Modeling spatial effects in multi-longitudinal-mode semiconductor lasers (original) (raw)
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Applied Physics B, 2018
Comprehensive theoretical investigation of the influence of external optical feedback on the dynamics of semiconductor lasers are introduced. The analyses are based on numerical simulation of the multimode rate equations superposed by Langevin noise sources that are generated in such a way as to keep the correlation of the modal photon number with the injected electron number. The gain saturation effect which causes mode-competition phenomena among longitudinal modes are considered in our multimode rate equation model. The dynamics of modes and the characteristics of the output spectrum are investigated for strong external optical feedback strength. Numerically simulated results show that the mode-competition phenomena induce quasi-periodic hopping among several longitudinal modes which reveals multimode-like output spectra in lasers. This mode-hopping phenomena is described in terms of asymmetric gain saturation effect.
This paper introduces a theoretical study of longitudinal mode competition in semiconductor lasers subject to optical feedback. The study is based on a model of time-delay multimode rate equations taking into account both symmetric and asymmetric suppressions of modal gain. The model is numerically solved and applied to the case of a short-external cavity. Mode competition is characterized along the feedback-induced period-doubling route to chaos as well as under chaotic dynamics. Contributions of symmetric and asymmetric gain suppressions to both mode dynamics and modal operation under OFB are clarified. The results show that under chaotic dynamics, mode competition induces multimode hopping giving rise to asymmetric multimode output spectra. In regimes of continuous-wave operation, mode competition supports single-mode oscillation, and the side-mode suppression ratio improves with the increase of feedback. In the regime of strong feedback, the lasing mode moves to either long-or short-wavelength side in a seemingly random fashion, which is strongly related to asymmetric gain suppression.
Modeling multi-longitudinal-mode semiconductor lasers with incoherent feedback
Physical Review A, 2007
We study numerically the dynamics of a multi-longitudinal-mode semiconductor laser subject to incoherent optical feedback. The feedback scheme is such that the polarization state of the feedback light is rotated 90°, so that the natural laser mode, TE, is coupled unidirectionally into the orthogonal, unsupported mode, TM. We use traveling-wave equations for the slowly varying complex amplitudes of the two counterpropagating optical fields circulating in the Fabry Pérot cavity, both with TE polarization, coupled to an equation for the carrier population. The carrier equation contains a time-delayed term that takes into account the effect of the incoherent feedback. The model considers a parabolic frequency-dependent gain and does not assume a priori a fixed number of active longitudinal modes. We find that moderate feedback levels reduce the total power and increase the number of oscillating longitudinal modes. Larger feedback levels lead to instabilities at both the external cavity frequency f ext and the relaxation oscillation frequency f ro. These findings are in good qualitative agreement with experimental observations by Houlihan et al. ͓Opt. Commun. 199, 175 ͑2001͔͒. For even stronger feedback there is square-wave periodic modulation of the total power, with a repetition period close to twice the delay time. In this regime, which consists of a sequence of turn-on and turn-off events driven by the incoherent feedback, the longitudinal modes show in-phase behavior at a frequency close to f ro accompanied by a slower out-of-phase drift, which is related to variations of the maximum and minimum values of the oscillation amplitude of the modal intensities.
Dynamics of multimode semiconductor lasers
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.
Rate-equation description of multi-mode semiconductor lasers
Physics and Simulation of Optoelectronic Devices XXII, 2014
We present a set of rate equations for the modal amplitudes and carrier-inversion moments that describe the deterministic multi-mode dynamics of a semiconductor laser due to spatial hole burning. Mutual interactions among the lasing modes, induced by high-frequency modulations of the carrier distribution, are included by carrier-inversion moments for which rate equations are given as well. We derive the Bogatov effect of asymmetric gain suppression in semiconductor lasers and illustrate the potential of the model for a two and three-mode laser by numerical and analytical methods.
Spatio-temporal dynamics of semiconductor lasers: Theory, modelling and analysis
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.
Spatio-temporal dynamics of gain-guided semiconductor laser arrays
IEEE Journal of Quantum Electronics, 1996
A continuous model based on the coupled fieldmatter Maxwell-Bloch equations for a two-level homogeneously broadened single mode laser is developed. The model includes a Langevin formulation to model thermal and spontaneous emission noises and accounts for carrier diffusion, optical field diffraction and current spreading. Our model is flexible enough to simulate any gain-guided longitudinally uniform laser geometry and is applied to both a single-stripe and a four-stripe gainguided semiconductor lasers where the influence of the injection current, the interstripe distance and carrier diffusion is discussed within the context of the laser dynamics, We show that an array operating with quasi-independent stripes may be achieved at low pumps and larger interstripe distances. However, as injection current is increased or the interstripe distance is decreased, the device passes through a variety of dynamical instabilities which can be analyzed in the context of lateral cavity modes. Moreover, we also show that the array dynamics is strongly influenced by carrier diffusion which may also lead to different thresholds for each element of the array.
Influence of Instantaneous Mode Competition on the Dynamics of Semiconductor Lasers
Comprehensive theoretical investigations of influence of instantaneous mode-competition phenomena on the dynamics of semiconductor lasers are introduced. The analyzes are based on numerical simulations of the multimode rate equations superposed by Langevin noise sources that account for the intrinsic fluctuations associated with the spontaneous emission. Numerical generation of the Langevin noise sources is performed in such a way as to keep the correlation of the modal photon number with the injected electron number. The gain saturation effects, which cause competition phenomena among lasing modes, are introduced based on a self-consistent model. The effect of the noise sources on the mode-competition phenomena is illustrated. The mode-competition phenomena induce instantaneous coupling among fluctuations in the intensity of modes, which induce instabilities in the mode dynamics and affect the state of operation. The dynamics of modes and the characteristics of the output spectrum are investigated over wide ranges of the injection current and the linewidth enhancement factor in both AlGaAs-GaAs and InGaAsP-InP laser systems. Operation is classified into stable single mode, stable multimode, hopping multimode, and jittering single mode. Based on the present results, the experimental observations of multimode oscillation in InGaAsP-InP lasers are explained as results of the large value of the linewidth enhancement factor.
Multimode dynamics of semiconductor lasers
2004
In this manuscript we analyze the modal dynamics of multimode semiconductor quantum-well lasers. Modal switching is the dominant feature of the devices analyzed and it obeys a highly organized antiphase dynamics which leads to an almost constant total intensity output. For each active mode a regular switching at frequencies of few MHz is observed. The activation order of the modes follows a well defined sequence starting from the lowest wavelength (bluest) mode to the highest wavelength (reddest) mode, then the sequence starts again from the bluest mode. Using a multimode theoretical model and a simpler phenomenological 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 to explain the optical frequency sequence.