Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers

Olejniczak, Lukasz; Panajotov, Krassimir; Thienpont, Hugo; Sciamanna, Marc; Mutig, A.; Hopfer, F.; Bimberg, D.

doi:10.1364/oe.19.002476

Cited by 31 publications

(42 citation statements)

References 17 publications

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“…3-(b). These two statistical features agree qualitatively well with what is seen in our experiment 33 . It is worth mentioning that the exponentially decaying statistical distribution of the dwell time is the result of polarization nonlinear deterministic dynamics and, in contrast to all previous studies, is not the result of a noise-driven Kramers hopping problem.…”

Section: Statistics Of the Deterministic Mode Hoppingsupporting

confidence: 92%

“…Our main contribution is the analysis of experimental data. Measurements of the data are already described elsewhere 33 and we will therefore focus on the method to reduce the noise in our dataset. Here we use a re-embedding procedure based on singular value analysis as described by Fraedrich 42 .…”

Section: Methodsmentioning

confidence: 99%

“…Figure 1 shows typical measured dynamics (b-c) of the polarization-resolved laser output power in a single-mode submonolayer 990-nm quantum dot VCSEL (a). The device characteristics, in particular its polarization and spectral properties as a function of the injection current, have been detailed elsewhere 33 . When increasing the current, the VCSEL switches from lasing with a linearly polarized emission to lasing in one of two elliptically polarized modes.…”

Section: Figure 1: Experimental Observations Showing Chaotic Polarizamentioning

confidence: 99%

“…The resulting six-dimensional set of rate equations explains polarization switching in VCSELs as resulting from a cascade of bifurcations on linearly polarized steadystates, which appear when increasing the injection current. Although nonlinear dynamics have been suggested in experiments 33,38 , no evidence of a chaotic behavior of a free-running VCSEL has been provided so far.…”

Section: Route To Polarization Chaosmentioning

confidence: 99%

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Deterministic polarization chaos from a laser diode

et al. 2012

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Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect -i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single-and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.The discovery of deterministic chaos -i.e. the aperiodic deterministic dynamics of a nonlinear system showing sensitivity to initial conditions -has been a major paradigm shift overthrowing two centuries of Laplacian viewpoint of dynamical systems [1][2][3][4][5] . Looking into a system behavior with the use of chaos theory has helped to interpret and control many of such ordered or disordered behaviors in our present day life, such as the bifurcations leading to epilepsy and cancer 6 , the stabilization of cardiac arrhythmias 7 , and the improvement of complex behavioral patterns in robotics 8 .Soon after the invention of the laser, the possibility to observe light chaos raised attention. In 1975, Haken discovered an analogy between the Maxwell-Bloch equations for lasers and the Lorenz equations showing chaos 9 . The Maxwell-Bloch equations are three equations for the field E, the polarization P and the carrier inversion N, each with its own relaxation time. However, while in Lorenz equations the relaxation times of the dynamical variables are of similar order of magnitude, they may take very different values in lasers. If one variable relaxes much faster than the others, this variable is adiabatically eliminated, hence resulting in a reduced number of dynamical equations. Therefore, so-called class A (ex: He-Ne, Ar and Dye), class B (ex: Nd:YAG, CO2 and semiconductor) or class C (ex: NH3) lasers have dynamics governed either by a single equation for the field, two equations for the field and population inversion or the full set of equations, respectively. In class A or class B laser systems chaos cannot be observed unless one adds one or several independent control parameters 10 . Chaos has then been reported in, for example, free-running NH3 lasers 11 , He-Ne lasers with modulation of the external field 12 , CO2

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Section: Statistics Of the Deterministic Mode Hoppingsupporting

confidence: 92%

Section: Methodsmentioning

confidence: 99%

Section: Figure 1: Experimental Observations Showing Chaotic Polarizamentioning

confidence: 99%

Section: Route To Polarization Chaosmentioning

confidence: 99%

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Deterministic polarization chaos from a laser diode

et al. 2012

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“…The polarization instability that mainly comes from the competition between two orthogonally polarized states generally occurs in small-area VCSELs [11]- [14]. It has been recently observed that the spatial morphologies of high-order transverse modes in broad-area VCSELs are strongly related to the directions of their polarization states [15], [16].…”

Section: Introductionmentioning

confidence: 99%

The Influences of Boundary Shapes on Polarization Characteristics and Lasing Modes in Broad-Area Vertical-Cavity Surface-Emitting Lasers With Cryogenic Detuning: Regular Versus Chaotic Cavities

Tuan

Chiang

et al. 2015

IEEE J. Select. Topics Quantum Electron.

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The broad-area rectangular-shaped and stadiumshaped VCSELs with nearly the same aspect ratio are designed to explore the influence of lateral boundary shapes on polarization states and lasing spectra with large detuning by cryogenic cooling. For the rectangular-shaped VCSEL, the lasing modes usually exhibit linearly polarized state and their far-field emissions mainly concentrate on four diagonal directions. On the other hand, the lasing modes of the stadium-shaped VCSEL generally display two orthogonally polarized states and their far-field emissions extensively spread on azimuthal directions. More intriguingly, the lasing spectra of the two devices clearly manifest the features of the energy-level distribution in regular and chaotic quantum billiards, respectively.

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Nonlinear Dynamics of Vertical-Cavity Surface-Emitting Lasers: Deterministic Chaos and Random Number Generation

Virte

Sciamanna

Thienpont

et al. 2015

Springer Proceedings in Physics

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Selected LecturesInternational audienceWe report on chaotic polarization fluctuations generated from a free-running vertical-cavity surface-emitting laser, and investigate in details the VCSEL dynamics and its potential application. We provide new experimental evidences of asymmetrical behaviour of VCSEL polarization dynamics, and show that considering a slight misalignment of the anisotropies of the laser cavity allows to reproduce these dynamics numerically. Finally, we propose a simple scheme for random bit generation exploiting polarization chaos , and experimentally demonstrate a 100 Gbps random generation rate

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Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers

Cited by 31 publications

References 17 publications

Deterministic polarization chaos from a laser diode

Deterministic polarization chaos from a laser diode

The Influences of Boundary Shapes on Polarization Characteristics and Lasing Modes in Broad-Area Vertical-Cavity Surface-Emitting Lasers With Cryogenic Detuning: Regular Versus Chaotic Cavities

Nonlinear Dynamics of Vertical-Cavity Surface-Emitting Lasers: Deterministic Chaos and Random Number Generation

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