The main goal of this study is to explore possibilities of using cavities with dielectric or semiconductor grating as a main building block of spin-injected vertical-cavity surface-emitting lasers (spin-VCSELs) for ultrafast data transfer up to hundreds of Gb/s. Spin-VCSELs allow direct control of emitted polarization by means of electron spin injection. Compared to intensity-modulated VCSELs, the information is encoded into polarization state of light. Shorter response time is offered as a result of introducing anisotropy, in this case via periodic grating, which couples circularly-polarized photons, emitted in spin-polarized quantum wells. Precise modeling of the lasing regime is essential and based upon theory developed in our previous work. Eigenmodes of cavity with periodic structures are extracted using effective medium theory implemented in the transfer matrix formalism. Mathematical tools allow us to calculate optimal parameters of birefringent grating and consequently to design the cavities with required functionality. Particular focus is put on calculation of photon lifetimes, generalized confinement factors and frequencies of eigenmodes, which are necessary for studying dynamical performance of grating-based spin-VCSELs. According to the numerical model, desired gratings and grating-based cavities can be fabricated using PVD deposition of dielectric material sophisticated by lithographic techniques along with sample etching.
Spin-VCSELs offer particularly rich polarization dynamics due to non-trivial interplay of spin-induced circular gain dichroism with microcavity-related linear anisotropies. One of their promising applications is a data transfer technology in which the information is carried by spin of electrons and photons, surpassing the standard intensity modulation technology in both speed and energy consumption. Over the years, modeling of spin-VCSELs has been basically monopolized by the so-called spin-flip model, which is however constructed assuming degenerate orthogonal modes. Moreover, any amplitude anisotropies are treated in a perturbative way using linear coupling terms. This can be misleading in case of gain anisotropies originating from QW strain or asymmetric light confinement. The situation is even more complicated in highly-birefringent devices such as grating-based spin-VCSELs, where the mode profile asymmetry leads to new coupling mechanisms of optical field components with opposite helicity. The aim of this work is to (i) explore the role of linear gain anisotropy in spin-VCSELs within the extended spin-flip model based on polarization-resolved coupled-mode theory and (ii) to further analyze the consequences of recently predicted coupling mechanisms appearing in highly-birefringent spin-VCSELs.
We experimentally demonstrate that circular oxide apertures with small side deformations of large-area 980 nm VCSELs contribute to an increase in the optical output power by more than 60% and in the quantum efficiency by more than 10%. We elaborate on the physical background of this behavior and its applicability to small aperture VCSELs. We show that the efficiency of stimulated emission can be enhanced by engineering the spectral structure of the resonator. Such an approach is used already to enhance spontaneous emission,but has been left unexplored in the context of the stimulated emission of VCSELs.
We present the nonlinear coupled-mode theory for anisotropic microcavity lasers, the birefringent spin-lasers in particular. The modeling technique is based on the decomposition of Maxwell-Bloch equations in a properly-chosen vectorial basis, imprinting all the important information about cavity geometry, gain medium and local anisotropies into the coefficients of coupled-mode equations. The formalism is applied to spin-lasers with high-contrast gratings, in which the interplay of spin dynamics and cavity birefringence offers new possibilities for near-future data-transfer technologies. The model can be used to investigate the effects of spin modulation and grating parameters on dynamical performance of realistic grating-based spin-laser. Moreover, it is used to derive the extended spin-flip model. We show, that the currently-used spin-flip model requires the corrections in order to describe the grating-based spin-VCSELs with extremely large frequency splitting.
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 [1]. 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. [2] 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.
[1] T. Fördös, et. al., J. Opt. 16 (2014) 065008, Phys. Rev. A 96, (2017) 043828.
[2] 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.
We present a general method for modeling spin-lasers such as spin-polarized vertical cavity surface emitting laser (spin-VCSELs) with multiple quantum wells including anisotropic effects such as i) the emission of elliptically-polarized photons and originating from unbalanced spin-up and spin-down pumps, ii) the linear gain dichroism originating from the reduction from Td to C2v symmetry group at the III-V ternary interfaces and iii) the locally linear birefringence due to the anisotropic strain field at surface of ½ VECSELs an optical birefringence of quantum wells from the Henry’s factor. New recurrence calculations, together with analytically gain tensor derived from Maxwell-Bloch equations, enable to model emission from multiple quantum well active zones to find the laser resonance conditions and properties of eigenmodes.
The method is demonstrated on real semiconductor laser structures. It is used for the extraction of optical permittivity tensors of surface strain and of quantum wells (QWs). The laser structures are also experimentally studied via ellipsometry methods by measurement of the rotation spectra of complete Mueller matrix in the reflection geometry. The anisotropic optical permittivity constants in the spectral range from 0.73 to 6.4 eV are modeled in order to disantangle surface and QWs contributions to the linear optical birefringence of the structures.
In our previous paper [T. Fördös, et al., J. Opt. 16 (2014) 065008] we have proposed a new approach for modeling of polarized light emission from anisotropic multilayers with active dipole layers. The method is suitable to model spin-polarized light emitting diodes (spin-LED) and spin-lasers. This paper deals with generalization of the approach to scattering matrix (S-matrix) formalism and to laterally periodic structures in the frame of rigorous coupled wave algorithm (RCWA). We use expansion of the permittivity tensor in a grating layer into Fourier series and the periodic electromagnetic field in the structure is expressed using a matrix method including appropriate boundary conditions. The new approach based on S-matrix formalism is also suitable for modeling of monomode emission from MQW laser structures with multiple source layers.
Using Yeh's matrix formalism, the approximate formulas for the magneto-optical effects in reflection from semi-infinite
orthorhombic crystal with symmetry axes parallel to the Cartesian axes are derived for a general orientation
of the magnetization vector. The magneto-optical (MO) effects in such structures are usually calculated
numerically, but theoretical formulas give us physical insight into these effects and an good understanding of
their symmetry properties. The near normal incidence approximation allows to study effects, which appear in the
case of small angle of incidence in the contrast to the normal incidence. Different dependencies of these effects
on the sample rotation allow us to distinguish between trigonal, tertragonal and hexagonal structures including
and missing two-fold in-plane symmetry axis. The theoretical description of the magneto-optical effects can be
applied to the magneto-optical ellipsometry, which is very sensitive nondestructive methods suitable for study
of magnetic anisotropy, magnetization reversal properties of nanostructures, and exchange coupling.
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