Perturbation approach to semiclassical laser theory with focus on spin-lasers

Abstract

Spin-lasers have attracted considerable attention due to the promising increase of modulation bandwidth by an order of magnitude via the polarization modulation. It has been understood using the so-called spin-flip model (SFM) that ultrafast polarization dynamics is the consequence of interplay between spin-dependent gain and cavity anisotropy, showing thus an importance of semi-analytic models in laser physics. However, the SFM lacks the predictive power in the sense of the first-principle design and does not describe correctly the linear gain anisotropy, which plays an important role in the polarization selection. Furthermore, the challenging semi-analytic modeling of complex gain media and nontrivial anisotropy is relevant also for other surface-emitting lasers, especially when their intriguing non-Hermitian and topological aspects are still being revealed nowadays. To make the design process and the analysis of novel surface-emitting devices, including spin-lasers, more practical, we perform the spectral decomposition of the effective Maxwell-Bloch equations in the basis of threshold lasing modes (TLMs) which allows us to view both stationary and non-stationary lasing as a perturbation problem. Concerning the stationary cases, we apply the first-order cavity perturbation theory (CPT) to derive the lasing condition, which allows to recover the differential generalization of the single-pole approximation steady-state ab initio lasing theory (SPA-SALT). Compared to SPA-SALT, it is not limited by the two-level atom approximation, permits a pump-induced frequency shift, and does not require the pre-determination of interacting lasing thresholds. As for non-stationary lasing, the perturbation approach allows to formulate a general theory of anisotropy rates. We directly apply the developed techniques to spin-lasers and derive the extended SFM including the linear gain anisotropy and a complete theory of anisotropy rates, making SFM directly applicable, for example, to grating-based spin-lasers. Most importantly, the extended SFM is used to predict the anisotropy-induced pair of exceptional points (EPs) connected by the Fermi-arc. It is shown that the Fermi-arc provides a new mechanism of polarization switching, thus paving an alternative way towards a long-desired dynamical polarization control in the sub-THz domain.