Recent technological and scientific interest in spin-polarized vertical-cavity surface emitting lasers (spin-VCSELs) leads to development of advanced laser modeling tools . The models describes arbitrary multilayer structure of spin-VCSELs including general anisotropy of optical properties of individual layers, and also anisotropy of gain. This important generalization allows not only for precise description of static properties of the resonant cavity, but can also be used to precisely calculate effective parameters used in dynamical models.  Applications of spin-lasers for high modulation and switching up to GHz/THz frequencies, advanced output beam shape manipulation, and use of active quantum dot structures leads to necessity to model spin-VCSELs with active and passive laterally periodic structures such as gratings, photonic crystals, and diffractive structures.
In this paper, we will show the generalization of existing matrix-based models to describe spin-lasers with lateral periodicity. The generalized rigorous coupled-wave analysis (RCWA) will be discussed in details and it will be compared with grid-based techniques such as finite element methods (FEM) and finite-difference time-domain analysis (FDTD). We will also discuss effects of incoherent propagation and random phase during light propagation in the structure. The method will be applied to structures of practical interest consisting of anisotropic grating used for ultrafast laser modulation and photonic structure.
 T. Fördös, et. al., J. Opt. 16 (2014) 065008, Phys. Rev. A 96, (2017) 043828.
 M. Drong, et al. Proc. SPIE 10926, (2019) 1092614.
Spin-polarized lasers such as spin-polarized vertical-cavity surface-emitting laser (spin-VCSELs) are prospective devices in which the radiative recombination of spin-polarized carriers results in an emission of circularly-polarized photons. Nevertheless, additional linear in-plane anisotropies in the cavity generally lead in preferential linearlypolarized laser emission and to possible coupling between modes. Optimization of room-temperature spinVCSELs thus relies on a proper modeling method and on a good understanding of these anisotropies that may reveal (i) a local linear birefringence due to strain fields at the surface or (ii) a birefringence in quantum wells (QWs) due to phase-amplitude coupling originating from the reduction of the biaxial D2d to the C2v symmetry group at the III-V ternary semiconductor interfaces. We present a novel method for the modeling of steady-state and dynamical properties of generally anisotropic multilayer semiconductor lasers containing multiple QWs active region. In order to solve the dynamical properties of spin-VCSELs, we combine here optical Bloch equations for a 4-level system with the scattering-matrix formalism, which treats VCSELs as a multilayer structure containing classical active dipole layers [T. F¨ord¨os et al., Phys. Rev. A 96, 043828 (2017)]. The method is then demonstrated on real semiconductor laser structures with InGaAs/GaAsP quantum wells. It is used for calculation of the laser resonance condition, the polarization properties of eigenmodes, the electromagnetic-field distribution inside the laser cavity, and time-dependent properties of the emitted light.