We present an experimental and numerical investigation of a sub-threshold optoelectronic oscillator (OEO) subject to injection from an external RF signal. A time-delayed numerical model is introduced and the agreement with experiments is discussed. The sub-threshold OEO exhibits frequency selective RF amplification. The OEO sensitivity is investigated for different subthreshold internal gain values. As the internal gain of the system increases and the oscillation threshold is approached, the OEO exhibits larger amplification of an injected RF signal. When the injected RF signal is on resonance, the OEO exhibits a maximum RF gain of approximately 28 dB near 0.5% below threshold. Furthermore, the injected RF signal frequency is scanned, and the amplified response is measured. Finally, we highlight the role of the intrinsic time-delay within the OEO’s temporal response to a pulsed, injected RF signal.
This paper will report on some features of a platform for the realization of an anti parity-time (anti-PT) symmetric system in a pair of time-delay coupled semiconductor lasers, with special emphasis on the delay induced dynamics in the system. The system is modeled by a modified Lang-Kobayashi rate equations model, augmented to include delayed coupling. The role of a phase accumulation factor that arises from the delayed coupling is elucidated. Finally, the novel exceptional point(s) behavior that is characteristic of the time-delay is investigated via numerics as well as analytically via the Lambert W function.
The purpose of this paper is to examine the behavior of exceptional points (EPs) in a time delayed anti-parity-time symmetric system composed of two delay-coupled semiconductor lasers (SCLs). Starting from a pseudo-2x2 rate equation model for the lasers’ electric fields we analyze the eigenvalues and eigenvectors of the system’s effective Hamiltonian and numerically search for EPs. Recent experimental work has suggested that the EP landscape in this system may be significantly different from the typical anti-PT dimer due to the time delay. Exceptional points in these PT dimers mark global phase changes from overall oscillatory behaviour to exponential growth/decay; in contrast, the time delay renders our effective Hamiltonian infinite-dimensional and allows for more than one EP. Specifically, we numerically demonstrate that by tuning the delay time or coupling strength our time delayed system may exhibit one, two, or zero EPs.
This paper describes our work on the realization of a non-hermitian Hamiltonian system in time-delay coupled semiconductor lasers consisting of two identical lasers, operated with a small frequency detuning between them, and bidirectionally coupled to each other through optical injection. The effective Hamiltonian for this system is non-hermitian, and, under some assumptions and conditions, reminiscent of two-site paritytime (PT) symmetric Hamiltonians, a topic that is under intense investigation. The dynamical response of the intensity of the lasers as a function of the detuning between them reveals characteristics of a PT symmetric system, and our emphasis is on the features that arise from the delayed coupling. Experimental measurements are in good agreement with numerical simulation of the nonlinear rate equation model that describes the coupled system.
We experimentally demonstrate the realization of a parity-time (PT) symmetry breaking in optically coupled semiconductor lasers (SCLs). The two SCLs are identical except for a detuning between their optical emission frequencies. This detuning is analogous to the gain-loss parameter found in optical PT systems. To model the coupled SCLs, we employ the standard rate equations describing the electric field and carrier inversion of each SCL, and show that, under certain conditions, the rate equations reduce to the canonical, two-site PT- symmetric model. This model captures the global behavior of the laser intensity as the system parameters are varied. Overall, we find that this bulk system (coupled SCLs) provides an excellent test-bed to probe the characteristics of PT-breaking transitions, including the effects of time delay.
We find that, although inversion noise has only a marginal effect on the linewidth of a semiconductor laser in CW operation, in the presence of dynamics it may play a key role in determining the final dynamical state. It is therefore essential to include both field noise and carrier noise of realistic strength when analysing semiconductor laser dynamics. Next we investigate the influence of quantum noise, both field and carrier noise, on the highly complex nonlinear dynamics that arise in a single-mode semiconductor laser subject to filtered optical feedback. Our numerical study based on stochastic rate equations shows that for a wide range of filter widths the noise may lead to qualitatively different dynamics than predicted by a deterministic analysis. In particular, we find that certain attractors that are predicted in the absence of noise may no longer be available when the effects of noise are correctly incorporated, while others show remarkable robustness instead. In general, the results confirm that carrier noise in the laser can influence the dynamics quite substantially. Finally, we present numerical results of noise-induced pulsations in a semiconductor laser with optical injection. We show that, close to the locking edge, patterns of single, two and three pulses can be excited and we suggest that experimental study of this multi-pulse excitability be based on pulse timing statistics.
Through simulations based on the rate equations for diode lasers with filtered optical feedback, we show that in the Coherence Collapse regime a large variety of dynamics is predicted such as periodic and quasiperiodic oscillations and chaos. The control of the transition through these dynamical regimes is achieved through the filter parameters : the filter's spectral width and its central frequency.
The dynamical behavior of an atom interacting with a coherent and a chaotic field is investigated. Langevin equations describing the time dependent behavior of the dipole moment and population inversion are numerically integrated using Monte-Carlo techniques. The model can account for a finite correlation time for the chaotic component. Results on fluctuations in the fluorescence intensity from an ensemble of two-level atoms and the power spectra of these intensity fluctuations are presented. The effect of detuning the pump field from the resonant frequency of the two-level atoms on the fluctuations in fluorescence is studied. The effect of field fluctuations on the macroscopic polarization produced by the atoms is also reported. The fluctuation behavior of the atomic fluorescence is found to be very sensitive to the correlation time of the stochastic component.
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