Phase-conjugate Feedback Research Articles

Research on secure communication technology based on phase conjugate feedback chaotic injection system

This paper presents an experimental scheme using optical method instead of phase conjugate light. We have implemented a phase conjugate feedback semiconductor laser chaotic system based on the four-wave mixing principle through an established optical fiber experimental platform. Based on the high-dimensional wideband chaotic signals generated by this system, we propose a two-channel secure communication scheme based on phase conjugate feedback, and analyze its delay hiding mechanism and synchronization characteristics. The effects of parameter mismatch and injection strength on synchronization performance and communication quality are also considered. Our experimental results show that by adjusting the injection strength and frequency detuning parameters, the system can produce signals with time-delay signature completely suppressed, thus achieving high-quality and high-security communications.

Time-Delay Signature Suppression and Communications of Nanolaser Based on Phase Conjugate Feedback

The nonlinear dynamics of nanolasers (NLs), an important component of optical sources, has received much attention. However, there is a lack of in-depth research into the high-quality chaotic output of NLs and their applications in chaotic secure communications. In this paper, we make the NLs generate broadband chaotic signals whose time-delay signatures (TDS) are completely hidden by a phase conjugate feedback structure. And in the two-channel communication scheme, we make the NLs achieve a combination of a low-latency high degree of synchronization and two-channel transmission technique, which enhances the security of message encryption and decryption. We also investigate the effects of system parameters, Purcell factor F, spontaneous emission coupling factor β, and bias current I on the TDS, as well as the effects of parameter mismatch and injection parameters on chaos synchronization and message recovery. The results show that the phase conjugate feedback-based NLs can achieve the suppression of the TDS within a certain parameter range, and it can achieve high-quality synchronization and enhance the security of chaotic communication under appropriate injection conditions.

High-frequency chaotic bursts in laser diode with optical-feedback

The diversity of observed nonlinear dynamics in laser diodes subjected to optical feedback shows promise as an excellent candidate for chaos-based commercial applications. Thus, works in the last decade have primarily focused on system performances, geometric configurations, and balancing their trade-offs. We demonstrate an optical feedback system operating on phase-conjugate feedback exhibiting state-of-the-art chaos bandwidth values reaching ≈ 30 GHz. We report numerous high-frequency, spatiotemporally complex, chaotic dynamics undocumented in the past four decades. We highlight the underlying physics involving a three-tier temporal interaction mechanism between laser relaxation oscillations, phase-conjugate feedback induced external cavity modes, and chaotic bursts repeating each delay time in the extended cavity. We show supporting real-time high-definition system outputs captured by modern large bandwidth oscilloscopes. The presented work shows to our knowledge, the highest bandwidth and complexity entropy to-date in an optical chaos from a single laser, thereby proving the unnecessary need for further complexity using cascading lasers.

Investigation on the complex and tunable laser chaos generated by the microresonator optical combs injection

A novel method to generate high complexity and wavelength-tunable laser chaos is proposed by injecting nonlinear frequency combs from a microresonator (MR) into a semiconductor laser. The nonlinear dynamics and chaotic characteristics are simulated. The results show that chaos with permutation entropy of 0.997, spectral entropy of 0.953, spectrum bandwidth of 32.4 GHz, the flatness of 0.38 dB/GHz can be generated. Compared with the conventional optical feedback injection system and the phase conjugate feedback injection system, the MR injection system can generate better chaos with bandwidth enhancement and complexity improvement at lower bias currents. The time delay signature introduced by the MR can be completely concealed, which provides support for chaotic secure communication. Furthermore, the microresonator injection (MRI) system is flexible and expandable. Laser chaos with tunable wavelength can be generated by changing the working wavelength of the slave laser. And if multiple lasers with free spectral range interval are connected to MR parallelly, up to 93 high-performance chaotic carriers with a cross-correlation as low as about 0.1 can be realized in short, conventional, and long wavelength bands simultaneously. This scheme provides a foundation for multiple parallel chaotic carriers and large-capacity chaotic secure communication.

Optimized properties of chaos from a laser diode

We perform an experimental parametric study of the chaos generated by a laser diode subjected to phase-conjugate feedback. In addition to the typical figure of merit, i.e., chaos bandwidth, the corresponding spectral flatness and permutation entropy at delay is analyzed. Our experimental observations reveal that the chaos can be generated with a bandwidth of ≈29GHz, a spectral flatness up to 0.75, and a permutation entropy at delay of up to 0.99. These optimized performances are maintained over a large range of parameters and have not been achieved in the conventional optical feedback configuration. Interestingly, reducing the pump current reduces the chaos bandwidth while keeping the spectral flatness and the permutation entropy at delay the same as observed for increased pump current. Our experimental findings are consistent with the presented numerical simulations produced using the Lang-Kobayashi model.

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.

Wideband chaos from a laser diode with phase-conjugate feedback.

We analyze experimentally and theoretically the chaotic dynamics generated by a laser diode subjected to phase-conjugate feedback. Phase conjugation is obtained from four-wave mixing in a BaTiO3 photorefractive crystal. We demonstrate that the chaos bandwidth first increases linearly with feedback ratio but then saturates to relatively high values. With a single optical feedback, a chaos bandwidth up to about 18GHz is achieved, which is about five times as large as the free-running laser diode relaxation oscillation frequency. Numerical simulations confirm our experimental observations and unveil that the finite depth penetration into the crystal is responsible for the observed saturation.

Numerical study of the time-delay signature in chaos optical injection system with phase-conjugate feedback

In this contribution, the effects of two key internal parameters, i.e. the linewidth-enhancement factor (α) and the gain nonlinearity (ε), on time-delay signature (TDS) concealment of the optical injection chaos system with phase-conjugate feedback (PCF-OICS) are numerically investigated. The results show that, as the injection and feedback parameters (injection and feedback strength, frequency detuning) are varied, higher linewidth-enhancement factor and lower gain nonlinearity are useful for concealing the TDS, and our simulations uncover that combining the mechanism of PCF and chaotic optical injection is beneficial for TDS concealment in the slave semiconductor lasers (SSL).

Stability analysis of a quantum cascade laser subject to phase-conjugate feedback.

We investigate the stability boundaries of a quantum cascade laser subject to phase-conjugate optical feedback. From a three-level model, we reduce our set of equations to the usual modified Lang-Kobayashi equations describing a semiconductor laser subject to phase-conjugate feedback. We then determine the Hopf bifurcation conditions, which we explore by using asymptotic methods. In the limit of large delays, we find approximations of the first Hopf bifurcation that is responsible for the destabilization of the system. We obtain an expression that depends only on three parameters: the feedback strength, the line-width enhancement factor, and the pump current. From this expression, we study the stability boundaries of our system. We compare our results with the initial three-level model using a continuation method. We find qualitative and quantitative agreements of the stability boundaries with the two methods. Finally, we compare our findings with the ones obtained for a quantum cascade laser subject to conventional optical feedback.

Dynamical characteristics of nano‐lasers subject to optical injection and phase conjugate feedback

The dynamics of nano-lasers has been analysed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. It is shown that when subject to optical injection and phase conjugate feedback, nano-lasers may exhibit remarkably stable small-amplitude oscillations with frequencies of order 300 GHz. Critically, it is established that such oscillations persist when the effects of noise are taken into account. The appearance of such high-frequency oscillations is associated with the effective reduction of the carrier lifetime for larger values of the Purcell factor, F, and spontaneous coupling factor, β. The effects of the feedback distance and bias currents are also considered. As the optical injection strength increases for fixed phase conjugate feedback and relatively short feedback distances, the nano-laser displays periodic dynamics and then enters stable locking. As the feedback distance increases, the quasi-periodic dynamics dominates. Increased bias current can also induce quasi-periodic behaviour albeit this may be ameliorated by reducing the strength of the phase conjugate feedback.

Mapping of external cavity modes for a laser diode subject to phase-conjugate feedback.

We numerically investigate the dynamics of a semiconductor laser subject to phase-conjugate optical feedback. We explore the effects of the laser model and feedback parameters for the generation of time-periodic oscillations of the output power at harmonics of the external cavity frequency, i.e., dynamical solutions that have been named external cavity modes. We point out that both the experimentally tunable and other parameters have an influence on the frequency of such dynamics. Since the delay has to exist, it is not the relevant parameter as we show that the feedback rate fixes the frequency of the periodic self-pulsations. The interaction length of the crystal and the ratio between carrier and photon lifetimes tend to filter out high frequencies as they increase. Finally, the linewidth enhancement factor unlocks high frequencies as it increases. We conclude by providing a situation which leads to periodic solutions with higher frequencies using a set of realistic values of parameters.

Concealment of Chaos Time-Delay Signature Through Phase-Conjugate Feedback and Chaos Optical Injection

In this paper, we numerically demonstrate that the concealment of time-delay signature (TDS) can be readily achieved via the combined mechanism of phase-conjugate feedback (PCF) and chaotic optical injection. To show the potential advantages of the proposed scheme, its counterpart, i.e., a slave semiconductor laser (SSL) subjected to chaotic optical injection from a master semiconductor laser (MSL) with conventional optical feedback (COF) is studied in parallel. In particular, we consider a fair situation where the MSL in both PCF and COF shows a comparable peak value in the autocorrelation function computed from the intensity time series. Our simulations uncover that combining the mechanism of PCF and chaotic optical injection is beneficial for TDS concealment in the SSL. To better understand this, the effects of some control parameters including injection and feedback are comparably studied. The results further prove that, as the injection or feedback parameters are varied, the proposed PCF-system always exhibits weaker autocorrelation around the feedback delay value when compared to the COF-system. In the meantime, the former system allows for larger bandwidth and, thus, paves way for important applications to secure communication and random-number generation.

High-order external cavity modes and restabilization of a laser diode subject to a phase-conjugate feedback

We experimentally report the sequence of bifurcations destabilizing and restabilizing a laser diode with phase-conjugate feedback when the feedback rate is increased. Specifically, we successively observe the initial steady state, undamped relaxation oscillations, quasi-periodicity, chaos, and oscillating solutions at harmonics up to 13 times the external cavity frequency but also the restabilization to a steady state. The experimental results are qualitatively well reproduced by a model that accounts for the time the light takes to penetrate the phase-conjugate mirror. The theory points out that the system restabilizes through a Hopf bifurcation whose frequency is a harmonic of the external cavity frequency.

Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback.

We demonstrate numerically that a semiconductor laser subjected to phase-conjugate feedback (PCF) can exhibit an enhancement in the complexity of chaos by comparison to conventional optical feedback. Using quantifiers from spectral analysis and information theory, we demonstrate that under similar parametric conditions, PCF exhibits a larger chaotic bandwidth and higher spectral flatness and statistical complexity. These properties are of utmost importance for applications in secure communications and random number generation.

Phase Conjugate Feedback Effects in Nano-Lasers

The response of the nanolasers subject to the phase conjugate feedback (PCF) has been analyzed. Calculations have been performed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. In the analysis, the influence of F and β is evaluated for varying the feedback rate. It is observed that, in general, the onset of chaos occurs at a higher feedback rate for PCF than for conventional mirror feedback (CMF), where PCF has lower intensity noise in comparison with the CMF.

High-frequency chaotic dynamics enabled by optical phase-conjugation.

Wideband chaos is of interest for applications such as random number generation or encrypted communications, which typically use optical feedback in a semiconductor laser. Here, we show that replacing conventional optical feedback with phase-conjugate feedback improves the chaos bandwidth. In the range of achievable phase-conjugate mirror reflectivities, the bandwidth increase reaches 27% when compared with feedback from a conventional mirror. Experimental measurements of the time-resolved frequency dynamics on nanosecond time-scales show that the bandwidth enhancement is related to the onset of self-pulsing solutions at harmonics of the external-cavity frequency. In the observed regime, the system follows a chaotic itinerancy among these destabilized high-frequency external-cavity modes. The recorded features are unique to phase-conjugate feedback and distinguish it from the long-standing problem of time-delayed feedback dynamics.

Numerical study of extreme events in a laser diode with phase-conjugate optical feedback.

Extreme intensity pulses sharing statistical properties similar to rogue waves have been recently observed in a laser diode with phase-conjugate feedback [A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 38, 703 (2013)], but remain unexplained. We demonstrate here that a rate equation model of a laser diode that includes an instantaneous phase-conjugate feedback field reproduces qualitatively well the statistical features of these extreme events as identified in the experiment, i.e., the deviation of the intensity statistics to a Gaussian-shape statistics and the statistics of the time separating extreme events. The numerical simulations confirm the importance of the feedback strength in increasing the number of such extreme events and allow us to explain how extreme events emerge from a sequence of bifurcations on self-pulsating solutions, the so-called external cavity modes.

Bifurcation to chaotic low-frequency fluctuations in a laser diode with phase-conjugate feedback.

We unveil theoretically the bifurcations to chaotic low-frequency fluctuations (LFF) in a laser diode with phase-conjugate feedback (PCF). LFF occur from a chaotic itinerancy among destabilized limit-cycle attractors that correspond to the external-cavity modes (ECMs) of the PCF laser system and with a directional motion toward a self-pulsating dynamics of increasing frequency and larger output power. When increasing the feedback strength, the frequency of the fast-pulsing dynamics changes about a multiple of the external-cavity frequency, which is a unique feature of LFF in a laser diode with PCF.

Extreme events in time-delayed nonlinear optics

We report experimentally on extreme events in the pulsating dynamics of an optical time-delayed system, i.e., a diode laser subject to a phase-conjugate feedback. We study the effect of the feedback strength on extreme events' properties. We show a transition to non-Gaussian statistics of the pulse intensity and an increased number of extreme events as the mirror reflectivity increases. The extreme event pulse is anticipated and followed by smaller pulses with time-delay periodicity.

Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.