Conventional Optical Feedback Research Articles

Enhanced performances of photonic reservoir computing using a semiconductor laser with random distributed optical feedback

We propose and experimentally demonstrate a photonic time-delay reservoir computing (TDRC) system with random distributed optical feedback under optical injection. To evaluate the performance, we calculate the memory ability and perform two benchmark tasks, i.e., chaotic time series prediction and nonlinear channel equalization task. Our numerical results show that the proposed TDRC has a superior performance compared with the case with conventional single optical feedback. This is attributed to the fact that the random distributed optical feedback offers multiple external cavity modes, which enhance the nonlinearity of the reservoir laser. Additionally, the experimental result also shows that our proposed TDRC scheme outperforms the computer with single optical feedback in the chaotic time series prediction task. To the best of our knowledge, our work offers a novel path to improve the performance of TDRC by introducing random distributed optical feedback.

Photonic reservoir computing using a self-injection locked semiconductor laser under narrowband optical feedback.

Photonic time-delay reservoir computing (TDRC) using a self-injection locked semiconductor laser under optical feedback from a narrowband apodized fiber Bragg grating (AFBG) is proposed and numerically demonstrated. The narrowband AFBG suppresses the laser's relaxation oscillation and provides self-injection locking in both the weak and strong feedback regimes. By contrast, conventional optical feedback provides locking only in the weak feedback regime. The TDRC based on self-injection locking is first evaluated by the computational ability and memory capacity, then benchmarked by the time series prediction and channel equalization. Good computing performances can be achieved using both the weak and strong feedback regimes. Interestingly, the strong feedback regime broadens the usable feedback strength range and improves robustness to feedback phase variations in the benchmark tests.

Fast physical random bit generation of wideband flat chaos signal based on filter feedback

<sec>Chaotic lasers feature wide spectrum and noise-like features, and extensively used in various fields, such as secure communications and random bit generation (RBG). Since the physical RBG using optical chaos was demonstrated first by Uchida et al., the optical chaos has been widely investigated in terms of chaos bandwidth and flatness, which determines the rate and randomness of RBG. Owing to the natural stability of semiconductor lasers, external perturbation is required to generate chaotic signals, such as optical injection, current modulation, and optical feedback. Among them, a semiconductor laser with optical feedback has attracted wide attention because of its simple structure and rich dynamic behaviors. Nonetheless, this configuration suffers the influence of the relaxation oscillation, which results in a limited bandwidth (a few GHz) and an uneven power spectrum. To obtain broad-spectrum chaotic signals, considerable efforts have been made in recent years. However, these solutions are associated with complex structures that require delicate manipulation because multiple parameters should be matched, so the cost of some of these schemes in terms of the system complexity can potentially outweigh the benefits.</sec><sec>In this work, we incorporate an optical filter and an amplifier into the feedback loop of a conventional optical feedback system to generate broadband chaotic signals. The effects of the filter detuning frequency and feedback power on the bandwidth and flatness of the chaotic output are investigated experimentally. The experimental results demonstrate that by appropriately adjusting the feedback power and detuning frequency, both the low-frequency components and the high-frequency components of the chaotic output power spectrum can be increased, and the maximum chaotic bandwidth can reach 24.4 GHz with a flatness of 5.7 dB. This phenomenon is attributed to the physical process of beating between the filtered mode and the internal modes of the laser. Furthermore, the optimized chaotic output is processed by retaining the 4 least significant bits and implementing the delayed exclusive-OR (XOR) operation. Our scheme is capable of generating physical random number of the bit rate of 320 Gbit/s, and successfully passes the standard randomness test, i.e. the NIST test (NIST SP 800-22).</sec>

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.

Permutation entropy analysis of the output of a laser diode under stimulated Brillouin scattering optical feedback.

The chaotic output emitted by a diode laser with optical feedback has fascinated the community for decades. The external cavity delay time imparts a weak level of periodicity to the laser output (the so-called "time delay signature", TDS) that is a drawback for applications that require random optical signals. A lot of efforts have focused in suppressing the TDS either by post-processing the signal or by using alternative ways to generate random optical signals. Here, we compare the signals generated by two optical feedback setups: in the first one, the stimulated Brillouin backscattered light from a standard optical fibre is re-injected into the laser (stimulated Brillouin scattering optical feedback, SBSOF); in the second one, the light transmitted through the fibre is re-injected into the laser (conventional optical feedback, COF). We analyse the permutation entropy, a well-known measure of complexity that captures order relations between values of a time series. We find that, on average, the signal generated by the SBSOF setup has slightly lower PE than the one generated by the COF setup, except when the sampling time of the intensity signal is an exact multiple of the delay; in that case, due to TDS, the entropy of the COF signal is lower than that of the SBSOF signal. We interpret the lower entropy value of the SBSOF signal as due to oscillations at the Brillouin frequency shift. Taken together, our results show that TDS suppression can have an undesirable side effect: a decrease of the entropy of the signal.

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.

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.

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.

Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback

In this work, we propose a new scheme of optical feedback using stimulated Brillouin scattering (SBS). A high-power laser diode emitting at 1450 nm stimulates Brillouin back-scattering in a 4km-long optical fibre and the back-scattered light is injected back into the laser diode for optical feedback. The experimental results with RF spectrum exhibit clearly the Brillouin frequency shift at 11.46 GHz. Although the frequency shift is very large, the laser diode subject to optical feedback using SBS shows abundant dynamics. RF spectrum maps are also established with respect to the laser drive current. The results are compared with the ones for conventional optical feedback and it is clearly shown that the dynamical behaviours for both the configurations are very different. The investigation with autocorrelation functions reveals that the time-delay signature vanishes completely using the SBS feedback scheme unlike the conventional feedback one.

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.

Wideband complex-enhanced chaos generation using a semiconductor laser subject to delay-interfered self-phase-modulated feedback.

A wideband complexity-enhanced chaos generation scheme is proposed by using a semiconductor laser subject to delay-interfered self-phase-modulated optical feedback. The influences of feedback strength, phase modulation index, and interference delay on the effective bandwidth and time-delay-signature (TDS) characteristics of the proposed scheme-generated chaos are extensively investigated both experimentally and numerically. The results demonstrate that with the joint effects of phase modulation-induced spectrum expansion and nonlinear filtering of delayed interference, wideband chaos with flat spectrum and excellent TDS suppression characteristics can be generated over a wide dynamic operation range. In comparisons with the relevant chaos generation schemes under conventional optical feedback, individual self-phase modulated optical feedback, and delay-interfered optical feedback, the proposed scheme cannot only significantly enhance the effective bandwidth of chaos but also considerably enhance the complexity of chaos by suppressing the TDS toward an indistinguishable level close to 0.

Simultaneous Chaos Time-Delay Signature Cancellation and Bandwidth Enhancement in Cascade-Coupled Semiconductor Ring Lasers

Optics chaos has been widely studied and its various applications have also been demonstrated in recent years. To improve the performance of chaos-based applications, several properties of the chaotic signals should be evaluated and enhanced accordingly. In this paper, we consider a chaotic system consisting of three cascade-coupled semiconductor ring lasers (SRLs), where the master SRL is subjected to conventional (parallel) optical feedback, while its output is injected to the intermediate SRL and further to the slave SRL. We focus on the time-delay signature (TDS) and bandwidth of the generated chaos and demonstrate the possibility of the simultaneous realization of TDS elimination and bandwidth enhancement in the parameter space of the injection strength against the frequency detuning. In addition, a proof-of-concept test of randomness is carried out, and it demonstrates that the chaotic properties could be greatly enhanced by the proposed cascade-coupling scheme compared with a single SRL with feedback and thus is suitable for use in high-speed random number generation.

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>

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.

Filtered Optical Feedback in Quantum Dot Light Emitting Diode

This research reports a theoretical investigation on the role of filtered optical feedback (FOF) in the quantum dot light emitting diode (QD-LED). The underlying dynamics is affected by a sidle node, which returns to an elliptical shape when the wetting layer (WL) is neglected. Both filter width and time delay change the appearance of different dynamics (chaotic and mixed mode oscillations ,MMOs). The results agrees with the experimental observations. Here, the fixed point analysis for QDs was done for the first time. For QD-LED with FOF, the system transits from the coherence collapse (CC) case in conventional optical feedback (COF) to a coherent case with a filtered mode in FOF. It was found that the WL washes out the modes which is an unexpected result. This may attributed to the longer capture time of WL compared with that between QD states. Thus, WL reduces the chaotic behavior.

Optimized chaotic Brillouin dynamic grating with filtered optical feedback

Chaotic Brillouin dynamic gratings (BDGs) have special advantages such as the creation of single, permanent and localized BDG. However, the periodic signals induced by conventional optical feedback (COF) in chaotic semiconductor lasers can lead to the generation of spurious BDGs, which will limit the application of chaotic BDGs. In this paper, filtered optical feedback (FOF) is proposed to eliminate spurious BDGs. By controlling the spectral width of the optical filter and its detuning from the laser frequency, semiconductor lasers with FOF operate in the suppression region of the time-delay signature, and chaotic outputs serving as pump waves are then utilized to generate the chaotic BDG in a polarization maintaining fiber. Through comparative analysis of the COF and FOF schemes, it has been demonstrated that spurious BDGs are effectively eliminated and that the reflection characterization of the chaotic BDG is improved. The influence of FOF on the reflection and gain spectra of the chaotic BDG is analyzed as well.

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.

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.

Quantum dots lasers dynamics under the influence of double cavity external feedback

This paper reports results on investigations of the dynamical behavior of a semiconductor laser with quantum dots active medium under the influence of a feedback from double external cavity. This configuration is treated in the framework of Lang-Kobayashi equations. The locus of external cavity modes is found to be elliptic, as in case of conventional optical feedback, but also represents different shapes, even with possible satellite bubbles. A bifurcation analysis is carried out revealing the points of saddle-node and Hopf bifurcations. Finally, the nature of bifurcations and the stability of steady state solutions are analyzed in dependence on different parameters.

External modes in quantum dot light emitting diode with filtered optical feedback

This research reports a theoretical investigation on the role of filtered optical feedback (FOF) in the quantum dot light emitting diode (QD-LED). The underlying dynamics is affected by a sidle node, which returns to an elliptical shape when the wetting layer (WL) is neglected. Both filter width and time delay change the appearance of different dynamics (chaotic and mixed mode oscillations, MMOs). The results agree with the experimental observations. Here, the fixed point analysis for QDs was done for the first time. For QD-LED with FOF, the system transits from the coherence collapse case in conventional optical feedback to a coherent case with a filtered mode in FOF. It was found that the WL washes out the modes which is an unexpected result. This may attributed to the longer capture time of WL compared with that between QD states. Thus, WL reduces the chaotic behavior.