Jan Albert

Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers

Intensity rate equations for two nearly degenerate modes are derived for current driven polarization switching (PS) in vertical-cavity surface-emitting lasers (VCSELs). We show that the introduction of a current-dependent gain that saturates with increasing optical power leads to a minimal description of a PS experiment. The main advantage of these rate equations compared to more sophisticated model equations is the possibility to describe analytically the PS dynamical phenomenon. We obtain a simple expression for the switching time which agrees with experimental observations.

Polarization behavior of vertical-cavity surface-emitting lasers: Experiments, models and applications

Due to the emission of light perpendicular to the surface of the quantum well and the usually symmetric vertical resonator there is a priori no intrinsic polarization anisotropy mechanism in VCSELs. Small residual strain explains the emission of linearly polarized light with a common orientation along [110] or [1–10] crystallographic directions. These two modes of linear polarization are strongly anti-correlated. Experimentally, polarization switching between them can be observed with increasing the injection current. It could happen from shorter to longer wavelength mode (type 1) or in the opposite way—from longer to shorter wavelength mode (type II). The polarization switching happens through a region of mode hopping or hysteresis. In the first case, the dwell time (the average time the laser spends in one mode) scales in several orders of magnitude. Thermal (carrier) effects influence the polarization behavior of VCSELs through the red (blue) shift of the gain maximum and through the dependence of the ...

Frequency response of polarization switching in vertical-cavity surface-emitting lasers

We present an experimental study of the current-driven polarization modulation properties of VCSELs. In some VCSELs, abrupt polarization switching (PS) between two polarization modes is observed at a particular value of the pump current. We investigate the dynamics and the associated dominating time scales of PS as these features are strongly linked with the underlying physical mechanism causing the PS. To this end, we measure both for gain- and index-guided VCSELs the critical modulation amplitude necessary to steadily force PS back and forth across the PS point as a function of the modulation frequency. This yields the current-driven polarization modulation frequency response, which we compare with the thermal frequency response of the studied devices. The dynamic behavior turns out to be strikingly different for the different VCSEL types. Thermal effects only play a minor role in the PS in our index-guided VCSELs, while they really seem to lie at the origin of PS in the gain-guided VCSELs. By implementing this in a rate-equation based theoretical model, we are able to explain the peculiarities of the measured response curves and to reproduce the experimental findings.

Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers

We present an experimental study of the current-driven polarization modulation properties of vertical-cavity surface-emitting Lasers (VCSELs). Some VCSELs exhibit a high-contrast polarization flip for a particular value of pump current. By modulating the current around this value we measure the critical modulation amplitude necessary to force current-driven polarization switching as a function of the modulation frequency. We thus obtain the polarization modulation frequency response, which shows the same cut-off frequency as the thermal frequency response. This indicates the necessity to incorporate a temperature-dependent variable in realistic models that describe the polarization behavior of these VCSELs.

Stochastic polarization switching dynamics in vertical-cavity surface-emitting lasers: theory and experiment

We present an analytical, numerical, and experimental study of the switching time and jitter of current-induced polarization switching in vertical-cavity surface-emitting lasers (VCSELs) as an example of switching in a nonlinear system in the presence of noise. Assuming that the switching is induced by changes in the dichroism, the problem can be reduced to the first-passage-time problem in gain-switched Class-A lasers. The theoretical results show excellent agreement both with numerical simulations based on the full-rate equations model and with experiments performed on oxide-confined VCSELs.

Laser Doppler velocimetry with polarization-bistable VCSELs

We present a rate equation model of a single mode vertical-cavity surface-emitting laser (VCSEL) with two states of linear polarization, subject to Doppler-shifted optical feedback. Recent experimental work has shown that the polarization bistability often observed in VCSELs can be exploited to enhance the responsivity of these semiconductor lasers in speed-sensing applications. We review these experimental results briefly and use the rate equation model to explain the increased signal-to-noise ratio.

Polarization switching and modulation dynamics in gain- and index-guided VCSELs

In this contribution, we bring forward and compare the polarization switching (PS) dynamics and the polarization modulation characteristics of gain- and index-guided VCSELs. We then discuss the steady-state and dynamic characteristics of both types of VCSELs. Finally we focus on the polarization modulation limit and the average mode hopping frequency, which both scale over 8 orders of magnitude when the switching current is varied from just above threshold up to 2 times the threshold current.

Polarization behavior of vertical-cavity surface-emitting lasers under the influence of in-plane anisotropic strain

It is well known that vertical-cavity surface-emitting lasers (VCSELs) can abruptly switch between two orthogonal linear polarization states if the current is changed. The impact of externally induced in-plane anisotropic strain on this switching was experimentally demonstrated in proton-implanted devices. In this contribution we present a further and thorough experimental investigation of the polarization behavior of different types of VCSELs (proton-implanted, air-post and oxide-confined), under varying strain conditions. We first measure the influence of the strain on the orientation of the axes of the linear polarization states. These axes can be rotated from the crystallographic direction [110] over [100] to [110]. At the same time, we monitor the exact birefringence. From the combination of these two measurements the amount of residual strain in these devices is deduced. Applying strain not only changes the frequency splitting between the two modes (due to birefringence) and their orientation, but also lifts the degeneracy in the gain of the polarization modes. We therefore also measure the gain difference (dichroism) as a function of the applied strain, via the mode suppression ratio and the optical spectrum. Due to the effect on both the birefringence and the dichroism, strain also changes the position of the polarization switching point as a function of current and can lead to the observation of double (consecutive) polarization switching. All this experimental evidence will help to build up a better understanding of the physics of polarization switching in VCSELs.

Polarization switching dynamics in single-mode VCSELs

We present an accurate experimental characterization of the dynamical properties of polarization switching (PS) in single transverse and longitudinal mode vertical-cavity surface-emitting lasers (VCSELs). When a VCSEL is driven with a constant current at its polarization switching point, it makes random jumps between its two linear polarization states. This phenomenon is called mode-hopping. The permanence times in the two polarization states show an exponentially decreasing distribution, according to Arrhenius? law. The average permanence time varies over several orders of magnitude depending on the relative difference between threshold and switching current. We have performed a statistical experimental characterization of the residence times of mode hopping VCSELs for both proton implanted and oxide confined samples, and find our results to be in excellent agreement with the theoretical predictions from a novel intensity rate equation model.

In-plane strain modification of polarization behavior of vertical-cavity surface-emitting lasers

We demonstrate experimentally how an external mechanical stress applied to a VCSEL wafer results in an in-plane anisotropic strain, which dramatically alters the polarization behavior of our VCSELs. In the presence of in-plane strain, the VCSEL still emits linearly polarized light but its direction strongly depends on the magnitude and the orientation of the strain (with respect to the crystal co-ordinate system). The latter behavior can be understood by taking into account the elasto-optic effect and the proper strain distribution. Furthermore, for a specific range in magnitude and orientation of the externally induced strain, current induced polarization switching between the two fundamental modes (with orthogonal linear polarization) is present in a reproducible way. The current at which switching occurs strongly depends on the magnitude of the external stress and can be tuned in the whole region of single-mode operation. These effects can be explained by accounting for the anisotropy of the valence band. The latter is induced by the in-plane uniaxial strain, leading to a modification of density of states and effective masses for different directions in the plane of the QW, and henceforth to a gain anisotropy and a different gain curve for each of the two polarization modes. Furthermore, the frequency splitting between the two cavity eigenmodes (also a result of the stress via the elasto-optic effect) has to be taken into account. We will discuss how the gain anisotropy changes with current, lattice temperature and carrier density, and how all these determine the polarization behaviour of VCSELs.