Spin-flip Model Research Articles

Time-delay signature of chaos in 1550 nm VCSELs with variable-polarization FBG feedback.

Based on the framework of spin-flip model (SFM), the output characteristics of a 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to variable-polarization fiber Bragg grating (FBG) feedback (VPFBGF) have been investigated. With the aid of the self-correlation function (SF) and the permutation entropy (PE) function, the time-delay signature (TDS) of chaos in the VPFBGF-VCSEL is evaluated, and then the influences of the operation parameters on the TDS of chaos are analyzed. The results show that the TDS of chaos can be suppressed efficiently through selecting suitable coupling coefficient and feedback rate of the FBG, and is weaker than that of chaos generated by traditional variable-polarization mirror feedback VCSELs (VPMF-VCSELs) or polarization-preserved FBG feedback VCSELs (PPFBGF-VCSELs).

Increasing spin-flips and decreasing cost: Perturbative corrections for external singles to the complete active space spin flip model for low-lying excited states and strong correlation.

An approximation to the spin-flip extended configuration interaction singles method is developed using a second-order perturbation theory approach. In addition to providing significant efficiency advantages, the new framework is general for an arbitrary number of spin-flips, with the current implementation being applicable for up to around 4 spin-flips. Two new methods are introduced: one which is developed using non-degenerate perturbation theory, spin-flip complete active-space (SF-CAS(S)), and a second quasidegenerate perturbation theory method, SF-CAS(S)1. These two approaches take the SF-CAS wavefunction as the reference, and then perturbatively includes the effect of single excitations. For the quasidegenerate perturbation theory method, SF-CAS(S)1, the subscripted "1" in the acronym indicates that a truncated denominator expansion is used to obtain an energy-independent down-folded Hamiltonian. We also show how this can alternatively be formulated in terms of an extended Lagrangian, by introducing an orthonormality constraint on the first-order wavefunction. Several numerical examples are provided, which demonstrate the ability of SF-CAS(S) and SF-CAS(S)1 to describe bond dissociations, singlet-triplet gaps of organic molecules, and exchange coupling parameters for binuclear transition metal complexes.

Simulated dynamics of optically pumped dilute nitride 1300 nm spin vertical‐cavity surface‐emitting lasers

The authors report a theoretical analysis of optically pumped 1300 nm dilute nitride spin-polarised vertical-cavity surface-emitting lasers (VCSELs) using the spin-flip model to determine the regions of stability and instability. The dependence of the output polarisation ellipticity on that of the pump is investigated, and the results are presented in two- dimensional contour maps of the pump polarisation against the magnitude of the optical pump. Rich dynamics and various forms of oscillatory behaviour causing self-sustained oscillations in the polarisation of the spin-VCSEL subject to continuous- wave pumping have been found because of the competition of the spin-flip processes and birefringence. The authors also reveal the importance of considering both the birefringence rate and the linewidth enhancement factor when engineering a device for high-frequency applications. A very good agreement is found with the experimental results reported by the authors' group.

Bistability of time-periodic polarization dynamics in a free-running VCSEL

We report experimentally a bistability between two limit cycles (i.e. time-periodic dynamics) in a free-running vertical-cavity surface-emitting laser. The two limit cycles originate from a bifurcation on two elliptically polarized states which exhibit a small frequency difference and whose main axes are symmetrical with respect to the linear polarization eigenaxes at threshold. We demonstrate theoretically that this peculiar behavior can be explained in the framework of the spin-flip model model by taking into account a small misalignment between the phase and amplitude anisotropies.

Dynamic characteristics of 1550 nm vertical-cavity surface-emitting laser subject to polarization-rotated optical feedback：the short cavity regime

Based on the extended spin-flip model (SFM), we investigate theoretically the dynamic characteristics of 1550nm vertical-cavity surface-emitting laser subject to polarization-rotated optical feedback: the short cavity regime. Results show that increasing the feedback strength will result in multiple polarization switching (PS) phenomena, and there will appear rich dynamics under the condition of medium feedback intensity, such as single period, period-doubling, quasi-periodic and chaotic states. At the same time, the increase of injection current will result in the reduction of working area of Y direction polarization mode. As the feedback delay time increases, under the condition of weak optical feedback polarization mode, the hopping phenomenon will take place at a particular frequency; the frequency of mode hopping will increase with the increase of moderate feedback strength, and the laser shows a variety of new dynamic characteristics, such as single period, pulse envelope, quasi-periodic and chaotic states, by taking a beat frequency signal. These dynamic characteristics are very sensitive to the phase change so the beat frequency effect between external cavity modes plays a key role. In addition, the hopping phenomenon between various dynamic states can also be found along with the mode hopping.

Dynamics of VCSELs Subject to Optical Injection of Arbitrary Polarization

New theoretical results are presented on polarized optical injection of vertical-cavity surface-emitting lasers (VCSELs) based on the spin-flip model extended to consider both the azimuth and ellipticity of the injected light. Experiments to investigate these effects are performed on two 1550-nm VCSELs with different frequency spacing between the resonances of the orthogonal polarizations of the fundamental transverse mode. Excellent agreement is found between experiment and theory for the stability and polarizations of the two VCSELs subject to polarized optical injection. The input polarization angle has a strong effect on both the dynamics and polarization of each VCSEL, whereas the ellipticity of the injected light affects only the polarization.

Nonlinear dynamics of 1550 nm VCSELs subject to polarization-preserved optical feedback and orthogonal optical injection

Based on spin-flip model (SFM), the nonlinear dynamics of 1550 nm vertical-cavity surface-emitting lasers (VCSELs) subject to polarization-preserved optical feedback (PPOF) and orthogonal optical injection (OOI) are theoretically investigated. The results show that two linear polarization (LP) modes can be simultaneously stimulated and polarization switching (PS) can be observed, which is different from the case that only y LP mode exists in a VCSEL with PPOF. Under the joint action of PPOF and OOI, the two LP modes will exhibit rich dynamical states, such as period one, period two, multiperiod and chaos oscillation. Different evolution routes to chaos can be also observed. Moreover, frequency detuning Δf (Δf = f m − f s, where f m and f s are the center frequencies of free-running master VCSEL and slave VCSEL, respectively) has an obvious influence on the PS. With the increase of the positive frequency detuning PS points shift toward larger injection strengths; meanwhile, a suitable negative frequency detuning value makes the injection strength for PS be the lowest.

Polarization dynamics and chaotic synchronization in unidirectionally coupled VCSELs subjected to optoelectronic feedback

Based on the framework of the spin-flip model (SFM), the polarization dynamics of vertical-cavity surface-emitting lasers (VCSELs) subjected to optoelectronic feedback has been investigated numerically. The results show that nonlinear dynamics are similar to what have been observed in VCSELs with negative optoelectronic feedback, such as polarization switching (PS), antiphase and inphase fluctuations, mode competition and quasi-period routes to chaos. The difference between them is that VCSELs subjected to optoelectronic feedback emit only in the yLP mode if the feedback strength is large enough. Moreover, the synchronization performance of unidirectionally coupled VCSELs subjected to optoelectronic feedback has also been investigated. The polarized mode in the single mode region (region A) can achieve complete synchronization. Within the mixed-mode region (region B), the synchronization quality of polarized modes is not ideal.

Optical generation of tunable millimeter-wave based on dual-beam optical injection Locked 1550 nm vertical-cavity surface-emitting laser

Based on the spin-flip model, the nonlinear dynamics of a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) subject to dual-beam optically injection is investigated theoretically. The results show that a slave 1550 nm-VCSEL (S-VCSEL) under the injection of dual-beam output from two master VCSELs (M-VCSELs) can be driven to enter into an injection locking state under suitable injection parameters. In this case, the outputs of both X and Y polarization modes of the S-VCSEL exhibit periodic oscillation whose frequency is equal to the frequency detuning between the two M-VCSELs, and its optical spectrum contains only two main frequency components and possesses a single sideband spectrum structure. As a result, two mutually orthogonal optical millimeter-waves can be obtained based on the periodic oscillation in a VCSEL subject to dual-beam optically injected locking. Through adjusting the frequency detuning between the two M-VCSELs, the frequency of the millimeter-wave can be tuned continuously in a large range, while the power and modulation depth can also be controlled by adjusting the system parameters.

Polarization switching dynamics of vertical-cavity surface-emitting laser subject to negative optoelectronic feedback

Using the extended spin-flip model, we theoretically investigate the polarization switching dynamics of a vertical-cavity surface-emitting laser subject to negative optoelectronic feedback. The results show that when the laser operates at two different the spin-flip rates, the feedback intensity and delay time have great influence on polarization switching dynamics. At a slow spin-flip rate, with the increase of feedback intensity, switching current increases linearly, that the X polarization mode is compressed is contrary to the reported results based on isotropic optical feedback. The reason may be due to the fact that the negative optoelectronic feedback improves the X polarization mode threshold; the effect of delay time will vary with feedback intensity. At a fast spin-flip rate, the effect of feedback strength is different from at a slow spin-flip rate, the switching point current undergoes a process in which the current increases first and then decreases gradually, the switching point current is more sensitively dependent on the feedback strength; while effect of the delay time is similar to that at a slow spin-flip rate. In addition, we find that the spontaneous emission noise has a great influence on polarization switching dynamics.

Violation of Leggett–Garg inequalities in quantum measurements with variable resolution and back-action

Quantum mechanics violates Leggett–Garg inequalities because the operator formalism predicts correlations between different spin components that would correspond to negative joint probabilities for the outcomes of joint measurements. However, the uncertainty principle ensures that such joint measurements cannot be implemented without errors. In a sequential measurement of the spin components, the resolution and back-action errors of the intermediate measurement can be described by random spin flips acting on an intrinsic joint probability. If the error rates are known, the intrinsic joint probability can be reconstructed from the noisy statistics of the actual measurement outcomes. In this paper, we use the spin-flip model of measurement errors to analyze experimental data on photon polarization obtained with an interferometric setup that allows us to vary the measurement strength and hence the balance between resolution and back-action errors. We confirm that the intrinsic joint probability obtained from the experimental data is independent of measurement strength, and show that the same violation of the Leggett–Garg inequality can be obtained for any combination of measurement resolution and back-action.

Analysis of Quantum-Dot Spin-VCSELs

The derivation of a set of rate equations (REs) to describe optically pumped quantum-dot (QD) spin-injected vertical-cavity surface-emitting lasers (VCSELs) is presented based on a modified version of the spin-flip model. The approach includes capture of spin-up and spin-down electrons from the wetting layer into the ground state of the QD and also coupling between left- and right-circularly polarized fields caused by birefringence and dichroism. Numerical solutions of the REs are presented in the form of stability maps in the plane of pump polarization and total pump intensity; examples of calculated time series of the polarized field components are also given for specific cases of interest. The values of the spin-relaxation rate, the carrier capture rate, and the gain parameter are shown to have a significant effect on the dynamics of quantum-dot spin-VCSELs.

Instabilities in quantum-dot spin-VCSELs

A modified spin-flip model is used to investigate the stability of optically-pumped quantum-dot spin-vertical cavity surface-emitting lasers. in terms of pump intensity and polarization. The stability maps exhibit pronounced polarization switching in the stable regions. Periodic oscillations in unstable regions are attributed to competition between spin relaxation and birefringence.

Optically-pumped dilute nitride spin-VCSEL

We report the first room temperature optical spin-injection of a dilute nitride 1300 nm vertical-cavity surface-emitting laser (VCSEL) under continuous-wave optical pumping. We also present a novel experimental protocol for the investigation of optical spin-injection with a fiber setup. The experimental results indicate that the VCSEL polarization can be controlled by the pump polarization, and the measured behavior is in excellent agreement with theoretical predictions using the spin flip model. The ability to control the polarization of a long-wavelength VCSEL at room temperature emitting at the wavelength of 1.3 µm opens up a new exciting research avenue for novel uses in disparate fields of technology ranging from spintronics to optical telecommunication networks.

Dynamics of vertical-cavity surface-emitting laser subject to optical injection and positive optoelectronic feedback

Based on the spin-flip model (SFM), we theoretically investigate the dynamics of a vertical-cavity surface-emitting laser (VCSEL) subject to optical injection and positive optoelectronic feedback. The results show that under the joint action of positive optoelectronic feedback and optical injection from a master VCSEL (M-VCSEL), two polarization modes of a slave VCSEL (S-VCSEL) will show many dynamic states such as period one, period two, multi-period and chaos, and the evolution routes of these states are different for two polarization modes. Mapping of dynamic region as a function of feedback strength f and injection strength is varied with frequency detuning between M-VCSEL and S-VCSEL (=m-s, where m ands are the free-running frequencies of M-VCSEL and S-VCSEL, respectively). Compared with the case for zero or negative frequency detuning, the region of chaotic state is expanded significantly under positive . For a fixed , the influences of f and on the chaotic bandwidth of S-VCSEL are discussed. Through selecting proper f and , chaotic bandwidth of S-VCSEL can be improved obviously.

Optical generation of high-quality millimeter-wave based on an optically injected VCSEL subject to polarization-rotated external optical feedback

A scheme of optical generation of high-quality millimeter-wave based on the optically injected vertical-cavity- surface-emitting laser (VCSEL) subject to polarization-rotated optical feedback is proposed in this paper. Based on the spin-flip model (SFM), wich external disturbances taken into account, the performances of the millimeter-wave generated by this scheme are numerically investigated. The results show that under suitable operation conditions, a slave VCSEL (S-VCSEL) injected by a master VCSEL (M-VCSEL) will operate in a period-one (P1) oscillation state and the output optical intensity of S-VCSEL looks like being modulated by a microwave signal. By adjusting the injection strength iand the frequency detuning between S-VCSEL and M-VCSEL, a millimeter-wave, whose frequency can be continuously adjusted in a large range from 30 GHz to 60 GHz, is obtained. After introducing polarization-rotated optical feedback, the linewidth of millimeter-wave can be obviously narrowed by adjusting the feedback strength i and the feedback delay time . For a millimeter-wave with a linewidth of 5.509 MHz, generated by the optically injected VCSEL, its linewidth can be reduced to 230.2 kHz under optimum feedback parameters. The results obtained in this paper are helpful for acquiring high-quality millimeter-wave used in high speed Radio-over-Fiber (RoF) system.

Nonlinear dynamics of 1550 nm vertical-cavity surface-emitting laser with polarization- preserved optical feedback

Based on the framework of the spin-flip model, the nonlinear dynamics of 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to polarization-preserved optical feedback is theoretically investigated. The results show that for a free-running 1550 nm-VCSEL, the current value for polarization switching (PS) is affected seriously by the internal parameters; with the increase of the gain anisotropy coefficient γa, the corresponding current for PS increases. Due to the introduction of the polarization-preserved optical feedback, the dominant polarized mode (Y polarized mode) will display different dynamical states for different injection currents while the other mode (X polarized mode) may be excited. As a result, the average output powers of the two polarized modes increase with fluctuation with the increase of current. For different feedback times, the dynamic states of 1550 nm-VCSEL with polarization- preserved optical feedback maybe route into chaos via different evolution paths such as period doubling bifurcation, quasi-periodic bifurcation and intermittent chaos.

Instabilities in Spin-Polarized Vertical-Cavity Surface-Emitting Lasers

We report a first comprehensive theoretical analysis of optically pumped spin-polarized vertical-cavity surface-emitting lasers, which combines the spin-flip model with the largest Lyapunov exponent technique to determine regions of stability and instability. The dependence of these regions on a wide range of fundamental device parameters is investigated, and results were presented in a new form of maps of the polarization versus the magnitude of the optical pump. We also reveal the importance of considering both the birefringence rate and the linewidth enhancement factor when engineering a device for high-frequency applications.

Numerical characterization of transient polarization square-wave switching in two orthogonally coupled VCSELs

We study the dynamics of two vertical-cavity surface-emitting lasers (VCSELs) mutually coupled such that the natural lasing polarization of each laser is rotated by 90 degrees and then is injected into the other laser. Simulations based on the spin-flip model show transient square-wave polarization switchings before a stationary state is reached. The influence of various model parameters on the duration of the stochastic transient time and on the lasers' dynamics in the stationary state is investigated.

Dynamics of Polarized Optical Injection in 1550-nm VCSELs: Theory and Experiments

We report novel theoretical results obtained from combining the method of largest Lyapunov exponent (LLE) with the spin-flip model (SFM), including noise, to model a vertical-cavity surface emitting laser (VCSEL) subject to polarized optical injection. The LLE is applied to the numerical solutions in order to automatically calculate stability maps that characterize the dynamics. The SFM has been extended and generalized to allow for optical injection of arbitrary polarization. Measurements on a 1550-nm VCSEL have been used to estimate the values of key parameters for use in the model and with these we demonstrate excellent agreement between theory and experiment.