Matrix approach for modeling of emission from multilayer spin-polarized light-emitting diodes and lasers

Spin-polarized light sources such as the spin-polarized light-emitting diodes (spin-LEDs) and spin-polarized lasers (spin-lasers) are prospective devices in which the radiative recombination of spin-polarized carriers results in emission of circularly polarized photons. The main goal of this article is to model emitted radiation and its polarization properties from spin-LED and spin-controlled vertical-cavity surface-emitting laser (spin-VCSEL) solid-state structures. A novel approach based on 4 × 4 transfer matrix formalism is derived for modeling of the interaction of light with matter in active media of resonant multilayer anisotropic structure and enables magneto-optical effects. Quantum transitions, which result in photon emission, are described using general Jones source vectors.Web of Science166art. no. 06500

Time-dependent laser cavity perturbation theory: Exploring future nano-structured photonic devices in semi-analytic way

We present a theoretical framework, which successfully combines two different fields of photonics: i) the laser rate equations and ii) the cavity perturbation theory, focusing particularly on micro-cavity lasers with optical anisotropies. Our approach is formally analogous to quantum-mechanical time-dependent perturbation theory, in which however the gain medium and permittivity tensor distribution are perturbed instead of the Hamiltonian. Using the general vectorial Maxwell-Bloch equations as a starting point, we derive polarization-resolved coupled-mode equations, in which all relevant geometric and anisotropy-related laser parameters are imprinted in its coefficients. Closed-form coupled-mode equations offer physical insights like rate equations approaches and the precision comparable to brute-force numeric routines, thus being the time-saving alternative to finite-difference time-domain methods. The main advantage is that one calculates numerically the shapes of cold-cavity modes used to derive coupled-mode equations for one set of parameters and the broad landscape of parameters of interest is further studied in a perturbative way. This makes the method particularly interesting for semi-analytic studies of state-of-art devices such as the photonic crystal lasers, the liquid-crystal lasers or specifically spin-lasers, in which the interplay between injected spin and cavity birefrigence creates very promising platform for ultrafast data transfer technologies.Web of Science40144745473

Magnetooptické jevy v nanostrukturách se sníženou symetrií

Import 04/07/2011Theoretical part of this bachelor thesis is focused to the theoretical description of magneto-optical effects in reflection from structures with reduced symmetry. Using Yeh's matrix formalism, the appropriate formulae for the magneto-optical effect from semi-infinite orthorombic crystal is derived. The sensitivity of quadratic magneto-optical effects to crystal symmetry can be used for study of symmetries of the structures. Experimental part is focused on characterization of layers consisting of the ferromagnetic Co and Fe nanoparticles embedded in SiO$_2$ matrix. Magnetic properties were measured using longitudinal magneto-optical Kerr effect. Magneto-optical hysteresis loop measurements show differences between Fe particular film with strong in-plane uniaxial anisotropy and Co one, which is almost isotropic. Nanoparticular film thicknesses and volume fractions of particles were obtained using spectroscopic ellipsometry. Ellipsometric data were fitted to the model based on the Bruggeman effective medium approximation.Teoretická část bakalářské práce je zaměřena na teoretický popis magnetooptických jevů ve strukturách se sníženou symetrií. Užitím Yehového maticového formalismu je odvozen přibližný vztah pro výpočet komplexního magnetooptického úhlu od polonekon- ečného ortorombického krystalu. Citlivost kvadratických jevů na symmetrii krystalu může být využita ke studiu symmetrií ve strukturách. Experimentální část je zaměřena na charakterizaci vrstev, které se skládají z feromagnetických Fe a Co nanočástic v prosteředí SiO$_2$. Magnetické vlastnosti byly měřeny s využitím longitudinálního magnetooptického Kerrova jevu. Z měření magnetooptických hysterezních smyček vyplývá rozdíl mezi Fe nanočásticovou vrstvou se silnou in-plane jednoosou anizotropií a téměř izotropní Co vrstvou. Tloušťky vrstev a objemový podíl částic byly stanoveny s využitím spektroskopické elipsometrie. Elipsometrická data byla fitována modelem efektivního prostředí.516 - Institut fyzikyvýborn

Modelování anizotropních tenkovrstevných laserových struktur

Import 26/06/2013Spin-polarized light sources such as the spin-polarized light-emitting diodes (spin-LEDs) and spin-polarized lasers (spin-lasers) are perspective devices in which the radiative recombinations of spin-polarized carriers result in emission of circularly polarized photons. Main goal of this thesis is modeling outside emited field and polarization properties of spin-LED and spin-controled vertical-cavity surface-emiting laser (spin-VCSEL) structures. New approach based 4x4 matrix formalism is derived for modeling of light interaction in resonant multilayer structure. Quantum transitions, which result in photon emission, are described using Jones source vectors.Spinově polarizované zdroje záření jako například spinově polarizované světelné emisní diody (spin-LED) a spinově polarizované lasery (spin-lasery) jsou perspektivní zařízení v nichž zářivé rekombinace spinově polarizovaných nosičů náboje vedou k emisi fotonů s kruhovou polarizací. Hlavním cílem této práce je modelování emitovaného pole a polarizačních vlastností spin-LED struktur a spinových laserů s vertikálním uspořádáním (spin-VCSEL). Je odvozen nový přístup založený na 4x4 maticovém formalismu, který popisuje interakci světla s rezonanční multivrstevnou strukturou. Kvantové přechody, které vedou k emisi fotonů, jsou popsány Jonesovými zdrojovými vektory.516 - Institut fyzikyvýborn

Světelné koherentní zdroje se spinově polarizovaným proudem.

Spin-lasers are semiconductor devices in which the radiative recombination processes involving spin-polarized carriers result in an emission of circularly polarized photons. Nevertheless, additional linear in-plane anisotropies in the cavity generally lead in preferential linearly-polarized laser emission and to possible coupling between modes. In this thesis, a general method for the modeling of semiconductor laser such as 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 (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. A novel scattering S-matrix recursive method is implemented using a gain tensor derived analytically from the Maxwell-Bloch equations. It enables to model the properties of the emission (threshold, polarization, 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 used for the extraction of optical permittivity tensors of surface strain and quantum wells in agreement with experiments. The method is 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 linear gain dichroism. In addition, the measurement of full 4x4 Mueller matrix for multiple angles of incidence and in-plane azimuthal angles has been used for extraction of optical permittivity tensors of surface strained layers and quantum wells. Such spectral dependence of optical tensor elements are crucial for modeling of spin-laser eigenmodes, resonance conditions, and also for understanding of sources of structure anisotropies.Spinové lasery jsou polovodičové zařízení v nichž zářivé přechody zahrnující spin nosičů vedou k emisi kruhově polarizovaných fotonů. Lokální anisotropie přítomné v rezonátoru však ovlivňují výslednou polarizaci a vedou k emisi lineárních nebo elipticky polarizovaných vlastních módů a k případné vazbě mezi nimi. V této práci je popsána obecná metoda modelování povrchově emitujících polovodičových laserů s vertikální geometrií zahrnující vícenásobné kvantové jámy a přítomné lokální anisotropie: i) linearní dvojlom a dichroismus na povrchu a ii) anisotropie v kvantových jámách pocházející z fázově-amplitudové vazby vzhledem k redukci D2d symetrie na C2v symetrii na rozhraní III-V ternárních polovodičů. Nová metoda zahrnující S-maticový přístup a využívající tenzor zesílení odvozený z Maxwell-Blochových rovnic umožňuje modelování vlastností spinového laseru (laserový práh, vyzářenou polarizaci, frekvenční rozestup módů) s vícenásobnými aktivními oblastmi. Metoda je demonstrována na příkladu reálné laserové struktury a je využita pro výpočet lokálních optických tenzorů permitivity na povrchu a v kvantových jamách. Metoda je dále zobecněna pro popis spinových laserů s elektrickým a optickým čerpáním a s lineárním dichroismem v zesílení. Pro výpočet anizotropních optických konstant bylo využito měření 4x4 Muellerovy matice pro různé úhly dopadu a různé azimutální úhly. Spektrální závislost optických konstant je klíčová pro modelování vlastních módu, podmínek rezonance a také pro pochopení rozdílných zdrojů anizotropie v laserových strukturách.516 - Institut fyzikyvyhově

Local and mean-field approaches for modeling semiconductor spin-lasers

Electrically and optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) seem to attain improved performance compared to their conventional counterparts. Their dynamical properties are studied mostly in the framework of effective rate equations containing parameters that are difficult to directly relate with fundamental material properties. Consequently, such approaches are not suitable for the precise design and optimization of future spin-lasers with desirable dynamical properties. We propose a method for extraction of dynamics-related parameters for the spin-flip model, which is widely used for the description of spin-laser dynamics. This method is based on the correspondence between robust local computational tools and effective models. A general matrix formalism based on S-matrices and generalized Maxwell-Bloch equations is used to determine approximate values of parameters such as cavity decay rate or birefringence rate. This would allow us to tune laser properties by changing the optical properties of the laser cavities and active media according to our needs. The method is demonstrated on realistic anisotropic spin-VCSEL structures containing a 12-quantum-well InGaAs/GaAsP active region. The potential limitations of already existing effective models are discussed.Web of Science225art. no. 05500

Mueller matrix ellipsometric study of multilayer spin-VCSEL structures with local optical anisotropy

Spin-laser structures such as spin-polarized vertical-cavity surface-emitting lasers are semiconductor devices in which the radiative recombination processes involving spin-polarized carriers result in an emission of circularly polarized photons. Nevertheless, additional linear in-plane anisotropies in the cavity, e.g., interfacial and surface anisotropies, generally lead to preferential linearly polarized laser emission and to possible coupling between modes. We present Mueller matrix ellipsometric study of non-intentionally doped InGaAs/GaAsP laser structures devoted for optical pumping operations in the spectral range from 0.73 to 6.4eV in order to disentangle surface and quantum wells contributions to the linear optical birefringence of the structures. The measurement of full 4 x 4 Mueller matrix for multiple angles of incidence and in-plane azimuthal angles in combination with proper parametrization of optical functions has been used for extraction of optical permittivity tensor components along [110] and [1 (1) under bar0] crystal axis of surface strained layers and quantum wells grown on [001]-substrate. Such spectral dependence of optical tensor elements is crucial for modeling of spin-laser eigenmodes, resonance conditions, and also for understanding of sources of structure anisotropies.Web of Science11222art. no. 22110

Spin vertical-cavity surface-emitting lasers with linear gain anisotropy: Prediction of exceptional points and nontrivial dynamical regimes

It is shown that when the linear gain anisotropy is properly accounted for, spin-injected vertical-cavity surface-emitting lasers (spin-VCSELs) offer interesting functionalities. Using the extended spin-flip model (SFM), we predict the existence of exceptional points (EPs) in spin-VCSELs and two interesting phenomena which accompany EPs, namely, (i) the polarization switching manifesting as induced change of field helicity sign and (ii) frequency comb generation without the need of external injection locking. Both effects have tremendous technological potential such as fast on-chip polarization switching, and most importantly, their concepts are not limited only to spin-VCSEL technology. We discuss the concept of anisotropy-engineered non-Hermitian microlasers and we provide a theoretical background to study their polarization dynamics near EPs.Web of Science1073art. no. 03350

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

We present a generalmethod 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 D-2d symmetry group to the C-2v 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.Web of Science964art. no. 04382

Spin-VCSELs with local optical anisotropies: Toward terahertz polarization modulation

We present a semiclassical model for spin-injected vertical-cavity surface-emitting lasers (spin-VCSELs) with local optical anisotropies. Particular focus is put on highly anisotropic spin lasers with broad application potential. A generalized matrix formalism for extraction of the laser modes is introduced, which enables us to calculate the spatial distribution of vectorial modes in arbitrary spin-VCSELs. The time dependence of such laser modes is further studied by means of the generalized coupled-mode theory, which is the natural anisotropic generalization of the conventional mode-decomposition approach. We use the circularly polarized optical modes as the basis for coupled-mode theory, which leads to extension of the well-known spin-flip model. In contrast to the conventional spin-flip model, the only input parameters are the geometric and local optical properties of the multilayer structure and properties of the gain media. The advantages of the theory are demonstrated in the design and optimization of spin-VCSEL structures with a high-contrast grating. We show that the proposed structures can be used for (i) polarization modulation in the terahertz range with tremendous applications for future ultrafast optical communication and (ii) as prospective compact terahertz sources.Web of Science151art. no. 01404