Eigenmodes of spin vertical-cavity surface-emitting lasers with local linear birefringence and gain dichroism

We present a general method for the modeling of semiconductor lasers such as a vertical-cavity surface-emitting laser and a vertical-external-cavity surface-emitting laser containing multiple quantum wells and involving anisotropies that may reveal (i) a local linear birefringence due to the strain field at the surface or (ii) a birefringence in quantum wells due to phase amplitude coupling originating from the reduction of the biaxial D2d symmetry group to the C2v symmetry group at the III-V ternary semiconductor interfaces. From a numerical point of view, a scattering S-matrix recursive method is implemented using a gain or amplification tensor derived analytically from the Maxwell-Bloch equations. It enables one to model the properties of the emission (threshold, polarization, and mode splitting) from the laser with multiple quantum well active zones by searching for the resonant eigenmodes of the cavity. The method is demonstrated on real laser structures and is presently used for the extraction of optical permittivity tensors of surface strain and quantum wells in agreement with experiments. The method can be generalized to find the laser eigenmodes in the most general case of circular polarized pumps (unbalance between the spin-up and spin-down channels) and/or dichroism allowing an elliptically polarized light emission as recently demonstrated experimentally when the linear birefringence is almost compensated [Joly, Opt. Lett. 42, 651 (2017)OPLEDP0146-959210.1364/OL.42.000651].