Spectral properties of the coherence collapsed state of asemiconductor laser with delayed optical feedback

A theoretical analysis of the coherence collapsed state for a single-mode semiconductor laser with a moderate amount of delayed optical feedback that is operating well above threshold is presented. Both phase fluctuations and the amplitude fluctuations satisfy a bivariate Gaussian distribution. The autocorrelation properties are determined self-consistently from the rate equations. The asymmetry of the optical power spectrum is discussed     

Stability analysis and the route to chaos for laser diodes withoptical feedback

The sequence of phenomena that lead from a narrow linewidth state to coherence collapse in semiconductor lasers for an increasing level of optical feedback has been identified. Undamping of the relaxation oscillations, which is shown to be accurately predicted by an analytical stability analysis, initializes the route to chaos, but the laser generally enters quasiperiodic and frequency-locked states before ending up in the chaotic state of coherence collapse. The analysis identifies the laser parameters which are relevant for reducing the feedback sensitivity     

Quasi-periodic route to chaos in erbium-doped fiber laser

We present experimental evidence of quasiperiodic route to chaos in erbium-doped fiber laser operating simultaneously at 1.550 μm and 1.536 μm. Starting from a CW state for high pumping rates the system becomes T-periodic, 2T-periodic, 3T-periodic and chaotic for decreasing pumping ratios. The low-frequency spectra shows two fundamental frequencies. The nT-periodic regimes correspond to a frequency locking of the low frequency on a subharmonic of the high frequency. An adapted model based on the rate equations is numerically investigated and leads to a good qualitative agreement with the experimental data     

光电反馈主动锁模

本文报道采用光电反馈法实现半导体激光器的主动锁模。在反馈环大增益工作状态下,得到了宽度为17.7ps、重复频率为926MHz、峰值功率为80mW的超短脉冲输出。     

Chaotic dynamics of oscillators based on circuits with VCO andnonlinear delayed feedback

An electronic oscillator that produces chaos with a dimensionality at least 20 times higher than the dimensionality obtained with previously published electronic chaos generators is reported     

单环掺铒光纤激光器光延迟反馈的混沌控制

为了找到更加简单稳定激光系统的混沌化方法,采用光延迟反馈方法对单环掺铒光纤激光器特性进行了数值仿真,得到了各种周期现象而且产生了混沌现象。结果表明,利用单模单环掺铒光纤激光器,在附加光延迟反馈环路的方法下可以实现混沌控制。这一结果对应用于保密通信的混沌化简化具有重要意义。     

Suppression of self-modulation in the self-oscillator with delayed feedback using the method for chaos control

A method to suppress self-modulationory in the self-oscillatory systems with delayed feedback (DF) is proposed. The method is based on an additional DF circuit whose parameters are chosen in such a way that the signal components at the fundamental and spurious frequencies having passed through the two branches of the DF circuit have equal and opposite phases, respectively, so that the spurious components are suppressed. The results of the numerical simulations show that the method allows a two- to threefold increase in the range of parameters that corresponds to the stability of the stationary single-frequency generation and an increase in the generation power by about 30%.     

Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback

Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback are studied both numerically and experimentally. Mappings of the dynamic states and bifurcation diagrams are compared between a delayed negative optoelectronic feedback system and a delayed positive optoelectronic feedback system. Both systems follow a quasiperiodic route to chaos, where regular pulsing, quasiperiodic pulsing, and chaotic pulsing states are observed. Frequency-locked pulsing states are also found in a delayed negative optoelectronic feedback system, but not in a delayed positive optoelectronic feedback system. These frequency-locked pulsing states are experimentally observed to exhibit a harmonic frequency-locking phenomenon, where the pulsing frequency is locked to a harmonic of the delay loop frequency instead of the delay loop frequency itself. The rotation numbers of these frequency-locked pulsing states show a Devil's staircase structure.     

Chaotic dynamics of delayed feedback klystron oscillator and its control by external signal

Complex nonlinear dynamics and applications of a microwave klystron oscillator with delayed feedback are studied in this paper on the basis of a system of delayed differential equations. Results of numerical simulation of self-modulation and chaotic regimes are presented, unveiling a complex bifurcation pattern in a wide range of parameters. Various types of chaotic attractors and transition to chaos scenarios are described. Experimental results for the five-cavity klystron oscillator are presented as well, showing good qualitative agreement with numerical simulations. Special attention is paid to application of the oscillator in direct chaotic communications. Information transmission using chaos shift keying (CSK) modulation and coherent reception is demonstrated via numerical simulation. The driving by an external signal is used to control the chaotic states of the transmitter oscillator for the purpose of generation of CSK basis functions.     

A simple method to determine carrier recombinations in asemiconductor laser optical amplifier

The contribution of nonradiative carrier recombinations to the characteristics of long-wavelength InGaAsP/InP semiconductor laser devices is verified by measuring the amplified spontaneous emission (ASE) power from a 1.5-μm semiconductor laser amplifier (SLA) against the bias current. This method provides a simple and straightforward way to determine the mathematical form of recombination rate in a long-wavelength semiconductor laser, provided that the structural parameters of the laser are known     

Small-signal analysis of modulation characteristics in asemiconductor laser subject to strong optical injection

Injection locking of a semiconductor laser can induce major changes in the modulation characteristics of the laser. A small-signal analysis using the lumped element model shows that both the frequency and damping of the characteristic resonances of the coupled complex field and free carriers (gain medium) are modified. The detuning between the injected field and the free-running oscillating field, the amplitude of the injection field relative to the free-running field, the linewidth enhancement factor, the cavity photon and spontaneous carrier decay rates, and the field enhancement of the decay rate are all key parameters in determining the changes to the modulation characteristics. For a broad range of parameters, there is simultaneous enhancement of the modulation bandwidth and stable, locked operation. The enhancement is a cavity phenomena and does not occur in a traveling wave amplifier. It requires that the frequency of the locking field be detuned from the injection-modified frequency of the cavity resonance. This causes a resonant enhancement of the modulation sideband associated with the preferred frequency of the optical cavity. Bandwidth enhancements beyond the free-running laser limit are possible over a range of injection levels and injection frequency detunings     

High-speed chaos in an optical feedback system with flexible timescales

We describe a new optoelectronic device with time-delayed feedback that uses a Mach-Zehnder interferometer as passive nonlinearity and a semiconductor laser as a current-to-optical-frequency converter. Band-limited feedback allows tuning of the characteristic time scales of both the periodic and high dimensional chaotic oscillations that can be generated with the device. Our implementation of the device produces oscillations in the frequency range of tens to hundreds of megahertz. We develop a model and use it to explore the experimentally observed Andronov-Hopf bifurcation of the steady state and to estimate the dimension of the chaotic attractor.     

Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop

We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electrooptical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as a function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.     

Self-excited oscillations in a ubitron oscillator with delayed feedback

The theory of a ubitron oscillator with external delayed feedback is constructed. Starting currents of the oscillator are determined. Microwave generation modes are studied at different currents of the relativistic electron beam.     

Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback

We numerically investigate the detailed characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback. The emission of the dominant TE mode of a drive laser is rotated 90 deg and fed back to the laser with time delay. The polarization-rotated TE mode is also injected with time delay into the TM mode of a second laser. Two types of synchronization with different time-lags are found, as in the case for synchronization in semiconductor lasers with nonrotated optical feedback. However, a significant difference to the nonrotated optical feedback case is that neither of the two types of synchronization requires matching of optical carrier frequency between the two lasers.     

Error performance of transmit beamforming with delayed and limited feedback

Feedback delay can severely affect the performance of transmit beamforming (TB) and the analytical quantification of the performance degradation has attracted much research interest recently. In this letter, we study the effect of delayed and limited-rate codebook index feedback on the error rate performance of TB systems over Rayleigh fading channels. We derive closed-form expressions for the moment generating function (MGF) and the probability density function (PDF) of the receiver output signal-to-noise ratio (SNR) including the effects of outdated and finite-rate feedback and further provide accurate analytical error rate expressions, which are verified by simulation results. The coding gain gap between the full-rate and limited-rate feedback and the coding gain advantage of multiple transmit antennas to the single antenna are analyzed, for limited and delayed feedback. These results are simple and concise and provide new analytical insight into the achievable diversity and combining gains and the loss caused by feedback delay for different system parameters and modulation formats.     

Model-based pilot and data power adaptation in psam with periodic delayed feedback

We consider the optimum design of pilot-symbolassisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized open-loop PSAM (i.e., the case where no feedback is provided from the receiver), our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in mediumrate fading channels. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.     

Multimode self-oscillating systems with a filter in a delayed feedback circuit

A chaotic self-oscillating system based on a delayed oscillator containing a filter in the feedback loop is considered. Results of the numerical analysis of equations describing such an oscillator are presented for symmetric and asymmetric amplitude characteristics enabling variation in their nonlinearity within wide limits. The mechanism of transition to chaos is considered. A two-stage delayed oscillator containing a filter between partial amplifiers is studied.     

Non-linear dynamics and chaos in semiconductor laser devices

The theoretical and experimental aspects of non-linear dynamics and chaos in semiconductor lasers are surveyed. Three novel scenaria for complex dynamical behaviour in semiconductor lasers are proposed for experimental investigation.     

Achievable rate of MIMO systems with multi-user diversity and delayed feedback

The effects are investigated of delayed feedback on the system achievable rate (AR) of a multi-user diversity multiple-input multiple-output (MIMO) system over uncorrelated Rayleigh fading channels in a general framework allowing for arbitrary numbers of transmit/ receive antennas and various spatial combining schemes. Exact AR expressions are derived for different MIMO schemes, including the selective combining, maximum ratio combining and space-time block codes. Numerical results are presented to examine the validity of the theory.