Time-delay Signature Research Articles

Ultra-wideband chaotic optical communication based on electro-optic differential feedback loop

A differential feedback electro-optical phase chaotic system is proposed to generate ultra-wideband optical chaos and realize high-speed long-distance chaotic communication. The nonlinear dynamics of this differential feedback loop are studied in detail. The numerical results show, firstly, in terms of chaos complexity, the highest permutation entropy of 0.993 and the largest spectral entropy of 0.945 are achieved. Regarding the key hiding, the time delay signature of phase chaos on both the autocorrelation function and delayed mutual information can be completely suppressed, so security can be guaranteed. Secondly, the maximum bandwidth of the radio spectrum is 46.75 GHz in the range of 50 GHz, and the minimum flatness is 1.62 dB/GHz. Finally, the reception of format-transparent messages can be realized by combining co-drive synchronization and coherent demodulation. The 50 GBaud QPSK signal can transmit 2400 km and the 25 GBaud 16 QAM signal can transmit 1500 km at an OSNR of 25 dB. This system realizes ultra-wideband high-complexity chaos and chaotic communication, which can greatly improve the security, transmission distance, and transmission rate of chaotic optical communication.

Electro-optical chaotic communication system based on additional chaotic phase-shift with time-delay signature concealment

We propose and demonstrate an electro-optical chaotic communication system with additional chaotic phase-shift based on the mutual coupling structure. Under the condition of complete concealment of time-delayed signatures (TDSs), the key space of the system is greatly enhanced and highly reliable chaotic communication is finally realized. The additional-phase introduced by the new branch is nonlinearly superimposed on the phase generated by the chaotic signal of the original branch, which improves the complexity and aperiodicity of chaos. For security performance, the system only needs a very small feedback gain (i.e., βi = 2.5) to conceal TDSs. Moreover, since the system has only one chaotic signal transmitted in the transmission link, it overcomes the exposure of TDSs caused by the cross-correlation characteristics between different links. At the same time, the system has strong synchronization robustness and can achieve high-quality communication when the parameters are well-matched. To sum up, the proposed system can effectively resist eavesdropping, which provides security for the physical layer of optical networks.

Evolution of the time delay signature of chaos generated in three types of optical injection systems.

The time delay signature (TDS) of chaos generated in three schemes of optical injection has been investigated, and the mechanism of TDS suppression (TDSS) is revealed. The first scheme is a continuous-wave (CW) laser unidirectionally injecting into a chaotic laser, and the TDS of the chaotic laser is suppressed below 0.08 in this structure. The second scheme is a chaotic laser unidirectionally injecting into a CW laser, where the parameter range of TDSS lower than 0.06 of this structure is the largest among the three schemes. The third scheme is two CW lasers coupling to each other, and two chaotic lasers with TDS (T D S<0.1) suppression can be obtained simultaneously. For the further analysis of the mechanism of TDSS, the quasi-linear relationship between the synchronization coefficient and TDS is revealed. This study will provide insight into the generation of chaotic lasers by optical injection and promote the application of chaotic lasers.

Critical dispersion of chirped fiber Bragg grating for eliminating time delay signature of distributed feedback laser chaos

Optical chaos has attracted widespread attention owing to its complex dynamic behaviors. However, the time delay signature (TDS) caused by the external cavity mode reduces the complexity of optical chaos. We propose and numerically demonstrate the critical dispersion of chirped fiber Bragg grating (CFBG) for eliminating the TDS of laser chaos in this work. The critical dispersion, as a function of relaxation frequency and bandwidth of the optical spectrum, is found through extensive dynamics simulations. It is shown that the TDS can be eliminated when the dispersion of CFBG is above this critical dispersion. In addition, the influence of dispersive feedback light and output light from a laser is investigated. These results provide important quantitative guidance for designing chaotic semiconductor lasers without TDS.

Security-Enhanced Electro-Optic Mutual Injection Secure Communication Scheme With Time-Delay Signature Suppressing

In this article, we propose and numerically demonstrate a novel dual-phase modulated time-delay signature (TDS) concealed communication system. The proposed system addresses the fatal disadvantage of conventional electro-optic chaotic systems in that TDS is vulnerable to detection. Combined with the dispersive devices ahead, which significantly expands the complexity of the signal, the scheme perturbs the transmitted data with the mutual injection of the feedforward and feedback branches in the phase, strengthening the nonlinear effect of the system considerably. In addition, the key space of the system against illegal users’ exhaustive attack within reasonable parameters reaches 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> , which is 14 orders of magnitude larger than that of the classical electro-optic system. A confidential 32 G/s OOK signal was transmitted over 100 km and successfully recovered. Numerical results demonstrate that the chaotic system can tolerate minor parameter mismatches which are controllable in practice, proving that the system can be used for secure communication.

Long-range chaotic Brillouin optical correlation domain analysis with more than one million resolving points

We propose and experimentally demonstrate a long-range chaotic Brillouin optical correlation domain analysis by employing an optimized time-gated scheme and differential denoising configuration, where the number of effective resolving points largely increases to more than one million. The deterioration of the chaotic Brillouin gain spectrum (BGS) and limitation of sensing range owing to the intrinsic noise structure, resulting from the time delay signature (TDS) and nonzero background of chaotic laser, is theoretically analyzed. The optimized time-gated scheme with a higher extinction ratio is used to eliminate the TDS-induced impact. The signal-to-background ratio of the measured BGS is enhanced by the differential denoising scheme to furthest remove the accumulated nonzero noise floor along the fiber, and the pure chaotic BGS is ulteriorly obtained by the Lorentz fit. Ultimately, distributed strain sensing along a 27.54-km fiber with a 2.69-cm spatial resolution is experimentally demonstrated, and the number of effective resolving points is more than 1,020,000.

Monolithically integrated laser with DBR for wideband and low time delay signature chaos generation

Chaotic laser has attracted a large amount of attention due to its broad spectrum, noise-like characteristics, and photonic integrated chaotic semiconductor lasers have further expanded the application field of chaotic laser for their small size and stable properties. Therefore, a monolithically integrated laser with a distributed Bragg reflector (DBR) is designed. This proposed chaotic laser consists of a distributed feedback (DFB) laser section, a phase section, and a DBR section. DBR grating can provide wavelength detuning to generate mode beating, which enhances chaotic bandwidth and distributed feedback to suppress time delay signature (TDS). The transmission line laser model (TLLM) of chaotic laser is constructed and chaotic characteristics of the integrated chip are investigated. A chaotic signal with a bandwidth of 12.34 GHz and TDS less than 0.065 is obtained. In addition, a map of dynamic states in the parameter space of phase section current and DBR section current is shown, and a wide range of chaotic regions are obtained. The results show that the broadband chaotic laser with a low TDS can be obtained by controlling the parameters reasonably, which is beneficial to realize the application of chaotic laser.

Security-enhanced electro-optic chaotic communication system based on the logistic map feedback and dynamic key

In this paper, a novel electro-optic chaotic system based on the logistic map feedback (EOLM) is proposed. The logistic map is used to introduce additional nonlinear effects into the electro-optic feedback loop. The simulation results show that, with the increase of logistic map iterations N, the bandwidth and permutation entropy of the chaotic output can be significantly increased, and the spectrum is flatter. The time-delay signature (TDS) of the system can be concealed within the appropriate range of values of parameters, which ensures the security of the key. Synchronization results show that the system is not only sensitive to time delay T but is also sensitive to the feedback intensity β, so β is also the key of the system. Utilizing the sensitivity to β, a dynamic EOLM communication system with changing key (DEOLM) is designed. Based on chaotic self-control, the chaotic optical signal is transformed nonlinearly to generate the control signal, which drives the gain coefficient of the amplifier to change dynamically, so as to realize the changing of β. Simulation of communication performance shows that the DEOLM system greatly raises the difficulty for the eavesdropper to crack the message and improves the confidentiality of communication.

Numerical and experimental investigation of a dispersive optoelectronic oscillator for chaotic time-delay signature suppression.

Chaos generation from a novel single-loop dispersive optoelectronic oscillator (OEO) with a broadband chirped fiber Bragg grating (CFBG) is numerically and experimentally investigated. The CFBG has much broader bandwidth than the chaotic dynamics such that its dispersion effect rather than filtering effect dominates the reflection. The proposed dispersive OEO exhibits chaotic dynamics when sufficient feedback strength is guaranteed. Suppression of chaotic time-delay signature (TDS) is observed as the feedback strength increases. The TDS can be further suppressed as the amount of grating dispersion increases. Without compromising bandwidth performance, our proposed system extends the parameter space of chaos, enhances the robustness to modulator bias variation, and improves TDS suppression by at least five times comparing to the classical OEO. Experimental results qualitatively agree well with numerical simulations. In addition, the advantage of dispersive OEO is further verified by experimentally demonstrating random bit generation with tunable rate up to 160 Gbps.

Strategy for Attacking the Key Parameters of Electro-Optic Self-Feedback Phase Encryption System

In this paper, we propose a method for cracking the key parameters of an electro-optic self-feedback temporal optical phase encryption system and experimentally demonstrate the feasibility of the scheme. By scanning a tunable dispersion compensation (TDC) module at the receiver, the time delay signature (TDS) of an encrypted signal can be exposed, making it possible to extract other key parameters of the system and reconstruct a decryption setup. The TDS characteristics for three typical modulation formats are investigated, revealing that while such an encryption system is secure against power detection attack, there is a risk of TDS leakage. The findings can guide the design of advanced optical encryption schemes with TDS suppression for security enhancement.

Time-delay signature suppression in single loop optoelectronic oscillators based on sine hyperbolic nonlinear amplifier

Time-delay signature suppression in single loop optoelectronic oscillators based on sine hyperbolic nonlinear amplifier

Time-Delay Signature Concealment in a Security-Enhanced Optical System With Dual-Loop Electro-Optic Self- Feedback Phase Encryption

In this paper, a novel phase encryption scheme based on a dual-loop electro-optic self-feedback structure is proposed for time-delay signature (TDS) concealment. As for a conventional single-loop feedback structure, the TDS is extremely vulnerable to exposure in the common link, resulting in a fatal weakness in the entire security system, whereas, the introduction of an additional feedback branch, brings about the mutual dynamics between the phase feedbacks, and effectively solves the problem. The modulation depth and dispersion values, which are two crucial variables affecting TDS concealment, are investigated in detail. In principle, the scheme is verified to have better robustness, more security, and can supply large key space. Error-free transmission of high-speed signals is possible. Thanks to the aforementioned benefits, the dual-loop electro-optic structure proposed could inspire fresh ideas for secure optical communication systems in the future.

Wideband and high-dimensional chaos generation using optically pumped spin-VCSELs.

We propose and numerically demonstrate wideband and high-dimensional chaos signal generation based on optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs). Here, we focus on the chaotic characteristics of spin-VCSELs under two scenarios: one is a spin-VCSEL with optical feedback and the other is optical heterodyning the outputs of two free-running spin-VCSELs. Specifically, we systematically investigate the influence of some key parameters on the chaotic properties, i.e., bandwidth, spectral flatness (SF), time delay signature (TDS), correlation dimension (CD), and permutation entropy (PE), and reveal the route to enhance these properties simultaneously. Our simulation results demonstrate for the first time that spin-VCSELs with simple auxiliary configurations allow for chaos generation with desired properties, including effective bandwidth up to 30 GHz and above, no TDS of greater than 0.2, the flatness of 0.75 and above, and the high complexity/dimensionality over a wide range of parameters under both schemes. Therefore, our study may pave the way for potential applications requiring wideband and high-dimensional chaos.

Security-enhanced watermark embedding and transmission based on synchronized chaotic semiconductor lasers

In this paper, we propose and numerically demonstrate a chaotic watermarking encryption and secure transmission scheme based on two synchronized response lasers (RLs) subject to identical injection from a driving laser (DL). In this proposed system, the chaotic signal from DL can be optimized after passing through a phase modulator and a dispersion component, then the chaotic signal with large bandwidth and low time delay signature is obtained. Simultaneously injecting this chaotic signal into two identical RLs, high-quality chaos synchronization between two RLs can be realized. Both synchronized chaotic signals are, respectively, divided into two parts. One is used to generate shared keys required by the watermarking encryption, and the other is used as chaotic carrier to realize the secure message transmission. After introducing the synchronized optical chaos into the watermarking encryption algorithm, the normalized correlation of the extracted watermark without long-distance transmission is 0.9554 and can still maintain above 0.9 over 200 km transmission fiber. The message transmission and watermark extraction have good robustness to the fiber parameter mismatches, and excellent performances can be maintained even within 20% mismatches range. In our method, synchronized high-quality optical chaotic signals from two RLs are used to watermark embedding and transmission, and double encryption can be realized, which can open a new path for future high-speed and security-enhanced watermark embedding and transmission.

Chaotic time-delay signature suppression in lasers using phase-controlled dual optical feedback

We experimentally study a semiconductor laser subject to two optical feedbacks in a free space setup. We show that control over the feedback phase is essential to adjust the time delay signature in the chaotic output intensity while affecting also the chaotic bandwidth. By optimizing the feedback phase, the time delay signature can be reduced by a factor of more than 2 while maintaining a large chaotic bandwidth.

Fast physical random bit generation based on a chaotic optical injection system with multi-path optical feedback.

Based on the chaotic signal provided by a simple chaotic system, a random bit sequence with a rate of 640 Gb/s is generated through adopting the circulating exclusive-or (CXOR) post-processing method. Such a simple chaotic system is built via a slave semiconductor laser subject to optical injection of a chaotic signal originated from a master semiconductor laser under multi-path optical feedback. First, through inspecting the dependences of the time-delay-signature (TDS) and bandwidth of the chaotic signal on some key operation parameters, optimized parameters are determined for generating a high-quality chaotic signal with a large bandwidth and low TDS. Second, the high-quality chaotic signal is converted to an 8-bit digital signal by sampling with a digital oscilloscope at 80 GSa/s. Next, through adopting the CXOR post-processing method, a bit sequence with a rate of 640 Gb/s is obtained. Finally, the randomness is estimated by the National Institute of Standard Technology (NIST) Special Publication 800-22 statistical tests, and the results demonstrate that the obtained random bit sequence can pass all the NIST tests.

Random number generator based on semiconductor nanoheterostructures with quantum dots and optical feedback

Subject of study. This study models the generation process of random bit sequences using an array of coupled lasers. It is based on quantum dot (QD) micropillars with optical feedback that is realized via a mirror positioned at some distance from the array. A model of the array of coupled micropillar lasers consists of QD laser rate equations accounting for the global optical feedback. Aim of study. This study aimed to numerically model and analyze a random number generator using an array of coupled lasers based on QD micropillars. Method. The dynamic behavior was modeled through numerical integration of the delayed differential equation system using a semi-implicit Euler method implemented using the Julia programming language. To generate sequences of random bits, an algorithm was used that involved the sampling of the total field intensity of the array, normalization and discretization with 12 bit resolution, conversion of discretized values to bit representation, selection of four less significant bits, and concatenation of the bit values into the final sequence. Main results. The process of generating a sequence of random bits at the rate of 400 Gb/s, which met the criteria of NIST 800-22 statistical tests for the p-value of 0.01 at the sampling rate of total field intensity of the array equal to 100 Gsamples/s and a sequence length of 11,142,860 bits, was modeled. The model of an array of coupled lasers based on QD micropillars with optical feedback was analyzed using bifurcation analysis. The feedback time delay signature was traced in the chaotic signal of the emission intensity. However, it did not affect the quality of the random number generation. Practical significance. The optical feedback resulted in the chaotic generation of an array of lasers based on the QD micropillars, which can be used to generate random numbers.

Secondary-encryption optical chaotic communication system based on one driving laser and two responding lasers

This paper theoretically investigates a secondary-encryption optical chaotic communication system scheme based on an optical injection structure with single optical feedback and dual-dispersion optical feedback lasers. In the scheme, a fiber reflector (FR) and Fabry–Perot interferometer (FPI) are selected as the laser feedback cavity and effectively conceals time delay signatures (TDSs) of the generated chaotic signals. By switching the responding laser connected to the driving laser with the message feeding method, messages directly participating in the process of encryption signal generation are avoided to generate the first encrypted chaotic sequence that can characterize a message. Subsequently, chaotic phase disturbance technology is used to complete the secondary encryption. By virtue of the spectral broadening effect of chaotic phase disturbance, the message rate and the randomness of the encrypted signal can be effectively enhanced. We use the synchronous power error to decrypt the message at the receiver, which simplifies the system structure and realizes the scheme with low hardware costs. The proposed scheme overcomes the shortcomings of existed schemes, which generate chaotic signal sensitive to channel noise and have complex system structures. In addition, the proposed scheme shows good robustness in terms of handling noise for transmitting digital signals, a bit error rate (BER) of 6.7 × 10−4 at a simulation signal-to-noise ratio of 10 dB, and good application prospects in harsh transmission environments, such as submarine optical fiber transmission.

Strong cluster synchronization in complex semiconductor laser networks with time delay signature suppression.

Cluster synchronization is a state where clusters of nodes inside the network exhibit isochronous synchronization. Here, we present a mechanism to realize the strong cluster synchronization in semiconductor laser (SL) networks with complex topology, where stable cluster synchronization is achieved with decreased correlation between dynamics of different clusters and time delay signature concealment. We elucidate that, with the removal of intra-coupling within clusters, the stability of cluster synchronization could be enhanced effectively, while the statistical correlation among dynamics of each cluster decreases. Moreover, it is demonstrated that the correlation between clusters can be further reduced with the introduction of dual-path injection and frequency detuning. The robustness of strong cluster synchronization on operation parameters is discussed systematically. Time delay signature in chaotic outputs of SL network is concealed simultaneously with heterogeneous inter-coupling among different clusters. Our results suggest a new approach to control the cluster synchronization in complex SL networks and may potentially lead to new network solutions for communication schemes and encryption key distribution.

Security-Enhanced Chaotic Optical Communication Based on External Temporal Self-Feedback Hardware Encryption and Decryption

Chaotic optical communication based on conventional external cavity semiconductor laser is a very promising solution for physical layer secure communication. However, the intrinsic time delay signature (TDS) associated with the external cavity length and the potential direct linear filtering (DLF) or synchronization utilization attack greatly threaten the system security. In this work, we propose and numerically demonstrate a novel scheme for TDS suppression and security enhancement of chaotic optical communication based on external temporal self-feedback hardware encryption and decryption. In this scheme, the confidential chaotic modulated signal is temporally scrambled in the time domain by two optical dispersion components and an electro-optic self-feedback phase modulation loop between them, which simultaneously conceal the TDS and enhance the security against malicious attacks. Proof-of-principle demonstration for a security enhanced chaotic optical communication system with error free transmission is successfully achieved. The proposed scheme may provide a promising way for pure-hardware based physical secure chaotic optical communication systems.