Chaotic Waveforms Research Articles

Polarization-diverse soliton transitions and deterministic switching dynamics in strongly-coupled and self-stabilized microresonator frequency combs

Dissipative Kerr soliton microcombs in microresonators have enabled fundamental advances in chip-scale precision metrology, communication, spectroscopy, and parallel signal processing. Here we demonstrate polarization-diverse soliton transitions and deterministic switching dynamics of a self-stabilized microcomb in a strongly-coupled dispersion-managed microresonator driven with a single pump laser. The switching dynamics are induced by the differential thermorefractivity between coupled transverse-magnetic and transverse-electric supermodes during the forward-backward pump detunings. The achieved large soliton existence range and deterministic transitions benefit from the switching dynamics, leading to the cross-polarized soliton microcomb formation when driven in the transverse-magnetic supermode of the single resonator. Secondly, we demonstrate two distinct polarization-diverse soliton formation routes – arising from chaotic or periodically-modulated waveforms via pump power selection. Thirdly, to observe the cross-polarized supermode transition dynamics, we develop a parametric temporal magnifier with picosecond resolution, MHz frame rate and sub-ns temporal windows. We construct picosecond temporal transition portraits in 100-ns recording length of the strongly-coupled solitons, mapping the transitions from multiple soliton molecular states to singlet solitons. This study underpins polarization-diverse soliton microcombs for chip-scale ultrashort pulse generation, supporting applications in frequency and precision metrology, communications, spectroscopy and information processing.

A method to design a fast chaotic oscillator using CCTA

This article introduces a novel method for designing a fast chaotic oscillator using a CCTA (Current Conveyor Transconductance Amplifier) based on Chua's circuit. The proposed method uses innovative configurations and advanced simulation techniques to overcome challenges in high-speed operation, nonlinear dynamics, and Analog Building Block (ABB) selection. The design begins with nonlinear negative resistance, essential for Chua's diode characteristics, including two negative resistances, NR1 and NR2. The circuit integrates one CCTA block, two grounded capacitors, two fixed resistors, one inductor, and one potentiometer. It is simulated using PSPICE with IC (Integrated Circuit) macro-models and 180nm CMOS (Complementary Metal Oxide Semiconductor) technology. Various chaotic waveforms and attractors are produced, validating the theoretical and mathematical predictions. By varying the resistance values (1450Ω, 1650Ω, 1800Ω, 1950Ω), the circuit exhibits different chaotic behaviors, such as large limit cycles, double-scroll attractors, Rossler-type attractors, and I-periodic attractors. FFT (Fast Fourier Transform) analysis confirms the highest dominant operating frequency of 37.5MHz. A Monte Carlo simulation with 100 runs shows maximum voltage variations in the chaotic waveforms of 5.21 % and 4.61 % across the capacitors, demonstrating robustness and reliability. This design offers significant advancements in implementing high-frequency chaotic oscillators, with potential applications in various fields requiring chaotic signal generation.•A novel design of Chua's diode and Chua's chaotic oscillator using only one CCTA block is presented in this paper.•The proposed chaotic oscillator achieves the highest operating frequency of 37.5MHz.•The proposed circuit is simulated using commercially available ICs (MAX435 and AD844) and CMOS 180nm technology in PSPICE to confirm its workability.

Statistical properties for an optically injected chaotic semiconductor laser with a high-pass filter.

Chaotic waveforms with Gaussian distributions are significant for laser-chaos-based applications such as random number generation. By exploring the injection parameter space of the optical injection semiconductor lasers, we numerically investigate the associated probability density functions of the generated chaotic waveforms when different high-pass filters with different cutoff frequencies are used. Our results demonstrate that the chaotic waveforms with Gaussian probability density functions can be obtained once the cutoff frequency of the high-pass filter is larger than the laser relaxation resonance frequency. Especially, we find that the Gaussian probability density function can reach a superhigh coefficient of determination R2 ≥ 99.5% and an ultralow skewness |S|<0.1 in a large parameter space by jointly controlling the injection parameter and cutoff frequency.

Experimental estimation of sample entropy in a semiconductor laser with optical feedback for random number generation

Estimating the entropy rate of physical random number generators with uncertainty is crucial for information security applications. We evaluate the sample entropy of chaotic temporal waveforms generated experimentally by a semiconductor laser with time-delayed optical feedback. We demonstrate random number generation with uncertainty using a quantitative measurement of the entropy rate.

Collision-free arbitrary-order chaotic path generator for differential robots

This article discusses a collision-free path generator based on arbitrary-order chaotic waveforms for differential robots. The novelty is that the robot can explore a predefined workspace with any irregular structure, avoiding obstacles and boundaries with any random shape. All positions of the differential robot are generated by the arbitrary-order chaotic dynamic system. The inverse Jacobian of the differential robot is used as control law. Therefore, the position error at each point of the chaotic path not only is iteratively reduced, but the angular velocities for each motion are also computed. Numerical simulations were performed within Matlab environment to evaluate the arbitrary-order chaotic path generator in a scenario and different starting positions. Numerical tests illustrate the usefulness of the proposed collision-free arbitrary-order chaotic path generator and it can be applied to various areas, such as household, agriculture, education, manufacturing, patrolling, medical care, military and so on.

Image encryption algorithm based on multi-bit superposition and optical chaos

Aiming at the problem that the leakage of single-layer key encryption may lead to the theft of image information, we propose an image encryption algorithm based on multi-bit superposition and optical chaos. The generated optical chaotic sequence is used to encrypt the encrypted image together with the user input key. In the scrambling stage, the 3D-cat map is used to encrypt the bit plane, and the multi-bit superposition method is used to encrypt the key space between the bit planes again by using the sub-block internal and external encryption methods. In the diffusion stage, the Logistic-tent map is used to diffuse the scrambling image to generate the ciphertext image, and the optical chaotic waveform is used as the carrier to mask the ciphertext image information in the transmission process. At the recipient, the ciphertext image information is obtained through the synchronized optical chaotic waveform, and the image is decrypted by using the synchronized optical chaotic sequence and the key transmitted through the secure channel. If only one of the two cannot decrypt the image, the security of image transmission is improved. The simulation results show that the correlation of adjacent pixels of the image encrypted by the algorithm is close to zero, the gray histogram is evenly distributed, the pixel change rate, the normalized average change intensity and the block average change intensity are close to the ideal value, and the sensitivity of the plaintext is further enhanced, which can effectively resist statistical attacks, differential attacks and exhaustive attacks.

Rogue wave generation using a chaotic semiconductor laser with energy redistribution.

We demonstrate for the first time that optical rogue waves (RWs) can be generated using a chaotic semiconductor laser with energy redistribution. Chaotic dynamics are numerically generated using the rate equation model of an optically injected laser. The chaotic emission is then sent to an energy redistribution module (ERM) that consists of a temporal phase modulation and a dispersive propagation. The process enables a temporal energy redistribution of the chaotic emission waveforms, where coherent summation of consecutive laser pulses leads to random generation of giant intensity pulses. Efficient generation of optical RWs are numerically demonstrated by varying the ERM operating parameters in the entire injection parameter space. The effects of the laser spontaneous emission noise on the generation of RWs are further investigated. The RW generation approach offers a relatively high flexibility and tolerance in the choice of ERM parameters according to the simulation results.

Low-disturbance automatic bias point control for optical IQ modulator using digital chaotic waveform as dither signals.

A low-disturbance automatic bias point control (ABC) method for optical in-phase and quadrature modulators (IQM) is proposed using digital chaotic waveform as dither signals. Two distinct chaotic signals, each with unique initial values, are introduced to the direct current (DC) port of IQM in conjunction with a DC voltage. Due to the robust autocorrelation performance and exceptionally low cross-correlation of chaotic signals, the proposed scheme is capable of mitigating the impact of low-frequency interference, signal-signal beat interference, and high-power RF-induced noise on transmitted signals. In addition, due to the broadwidth of chaotic signals, their power is distributed across a broad frequency range, resulting in a significant reduction in power spectral density (PSD). Compared to the conventional single-tone dither-based ABC method, the proposed scheme exhibits a reduction in peak power of the output chaotic signal by over 24.1 dB, thereby minimizing disturbance to the transmitted signal while maintaining superior accuracy and stability for ABC. The performance of ABC methods, based on single-tone and chaotic signal dithering, are experimentally evaluated in both 40Gbaud 16QAM and 20Gbaud 64QAM transmission systems. The results indicate that the utilization of chaotic dither signals leads to a reduction in measured bit error rate (BER) for 40Gbaud 16QAM and 20Gbaud 64QAM signals, with respective decreases from 2.48% to 1.26% and from 5.31% to 3.35% when the received optical power is -27dBm.

Toward Chaotic Secure Communications: An RIS Enabled M-Ary Differential Chaos Shift Keying System With Block Interleaving

Chaotic secure communication systems using chaotic waveforms as their spreading carriers can hide the transmitted information bits over a wide frequency range of chaotic waveform, which disguises the transmitted information waveform as noise. In this paper, a reconfigurable intelligent surface (RIS) enabled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary differential chaos shift keying with block interleaving (RIS-MDCSK-BI) system is proposed for chaotic secure communications, where an RIS is deployed at the transmitter to assist communications and a pair of block interleaving patterns are used to interleave <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary information-bearing signals to enhance security performance. Moreover, we propose a chaotic merging sort algorithm to generate different block interleaving patterns, where these interleaving patterns are encrypted by using the non-periodic and noise-like properties of chaotic signals. To estimate information bits at the legitimate receiver, we propose a sequential detection algorithm and a joint detection algorithm. Then, theoretical bit error rate (BER) performances of the proposed RIS-MDCSK-BI system with the legitimate receiver and the eavesdropping receiver are derived. The security performance metrics, including information leakage and secrecy outage probability, are also analyzed. Monte Carlo simulations are performed to verify the superior BER performance and security performance of the proposed RIS-MDCSK-BI system compared to benchmark systems.

0271 Patterned Planar Bed Surface Vibration Is Effective in Shortening Time to Onset of Sleep (As Good as a Sleeping Pill?)

Abstract Introduction 70 million Americans suffer from poor sleep, 42 million have a chronic sleep disorder, and an estimated 64% report regularly taking a pharmacological sleep aid regularly with well-known risks. A link between vibration and sleep was first observed during investigations of highway hypnosis. We developed a prototype bed producing sub-audible, tactilely perceptible traveling-wave vibration where noninvasive sleep monitors could objectively measure sleep. Methods A bed was outfitted with low-frequency effectors (LFEs) and phasers to create infrasonic, low-frequency vibration that traversed the mattress in patterns. Amplitude was adjusted to comfort using a bedside dial. Sleep was monitored over four sequential weeks in a single 22-year-old healthy male subject with 3 devices each employing a unique mechanism: the OuraRing (actigraphy), Google NestHub (GHz radar chip), and SleepScore (ultrasound). No vibration was used during weeks 1 and 4 to establish a baseline/return to baseline. Week 2 vibration was a highly periodic waveform (25 Hz, migrating at 1 Hz), while week 3 vibration was an irregular, chaotic waveform. Objective data was collected from the 3 devices to plot total sleep duration and latency of onset. Results 1. Strong agreement was seen among the 3 different sensors 2. Patterned, highly periodic, low-frequency vibration shortened sleep latency by nearly 50% consistently for one week (from 15 to 8 minutes) 3. Chaotic, irregular vibration of week 3 also shortened latency, but less so (from 15 to 12 minutes) 4. Baseline and repeat baseline were statistically nearly identical 5. Sleep duration was not impacted by vibration (mean 7 hours 45 minutes) Conclusion The primary mechanism of improved latency with vibration may be somatic/mental distraction. The subject reported that vibration diverted away from pre-occupying thoughts and was highly pleasant. These observations were reflected in nearly 50% reduction of latency in week 2 and more modest reduction in week 3. Patterned planar vibration appears as effective as prescribed sleep medications, suggesting it may be a useful non-pharmacologic sleep adjunct. Support (if any) Jacob Bentley is the recipient of scholarship support for this research from the American Medical Association and AASM.

Chaotic waveform for optimal joint radar communication systems

Due to the increased spectrum congestion, there has been a tremendous interest in radar and communication devices operating on a shared platform. Therefore, the waveform design for joint radar communication (JRC) systems has recently gained significant attention. Despite several efforts, most state-of-the-art waveforms are far from achieving ideal radar and communication performance. To address this issue, we design a family of chaotic maps whose output yields waveforms with optimal JRC features. We adopt the antipodal chaos shift keying (ACSK) scheme, where the segments of the chaotic signal are multiplied by ±1 to encode the binary information. This ACSK waveform is further used for the JRC system transmission. Once the synchronization between the receiver and transmitter is established, the information is recovered by cross-correlating the received and the synchronized waveforms. This technique yields bit error rates (BER) similar to the theoretical values of the BPSK waveform. The same transmitted waveform results in a thumb-tack ambiguity function which is essential for high-resolution radar imaging. The variance analysis of the ambiguity function shows that the proposed waveform is comparable to the noise-modulated waveforms. We also show that the multiplexed ACSK waveforms yield similar optimal behavior. Furthermore, we demonstrate the potential of the family of chaotic maps for multiple-input, multiple-output (MIMO) JRC systems.

Performance Analysis of Vilnius Chaos Oscillator-Based Digital Data Transmission Systems for IoT

The current work is devoted to chaos oscillator employment in digital communication systems for IoT applications. The paper presents a comparative performance analysis of two different chaos data transmission systems: frequency-modulated chaos shift keying (FM-CSK) and quadrature chaos phase-shift keying (QCPSK), and a comparison to their non-chaotic counterparts: frequency-shift keying (FSK) and quadrature amplitude modulation (QAM). For both chaotic communication systems, the Vilnius oscillator and substitution method of chaotic synchronization are chosen due to simple circuitry implementation and low power consumption properties. The performance of the systems in the fading channel with additive white Gaussian noise (AWGN) is evaluated. Also, the systems’ performance in the case phase noise is investigated, and the benefits of chaotic waveforms employment for data transmission are demonstrated.

Improving the processing rate of VCSEL-based reservoir computing through adopting variable polarization information injection

A novel information injection method is proposed for improving the information processing rate in reservoir computing (RC) systems based on vertical-cavity surface-emitting lasers (VCSELs), and its effectiveness is numerically verified via Santa-Fe chaotic time series prediction task and waveform recognition task. For VCSEL-based RC systems, conventional information injection (CII) method is usually adopted, namely the polarization direction of the injection light loaded by the information is along either X-polarization component (X-PC) or Y-polarization component (Y-PC) of VCSEL. In this work, the polarization direction of the injection light loaded by the information is set at 45-degree deviated from the X-PC of the VCSEL, which is named as variable polarization information injection (VPII) method. By utilizing the VCSEL-based RC to deal with two different scenarios of single task and two tasks in parallel, the numerical results demonstrate that after adopting VPII to replace CII, the processing rate can be doubled while the system performance maintains the same level.

Design and implementation of a robust random number generator based on chaotic ring oscillators

In this paper, the design and implementation of a robust random number generator (RNG) based on chaotic ring oscillators is presented. The RNG output bits are generated through the chaotic sampling of chaotic waveform (CSCW) where the chaotic signals are obtained from two separate nodes of a chaotic ring oscillator (CRO). The proposed RNG is implemented on a FPGA (field-programmable gate array) combined with lumped elements on a breadboard circuit. The output bitstream of the proposed RNG passed the NIST 800-22 statistical randomness test suite without any need for post processing. To analyze the robustness of the CSCW method, a comparative analysis is conducted between chaos-based bit generation methods in terms of robustness against external interference. It is demonstrated that the proposed CSCW method ensures higher immunity of the RNG against external interference.

Misestimate of the performance in VCSEL-based reservoir computing systems with optical information injection by high surface reflectivity.

In reservoir computing (RC) systems based on semiconductor lasers (SLs), the information that must be processed usually enters the reservoir through optical injection. Part of the injection information directly reflected by the front facet of the SLs is inevitably hybridized into the output of the SLs and contributes to the state of virtual nodes. For an RC system based on vertical-cavity surface-emitting lasers (VCSELs), the proportion of the reflected information coupled to the laser output is relatively huge due to the high surface reflectivity. Thus the influence of the directly reflected information will be much more obvious. Using a Santa Fe chaotic time series prediction task and waveform recognition task, we theoretically investigate the influence of high front facet reflectivity on the evaluation of the performance of a VCSEL-based RC system with optical information injection. The simulation results demonstrate that, after taking the directly reflected information into account, a lower error rate is obtained for each benchmark task. The physical mechanism to misestimate the RC performance has been studied through memory correlation and a statistical histogram of virtual node states.

Self-generation of Möbius solitons and chaotic waveforms in magnonic-optoelectronic oscillators under simultaneous action of optic and magnonic nonlinearities

Self-generation of microwave nonlinear waveforms in the magnonic-optoelectronic oscillator (MOEO) was investigated. Nonlinear dynamics of the MOEO was due to both optical and magnonic paths of the oscillator circuit. Four-magnon parametric interactions in the magnonic path and cosine transfer function of the electro-optical modulator caused double nonlinearity of the MOEO. Gain coefficient was used as a control parameter. We found that during a route from regular to chaotic dynamics, the oscillator generates two unusual waveforms: symmetry-breaking soliton-like modes of Möbius type and periodic pulses with chaotic amplitude modulation. Nonlinear waveforms were characterized using a time series analysis. Peculiarities of the signals and their spectra in regular and chaotic regimes of self-generation are discussed. We expect that the multiple nonlinearity of the MOEO may be useful for investigation of various fundamental effects in complex time-delayed systems and for development of novel circuits for neuromorphic computing.

Use of Chaotic Oscillations for Precoding and Synchronization in OFDM

This paper proposes a novel linear precoding method for Orthogonal Frequency Division Multiplexing (OFDM) based on the employment of the chaotic waveforms generated by the fourth-order chaotic oscillator and orthonormalized by the Gram-Schmidt process. The proposed linear precoding method is aimed to increase resilience to the multipath propagation issues and reduce the Peak-to-Average Power Ratio (PAPR) of the transmitted signal. Moreover, the chaotic waveform enables novel timing synchronization methods to be implemented in the receiver. The modelling of baseband Linear Precoded OFDM (LP-OFDM) data transmission system with Rayleigh channel has been performed in Simulink environment to validate the proposed method and to compare the performance to the classic precoding methods, such as Walsh-Hadamard Transform (WHT). Experiments have shown that in a high Signal-to-Noise Ratio (SNR) scenario, the employment of the novel precoding scheme allows reducing Bit Error Ratio (BER) by several dB compared to non-precoded OFDM. The proposed precoding method leads to the reduction of PAPR; however, it is not as efficient as classical precoding schemes, such as WHT. Experimental evidence of synchronization of the chaotic oscillators within 50 samples long time interval is presented.

Discovering Chaos-Based Communications by Recurrence Quantification and Quantified Return Map Analyses

Many studies show the possibility of transmitting messages in a protected and covert manner using a noise-like chaotic waveform as a carrier. Among popular chaotic communication system (CCS) types, one may distinguish chaotic shift keying (CSK) and parameter modulation (PM) which are based on the manipulation of the transmitting chaotic oscillators. With the development of direct digital synthesis (DDS), it became possible to modulate chaotic signals by varying the properties of the numerical method used in digital chaos generators. The symmetry coefficient modulation (SCM) is such an approach potentially able to provide higher secrecy. However, the actual security of chaos-based communications is still a questionable and controversial feature. To quantitatively evaluate the CCS security level, a certain numerical metric reflecting the difficulty of breaking a communication channel is needed. Return maps are commonly used to attack chaotic communication systems, but the standard algorithm does not involve any kind of quantification. In this study, we propose a new method for estimating the differences between two return maps based on a two-dimensional (2D) histogram. Then, we investigate the resistance of chaotic shift keying, parameter modulation, and SCM communication schemes against three types of attacks: the proposed quantified return map analysis (QRMA), recurrence quantification analysis (RQA), which had not been previously reported for attacking chaos-based communications, and the classical approach based on spectral analysis. In our experiments we managed to recover the plain binary message from the waveform in the channel when transmitted using all three chaos-based messaging techniques; among them, SCM appeared to be the most secure communication scheme. The proposed QRMA turned out to be the most efficient technique for message recovery: the sensitivity of the QRMA appeared to be 2–5 times higher than that in the case of spectral analysis. The proposed QRMA method can be efficiently used for evaluating the difficulty of hacking chaos-based communication systems. Moreover, it is suitable for the evaluation of any other secure data transmission channel.

Decision making for large-scale multi-armed bandit problems using bias control of chaotic temporal waveforms in semiconductor lasers

Decision making using photonic technologies has been intensively researched for solving the multi-armed bandit problem, which is fundamental to reinforcement learning. However, these technologies are yet to be extended to large-scale multi-armed bandit problems. In this study, we conduct a numerical investigation of decision making to solve large-scale multi-armed bandit problems by controlling the biases of chaotic temporal waveforms generated in semiconductor lasers with optical feedback. We generate chaotic temporal waveforms using the semiconductor lasers, and each waveform is assigned to a slot machine (or choice) in the multi-armed bandit problem. The biases in the amplitudes of the chaotic waveforms are adjusted based on rewards using the tug-of-war method. Subsequently, the slot machine that yields the maximum-amplitude chaotic temporal waveform with bias is selected. The scaling properties of the correct decision-making process are examined by increasing the number of slot machines to 1024, and the scaling exponent of the power-law distribution is 0.97. We demonstrate that the proposed method outperforms existing software algorithms in terms of the scaling exponent. This result paves the way for photonic decision making in large-scale multi-armed bandit problems using photonic accelerators.

Chaotic optical communications at 56 Gbit/s over 100-km fiber transmission based on a chaos generation model driven by long short-term memory networks.

Chaotic optical communication technology is considered as an effective secure communication technology, which can protect information from a physical layer and is compatible with the existing optical networks. At present, to realize long-distance chaos synchronization is still a very difficult problem, mainly because well-matched hardware cannot always be guaranteed between the transmitter and receiver. In this Letter, we introduce long short-term memory (LSTM) networks to learn a nonlinear dynamics model of an opto-electronic feedback loop, and then apply the trained deep learning model to generate a chaotic waveform for encryption and decryption at the transmitter and receiver. Furthermore, to improve the security, we establish a deep learning model pool which consists of different gain trained models and different delay trained models, and use a digital signal to drive chaos synchronization between the receiver and transmitter. The proposed scheme is experimentally verified in chaotic-encrypted 56-Gbit/s PAM-4 systems, and a decrypted performance below 7%FEC threshold (BER = 3.8×10-3) can be achieved over a 100-km fiber transmission.