Light-polarization dynamics in surface-emitting semiconductor lasers

Miguel, M. San; Feng, Quanyuan; Moloney, Jerome V.

doi:10.1103/physreva.52.1728

Cited by 638 publications

(399 citation statements)

References 38 publications

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“…Chaos is unambiguously identified in the light polarization output of a vertical-cavity surface-emitting laser (VCSEL). Moreover, both the route to chaos and the mode dwell time -time the laser stays emitting in one mode -characteristics agree qualitatively very well with the longstanding and so far unconfirmed prediction of the spin-flip model 20 : a nonlinear coupling between two polarization modes induced by carrier spin relaxation leads to deterministic nonlinear dynamics. Today applications of laser diodes such as secure communications [21][22][23] and random number generation 24,25 make use of high-dimensional chaos obtained from time-delayed optical feedback.…”

Section: Figure 1: Experimental Observations Showing Chaotic Polarizasupporting

confidence: 63%

“…These polarization characteristics call for an interpretation that is different from a stochastic Kramers hopping problem applied to symmetric bistable states, as is typically done for VCSELs 34 .Our experiment can qualitatively be reproduced well using the San Miguel, Feng and Moloney (SFM) model. The model considers two competing emission processes for the right and left circular polarization with two coupled carrier reservoirs 20,36 ; the coupling comes from multiple complex spin-flip processes, i.e. sub-picosecond mechanisms that contribute to the relaxation of electron spin (see e.g.…”

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: Figure 1: Experimental Observations Showing Chaotic Polarizasupporting

confidence: 63%

Section: Route To Polarization Chaosmentioning

confidence: 99%

Deterministic polarization chaos from a laser diode

et al. 2012

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“…As explained in Ref. [9], physically these two pairs of transitions are associated with two z-components J z = ±1/2 of the total angular momentum J = 1/2 of the electrons in the conduction band and corresponding z-components J z = ±3/2 for J = 3/2 of the heavy holes in the valence band. The constants γ a and γ b are the decay rates of the populations of the upper and lower levels, γ ⊥ (not shown in Fig.…”

Section: Quantum Spin-flip Theory Of Vcsels a Resume Of The Modelmentioning

confidence: 99%

“…The semiclassical four-level spin-flip model of VCSELs was developed by San Miguel, Feng and Moloney [9]. This model describes very well the dynamics of these semiconductor lasers and is widely used for understanding of such phenomena, for example, as polarization switching.…”

Section: Quantum Spin-flip Theory Of Vcsels a Resume Of The Modelmentioning

confidence: 99%

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Polarization squeezing in vertical-cavity surface-emitting lasers

et al. 2004

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We further elaborate the theory of quantum fluctuations in vertical-cavity surfaceemitting lasers (VCSELs), developed in Ref. [1]. In particular, we introduce the quantum Stokes parameters to describe the quantum self-and cross-correlations between two polarization components of the electromagnetic field generated by this type of lasers. We calculate analytically the fluctuation spectra of these parameters and discuss experiments in which they can be measured. We demonstrate that in certain situations VCSELs can exhibit polarization squeezing over some range of spectral frequencies. This polarization squeezing has its origin in sub-Poissonian pumping statistics of the active laser medium.

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Optical Response and Spin Relaxation in Semiconductor Systems under Excitation with Arbitrary Polarization

Rößler

2002

phys. stat. sol. (b)

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(accepted for publication in Phys. Stat. Sol. (b) 234 (2002)) The equations-of-motion for the density matrix are derived in a multiband model to describe the response of semiconductors (bulk or quantum well structures) under optical excitation with arbitrary polarization. The multiband model used, comprising the twofold conduction band and the fourfold topmost valence band (or heavy-and light-hole states), incorporates spin-splitting of the single-particle states. The interaction terms include besides the direct Coulomb coupling between carriers also the electron-hole exchange interaction, which together with the spin-splitting terms is responsible for spin relaxation. Applying the Hartree-Fock truncation scheme leads to a set of coherent semiconductor Bloch equations for the multiband case. This concept provides the theoretical frame for describing phenomena connected with optical response under excitation with arbitrary light polarization and spin relaxation: polarized optical response, polarization dynamics of VCSELs, spin relaxation, and the circular photovoltaic effect. PACS Num. 72.25.Fe, 72.25.Rb, 78.47.+p

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Light-polarization dynamics in surface-emitting semiconductor lasers

Cited by 638 publications

References 38 publications

Deterministic polarization chaos from a laser diode

Deterministic polarization chaos from a laser diode

Polarization squeezing in vertical-cavity surface-emitting lasers

Optical Response and Spin Relaxation in Semiconductor Systems under Excitation with Arbitrary Polarization

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