Physical secure optical communication based on private chaotic spectral phase encryption/decryption

Sliced chaotic encrypted transmission scheme based on key masked distribution in a W-band millimeter-wave system

In order to guarantee the information of the W-band wireless communication system from the physical layer, this paper proposes the sliced chaotic encrypted (SCE) transmission scheme based on key masked distribution (KMD). The scheme improves the security of free space communication in the W-band millimeter-wave wireless data transmission system. In this scheme, the key information is embedded into the random position of the ciphertext information, and then the ciphertext carrying the key information is encrypted by multi-dimensional chaos. Chaotic system 1 constructs a three-dimensional discrete chaotic map for implementing KMD. Chaotic system 2 constructs complex nonlinear dynamic behavior through the coupling of two neurons, and the masking factor generated is used to realize SCE. In this paper, the transmission of 16QAM signals in a 4.5 m W-band millimeter-wave wireless communication system with a rate of 40 Gb/s is proved by experiments, and the performance of the system is analyzed. When the input optical power is 5 dBm, the bit error rate (BER) of the legitimate encrypted receiver is 1.23 × 10-3. When the offset of chaotic sequence x and chaotic sequence y is 100, their BERs are more than 0.21. The key space of the chaotic system reaches 10192, which can effectively prevent illegal attacks and improve the security performance of the system. The experimental results show that the scheme can effectively distribute the keys and improve the security of the system. It has great application potential in the future of W-band millimeter-wave wireless secure communication.

Collision in double-image encryption scheme based on spatial encoding and phase-truncation Fourier transforms

In this paper, the security strength of a double-image cryptosystem using spatial encoding and phase-truncation Fourier transforms (PTFTs) is evaluated. Unlike the conventional PTFT-based cryptosystem, where two random phase masks (RPMs) are used as public keys to provide enough phase constrains in the estimation, in the improved cryptosystem, the RPM generated by a random amplitude mask (RAM) is treated as an unknown parameter. Due to this fixed RAM, the number of constraints in the estimation decreases to achieve high robustness against potential iterative attacks. Moreover, instead of two phase-only masks (POMs), here the two POMs and the RAM are utilized as the private keys in the improved cryptosystem; thus, the key space of the double-image cryptosystem has been enlarged. However, we noticed that the RAM used to encode plaintexts spatially and to generate the phase encryption key is independent of the plaintexts. This could be recovered by a known pair of plaintexts and the ciphertext. Once the information of the RAM is retrieved, the phase key RPM can also be produced making the cryptosystem vulnerable. Based on this finding, new hybrid algorithms, including a known-plaintext attack and a known key attack are proposed to crack the enhanced PTFT-based cryptosystem. The information of the plaintexts can be retrieved from one POM using the proposed algorithms without any knowledge of another POM and the corresponding ciphertext. Numerical simulations have been carried out to validate the information disclosure problem still exists in the double-image cryptosystem based on spatial encoding and PTFTs.

Phase stability diagram, self-similar structures, and multistability in a free-running VCSEL with a small misalignment between the phase and amplitude anisotropies

We report on the global dynamics of a free-running vertical-cavity surface-emitting laser (VCSEL) with misalignment between the linear phase and amplitude anisotropies due to the fact that this case might occur in practice caused unintentionally by minor manufacturing variations or design, in virtue of high-resolution phase stability diagrams, where two kinds of self-similar structures are revealed. Of interest is that the Arnold tongue cascades covered by multiple distinct periodicities are discovered for the first time in several scenarios specified in the free-running VCSEL, to the best of our knowledge. Additionally, we also uncover the existence of multistability through the basin of the attraction, as well as the eyes of anti-chaos and periodicity characterized by fractal. The findings may shed new light on interesting polarization dynamics of VCSELs, and also open the possibility to detect the above-mentioned structures experimentally and develop some potential applications.

Wideband chaos synchronization using discrete-mode semiconductor lasers

Optical chaos communication encounters difficulty in high-speed transmission due to the challenge of realizing wideband chaos synchronization. Here, we experimentally demonstrate a wideband chaos synchronization using discrete-mode semiconductor lasers (DMLs) in a master-slave open-loop configuration. The DML can generate wideband chaos with a 10-dB bandwidth of 30 GHz under simple external mirror feedback. By injecting the wideband chaos into a slave DML, an injection-locking chaos synchronization with synchronization coefficient of 0.888 is realized. A parameter range with frequency detuning of -18.75 GHz to approximately 1.25 GHz under strong injection is identified for yielding the wideband synchronization. In addition, we find it more susceptible to achieve the wideband synchronization using the slave DML with lower bias current and smaller relaxation oscillation frequency.

Fingerprint construction of optical transmitters based on the characteristic of electro-optic chaos for secure authentication

In this paper, an optical transmitter authentication method using hardware fingerprints based on the characteristic of electro-optic chaos is proposed. By means of phase space reconstruction of chaotic time series generated by an electro-optic feedback loop, the largest Lyapunov exponent spectrum (LLES) is defined and used as the hardware fingerprint for secure authentication. The time division multiplexing (TDM) module and the optical temporal encryption (OTE) module are introduced to combine chaotic signal and the message to ensure the security of the fingerprint. Support vector machine (SVM) models are trained to recognize legal and illegal optical transmitters at the receiver. Simulation results show that LLES of chaos has the fingerprint characteristic and is highly sensitive to the time delay of the electro-optic feedback loop. The trained SVM models can distinguish electro-optic chaos generated by different feedback loops with a time delay difference of only 0.03ns and have a good anti-noise ability. Experimental results show that the recognition accuracy of the authentication module based on LLES can reach 98.20% for both legal and illegal transmitters. Our strategy can improve the defense ability of optical networks against active injection attacks and has high flexibility.

Physical-layer security of optical communication based on chaotic optical encryption without an additional driving signal

We propose and numerically demonstrate a scheme for physical-layer security based on chaotic phase encryption, where the transmitted carrier signal is used as the common injection for chaos synchronization, so there is no need for additional common driving. To ensure privacy, two identical optical scramblers consisting of a semiconductor laser and a dispersion component are used to observe the carrier signal. The results show that the responses of the optical scramblers are highly synchronized but are not synchronized with the injection. By properly setting the phase encryption index, the original message can be well encrypted and decrypted. Moreover, the legal decryption performance is sensitive to the parameter mismatch, since it can degrade the synchronization quality. A slight drop in synchronization induces an evident deterioration in decryption performance. Therefore, without perfectly reconstructing the optical scrambler, the original message cannot be decoded by an eavesdropper.

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.

Experimental demonstration of an 8-Gbit/s free-space secure optical communication link using all-optical chaos modulation

For the first time, to the best of our knowledge, we experimentally demonstrate a high-speed free-space secure optical communication system based on all-optical chaos modulation. The effect of atmospheric turbulence on optical chaos synchronization is experimentally investigated via a hot air convection atmospheric turbulence simulator. It is shown that, even under moderately strong turbulent conditions, high-quality chaos synchronization could be obtained by increasing the transmission power. Moreover, a secure encryption transmission experiment using a high bias current induced chaotic carrier for 8-Gbit/s on-off-keying data over a ∼10-m free-space optical link is successfully demonstrated, with a bit-error rate below the FEC threshold of 3.8 × 10^-3. This work favorably shows the feasibility of optical chaotic encryption for the free-space optical transmission system.

Performance improvement of coherent optical chaos communication using probabilistic shaping

We numerically investigate the effects of probabilistic shaping on the performance improvement of coherent optical chaos communication. Results show that the decryption bit-error ratio (BER) of the 16-ary quadrature amplitude modulation (QAM) signal decreases upon increasing the probabilistic shaping factor. It is predicted that the BER of 10-GBd 16QAM can be decreased by one order of magnitude. On the other hand, for the forward error correction threshold of the BER, the requirement for synchronization quality is no longer strict for successful decryption. This means that probabilistic shaping improves the system's tolerance to residual synchronization error. Thus, the transmission rate can be increased by approximately 30∼60%. The side effect of probabilistic shaping is that the valid masking coefficient range is narrowed.

56 Gb/s PAM4 physical secure communication based on electro-optic self-feedback hardware temporal phase encryption and decryption

To guarantee information security from the lowest level of optical networks, it is essential to provide physical layer security in fiber-optic communication systems. However, it is challenging to realize high speed physical secure optical communication based on advanced optical modulation formats and pure commercial hardware components. In this work, we report an experimental demonstration of a high-speed 56 Gb/s PAM4 physical-layer secure optical communication system by employing an electro-optic self-feedback hardware module for temporal self-phase encryption and decryption without consuming any additional encryption channel. An encrypted 56 Gb/s PAM4 confidential signal is successfully decrypted after transmitting over 60 km single-mode fiber. The demonstrated scheme can not only be integrated with existing optical communication networks, but can also be used as a pluggable module, which may provide a promising solution for ultra-high speed physical secure optical communication by combining with advanced multiplexing technology in future.

Mode division multiplexing chaotic encryption scheme based on key intertwining and accompanying transmission

A mode division multiplexing (MDM) chaotic encryption scheme based on key intertwining and accompanying transmission is proposed in this paper. Based on the weakly coupled few-mode fiber (FMF), data and time-varying keys can be accompanied by transmission in two modes, LP01 and LP11, respectively. In order to generate a new key, the current key is XORed with all of the keys from all the preceding moments, one by one. To implement chaotic masking in the digital domain, the three chaotic sequences corresponding to the new key are adopted to encrypt the data at the constellation phase, data symbol block, and subcarrier levels. An 8.89 Gb/s encrypted 16QAM-OFDM signal transmission over 1 km weakly-coupled FMF is experimentally demonstrated. The receiver with the correct key can recover the data normally, while the BER of the illegal receiver remains around 0.5. In the case of the key transmission bit rate of 1 Gb/s, the cracking efficiency threshold of the time-varying key encryption scheme is 5.21 × 10⁶ times that of the time-invariant key encryption scheme, which suggests that the proposed work is a promising candidate for future physical layer security.

Photonic-layer secure 56 Gb/s PAM4 optical communication based on common noise driven synchronous private temporal phase en/decryption

Achieving photonic layer security at the lowest network layer to supplement the upper layer digital cryptography in fiber-optic networks is a constant pursuit but a critical challenge. In this Letter, we propose and experimentally demonstrate a high-speed photonic-layer secure optical communication system based on a novel, to the best of our knowledge, common noise driven synchronous private temporal phase en/decryption scheme, which is capable of supporting high-order modulation formats and enhancing security. A record high bit rate of 56 Gb/s 4-level pulse amplitude modulation (PAM4) confidential signal is successfully encrypted and decrypted by remotely synchronized private noise-like en/decryption signals after secret transmission over 20 km of optical fiber with a bit-error-rate (BER) lower than the hard-decision forward error correction (HD-FEC) limit. The demonstrated scheme may provide a promising way for future ultrahigh-speed photonic-layer secure optical communication.

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.

Experimental demonstration of synchronous privacy enhanced chaotic temporal phase en/decryption for high speed secure optical communication

Protecting confidential high speed optical signal transmission at the lowest physical layer is a critical challenge for modern fiber-optic communication systems. In this paper, we experimentally demonstrate a novel synchronous privacy enhanced chaotic temporal phase en/decryption scheme for high-speed physical layer secure optical communication. A remote chaos synchronization architecture relying on common source signal driving and private response hardware modules comprising of dispersive components and slave lasers is employed to generate synchronized private chaotic en/decryption signals, and simultaneously suppress residual driving-response correlation for enhancing the security. A proof-of-principle demonstration by secure transmission of a 28 Gb/s on-off-keying modulated confidential signal over 100 km single mode fiber link based on the private chaotic temporal phase en/decryption scheme is successfully achieved. The demonstrated hardware optical en/decryption approach may provide a promising way towards future ultra-high speed physical layer secure optical communication systems.

A time-delay signature elimination and broadband electro-optic chaotic system with enhanced nonlinearity by deep learning

In this paper, a novel electro-optic chaotic system with enhanced nonlinearity by deep learning (ENDL) is proposed to achieve time-delay signature (TDS) elimination. A long-short term memory network (LSTM) is trained by a specially designed loss function to enhance the nonlinear effect that can hide the TDS of the system. For the first time, the trained deep learning module is put into a single feedback loop to participate in chaos generation. Simulation results show that the ENDL system can eliminate TDS and increase the bandwidth to more than 31GHz when the feedback intensity is very low (α = 4V). Moreover, the complexity of the chaotic output can be improved with permutation entropy (PE) reaching 0.9941. The synchronization result shows that the ENDL system has high sensitivity to TDS but has low sensitivity to the feedback intensity, thus the system has both high security and high robustness. This system has an uncomplicated synchronization structure and high flexibility, and it opens up a new direction for high-quality chaos generation.

32 Gb/s physical-layer secure optical communication over 200 km based on temporal dispersion and self-feedback phase encryption

Providing physical layer security at the lowest network layer in fiber-optic communication systems is a technical challenge worldwide. Here, we propose and experimentally demonstrate a pure hardware optical encryption scheme based on temporal spreading and self-feedback phase encryption for high-speed and long-distance physical-layer secure optical communication. A record high bit-rate-distance product of 6400 Gb/s km is successfully achieved by the secure transmission of a 32 Gb/s on-off-keying modulated confidential signal over a 200 km optical fiber link. The demonstrated scheme is fully compatible with conventional optical transmission systems and can be operated in a pluggable manner, which may pave a new path to ultra-high-speed physical-layer secure optical communication in the future.

Chaotic time-delay signature suppression using quantum noise

The time-delay signature (TDS) suppression of semiconductor lasers with external optical feedback is necessary to ensure the security of chaos-based secure communications. Here we numerically and experimentally demonstrate a technique to effectively suppress the TDS of chaotic lasers using quantum noise. The TDS and dynamical complexity are quantified using the autocorrelation function and normalized permutation entropy at the feedback delay time, respectively. Quantum noise from quadrature fluctuations of the vacuum state is prepared through balanced homodyne measurement. The effects of strength and bandwidth of quantum noise on chaotic TDS suppression and complexity enhancement are investigated numerically and experimentally. Compared to the original dynamics, the TDS of this quantum noise improved chaos is suppressed up to 94%, and the bandwidth suppression ratio of quantum noise to chaotic laser is 1:25. The experiment agrees well with the theory. The improved chaotic laser is potentially beneficial to chaos-based random number generation and secure communication.

Evolution of time-delay signature of polarized chaos in a unidirectional-coupling VCSEL system with variable-polarization optical injection

The evolution characteristics of the time-delay signature (TDS) of polarized chaos is systematically investigated in a unidirectional-coupling vertical-cavity surface-emitting (VCSEL) scheme with variable-polarization optical injection (VPOI), by means of the time series, optical spectra, power spectra, and autocorrelation function. In this scheme, the polarized chaos with TDS from a master VCSEL (M-VCSEL) with the external cavity is unidirectionally injected into another solitary slave VCSEL (S-VCSEL) through VPOI. The numerical results show that the VPOI can exert significant influence on the TDS characteristics of polarized chaos in the S-VCSEL. Under special injection parameters, as the polarization injection angle (θ_p) of VPOI varies, the TDS evolution for the X polarization component can exhibit almost an opposite evolutionary pattern to that for the Y polarization component in the S-VCSEL. A series of TDSs is mapped in the θ_p plane, and the injection strength and frequency detuning have been simulated to thoroughly elaborate the TDS evolution of polarization-resolved chaos in the S-VCSEL. Moreover, the optimal parameter spaces with effectively suppressed TDS are also determined for each polarization component in those maps.

Instability of optical phase synchronization between chaotic semiconductor lasers

The instability of optical phase chaos synchronization between semiconductor lasers under master-slave open-loop configuration is investigated. The phase difference between the master and slave lasers is obtained and analyzed in experiment by heterodyne detection and Hilbert transform, and in simulation by solving the rate equations. The results show that the phase difference only maintains in a short duration time and then jumps to another value. A statistical analysis shows that both duration time and jumping values are random, proving that the phase chaos synchronization is unstable. A theoretical analysis shows that the instability of phase synchronization is caused by the jumping of the external cavity mode in the master laser.

Analog-digital hybrid chaos-based long-haul coherent optical secure communication

We propose and numerically investigate a chaotic optical coherent secure communication scheme, which supports long-haul secure transmission for signals in advanced modulation formats. A hybrid optical chaos system is designed with coordination of digital and analog signals. The hybrid entropy source provides a broadband analog optical chaos signal, which could serve as the carrier to load quadrature amplitude modulation (QAM) data. Simultaneously, a digital binary signal generated from the entropy source is transmitted to establish long-haul chaotic synchronization. Coherent detection is utilized at the receiver, and a digital signal processing (DSP) algorithm is adopted to reduce transmission distortion. A 5 Gbaud 16QAM signal is encrypted by a phase chaos carrier with the effective bandwidth of 5.8 GHz. A bit error rate (BER) below forward error correction (FEC) can be achieved after transmitting over 1600 km based on digital-signal-induced chaos synchronization technology. Optimal launch power is investigated to minimize nonlinear effects of transmission links. System security is guaranteed by the high dynamical complexity of the chaotic source and the sensitive time delay as the secret key.

Time-delay signature concealing electro-optic chaotic system with multiply feedback nonlinear loops

A novel time-delay signature (TDS) concealing electro-optic (EO) chaotic system with multiply feedback nonlinear loops is proposed and analyzed by numerical simulation. The proposed system employs mutual injection structure implemented by two asymmetric branches named as multiply feedback nonlinear loop which introduces an extra nonlinear factor to the system dynamic equation. The complexity of the chaos system is increased by introducing this multiply feedback nonlinear loop. The permutation entropy (PE) of the proposed system is improved to higher than 0.96 when feedback strength (β) equals 5. The proposed system can enter to chaos regime with a small β (β = 0.8). The TDS is concealed effectively due to the extra nonlinear factor introduced by multiply feedback nonlinear loop. Meanwhile, key-space of the proposed system is about 10¹² times that of the classical EO system because more tunable time delay parameters are introduced. Furthermore, the performance of a secure communication system based on the proposed chaotic system is discussed, and the simulation results show that the system is sensitive to time delay parameters and robust to feedback strength, which proves the proposed system is suitable for secure communication.

Flat broadband chaos generation in a discrete-mode laser subject to optical feedback

Chaos generation in a discrete-mode (DM) laser subject to optical feedback is experimentally explored. The results show that a DM laser with only optical feedback can produce flat broadband chaos under an optimized feedback ratio. The effect of the laser bias current on the bandwidth and flatness of chaos is also investigated. It shows that the higher bias current, the better the flatness that can be obtained at the optimal feedback ratio.

Flexible multipoint-to-multipoint communication in semiconductor laser networks using one-way isolation

We propose a type of semiconductor laser (SL) network that supports flexible chaos synchronization and multipoint-to-multipoint communications by using one-way isolation (OWI). The properties of chaos synchronization, influences of coupling strength and time delay mismatches on the quality of chaos synchronization, and the performance as well as the security of the SL network-based chaotic communications are systematically discussed. The numerical results demonstrate that, with the introduction of OWI, flexible chaos synchronization can be easily achieved in arbitrary-size SL clusters over wide parameter spaces of coupling strength and current factor. Based on the high-quality flexible chaos synchronization, satisfactory performance for Gb/s chaotic communications can be achieved in arbitrary-size clusters in the SL networks. Moreover, it is also indicated that in the SL networks, the security of intra-cluster communications can be guaranteed in three aspects. Firstly, the eavesdroppers cannot intercept any useful information by using a typical illegal attack. Secondly, due to the OWI, the chaotic carriers are only transmitted in the corresponding clusters, not transmitted among clusters, as such the security can be further improved. Thirdly, the high sensitivity of cross-correlation coefficient to the injection delay mismatches indicates that the injection delays of idle SLs to communicating SLs can be regarded as the keys of the communication clusters. The proposed scheme offers an alternative solution to flexible secure network-type communications.

Scheme of coherent optical chaos communication

We propose and numerically demonstrate a scheme of coherent optical chaos communication using semiconductor lasers for secure transmission of optical quadrature amplitude modulation (QAM) signals. In this scheme, a laser intensity chaos and its delayed duplicate are used to amplitude-quadrature modulate a continuous-wave light to generate a chaotic carrier. High-quality chaotic carrier synchronization between the transmitter and receiver is guaranteed by laser intensity chaos synchronization, avoiding laser phase fluctuation. Decryption is implemented by a 90 deg optical hybrid using the synchronous chaotic carrier as local light. Secure transmission of an optical 40 Gb/s 16QAM signal is demonstrated by using a laser intensity chaos with a bandwidth of 11.7 GHz. The system performances are evaluated by analyzing a bit error ratio with different masking coefficients, signal rates, synchronization coefficients, parameter mismatches, and dispersion compensation. It is believed that this scheme can pave a way for high-speed optical chaos communication.

Wideband complex-enhanced bidirectional phase chaotic secure communication with time-delay signature concealment

A novel bandwidth-enhanced bidirectional phase chaotic secure communication system with time-delay signature (TDS) concealment is proposed and analyzed by numerical simulation. This bidirectional system based on two mutually coupled electro-optic (MCEO) phase feedback loops is driven by a common all-optical (AO) chaotic source. The AO driving source makes the amplitude and phase terms in the Ikeda-based MCEO equation chaotic. Two mutually coupled optoelectronic delayed feedback loops also greatly increase the complexity of the chaotic carrier. By replacing the semiconductor laser in the existing bidirectional communication scheme with an electro-optic feedback loop, the problems of narrow carrier bandwidth and poor synchronization performance can be compensated. Compared to the single MCEO system, the permutation entropy of the AO-MCEO cascaded system with a bit rate of 10 Gbit/s is improved by 0.13 to 0.98. The TDS of the AO-MCEO system is suppressed 35 times to less than 0.01 to be completely hidden when the EO gain is reduced by half to 2.75. The chaos effective bandwidth is increased by 5 GHz to 32.05 GHz, and the spectrum flatness is reduced by 0.33 dB/Hz to 0.82 dB/Hz. Meanwhile, the security is further enhanced by reducing the cross-correlation coefficient to 0.001 between the AO driving source and the electro-optical chaotic carrier. The results show that the proposed model has potential applications in bandwidth-enhanced bidirectional secure chaotic systems.

Time-delay signature suppression of polarization-resolved wideband chaos in VCSELs with dual-path chaotic optical injections

The combining investigation on the time-delay signature (TDS) and chaos bandwidth have been theoretically investigated in a vertical-cavity surface-emitting laser (VCSEL) system with dual-path chaotic optical injections. In this scheme, the polarized chaos with the TDS from an external-cavity master VCSEL is routed into two different paths and then unidirectionally injected into another solitary slave VCSEL. With the aid of the autocorrelation function and the effective bandwidth calculation, the TDS and bandwidth of polarized chaos from the chaotic system are quantitatively evaluated. The results show that, in such a dual-path chaotic optical-injection system, the high-quality polarized chaos with the successful TDS suppression and chaotic bandwidth enhancement can be achieved in wider parameter regions in contrast with the case for the single-path chaotic optical injection. Further research also finds that the injected time-delay difference between two injection paths is desired to mismatch the feedback time delay, which is conducive to suppressing TDS and expanding bandwidth of polarized chaos. Besides, the better chaotic quality with low TDS and wide bandwidth can be expected by choosing the appropriate injection strengths of two injection paths.

Generation of synchronized wideband complex signals and its application in secure optical communication

We propose and demonstrate a novel secure optical communication scheme, in which the message signal is encrypted and decrypted by two synchronized wideband complex signals. In our scheme, the wideband complex signals are generated by two private chaotic driving signals which are obtained from two local conventional external-cavity semiconductor lasers (ECSLs) subject to a common injection. Both the experimental and simulation results show that, the effective bandwidths of the chaotic driving signals are significantly improved and the time-delay signatures are completely suppressed, in virtue of the spectral broadening effect of chaotic phase-modulation and the phase-to-intensity conversion effect of dispersive components. Furthermore, the generated wideband complex signals are used as the optical carriers for achieving secure transmission. The message signal with a bit rate up to 10 Gb/s can be well hidden into the carrier, and cannot be recognized by the eavesdropper. The high-quality synchronization ensures that the message signal can be correctly recovered at the receiver.

Chaos synchronization and communication in global semiconductor laser network with coupling time delay signature concealment

Chaos synchronization and pairwise bidirectional communication with coupling time delay signature (CTDS) concealment in a global heterogeneous coupled semiconductor laser (SL) network are achieved by introducing identical chaotic injections from an external SL with self-feedback. The properties of chaos synchronization and CTDSs in four indicative cases are comparatively discussed. Moreover, the influences of key parameters on the quality of chaos synchronization and the CTDS characteristics are thoroughly investigated. On the basis of the chaos synchronization, the chaotic communication performance is further analyzed. The numerical results demonstrate that with the joint contributions of heterogeneous couplings and external identical chaotic injections, isochronous chaos synchronization can be achieved between two arbitrary SLs, and simultaneously the CTDSs are suppressed to a distinguishable level close to zero, over a wide parameter range. Besides, bidirectional transmission with a bit rate beyond 6 Gbit/s can be achieved between the synchronized SLs. Comparing with the conventional two-user communication system, the proposed SL network with CTDS concealment supports flexible network-type message exchanges between pairwise SLs.

High security OFDM-PON with a physical layer encryption based on 4D-hyperchaos and dimension coordination optimization

In this article we have enhanced the security of an orthogonal frequency division multiplexed passive optical network (OFDM-PON) based on four dimensional (4D) encryption, including constellation, subcarrier, symbol and time, which is proposed for the first time in this paper. 4D-hyperchaotic mapping is used to generate four masking factors to achieve ultra-high security encryption in four different dimensions. During the encryption, dimension coordination optimization is adopted, which effectively reduces the time cost of the system and improves the encryption efficiency by 3 times. At the same time, probabilistic shaping (PS) technology is used to further optimize the system that has effectively improved the bit error performance by about 1 dB. The proposed encryption technique for OFDM-PON has been demonstrated successfully with the help of experiments. The generated OFDM signal is modulated by the quadrature amplitude modulation (QAM) technique, which transmitted 16 Gb/s data rate across a 25 km fiber span of standard single-mode fiber. The values of bit error rate (BER) and peak-to-average-power ratio (PAPR) are analyzed during the experiments, and the obtained results show that the proposed security-enhanced OFDM-PON has high sensitivity and security and can be well compatible with PS and OFDM technologies. The proposed scheme has very reliable security performance and also has excellent benefit improvement, which is very promising in the future PS-OFDM-PON.

Generation of laser chaos with wide-band flat power spectrum in a circular-side hexagonal resonator microlaser with optical feedback

We numerically demonstrate the generation of wide-band laser chaos with flat power spectrum in a 2D circular-side hexagonal resonator (CSHR) microlaser subject to long-cavity optical feedback. The bandwidth and flatness of the chaotic power spectrum are investigated under different bias currents and optical feedback rates. Under low bias current, the bandwidth under an optimized optical feedback rate increases obviously as raising bias current and the power spectrum flatten simultaneously. Under high bias current, the optimized bandwidth gradually tends toward stabilization, with corresponding flatness less than 5 dB. We compare the chaotic power spectra with small-signal modulation response (SSR) curves under different bias currents. It can be concluded that wide-band and flat SSR indicates wide-band and flat chaotic power spectrum. This work argues that we can enhance laser chaos by using a laser device with wide-band and flat SSR and simple optical feedback configuration, which is significantly beneficial to synchronization-based applications including chaos communication and key distribution.

Unveil the time delay signature of optical chaos systems with a convolutional neural network

We propose a time delay signature extraction method for optical chaos systems based on a convolutional neural network. Through transforming the time delay signature of a one-dimensional time series into two-dimensional image features, the excellent ability of convolutional neural networks for image feature recognition is fully utilized. The effectiveness of the method is verified on chaos systems with opto-electronic feedback and all optical feedback. The recognition accuracy of the method is 100% under normal conditions. For the system with extremely strong nonlinearity, the accuracy can be 93.25%, and the amount of data required is less than traditional methods. Moreover, it is verified that the proposed method possesses a strong ability to withstand the effects of noise.

Generation and synchronization of wideband chaos in semiconductor lasers subject to constant-amplitude self-phase-modulated optical injection

We propose a novel wideband chaos generation scheme by using an external-cavity semiconductor laser (ECSL) subject to optical-electronic hybrid feedback. In this scheme, the output of ECSL is photo-detected and used to modulate the output of a continuous wave laser by an electro-optical phase modulator, the constant-amplitude self-phase-modulated light is then injected back into the ECSL. The experimental results indicate that, compared with the chaos generation with conventional optical feedback (COF), significant bandwidth enhancement is achieved in the proposed scheme. The effective bandwidth of generated chaos is increased from a few GHz to over 20 GHz, and moreover, the spectrum flatness and the complexity of generated chaos are also considerably improved. Furthermore, we propose a wideband chaos synchronization system based on the proposed chaos generation scheme. It is experimentally demonstrated that high-quality synchronization between two wideband chaos signals with an effective bandwidth greater than 20 GHz is achieved. This work simultaneously achieves the generation and the synchronization of wideband chaos, which shows valuable potential in chaos-based secure communication, such as enhancing the transmission capacity and improving the security.

Robust chaotic-shift-keying scheme based on electro-optical hybrid feedback system

A chaotic-shift-keying (CSK) scheme is designed based on a chaos system with electro-optical hybrid time delayed feedback structure. By switching the time delay parameter as a message feeding method, the generated chaotic signal is no longer suffered from return map attack, which is an innate vulnerability of traditional CSK. When the coupling of the seed electrical chaotic system and the nonlinear optical time delay feedback loop is carefully weighed, this CSK scheme shows a good robustness in terms of handling noise for transmitting digital signals. By demodulating the digital signals with the chaotic coherent detection method, a bit error rate of 6×10^-4 is achieved at the signal-to-noise ratio of 10dB in the simulation. The proposed method has a promising application prospect in some harsh environments.

Optical chaotic flip-flop operations with multiple triggering under clock synchronization in the VCSEL with polarization-preserved optical injection

We investigate the evolution of nonlinear dynamic behaviors of two polarization components (x-PC and y-PC), as well as the interplay of polarization bistability and injection strength in the vertical-cavity surface-emitting laser (VCSEL) with polarization-preserved optical injection. We explore a new threshold mechanism to judge two logic outputs encoded in different dynamic behaviors of the x-PC and y-PC emitted by the VCSEL with polarization-preserved optical injection. We demonstrate implementations of two parallel optical chaotic reset-set flip-flop operations and two parallel chaotic toggle flip-flop operations that are synchronized by a clock signal and response for as short as 1 ns bit time. We further observe the reconfiguration of these two kinds of flip-flop operations with clock synchronization in different time periods by controlling the duration-time of the reset (toggle) signal with high-level. The probability of the correct trigger responses for these two kinds of flip-flop operations is controlled by the interplay of the duration-time of the reset (toggle) signal and the noise strength of the spontaneous emission. The probability that is equal to 1 for the reset-set flip-flop operations occurs in the long duration-time of the reset (toggle) signal ranging from 480 ps to 592 ps. The probability with 1 for the toggle flip-flop operations takes place in the short duration-time between 116 ps and 170 ps. Moreover, these two kinds of flip-flop operations have strong robust to the spontaneous emission noise. The optical chaotic flip-flop operation device with clock synchronization and reconfigurable trigger function proposed in our scheme offers interesting perspectives for applications where noise is unavoidable and synchronized multiple triggering is required.

Injection-locking chaos synchronization and communication in closed-loop semiconductor lasers subject to phase-conjugate feedback

The properties of injection-locking chaos synchronization and communication in closed-loop external-cavity semiconductor lasers (ECSL) subject to phase-conjugate feedback (PCF) are investigated systematically. We theoretically analyze the general conditions for the injection-locking, and numerically investigate the properties of injection-locking chaos synchronization in the phase and intensity domains, the influences of frequency detuning and intrinsic parameter mismatch on the injection-locking chaos synchronization, as well as the performance of injection-locking chaos synchronization-based communication in closed-loop PCF-ECSL systems. The numerical results demonstrate that with respect to the conventional optical feedback (COF) scenario, the injection-locking chaos synchronization in a PCF-ECSLs configuration shows a significantly wider high-quality synchronization region and excellent feasibility, and the performance of chaos communication can also be enhanced.

Enhancing time-delay suppression in a semiconductor laser with chaotic optical injection via parameter mismatch

Time-delay signature (TDS) suppression of an external-cavity semiconductor laser (ECSL) is important for chaos-based applications and has been widely studied in the literature. In this paper, the chaotic output of an ECSL is injected into a semiconductor laser and TDS suppression in the regenerated time series is revisited. The focus of the current work is the influence of parameter mismatch on the TDS evolution, which is investigated experimentally and compared systematically to simulations. The experimental results demonstrate that it is much easier to achieve desired TDS suppression in the configuration composed of mismatched laser pairs. Numerical simulations confirm the validity of the experimental results. In the experiments and simulations, the influence of the injection parameters on TDS suppression is also studied and good agreement is obtained.

Simultaneous bandwidth-enhanced and time delay signature-suppressed chaos generation in semiconductor laser subject to feedback from parallel coupling ring resonators

We propose and demonstrate an external-feedback semiconductor laser-based chaos generation scheme supporting simultaneous bandwidth enhancement and excellent time-delay-signature (TDS) suppression, by using parallel-coupling ring resonators (PCRR) as reflector. The characteristics of effective bandwidth and TDS of chaotic signals generated in three indicative PCRR configurations are thoroughly investigated. The numerical results demonstrate that with the nonlinear feedback of PCRR, the TDS of chaos can be efficiently suppressed toward an indistinguishable level, and the bandwidth of chaos in the proposed scheme can also be enhanced, with respect to the conventional optical feedback configuration. The proposed scheme shows a flexible way to generate wideband complex chaos.

Correlated random bit generation based on common-signal-induced synchronization of wideband complex physical entropy sources

We propose and experimentally demonstrate a novel, to the best of our knowledge, correlated random bit generation (CRBG) scheme in virtue of the synchronization of two physical entropy sources that are composed of a continuous-wave laser, a phase modulator that is driven by the output of a local laser subject to constant-amplitude and random-phase (CARP) injection, as well as a dispersive component. It is experimentally indicated that wideband complex physical entropy sources with an effective bandwidth of 22 GHz can be achieved, and high-quality synchronization with a large cross-correlation coefficient (∼0.95) can be achieved by introducing symmetric CARP injections into the local lasers at Alice and Bob ends. Based on this, two distributed CRBSs with a bit rate over 3 Gb/s and satisfactory consistency are independently generated at Alice and Bob ends; the excellent randomness of CRBSs is verified using a test suite of the National Institute of Standards and Technology.

Isochronous cluster synchronization in delay-coupled VCSEL networks subjected to variable-polarization optical injection with time delay signature suppression

The isochronous cluster synchronization with time delay (TD) signature suppression in delay-coupled vertical-cavity surface-emitting laser (VCSEL) networks subject to variable-polarization optical injection (VPOI) is theoretically and numerically studied. Based on the inherent symmetries of network topology, parameter spaces for stable cluster synchronization are presented, and zero-lag synchronization are achieved for VCSELs in same clusters. Additionally, the TD signature reduction for the dynamics of VCSELs in the stable clusters are systematically discussed. It is shown that both moderate polarizer angle and frequency detuning between different clusters have strengthen the effect of TD signature suppression. Moreover, the isochronous cluster synchronization with TD signature concealment is also verified in another VPOI-VCSEL network with different topology, indicating the generality of proposed results. Our results shed a new light on the research of chaos synchronization and chaos-based secure communications in VCSEL networks.

Optical chaotic data-selection logic operation with the fast response for picosecond magnitude

We investigate the evolution of nonlinear dynamic behaviors of two polarization components (x-PC and y-PC), as well as the interplay of polarization bistability, frequency detuning and injection strength in the vertical cavity surface emitting laser with optical injection. Specifically, by encoding two logic inputs and one clock input in the amplitude of the light from a sampled grating distributed Bragg reflector laser, and by decoding two output logic responses from the x-PC and y-PC emitted by the laser, we demonstrate two parallel data-selection computing. The correct logic output encoded in two emitted PCs response for as short as 100 ps bit time and the response bit time of the correct logic output encoded in the y-PC may be 67 ps by the optimization of the injection strength. The probability of a correct response is controlled by the interplay of the bit time, the injection strength and noise strength, and is equal to 1 in a wide region of the injection strength and noise strength. The chaotic data-selection computing in an optically VCSEL offer interesting perspectives for applications where noise is unavoidable and fast switching is required.

Common-injection-induced isolated desynchronization in delay-coupled VCSELs networks with variable-polarization optical feedback

We have investigated the cluster isolated desynchronization, a symmetry-breaking state, in the delay-coupled vertical-cavity surface-emitting lasers (VCSELs) networks subject to variable-polarization optical feedback (VPOF). It is shown that, in the VPOF-VCSELs networks, the elusive isolated desynchronization phenomenon could emerge out of the cluster synchronization by the common-signal injection approach from an additional auxiliary VCSEL. The influences of parameters in VPOF-VCSELs networks on the existence and stability of isolated desynchronization are systematically investigated. Moreover, the generality of the proposed scheme is validated in the VPOF-VCSELs network with real-world network topology (Nepal power grid network). Our results offer a new insight to manage the synchronization patterns of a VCSELs network.

Observation of flat chaos generation using an optical feedback multi-mode laser with a band-pass filter

We demonstrate experimentally that flat and broadband chaotic signals can be easily generated by combining a multi-mode laser diode subject to optical feedback with a band-pass filter. Measurements are made of the RF spectra of multi-mode and single-mode outputs from an external cavity Fabry-Perot (FP) semiconductor laser before and after the filtering procedure. In this way it is found that in the chaos regime the low-frequency energy of the single-mode output is enhanced by about 25 dB comparing with that of the multi-mode output. Moreover, the associated 3-dB chaos bandwidth can reach around 6 GHz for the single mode case. Numerical demonstrations show mode competition is the physical origin of the low-frequency enhancement in the single-mode chaotic outputs.