Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach (original) (raw)
Related papers
Physical Review E, 2009
We report theoretically on the interplay between polarization switching and bifurcations to nonlinear dynamics in a vertical-cavity surface-emitting laser ͑VCSEL͒ subject to orthogonal optical injection. Qualitatively different bifurcation scenarios leading to polarization switching are found and mapped out in the plane of the injection parameters, i.e., the frequency detuning vs injection strength plane. A Hopf bifurcation mechanism on the two-polarization-mode solution determines the injection-locking boundaries and influences polarization switching induced by optical injection. We furthermore report on a torus bifurcation emerging from a two-linearly polarized ͑LP͒ mode time-periodic dynamics before polarization switching and injection locking appear. It corresponds to an interesting combination of relaxation oscillation dynamics in the x-LP mode together with wave mixing dynamics in the injected y-LP mode. In agreement with recent experiments, we unveil a period-doubling route to chaos that involves both VCSEL orthogonal LP modes. The corresponding region of chaotic dynamics coincides with abrupt changes in the polarization switching boundaries in the plane of the injection parameters.
Physical Review A, 2006
We present a comprehensive study of the bifurcation routes in a generic model of a two-polarization-mode semiconductor laser when subject to orthogonal optical injection, relevant to a single-transverse-mode verticalcavity surface-emitting laser. For positive detunings, polarization switching (PS) occurs as the intensity of the noninjected mode gradually decreases and eventually shuts down, in some cases accompanied along the way by the onset and the subsequent vanishing of relaxation oscillations. We identify a Hopf bifurcation on a twopolarization-mode solution, which supports the onset of relaxation oscillation time-periodic dynamics in both injected (x-linearly polarized) and noninjected (y-linearly polarized) modes. For sufficiently large negative detunings, PS is a sharp transition occurring either at the injection-locking point or at a subcritical Hopf bifurcation and is often part of a hysteresis cycle.
IEEE Journal of Quantum Electronics, 2009
In this paper, we summarize our recent results on nonlinear polarization-and transverse-mode dynamics of vertical-cavity surface-emitting lasers (VCSELs) induced by optical injection (OI) or current modulation. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching (PS). Furthermore, VCSELs may emit light in multiple transverse modes. This provides new features to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We demonstrate for the case of orthogonal OI that new Hopf bifurcation on a two-polarization-mode solution delimits the injection locking (IL) region and that PS and IL of first-order transverse mode lead to a new resonance tongue for large positive detunings. Similarly, the underlying polarization-mode competition leads to chaotic-like behavior in case of gain switching and the presence of two transverse modes additionally reduces the possibility of regular dynamics.
Optical and Quantum Electronics, 2006
Bistability as well as dynamics associated to polarization switching in a vertical-cavity surface-emitting laser (VCSEL) submitted to orthogonal optical injection from an external master laser are investigated. Intensity-polarization switching bistability is studied by increasing and decreasing the intensity of the injected beam and for a fixed frequency detuning, i.e. the frequency offset between master and the free running VCSEL. Depending on the frequency detuning, bistable switching is experimentally found to occur with or without injection locking of the fundamental mode to the master laser frequency. For large positive detuning, injection locking of the first-order transverse mode with a strong depression of the fundamental mode has been observed. The case of frequency – polarization switching bistability, i.e. when the frequency detuning is first decreased and then increased for a fixed injected power, has also been theoretically analyzed. Qualitative comparison with previous experimental work is presented for the dependence of the width of the bistable switching region on the injection strength level. Finally we show an experimental result of complicated dynamics including period doubling route to chaos that accompany polarization switching and which motivates future theoretical investigations.
Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers
Optics Letters, 2002
We analyze the bifurcation mechanisms leading to polarization self-modulation (PSM) in a vertical-cavity surface-emitting laser (VCSEL) subject to a 90° polarization rotating external optical feedback. We show that the laser system undergoes a sequence of steady states and Hopf bifurcations to time-periodic solutions as we increase the feedback rate. Branches of PSM are obtained for moderate to high feedback rates and, using continuation methods, we show that they connect two orthogonally polarized external cavity modes (ECMs). This last result allows us to interpret PSM as a beating mechanism between ECMs and is in agreement with previous experiments.
Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata
Optics Letters, 2002
We analyze the bifurcation mechanisms leading to polarization self-modulation (PSM) in a vertical-cavity surface-emitting laser (VCSEL) subject to a 90° polarization rotating external optical feedback. We show that the laser system undergoes a sequence of steady states and Hopf bifurcations to time-periodic solutions as we increase the feedback rate. Branches of PSM are obtained for moderate to high feedback rates and, using continuation methods, we show that they connect two orthogonally polarized external cavity modes (ECMs). This last result allows us to interpret PSM as a beating mechanism between ECMs and is in agreement with previous experiments.
Physical review. E, 2018
We present experimental and theoretical results of noise-induced attractor hopping between dynamical states found in a single transverse mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. These transitions involve dynamical states with different polarizations of the light emitted by the VCSEL. We report an experimental map identifying, in the injected power-frequency detuning plane, regions where attractor hopping between two, or even three, different states occur. The transition between these behaviors is characterized by using residence time distributions. We find multistability regions that are characterized by heavy-tailed residence time distributions. These distributions are characterized by a -1.83±0.17 power law. Between these regions we find coherence enhancement of noise-induced attractor hopping in which transitions between states occur regularly. Simulation results show that frequency detuning variations and spontaneous emission noi...
IEEE Journal of Quantum Electronics, 2006
In this paper, the output characteristics of an oxide-confined AlGaAs-As quantum well vertical-cavity surfaceemitting laser (VCSEL) under orthogonal optical injection are mapped as a function of the strength of the optical injection and the detuning between the injection frequency and the free-running frequency of the solitary laser, for a very large range of frequency detuning (from 82 to 89 GHz). The injection light is polarized orthogonally with respect to the solitary VCSEL output light. As the injection strength increases the VCSEL switches to the master laser polarization. Polarization switching is accompanied by a rich nonlinear dynamics, including limit cycle, wave mixing, subharmonic resonance and period doubling route to chaos. Polarization switching is found with but also without injection locking. Injection locking occurs with the slave fundamental transverse mode or, for large positive detunings, with the first-order transverse mode.