Time Delay Concealment in Feedback Chaotic Systems With Dispersion in Loop

Concealment of time delay signature of chaotic output in a slave semiconductor laser with chaos laser injection

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

In this paper, a novel chaotic secure communication system based on vertical-cavity surface-emitting lasers (VCSEL) with a common phase-modulated electro-optic (CPMEO) feedback is proposed. The security of the CPMEO system is guaranteed by suppressing the time-delay signature (TDS) with a low-gain electro-optic (EO) feedback loop. Furthermore, the key space is enhanced through a unique secondary encryption method. The first-level encrypted keys are the TDS in the EO feedback loop, and the second-level keys are the physical parameters of the VCSEL under variable-polarization optical feedback. Numerical results show that, compared to the dual-optical feedback system, the TDS of the CPMEO system is suppressed 8 times to less than 0.05 such that they can be completely concealed when the EO gain is 3, and the bandwidth is doubled to over 22 GHz. The error-free 10 Gb/s secure optical transmission can be realized when the time-delay mismatch is controlled within 3 ps. It is shown that the proposed scheme can significantly improve the system performance in TDS concealment, as well as bandwidth and key space enhancement, which has great potential applications in secure dual-channel chaos communication.

A linear time-invariant system with time delays is considered. It is assumed that the delays are nontrivial in the sense that they affect the characteristic equation (i.e., the characteristic quasi-polynomial is not a polynomial of one complex variable). It is proved that if any of such delays grows to infinity then either the system becomes unstable or, at least, some of its eigenvalues approach the imaginary axis. In the latter case, of course, the system may become extremely sensitive to changes of other parameters, which means practical instability. The theoretical results of this paper support well-known real-world observations concerning the stability of systems with large delays in the feedback loop.

We numerically investigate the time delay signature (TDS) properties of a chaotic semiconductor laser subject to nonlinearly-modulated feedback. In the proposed scheme, two semiconductor lasers that play the role of a built-in nonlinear modulator is positioned in the external cavity of the chaos generator laser, which forms a structure of semiconductor laser ring. The simulation results show that the TDS of the chaos generator in the laser ring is quite smaller than that of the chaos induced by the conventional optical feedback. Moreover, the TDS embedded in the intensity and phase time-series of the chaotic signal can be further concealed, by introducing an additional optical feedback into the built-in nonlinear modulator.

Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback

To quantitatively evaluate the time-delay (TD) signatures of chaotic signals generated by vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated optical feedback (PROF), we propose four cases of resolution coefficients R based on correlation functions. The resolution coefficient characteristics for the x-polarization (XP) mode, y-polarization (YP) mode and the total output are considered. The dependences of R on the feedback strength and feedback delay are discussed and compared carefully. The two-dimensional maps of R show that the TD signatures for the single polarization mode (i.e., XP or YP mode) are much more difficult to retrieve than those for the total output in the entire parameter space. Thus, by using single polarization mode as a chaotic carrier, the TD signatures are extremely difficult to be identified, which contributes a lot in the security-enhanced VCSELs-based chaotic optical communication systems.

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

In this paper, we investigate the possibility of using optical injection to efficiently suppress the time-delay (TD) signatures of chaotic signals in a large experimentally accessible parameter range of semiconductor ring lasers (SRLs). We also study how this optical injection can improve the signal bandwidths. The injection signal is obtained from a master SRL with either optical self- or cross-feedback. For optical self-feedback configurations, it is found that the suppression of TD signatures is similar to what has been found in injected Fabry–Perot semiconductor lasers, i.e., narrow range of parameters with respect to the detuning and injection strengths. For cross-feedback configurations, however, the TD signatures can be suppressed in a wide range of parameters; meanwhile, the bandwidths are significantly improved for the same range of parameters. This is particularly useful for the security in chaos-based communications and also for generating random bits with improved properties.

A novel chaos system with XOR operations and multi-bit PRBS is proposed to improve the sequence complexity and the security of the classic electro-optic intensity chaos system. Through the bifurcation diagram and permutation entropy analysis, the PE can be increased to 0.99. The key space is enlarged because additional DSP parameters and PRBS are introduced. The impacts of ADC/DAC characteristics and PRBS characteristics are analyzed in detail. The simulation results show that the time delay signature can be concealed with the appropriate DSP parameters.

We demonstrate that a semiconductor laser perturbed by distributed feedback with random time delays from a large number of scattering centers along a fiber random grating can emit light chaotically without the time-delay signature (TDS). A theoretical model is developed based on the modified Lang-Kobayashi model to numerically explore the chaotic dynamics of the laser diode subjected to random feedback. It is predicted that the random distributed feedback destroys the phase-correlated mode condition and hence suppresses the TDS. The fiber random grating is fabricated with random index modulation periods through point-by-point inscription, which introduces large numbers of phase-uncorrelated cavity modes into the semiconductor laser, leading to high dimensional chaotic dynamics and thus the concealment of the TDS. The experimentally obtained TDS value is negligible with a minimum of 0.0088, which is the smallest to date.

Aiming at the problems of limited bandwidth and periodicity of chaotic laser, a monolithically integrated chaotic semiconductor laser subject to random feedback and mutual injection is proposed. The chaotic laser consists of two distributed feedback laser diodes (DFB-LD), two semiconductor optical amplifiers (SOA) and a passive optical waveguide. Optical injection of two coupled DFB-LDs achieves chaotic signal shaping and bandwidth enhancement. Random grating along the passive waveguide provides stochastic feedback to suppress the time delay signature (TDS). A theoretical model is established based on the Lang-Kobayashi model to explore the dynamics of the proposed chaotic laser. A chaotic signal with TDS of 0.06 and bandwidth of 13.12 GHz is obtained by simulation. Furthermore, the effects of parameters including feedback ratio, mutual injection ratio, and detuning frequency on the TDS and bandwidth of chaotic signal are investigated. The results show that the broadband chaotic laser signal with TDS suppression can be obtained by controlling parameters reasonably.

We mainly investigate the influence of group velocity dispersion (GVD) and self-phase modulation (SPM) in single-mode fiber on chaotic time delay signature (TDS) of single feedback semiconductor laser. In the simulation, the second-order dispersion coefficient and the average input optical power in fibers are adjusted to control GVD and SPM. The results show that after the fiber length reaches the dispersion length of the chaotic laser, the chaotic TDS caused by single optical feedback begins to be suppressed due to the significant enhancement of GVD, and then the value of the autocorrelation coefficient at the chaotic TDS descends at the fastest suppression rate of 0.5 dB/km. When chaos laser propagates about 20 km in the fibers, duo to the accumulation of SPM to the significant range of action, the chaotic TDS achieves the best stable suppression state, and the suppression effect can reach 11.6 dB.

The practical application of chaotic optical communications has been limited by two aspects: the difficulty in concealing the time delay - a critical security parameter in feedback chaotic systems, and the difficulty of significantly enlarging the key space without complicating the implementation. Here we propose an architecture to break the above limits. By introducing a frequency-dependent group delay module with frequency tuning resolution of 1 MHz into the chaotic feedback loop, we demonstrate excellent time delay concealment effect, and an additional huge key space of 1048 can be achieved at the same time. The effectiveness is proved by both numerical simulation and experiment. Besides, the proposed scheme is compatible with the existing commercial optical communication systems, thus pave the way for high-speed secure optical communications.

We study the coherence resonance in a Schmitt-trigger inverter with a delayed feedback loop. The output of the system is analyzed changing the input noise amplitude and the delay time of the feedback loop. The regularity of the output shows resonance-like dependence on the input noise amplitude. At the optimum input noise amplitude, the system outputs well-regulated rectangular wave, and corresponding peaks in the output spectrum become large and sharp. This optimization of the system is accomplished when the period of the output rectangular wave almost coincides with the feedback delay time.