We consider four different laser arrangements with the nonlinear loops of Kerr type, and discuss square wave pulse operation using modeling based on delay differential equation (DDE) approach. We reduce DDE models to 1D maps, which enable square wave operation and analyze numerically the possible dynamical scenarios of the square wave evolution.
Long cavity fibre-based wavelength sweeping lasers are promising devices with a wide range of potential applications ranging from communications to life sciences. For example, Fourier Domain Mode-Locked (FDML) lasers, which are commonly used for Optical Coherence Tomography (OCT) imaging applications are long cavity lasers incorporating an intra-cavity resonator driven in resonance with the cavity round trip time. The coherence properties of such swept sources are of major importance as they define the image quality. The purpose of this work is to analyze the mechanism that deteriorates the coherence of long lasers. In our experiment, the laser included a 100nm wide semiconductor optical amplifier at 1310nm and a fibre cavity that could vary from 20m to 20km. the laser emission wavelength was controlled using a fibre based intra-cavity filter with a bandwidth of 10GHz. Near the lasing threshold and/or for fast carrier decay rate, we observed the appearance of periodic power dropouts with stable Nozaki-Bekki holes (NBH) that circulate in the laser cavity. As a function of the injection current, the laser could operate in various regimes including bi-stability between NBH and stable (cw) operation, unstable NBH or chaotic operation. Such behavior indicates that the interplay between the injection current and carrier decay rate can lead to highly coherent emission of a long cavity laser.
We analyze the properties of a unidirectional class-A ring laser containing a nonlinear amplifying loop mirror (NALM). The NALM is a Sagnac interferometer consisting of an amplifier and a Kerr-type nonlinear element, and has a reflectivity that periodically varies with the intra-cavity power. To model the dynamics of these lasers, we use the approach based on Delay Differential Equations (DDEs) that has been successfully applied to describe the properties of passively mode-locked semiconductor lasers. The proposed model allows us to investigate mode locking operation in this laser. The analysis of this DDE model for mode-locked operation was performed numerically and analytically in the limit of large cavity round trip times. We demonstrate that mode-locked pulses are born though a modulational instability of the steady state solutions when the pseudo- continuous branch crosses the imaginary axis. These asymmetric pulses always co-exist with the stable laser-off solution. Hence, they can be viewed as temporal cavity solitons having similar properties with localized structures observed in bistable spatially-extended systems.
A set of differential equations with distributed delay is derived for modeling of multimode ring lasers with intracavity chromatic dispersion. Analytical stability analysis of continuous wave regimes is performed and it is demonstrated that sufficiently strong anomalous dispersion can destabilize these regimes.
A novel, time-resolved interferometric technique is presented allowing the reconstruction of the complex electric field output of a fast frequency swept laser in a single-shot measurement. The power of the technique is demonstrated by examining a short cavity swept source designed for optical coherence tomography applications, with a spectral bandwidth of 18 THz. This novel analysis of the complete electric field reveals the modal structure and modal evolution of the device as well as providing a time-resolved real-time characterization of the optical spectrum, linewidth and coherence properties of a dynamic rapidly swept laser.
We analyse the dynamical behaviour of a Fourier domain mode locked laser experimentally and theoretically. Heterodyne measurements of laser dynamics allows some insight into the frequency behaviour of the laser which coupled with theoretical arguments from previous work allow for a clear interpretation of the observations. Direct simulations using a delay differential equation model in full FDML mode display excellent agreement with the experimental results.
An experimental and theoretical analysis of the dynamics of a Fourier domain mode locked laser, currently one of the fastest swept source lasers applied in optical coherence tomography, is performed. A novel time- resolved technique to measure the laser output electric field allows access to the phase dynamics of the laser and thus the coherence properties. A delay-differential equation model for the laser is used to analyse the system theoretically and via direct simulation. Numerical simulations of the laser output are in excellent agreement with experimentally measured data.
We analyse the dynamical behaviour of a short cavity OCT swept-source laser experimentally and theoretically. Mode-hopping, sliding frequency mode-locking and chaos are all observed during the laser sweep period. Hetero- dyne measurements of laser dynamics allows some insight into the behaviour of the laser, while interferometric techniques allow the full phase reconstruction of the laser electric field. A delay differential equation enables modelling of the laser output, and laser parameters can be altered to provide optimisation conditions for future laser designs.
We consider a broad area vertical-cavity surface-emitting laser(VCSEL) subject to injection and to time-delayed feedback. We present analytical and numerical analysis of the dependence of the drift instability threshold and on the feedback strength, feedback phase, and carrier relaxation time. we demonstrate that due to finite carrier relaxation rate the delay induced drift instability can be suppressed to a certain extent. We give analytical estimation of the soliton velocity near the drift instability point which is in a good agreement with numerical results obtained using the full model equations.
We investigate the dynamical properties of broad area lasers with a V-shaped external cavity formed by two
off-axis feedback mirrors that allow to select a single transverse mode with transversely modulated intensity
distribution. We derive and study a reduced model of a multi-stripe array. Bifurcation analysis of this system
reveals the existence of single mode and multimode instabilities leading to a periodic and irregular time
dependence of the output intensity. We observe within reduced model the multimode instability leading to a
periodic regime, where the fields traveling in the opposite directions oscillate in antiphase. This result is in
agreement with that obtained with the help of 2+1 dimensional traveling wave model.
We consider a broad area vertical-cavity surface-emitting laser (VCSEL) subject to injection and to time-delayed feedback. We show that near the nascent optical bistability regime, the space-time dynamics of this device is described by a generalized Swift-Hohenberg equation with delay. We classify different regime of stability of the homogeneous steady states in terms of dynamical parameters. We show that the delay modifies strongly the stability domain of both periodic and localized structures solutions. Finally, we show that the delay feedback induces a spontaneous motion of bright peaks in one and in two-dimenional transverse plane. Bifurcation diagram associated with these localized structures is constructed.
We analyze the dynamics of a mode-locked quantum-dot edge-emitting semiconductor laser consisting of reversely
biased saturable absorber and forward biased amplifying sections. To describe spatial non-uniformity of laser
parameters, optical fields and carrier distributions we use the traveling wave model, which takes into account
carrier exchange processes between wetting layer and quantum dots. A comprehensive parameter study and an
optical mode analysis of operation regimes are presented.
Hybrid mode-locking in monolithic quantum dot lasers is studied experimentally and theoretically. A strong asymmetry of the locking range with respect to the passive mode locking frequency is observed. The width of this range increases linearly with the modulation amplitude for all operating parameters. Maximum locking range found is 30 MHz. The results of a numerical analysis performed using a set of five delay-differential equations taking into account carrier exchange between quantum dots and wetting layer are in agreement with experiments and indicate that a spectral filtering element could improve locking characteristics. Asymptotic analysis of the dependence of the locking range on the laser parameters is performed with the help of a more simple laser model consisting of three delay differential equations.
The scenario for stability loss of laser solitons is analyzed. The process of radial symmetry breaking and bistability between symmetrical and rotating solitons is demonstrated. New, rotating and oscillating soliton state is founded. The consequent period-doubling of symmetrical oscillations is found as a route to chaotic behavior.
The SAGE III is a joint Earth Observing System (EOS) mission between the US NASA and the Russian Space Agency (RSA) to fly aboard the Russian Meteor-3M(1) spacecraft to be launched from the Baikonur Cosmodrome in mid-1999. SAGE III is a spectrometer that measures attenuated radiation in the 282 nm to 1550 nm wavelength range which can be inverted to yield vertical profiles of ozone, aerosols and other species that are critical in studying trends and global change. In addition to SAGE III, the Meteor-3M(1) spacecraft carries nine Russian instruments for analyzing and forecasting environmental change and climate, for hydro-meteorological monitoring and for helio-geophysical research. Both the RSA and NASA are coordinating the activities associated with the joint mission development and implementation, including instrument development, spacecraft development, and mission operations.
For the complex Lorenz model, which is one of basic laser models, it is shown that the phase space has the geometric structure associated with a fiber bundle. Using the equation of motion in the base space of the fiber bundle, we find the surfaces bounding the attractors in this space. The homoclinic `butterfly' responsible for the Lorenz-like attractor appearance is shown to correspond to a codimension-two bifurcation.
Model equations for a ring class B laser operating in three Gauss-Laguerre modes are derived and studied. Bifurcation mechanisms leading to the appearance of low-frequency antiphase oscillations of mode intensities are investigated. The spontaneous phase symmetry breaking effect leading to transverse patterns with rotating crystal generated by four optical vortices is described.
Two coupled complex Ginzburg-Landau equations are derived to described multimode operations of a ring unidirectional laser with a saturable absorber near the lasing threshold. We show that unlike a laser without absorber this laser can exhibit in low-intensity domain the Benjamin-Feir instability which is known to lead to very complicated behaviors including chaotic ones.