We extend our layer-by-layer model of photonic eigenmodes (resonance, polarization) of semiconductor laser and VCSELs (Fordos PRA 2017) by considering local optical properties in order to describe the above-threshold lasing even in the multimode regime. Such generalization, consistent with the semi-classical description based on the optical Bloch equations, allows to describe the optical gain and the wave propagation within the cavity in a more realistic way. The formalism is suitable to study the mode competition, since the important physical effects such as spatial-hole burning or cross-saturation mechanisms are included self-consistently. The only input parameters are those describing geometrical and local material properties of the cavity and the gain media, without using any mean-field approximations. We will present our generalized approach for modelling real devices and will show how it can serve in determining the main optical and physical properties of such devices.
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.
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