896 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 42, NO. 9, SEPTEMBER 2006 The Effects of Stress, Temperature, and Spin Flips on Polarization Switching in Vertical-Cavity Surface-Emitting Lasers Guy Van der Sande, Michael Peeters, Member, IEEE, Irina Veretennicoff, Jan Danckaert, Member, IEEE, Guy Verschaffelt, and Salvador Balle, Member, IEEE Abstract—We discuss the effect of uniaxial planar stress on polarization switching in vertical-cavity surface-emitting lasers (VCSELs). The approach is based on an explicit form of a fre- quency-dependent complex susceptibility of the uniaxially stressed quantum-well semiconductor material. In this mesoscopic frame- work, we have taken cavity anisotropies, spin carrier dynamics, and thermal shift of the gain curve into account. In this way, we present a model that provides a global overview of the polarization switching phenomenon. The results are compared with experi- ments on an air-post VCSEL operating at 980 nm. Index Terms—Numerical analysis, optical polarization, quantum theory, stress, surface emitting lasers. I. INTRODUCTION V ERTICAL-CAVITY surface-emitting lasers (VCSELs) are of particular interest because they offer several ad- vantages compared to conventional edge-emitting lasers. They show an improved beam quality, they exhibit low threshold cur- rents and high efficiency, and their parallel growth allows for on wafer testing. One of the most intriguing properties of VCSELs lies in their polarization behavior, which differs from the one of edge-emitting lasers due to the lack of a dominating polariza- tion selection mechanism in the quasi-cylindrically symmetric structure [1]. Usually VCSELs emit linearly polarized light. The polarization direction exhibits a certain randomness, with preferences, however, for the [1 10] and [110] crystallographic directions. This has been attributed to an inherent birefringence Manuscript received March 9, 2006; revised May 10, 2006. This work was supported in part by the European RTN network VISTA under Contract HPRN-CT-2000-00034 and the COST 288 action, and in part by the Interuni- versity Attraction Pole program (IAP V/18), in part by the Concerted Research Action “Photonics in Computing”, and in part by the Research Council of the Vrije Universiteit Brussel. The work of G. Van der Sande, G. Verschaffelt, and J. Danckaert was supported in part by the Fund for Scientific Research—Flan- ders (FWO). The work of S. Balle was supported in part by the Ministerio de Ciencia y Tecnología, Spain, through Project TIC2002-04255-C04-03. G. Van der Sande is with the Department of Applied Physics and Photonics (TW-TONA),Vrije Universiteit Brussel, 1050 Brussels, Belgium and also with the Optique Nonlinéaire Théorique, Université Libre de Bruxelles, 1050 Brus- sels, Belgium (e-mail: guy.van.der.sande@vub.ac.be). M. Peeters, I. Veretennicoff, J. Danckaert, and G. Verschaffelt are with the Department of Applied Physics and Photonics (TW-TONA), Vrije Uni- versiteit Brussel, 1050 Brussels, Belgium (e-mail: mpeeters@vub.ac.be; ivereten@vub.ac.be; jandan@vub.ac.be; gverscha@vub.ac.be). S. Balle is with the Departamento de Física Interdisciplinar, Instituto Mediterráneo de Estudios Avanzados, Consejo Superior de Investigaciones Científicas, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain (e-mail: salvador@imedea.uib.es). Digital Object Identifier 10.1109/JQE.2006.879816 in the cavity caused by stresses and strain unintentionally in- duced during manufacturing [2]–[4], and/or to the electrooptic effect arising from the drive voltage [5], [6]. Furthermore, it has been observed that often this linear polarization can switch between two orthogonal states while preserving operation in the fundamental transverse mode of the laser [7]–[10]. Experiments described in [11] show that a mechanical stress, applied externally to the VCSEL package, dramatically alters its polarization behavior. These – (optical output power versus injected current) measurements on an oxide-confined VCSEL show that the switching current changes when the stress is applied. This work proves the importance of stress on the quantum-well (QW) gain spectra and henceforth on the polarization selection in VCSELs. It is clear from these and other experiments by van Doorn et al. [3], [4], Verschaffelt et al. [9], Panajotov et al. [11], [12], Peeters et al. [13], and Sondermann et al. [14] that stress plays a crucial role on the polarization properties of VCSELs. Different physical models have been investigated in the liter- ature to describe polarization switching (PS) in VCSELs. The first model is of thermal nature and attributes PS to a spectral shift of the gain maximum with respect to the cavity resonances for the two frequency-split polarization modes [15]. Extending this idea one can also explain PS due to thermal lensing [16], or by incorporating the temperature and frequency dependence of both losses and gain [17]. A distinctively different model called the spin-flip model (SFM) for PS is developed in [18] and is extended to include frequency and gain anisotropies in [19]. This model describes the active semiconductor QW in terms of a spin-split two-level system, where the two spin subsystems are coupled through spin-flip processes. These two effects, tem- perature and spin-flip processes, have been combined by Balle et al. [20] by introducing an approximate frequency-dependent susceptibility for QW media [21]. This approach permits to in- clude the thermal shift of the cavity resonances over the gain spectrum of the system, and has allowed reproduction of the ex- perimental observations of PS [20], [22] two-frequency emis- sion at threshold [23], and the emission of elliptically polar- ized states [14]. In all these modeling attempts, strain effects are introduced phenomenologically through the dichroism and birefringence parameters. These parameters, which as already commented describe the residual anisotropies in the structure that may result from unintentional residual strain left after the growth process or from the electrooptic or elastooptic effects in the VCSEL cavity [5], play a key role in the preference for a particular polarization orientation. 0018-9197/$20.00 © 2006 IEEE