Dynamics of patterns in lasers with delayed feedback

Optics Communications, 1998

We experimentally investigate low frequency fluctuations LFF in a Fabry-Perot semiconductor laser with optical feedback from an external mirror. During LFF, the time resolved optical spectrum shows that many longitudinal modes of the solitary laser enter into the transients. After each LFF event, the excited solitary-laser modes recover similarly. However, the recovery for the power in each mode is much slower than the recovery of the total power. The intermode exchange of energy during the recovery indicates that a single-longitudinal mode description of such LFF behavior will not capture important underlying dynamics. The relevance of multimode dynamics is confirmed in a feedback experiment where the external mirror is substituted by a diffraction grating. q 1998 Elsevier Science B.V.

Wireless Personal Communications, 2018

In this work, we first analyse the behaviour of semiconductor laser in the presence of weakto-moderate feedback from a single (lumped) and double external cavity setting. Analysis of laser diode in dynamic double cavity configuration shows that the dynamic double cavity does not disturb the stability of the laser device, but it introduces a considerable shift in the emission frequency that is directly related to the feedback strength and the relative phase difference between the phase of the two mirrors, and the phase of electric field inside the laser diode. Conditions for maximum and minimum impact of the laser emission wavelength have been derived. Addressing the issue of distributed optical feedback, optical feedback produced by more than two external mirrors has been also studied. To this aim we have first generalized the Lang and Kobayashi deterministic rate equations model to arbitrary number of external reflectors and provide the corresponding steady-state solution, which is done for the first time. To the best of our knowledge, this kind of study is carried out for the first time.

Physical Review E, 2006

We investigate the dynamics of a semiconductor laser subject to coherent, delayed filtered optical feedback. This system produces multi-stable continuous wave, relaxation and pure frequency oscillations. We show that the feedback phase is a key quantity for controlling this dynamical complexity. A systematic analysis with the feedback phase as one bifurcation parameter reveals the system's overall dynamical structure. PACS numbers: 42.65.Sf, 05.45.Xt, 02.30.Ks, 42.55.Px In a system with feedback a part of the output re-enters into the system, possibly after having been manipulated externally. Typically, the feedback mechanism involves a time delay, which is substantial in many applications; see, e.g., the recent studies Refs. . Laser systems with delayed feedback are of particular interest, because of their possible practical applications, for example, for secure communication via a chaotic carrier .

IEEE Journal of Quantum Electronics, 2000

We report on the systematical investigation of the steady-state regime and the dynamical behavior of a semiconductor laser subject to delayed filtered optical feedback. We study a Fabry-Perot (FP) interferometer type of filter placed in the external feedback loop of a diode laser. The effects of the filter on the locking of the diode laser frequency to the external cavity modes are described. We report and observe hysteresis, bistability, and multistability and show that all these are well described by a set of rate equations for the coupled laser and FP cavity system. We also present an experimental stability diagram that summarizes the dynamical behavior of the system.

IEEE Journal of Quantum Electronics, 1990

We experimentaly investigate the spectrum of a semiconductor laser with incoherent feedback from a distant mirror, i.e., the external round-trip time exceeds the coherence time of the laser. As the amount of feedback increases, the optical spectrum evolves from a central line with enhanced isolated satellite peaks caused by the relaxation oscillation to a very broad ( -20 GHz) line, where the relaxation oscillation gives rise to shoulders. Moreover, there is an asymmetry for frequencies above or below the central frequency. This drastic change of the spectrum is also found from a recent theoretical description of a semiconductor laser in the coherence collapsed state. The amount of feedback and the damping rate of the relaxation oscillation are obtained from a fit of the theory to the observed time-autocorrelation function. This analysis reveals that, owing to incoherent feedback, the damping rate of the relaxation oscillation behaves as an effective damping rate that depends almost linearly on the feedback rate.

Optical and Quantum Electronics, 2008

Abstract We experimentally and theoretically study the impact of optical feedback from an extremely short external cavity (tens of μm) on the spectral behavior of edge emitting lasers (EELs). We are able to investigate a broad range of external cavity lengths and feedback ...

Physical Review A, 2004

We analyze multi-longitudinal-mode semiconductor lasers experimentally. We show that the intensity of each mode displays large amplitude oscillations but obeys a highly organized antiphase dynamics leading to an almost constant total intensity output. For each mode, regular switching is observed in the megahertz range, while the optical frequency as a function of time follows a well defined sequence from blue to red. Using a multimode theoretical model, we identify that four-wave mixing is the dominant mechanism at the origin of the observed dynamics. The asymmetry of the susceptibility function of semiconductor materials allows us to explain the optical frequency sequence.

2006

In the filtered optical feedback (FOF) scheme a part of the emission of the laser is spectrally filtered, for example by a Fabry-Perot filter, and than fed back into the laser. If a semiconductor laser is subject to such delayed FOF qualitative different types of oscillations are possible: the well known relaxation oscillations and, more remarkably, frequency oscillations. We explain

Progress in Quantum Electronics, 1996

The spatio-temporal dynamics of semiconductor lasers is studied theoretically on the basis of semiclassic laser theory. The carrier dynamics is described in a density-matrix approach and the coupled set of equations of motion for the active medium and the light field are derived. Several approximafions related to separations of length and time scales are discussed, resulting in a hierarchy of model equations leading from microscopic to macroscopic levels of description. By numerically solving space-dependent coupled partial differential equations for the (complex) optical fields, the interband polarization and the charge carrier distribution functions on the various levels of the hierarchy the formation and longitudinal propagation of unstable transverse optical filamentary structures is analyzed in a model configuration for typical doubleheterostructure multi-stripe and broad-area lasers. Spectral and spatial hole burning which is observed in the simulated carrier distributions reflects the interplay between stimulated emission and the relaxation dynamics of the carrier distributions as well as the polarization. Its details are strongly influenced by the momentum and density dependence of the microscopic relaxation rates. The transverse hole burning leads to complex spatio-temporal patterns in the macroscopic intensity picture. This complex spatio-temporal dynamic behavior in multi-stripe and broad-area lasers is analyzed by various theoretical tools which allows one to quantify the degree of complexity. CONTENTS * It should be mentioned that these assumptions break down if the the scattering probabilities are strongly peaked around a single final state as is the case in pure LO-phonon scattering or for carrier-carrier scattering at low densities, where most scattering processes are in the forward direction. (57,6s) In the present case of high densities with strong large-angle carrier-carrier scattering the assumptions are well satisfied. * Strictly speaking, p, is not exactly the linear part. Due do the band gap renormalization and the density dependent dephasing rate it includes already parts which are nonlinear in the field.

Journal of Optics B: Quantum and Semiclassical Optics, 2002

We study the multimode dynamics of a semiconductor laser with optical feedback operating in the low-frequency fluctuation regime. A multimode extension of the Lang-Kobayashi (LK) model shows, in agreement with experimental observations, that the low-frequency power dropouts exhibited by the main modes are accompanied by sudden, asymmetric, activations of dormant longitudinal side modes. Furthermore, these activations are delayed with respect to the dropouts of the active modes. In order to satisfactorily reproduce both the asymmetric activation of side modes and their delay with respect to the dropouts, the generalized LK model has to include a parabolic gain profile, together with a frequency shift of the gain curve with carrier population.