotic series with weak time-delay (TD) signature, a chaotic system based on a vertical-cavity surface-emitting laser (VCSEL) subject to double variable-polarization optical feedback (DVPOF) has been proposed. With the aid of the peak signal to mean ratio (PSMR) calculated from the self-correlation function (SF), the TD signature of chaotic output generated by this system has been investigated numerically and compared with that generated by a VCSEL with single variable-polarization optical feedback (SVPOF). After evaluating the variation of PSMR with the polarizer angle under different feedback strengths and injection currents for this presented chaotic system, the results show that such a DVPOF system is more conducive to generate low TD signature chaotic series than a SVPOF system.

Unidirectional open-loop chaotic synchronization communication based on a semiconductor laser with double optical feedback

Using a semiconductor laser with double optical feedback as a chaos transmitter, a unidirectional chaotic synchronization communication system is constructed, and the performances of such a system are investigated numerically. The results show that by selecting reasonable parameters, the time delay behaviour of chaotic carrier generated by the semiconductor laser with double optical feedback can be suppressed efficiently; through the strong injection from transmitter to receiver, the perfect synchronization between transmitter and receiver can be realized, and the synchronization quality has a high tolerance to frequency detuning between transmitted laser and received laser; under the additive chaos modulation encryption scheme, the 500 Mbits/s encoded message can be hidden efficiently in the chaotic carrier and successfully extracted at the receiver.

Extracting the external-cavity key of a chaotic semiconductor laser with double optical feedback by spectrum analyzer

Optical-feedback laser diodes have been widely applied in chaotic optical communication, because it can simply generate wideband and high-dimension chaos and its external-cavity length is often regarded as an additional key. In this paper, it is experimentally demonstrated that the time delay signature of a chaotic laser diode with optical feedback can be identificated. Through locally enlarging the power spectral of chaotic light and observing its fine structure, the external-cavity key can be directly extracted by the spectrum analyzer, regardless of the laser diode with single or dual optical feedback of different external cavity length ratio.

双光反馈半导体激光混沌高复杂度优化分析

双光反馈半导体激光混沌高复杂度优化分析

Suppression of time delay feedback signatures in a semiconductor laser with double optical feedback

In a double optical feedback semiconductor laser chaotic system, by fixing the feedback time and feedback strength of the one mirror (named as fixed cavity M1), the influences of the feedback time and feedback strength of the other mirror (named as tunable cavity M2) on the time delay feedback signatures of the chaotic system have been investigated experimentally. The results show that, for the case of the two cavities with identical feedback strengths, time delay feedback signatures of chaotic output can be suppressed efficiently when the cavity length of M2 is approximately equal (but can not exactly equal) to the cavity length of M1 (or half of the cavity length of M1). Fixing the length of M2 to approximately equal to the cavity length of M1 (or half of the cavity length of M1), the time delay feedback signature suppression can be further improved through adjusting the feedback strength of M2 carefully. Therefore, adopting a double optical feedback semiconductor laser chaotic system can make the system behave with higher security due to the efficient hiding of delay feedback parameter of the system.

双光反馈半导体激光混沌系统的外腔反馈强度对延时特征的影响

Through constructing a double optical feedback semiconductor laser chaotic system,the time delay signatures of chaos are investigated experimentally under different working conditions.The results show that,time delay signatures of chaotic output can be suppressed efficiently through adjusting the feedback strength of one cavity carefully and fixing the feedback strength of another cavity.Meantime,there is a big time shift which is the deviation between extracted delay time and real system delay time.Therefore,double optical feedback semiconductor laser chaotic system can efficiently hide the delay time signature of chaotic laser output,and also improve the performance in related application fields.