We present experiments measuring the complex degree of coherence of a Broad-Area Vertical-Cavity Surface-Emitting Laser (BA-VCSEL) when it is driven into a regime of spatially incoherent emission. This high-power,
spatially incoherent emission regime is quite uncommon for semiconductor lasers but can be useful in e.g. illumination
and projection systems, as the low degree of spatial coherence may help to reduce speckle. The
near-field coherence properties are measured for different positions in the VCSEL's aperture using a 180 degrees
reversing-wavefront Michelson interferometer. We give evidence that the coherence area is much smaller than
the VCSEL's aperture and that the intensity fluctuations across the coherence area are small, therefore allowing
the BA-VCSEL to be considered a quasi-homogeneous source. We explain the reason for the relatively small
coherence radius of about 1.4 μm based on the mode size in a planar cavity together with the thermal gradient
within the VCSEL aperture.
We develop a rate equation model describing the polarization switching phenomenon in vertical-cavity surface-emitting lasers taking into account the major underlying physical origins of this behavior: spin flip relaxation effects, temperature variations and both residual strain in the quantum well and stresses externally applied to the device. To include effects of temperature and stress or strain, we describe the optical material properties of the quantum well by way of a recently derived analytical approximation for the optical susceptibility of uniaxially stressed quantum-well lasers at low temperatures. We review the influence of temperature and stress on the polarization-dependent gain and the linewidth enhancement factor. Combining this information with cavity anisotropies and spin carrier dynamics, we present a model that provides a unified overview of the polarization switching phenomenon. By way of a linear stability analysis, the polarization mode stability is discussed and compared with earlier experimental results.
An overview of the idiosyncratic emission characteristics of pulsed broad-area VCSELs is presented, together with a statistical model which describes these devices as quasi-homogeneous sources. The predicted properties of such sources, which include two reciprocity relations between near and far field aspects of the cross-spectral density as well as its propagation, are verified experimentally. We finish by showing how and which thermal effects are at the origin of this nonmodal emission.
Vertical Cavity Surface Emitting Lasers (VCSELs) often present switching between two orthogonal polarization states when varying parameters like e.g. current or temperature. Around such a switching point, the system randomly jumps between these two polarization states (mode hopping), driven by noise. In this contribution, we present experimental and numerical results showing the effect of coloured noise, externally added to the current, on the switching characteristics of a VCSEL.
We present a study of the time-scale at which current induced polarization switching (PS) in VCSELs takes place. To this end, we measure the step and frequency response in three different types of PS VCSELs, showing that the dominating time-scales differ strongly from one VCSEL structure to another. We characterize the current-driven polarization modulation frequency response by measuring the critical modulation amplitude necessary to steadily force PS back and forth across the PS point as a function of the modulation frequency. The polarization step response is obtained by measuring the stochastic properties of the delay between the applied current step and the resulting change in the polarization, for various values of the initial and final current. For the studied proton-implanted VCSEL the polarization response is characterized by the thermal relaxation time. The measured polarization response of the air-post VCSEL also shows a clear signature of thermal effects, however PS is not at all inhibited at higher frequencies. In the oxide-confined device studied, there seems to be no thermal influence on the PS at all. Comparing the frequency response and the step response measurements done on the same device leads to similar conclusions and allows us to crosscheck our results. In all cases, we are able to reproduce our experimental findings using a rate-equation model, where PS is supposed to be induced by changes in the gain balance between the two polarization modes.
We have derived and implemented a simplified dynamical multi-mode
model for vertical-cavity surface-emitting lasers (VCSELs) requiring
minimal computing resources while remaining realistic. A set of
spatially independent rate equations with a minimum of parameters is
extracted from the general spatially resolved equations and reduced to
dimensionless form to expose its essentials. The shape of the carrier
density distribution is approximated with a linear sum of the modal
shapes which are considered to be bias independent for index-guided
devices. Despite this simplification the model, which can be
extended to any number of laser modes, includes important effects like
spatial hole burning (SHB), carrier diffusion and inhomogeneous
injection and shows good agreement with spatially resolved models.
We describe the reduction and nondimensionalization of the general
spatially resolved equations. The implementation inside a C++ rate-equation framework is discussed and shown to provide a powerful and flexible environment to efficiently study the contribution of different factors. The effect of spatial hole burning (SHB) and mode competition on the small signal modulation response is investigated in three basic cases. The comparison between a single mode VCSEL without SHB, a single mode VCSEL including SHB and two mode VCSEL including SHB enables us to pinpoint which contributions are due to SHB and which are due to the modal competition. Finally,the possibility of using this approach to model polarization switching in VCSELs is discussed. The unavoidable small birefringence (with elasto-optic and electro-optic contributions) present in all VCSELs leads to a doubling of each mode into two orthogonal polarization states which are almost degenerate. Although small, the birefringence causes gain differences: part of which are due to frequency dependent gain and loss of the materials and part of which are due to slightly different transverse modal shapes. As these gain differences depend on the
injected current, they can be one of the causes of polarization
switching.
We present an experimental and rate-equation based theoretical 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 of the current-driven polarization modulation properties of VCSELs we are able to explain the peculiarities of the measured response curves and to reproduce the experimental findings.
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.
We present an experimental and rate-equation based theoretical study of the current-driven polarization modulation properties of VCSELs. In such lasers a high-contrast polarization flip is often observed at a particular value of the pump current. When modulating the current around the polarization switching value, we measure the critical modulation amplitude necessary to force synchronized back-and-forward polarization flips, as a function of the modulation frequency. This yields the polarization modulation frequency response. For a proton-implanted VCSEL the shape of the measured response curve is characterized by time constants that are very long compared with the usual time scales of laser dynamics (such as photon and carrier lifetimes), and compatible with the measured thermal relaxation time. Indeed, both the polarization modulation and the thermal frequency response curves show a cut-off frequency of about 90kHz, independent of the particular value of the switching current. In the frequency response curve of an air-post VCSEL one clearly sees remnants of the thermal influence on the switching. However, one cannot say that a thermal cut-off inhibits polarization switching above a certain modulation frequency. Notwithstanding the difference in impact of thermal effects depending on the type of device under study, our results indicate that it is necessary to incorporate a temperature-dependent variable in realistic models describing the dynamical polarization properties of VCSELs.
Current driven switching between two orthogonal linear polarizations in the fundamental mode of VCSELs is the object of intensive experimental and theoretical work. We developed a model based on the experimental evidence that the gain/loss difference between the two modes is an important factor in polarization switching. We analytically and numerically study a nearly-degenerate two-mode intensity rate equation model. The gain coefficients we use are current dependent and gain saturation with increasing optical power is also taken into account. Two types of stationary solutions emerge: pure-mode solutions (one mode lases) and mixed mode solutions (both modes lase). Stability analysis shows that when the gains equalize, switching between the two pure-mode solutions occurs. The nonlinear gain induces a region of bistability around the switching point. Taking into account the different time scales present in the model and using asymptotic techniques, we can further reduce the model to a single dynamical equation, which can be solved analytically. Stochastic effects (e.g. due to spontaneous emission) can be incorporated in this 1D Langevin-type equation. This allows us to explain the mode hopping in terms of a First Passage Time over the potential barrier in a double potential well.
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.
The intriguing polarization properties of Vertical-Cavity Surface-Emitting Lasers (VCSELs) are discussed and different physical mechanisms to explain this behavior are proposed. Experimental results obtained on different types of VCSELs will be confronted with the predictions from different theoretical models.
An array compatible, fast and high contrast opto-electronic polarization sensitive switch is proposed. The element's electrical configuration is a standard p-i-n heterostructure under reverse bias voltage. Its optical configuration is very similar to an asymmetric Fabry-Perot resonator (AFPR) where an electroabsorptive i-layer is included between the p and n layers, as in a SEED. Both p- and n-layers are Bragg- reflectors. The front mirror of the AFPR is made slightly polarization dependent using a subwavelength grating etched in the top layer of the p-type reflector stack. We calculate the polarization dependent overall absorption and reflection of the device and model the steady state behavior and polarization induced switching properties, for an electroabsorption coefficient that increases linearly with applied voltage. Using a standard load-line analysis we show that changing the input polarization from TE to TM can lead to a dramatic decrease or increase in overall reflectivity.
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