Broadband Chaos Research Articles

Entropy analysis on chaos excited through destabilization of semiconductor lasers at period-one nonlinear dynamics for physical random number generation.

This study analyzes entropy of broadband chaos excited in a semiconductor laser subject to intensity-modulated optical injection for random number generation with guaranteed unpredictability. It is identified that the flattening of spectral profile around the laser relaxation resonance blurs the periodicity it brings, and thus leads to a high entropy value and a high random number generation rate. The effect of measurement device noise on entropy suggests that both the power of chaos needs to be kept at a level to achieve an adequate signal-to-noise ratio, 24 dB or more, and the entropy contribution of the measurement device noise is excluded in order to assert entropy that can be extracted solely from the intrinsic property of chaos. The effect of data sampling rate on entropy shows that entropy reaches its maximum at the Nyquist rate, which is two times the standard bandwidth of chaos, and the rate of change in entropy is much slower than that in sampling rate as the sampling rate varies, which leads to the dominance of the sampling rate, not entropy, in determining the random number generation rate. It is highly likely that modest oversampling (i.e., a sampling rate modestly higher than the Nyquist rate) gives rise to a higher random number generation rate while entropy slightly decreases.

Broadband chaos of an interband cascade laser with a 6-GHz bandwidth.

Near-infrared semiconductor lasers subject to optical feedback usually produce chaos with a broad bandwidth of a few GHz. However, the reported mid-infrared interband cascade lasers (ICLs) only show chaos with a limited bandwidth below 1 GHz. Here we show that an ICL with optical feedback is able to generate broadband chaos as well. The mid-infrared chaos exhibits a remarkable bandwidth of about 6 GHz, which is comparable to that of the near-infrared counterpart. In addition, the spectral coverage in the electrical domain reaches as high as 17.7 GHz. It is found that the chaos bandwidth generally broadens with increasing feedback ratio and/or increasing pump current of the laser, while it is insensitive to the feedback length.

Nonlinear dynamics of an interband cascade laser with optical injection

This work reports the nonlinear dynamics of a mid-infrared interband cascade laser (ICL) subject to optical injection. It is shown that the stable locking regime is asymmetric and broadens with increasing injection strength. Outside the locking regime, the ICL mostly produces period-one oscillations. However, three categories of periodic pulse oscillations are observed in the vicinity of the Hopf bifurcation and the saddle-node bifurcation. In particular, it is found that the ICL generates broadband chaos at a near-threshold pump current, and the chaos bandwidth is over 300 MHz.

Broadband chaos generation in a distributed-feedback laser by selecting residual side modes.

Chaotic dynamics with spectral broadening is experimentally obtained by selective excitation of residual side modes in a distributed-feedback (DFB) laser. For the single-mode laser that emits only at the main mode when free-running, feedback to a residual side mode is introduced via a fiber Bragg grating (FBG). The FBG feedback suppresses the main mode, selectively excites the residual side mode, and generates broadband chaotic dynamics. Such a chaos of the residual side mode has a broad electrical bandwidth reaching at least 26 GHz, which corresponds to a significant broadening by over 50% when compared with the main mode. The dynamics are attributed entirely to the one selected mode without invoking multimode interactions. The wavelength is tunable beyond 10 nm by using different FBGs. Through avoiding multimode interactions, this approach of broadband chaos generation is potentially simple to model and thus promising for applications.

Broadband Chaos Generation and Synchronization Induced by Integrated Tri-section Laser

Broadband Chaos Generation and Synchronization Induced by Integrated Tri-section Laser

Optical time domain reflectometry based on a self-chaotic circular-sided microcavity laser.

A self-chaotic circular-sided square microcavity laser, with a chaos bandwidth of 12.9GHz and a flatness of ±3d B, was applied in optical time domain reflectometry (OTDR). Using the broadband chaos laser, we demonstrated a range resolution of 4.5mm and a 25-km detection distance experimentally. The solitary wide-bandwidth microcavity chaos laser, without the extra correlation peaks in optical feedback chaotic lasers, has shown potential advantages for correlation OTDR in practical application.

Multi-Wavelength Broadband Chaos Generation and Synchronization Using Long-Cavity FP Lasers

Simultaneous generation and synchronization of multiple broadband laser chaos with different wavelengths are numerically demonstrated by using long-active-cavity Fabry-Perot (LC-FP) semiconductor lasers based on multi-mode beating effect. Simulation results show that the LC-FP laser under simple optical feedback can produce broadband chaos with a bandwidth up to 37 GHz with an active cavity length of about 1500um. Furthermore, common-signal-induced chaos synchronization is predicted. Driven by a common chaos from the optical-feedback LC-FP laser, two response LC-FP lasers can reach broadband chaos synchronization with a correlation coefficient beyond 0.98. Meanwhile, the drive-response correlation is low at around 0.4. More interestingly, by optical filtering, parallel multiple broadband chaotic signals at different wavelengths are obtained with bandwidths exceeding 25 GHz and cross-correlation values lower than 0.2. The chaos synchronization keeps for the identical wavelengths. This work will pave a way for increasing capacity of chaos communication.

High-entropy-rate broadband chaos generation by using short-resonant-cavity DFB semiconductor laser with optical feedback.

Semiconductor lasers with delayed optical feedback are a promising source of optical chaos for practical applications, owing to simple configurations that are easy to integrate and synchronize. However, for traditional semiconductor lasers, the chaos bandwidth is limited by the relaxation frequency to several gigahertz. Here, we propose and experimentally demonstrate that a short-resonant-cavity distributed-feedback (SC-DFB) laser can generate broadband chaos only with simple feedback from an external mirror. The short distributed-feedback resonant cavity not only enhances laser relaxation frequency but also makes the laser mode more susceptible to external feedback. Experiments obtained a laser chaos with 33.6 GHz bandwidth and a spectral flatness of 4.5 dB. The corresponding entropy rate is estimated as more than 33.3 Gbit/s. It is believed that the SC-DFB lasers will promote development of chaos-based secure communication and physical key distribution.

Dual-Channel Secure Communication Based on Wideband Optical Chaos in Semiconductor Lasers Subject to Intensity Modulation Optical Injection

Chaotic optical communication was initially proposed to provide advanced physical layer security for optical communication. Here, we propose and numerically demonstrate an optical chaos communication scheme based on semiconductor lasers subject to intensity modulation optical injection for secure transmission of quadrature amplitude modulation (QAM) messages. In this scheme, two chaotic sources were generated with different modulation parameters and acted as chaotic carriers at the transmitter side, which were subsequently used to drive two receivers in two separate channels. Numerical results demonstrate that this scheme allows for broadband chaos generation and high-quality chaos synchronization can be achieved to simultaneously encrypt two messages for secure communication; a 20 GBaud 16-QAM message was recovered correctly with a transmission distance in standard single mode fiber (SMF) over 120-km, while the other 20 GBaud 64-QAM message was limited to a 20-km fiber transmission distance. The system performance was systematically evaluated by analyzing the bit error ratio (BER) of the recovered message versus the masking coefficient and the transmission distance. Furthermore, our simulations justify the robustness against the mismatch of parameters. Therefore, we hope that this scheme can be experimentally implemented for high-speed chaos communication and secure key distribution.

Broadband chaos generation in VCSELs with intensity-modulated optical injection

We propose and numerically demonstrate broadband chaos generation based on vertical-cavity surface-emitting lasers (VCSELs) subject to intensity-modulated (IM) optical injection. Herein, we consider two scenarios, i.e., parallelly-polarized IM optical injection (PPIOI) and orthogonally-polarized IM optical injection (OPIOI). Specifically, we investigate the effect of injection parameters (injection strength and frequency detuning) and modulation parameters (modulation depth and modulation frequency) on the chaotic dynamic behaviors. The results confirm that both PPIOI and OPIOI can enhance the chaotic regions, bandwidth, and correlation dimension (CD) compared with continuous-wave (CW) optical injection. Besides, OPIOI seems to be more beneficial for obtaining chaotic signals with broader bandwidth and higher dimension compared with PPIOI. Therefore, this study paves the way for prosperous potential in the chaos-based applications.

Broadband chaos generation utilizing a wavelength-tunable monolithically integrated chaotic semiconductor laser subject to optical feedback.

We demonstrate a broadband and wavelength-tunable chaotic laser by using a monolithically integrated wavelength-tunable chaotic semiconductor laser subject to optical feedback. The chip consists of a gain section, a distributed Bragg reflection grating section, a semiconductor optical amplifier section, and a phase section. By applying an optical feedback loop to the chaotic semiconductor laser chip, a nonlinear frequency mixing is stimulated in the laser cavity, and the chaos bandwidth is expanded to 33.6 GHz, which is 4.4 times larger than the bandwidth without optical feedback. Furthermore, the effect of feedback optical power on the bandwidth is investigated. The results show that the wide power spectrum of chaotic laser is available in a large wavelength range from 1556.44 nm to 1566.42 nm. This work explores a broadband and wavelength-tunable chaotic semiconductor laser for the wavelength division multiplexing to enlarge the capacity in chaotic secure optical communications.

60 Gb/s coherent optical secure communication over 100 km with hybrid chaotic encryption using one dual-polarization IQ modulator

We propose and experimentally study a coherent optical secure transmission system based on one dual-polarization in-phase and quadrature modulator (IQM). One beam of the polarized light is used to generate broadband chaos by configuring a nonlinear opto-electronic oscillator while the other beam carries the encrypted signal. The encrypted signal is obtained through sequential encryption of the analog and digital chaos. The mutual mask of the hybrid chaotic signals can effectively enhance the security performance. Moreover, by varying the encryption depth of analog and digital vectors, the transmission performance can be flexibly adjusted. A commercial dual-polarization IQM could simultaneously generate a chaotic signal and a load message, which provides a high-integration solution. A fast independent component analysis (ICA) algorithm is adopted to compensate for the rotation of state of polarization (RSOP). 60 Gb/s encrypted quadrature phase shift keying (QPSK) signal transmission over 100 km single-mode fiber is realized, and the decrypted bit error rate (BER) performance is below the 7% forward error correction (FEC) threshold (BER = 3.8 × 10-3).

Fast physical random bit generation using a millimeter-wave white noise source.

A broadband millimeter-wave (MMW) white noise signal generated by optical heterodyning of two Fabry-Perot laser diodes (FP-LDs) subject to optical feedback is demonstrated and employed for fast physical random bit generation with a simple least significant bits (LSBs) retaining method. Firstly, under suitable feedback conditions, two external-cavity feedback FP-LDs can be easily driven into chaotic states. In this process, the optical spectra of multi-longitudinal modes are significantly broadened. Then, two spectral broadening multi-longitudinal chaotic signals are mixed and converted into an MMW white noise signal through the heterodyne beating technique combined with a fast photodetector. With such an approach, a high dimensional broadband chaos with perfect characteristics of MMW white noise (3-dB bandwidth beyond 50 GHz without any time-delay signature) is experimentally achieved. Finally, taking the generated MMW white noise as the entropy source, 640 Gb/s physical random bit generation is realized by directly selecting 4-LSBs at 160 GS/s sampling rate after an 8-bit analog-digital-convertor.

Flat Broadband Chaos Generation Using a Semiconductor Laser Subject to Asymmetric Dual-Path Optical Feedback

A method of generating flat broadband chaos by using a semiconductor laser subject to asymmetric dual-path optical feedback is proposed and demonstrated experimentally. In the asymmetric dual-path optical feedback, one path is connected with an optical band-pass filter (OBPF) to form filtered path, and the other is a traditional optical feedback path named non-filtered path. Through the beating frequency effect between the filtered mode and the non-filtered chaos mode, a chaotic signal with the standard bandwidth of 36.1 GHz and the spectrum flatness of 5.8 dB is generated experimentally. Furthermore, the effects of filter frequency detuning, filter bandwidth and feedback strength on the bandwidth and flatness of chaos are investigated. The results show that the bandwidth enhancement and the flat spectrum can be achieved simultaneously in a wide range of operating parameters.

Experimental demonstration of a broadband optoelectronic chaos system based on highly nonlinear configuration of IQ modulator.

We experimentally investigated a novel broadband optoelectronic chaos generation scheme. The proposed system is achieved by adopting the highly nonlinear operation of an electro-optical exclusive-NOR (XNOR) logic gate and two delayed feedback loops that refer to the Boolean chaos model. The XNOR gate is established by a commercial use inphase and quadrature-phase (IQ) modulator that works at a specific bias point. The resulting power spectrum of the broadband chaos signal extends from DC to 29.1 GHz (10 dB bandwidth), and the probability density distribution is Gaussian distribution like. Owing to the strong nonlinearity of XNOR operation, the conditions to enter the chaos region are more relaxed compared to traditional optoelectronic oscillator (OEO) chaos systems, and the time delay signature (TDS) of the feedback loop is also suppressed. Moreover, to further enhance the performance of the generated chaos signal, we injected the optoelectronic chaotic signal into a semiconductor laser. Experimental results indicate that after the cascade optical injection, the bandwidth of the output chaos signal is extended to 38.4 GHz and the TDS is completely concealed; meanwhile, a perfect Gaussian distribution can be obtained.

Broadband Chaos Signal Generation Based on Dual-mode DFB Laser with Optical Feedback

Broadband Chaos Signal Generation Based on Dual-mode DFB Laser with Optical Feedback

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.

Optically injected nanolasers for time-delay signature suppression and communications.

A large number of studies have been carried out to understand the nonlinear dynamics of nanolasers, yet there is a lack of comprehensive consideration on the optimization of chaotic output and its application to chaos secure communications. In this paper, we used an optically injected nanolaser structure to generate broadband chaos without a time-delay signature (TDS), which acts as the chaotic carrier in the proposed communication scheme. Due to the combination of desired TDS suppression enabled by the nanolasers and a two-channel transmission technique, the proposed scheme offers enhanced security for message encryption and decryption. We also considered the influence of some key parameters on the TDS suppression and that of parameter mismatch on chaos synchronization and message recovery. The detailed studies indicate that the proposed nanolaser-based scheme offers satisfactory TDS suppression performance over a wide range of parameters considered and is robust to resist fabrication imperfections-induced mismatch under proper injection conditions.

Dynamic strain measurement by a single-slope-assisted chaotic Brillouin optical correlation-domain analysis.

We propose a novel, to the best of our knowledge, method to enhance the measurement range of dynamic strain using a single-slope-assisted chaotic Brillouin optical correlation-domain analysis. The broadband chaos provides a Gaussian-shape pump-probe beat spectrum so that not only the centimeter-level spatial resolution is achieved but also the linewidth of the chaotic Brillouin gain spectrum is naturally broadened. Thus, the enlarged linear region could be employed to dynamically measure a large-range stretched strain. This experiment is the first to accurately identify the maximal strain of 1200 $\unicode{x00B5}\unicode{x03B5}$µε with a high spatial resolution of 3.45 cm using the single-slope-assisted technology. The dynamic frequency is 4.67 Hz in the highest but limited by the practical devices.

Flat chaos generated by optical feedback multi-mode laser with filter

<sec> Optical chaos has a wide range of applications in communications, such as secure communication, high-resolution lidar ranging, optical time domain reflectometer, and high-rate physical random bit generator.</sec><sec> In recent years, external-cavity feedback semiconductor lasers (ECLs) are the most common chaotic laser generation systems due to their characteristics of wide bandwidth, large amplitude, and simple structure, and the dynamic characteristics of chaotic signals have attracted much attention. However, limited by the relaxation oscillation of the laser, the energy of the chaotic signal directly generated by ECL is mainly concentrated at high relaxation oscillation frequency. Thus, the low-frequency component encounters the problem of energy loss.</sec><sec> In practical applications, the signal detection/acquisition device usually responds to a 3-dB low-pass filtering characteristic. Therefore, the available effective bandwidth of the chaotic signal should actually be 3-dB bandwidth. The lack of low-frequency components will limit the energy utilization rate of chaotic signals and restrict the relevant performances of chaotic applications (such as reliability and transmission of chaotic secure communication, randomness and generation rate of physical random bits, measurement accuracy and range of lidar ranging or optical time-domain reflectometer).</sec><sec> In the paper, we propose a broadband chaos generation scheme with simple structure and losing no low-frequency components. Specifically, we experimentally analyze the radio frequency (RF) spectra of the single-mode and the multi-mode output from an optical feedback Fabry-Perot (FP) semiconductor laser after and before filtering. The experimental results show that comparing with the multi-mode chaotic signal, the low-frequency energy of the single-mode chaotic spectrum is enhanced by 25 dB, and the 3-dB bandwidth of the single-mode chaotic signal can reach 6 GHz. Further theoretical analysis demonstrates that the enhancement of low-frequency component in the single-mode chaotic signal is caused by the mode-competing in multi-mode laser. It is concluded that this method can well solve the problem of low-frequency energy loss in conventional optical feedback chaotic systems, and is beneficial to improving the energy utilization rate of chaotic signals, which is of great significance for improving the performance of chaotic secure communication, random bit generation, lidar ranging, optical time domain reflectometer, and other relevant applications. </sec>