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Quantum interference control has is a well described effect in bulk and infinite well super-lattice crystals. In this thesis, we describe this effect in nanocrystals. We use a 8-band model for the description of the electron band structure in the crystal. We then break its inversion symmetry with a linear potential. We then apply external electro- magnetic field and calculate its effect on the crystal with the help of perturbation theory. The fields applied are of two kinds, one harmonic, the other instant in time. We follow with the calculation of the generated current, with detailed numerical tests of several pa- rameters of the model. Conductivity for a non-linearity of the 3rd order is then formally calculated. 1

We explore the conductivity of Dirac electrons in the terahertz range, especially in graphene. We are trying to find a boundary condition that is suitable both for the eigen states around the Dirac points and the nanocrystalline structure of graphene. Ultimately we analyze the conductivity of these bound states. 1

Conductivity of semicoductor nanostructures has its maximum in terahertz spectral range. Linear response is described in reasonable detail. With high intensity light sources it is also needed to be concerned with nonlinear response. In this thesis, there is firstly described already existing quantum model of linear conductivity which is using perturbation theory. This model is then extended by adding another perturbations, getting us quantum model for calculating nonlinear conductivity of arbitrary order. Model is then applied for calculation of third order nonlinear conductivity spectra for cubic nanocrystal. There is described spectra for varying parametres, such as tempera- ture, volume, electron density or scattering rate. In the end it is compared with semiclassical compuptation using Monte-Carlo simu- lation. 1

Magnetic properties of matter have an effect on their optical response. These properties depend on the microscopic structure of the matter and we distinguish several basic types of magnetism. In the latest research, scientists focus on tri- angualr antiferromagnets and their use in technology, for example in spintronics. We describe the magnetic material by permittivity tensor. Description of the response of the material is derived from Maxwell equations and the reflected light is described by its polarization and ellipticity. Then we model triangular antiferromagnets Γ5g and Γ4g configuration. 1

V této teoretické práci se zabýváme kvantově mechanickými jevy, jež jsou spjaté s vodi- vostními elektrony uzavřenými v kvantových tečkách. Nejprve je odvozen model nanokrys- talu jakožto potenciálové jámy. Při tom se ukazuje, že pouze objem, ne tvar, je významným parametrem modelu pro účely terahertzové spektroskopie. Studované geometrie jsou tak vzájemně zaměnitelné a výběr mezi nimi m·že zjednodušit dané úlohy. Pro zkoumání depo- larizačních efekt·, které jsou zahrnuty v depolarizačním faktoru v Maxwell Garnettově teorii efektivního prostředí, je zvolena sférická symetrie. V rámci poruchy prvního řádu je vyřešena Poissonova rovnice pro elektrony rozmístěné uvnitř koule podle vlnové funkce a je určen depo- larizační faktor. Zatímco v klasické limitě tento nabývá p·vodní hodnoty, pro nanokrystaly se zvyšuje a maxima je dosaženo v ne-degenerovaném režimu, kdy je obsazen pouze základní stav. Navýšení depolarizačního faktoru posouvá plasmonovou rezonanci směrem k vyšším frekvencím. 1

We explore conductivity of nanostructures in the terahertz range. We model the nanostructure as a square potential well with a barrier inside. We examine how the conductivity depends on temperature, material constants and dimensions of the potential well. The conductivity of the material determines the complex refractive index and thus influences its optical properties such as reflexivity, transmittance and attenuation coefficient. We construct the functional dependency of the conductivity on the electric field frequency. The maxima of this functional dependency correspond to spectral lines. We examined the dependency of the frequencies of the maxima (spectral lines) on various parameters. We got the most interesting result when we continuously changed the position of the barrier inside the potential well. For different heights of the barrier we got qualitatively different results. With high barrier the system behaves as two separate potential wells where we can see monotonous functional dependency of the spectral lines on the position of the barrier. With low potential barrier we get oscillating dependencies. For gallium arsenide and 2 nm width of the potential barrier, high barrier is higher than 1 eV, while low barrier is lower than 0, 05 eV.

In my research work, I study diffraction by planar periodic structures (diffraction grating). In the first chapter, I try to familiarize the importance of diffraction gratings in spectroscopy. The second chapter explains the basic principle of diffraction without involving difficult mathematical tools. In the third chapter, I deduce Fourier modal method from Maxwell equations, a modern mathematical approach used for calculating the electromagnetic response of diffraction. The most important part of my work consists of the fourth and fifth chapter. At first, I try to utilize Fourier modal method for deriving formulas involving just 0th and (-1)st diffraction orders. Because of the unreasonable difficulty of uncovered formulas, I decided to consider only a special case - so-called Littrow configuration, in which the solution can be superposed from symmetric and antisymmetric couples of rays. I further develop so-called Local modal method - very inaccurate, but mathematically fairly simple, and discuss its physical limitations. Whole work is finished by the sixth chapter, which compares accurate computations gained from simulation and derived analytical formulas for both methods.

Ultrashort laser pulses are nowadays widely used in both the basic and applied reseach as well as in a wide range of applications. Application of laser pulses requires their complete characterization from the point of view of temporal evolution of field amplitude and frequency on femtosecond timescales. This thesis is focused on a new method for ultrashort pulse characterization, which involves measuring spectral interference between input pulse and the pulse transmitted through a medium with cubic nonlinear susceptibility. The new method is inte- resting compared to the established techniques mainly because of its simplicity, as it requires only one medium with cubic nonlinear susceptibility and a spectro- meter. We have implemented the technique experimentally and determined pulse duration and phase for ideally compressed pulse.

of Doctoral Thesis Title: Ultrafast response of electrons in nanostructured and disordered semiconductor systems studied by time-resolved terahertz spectroscopy Author: Vít Zajac Department / Institute: Institute of Physics of the Czech Academy of Sciences Supervisor of the doctoral thesis: doc. RNDr. Petr Kužel, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: This thesis deals with charge transport in semiconducting nanomaterials on the picosecond time scale studied by time-resolved terahertz spectroscopy. The problematics of the effective response of composite materials is reviewed and the VBD effective medium model is formulated. The wave equation for the THz probing pulse propagating through inhomogeneously excited percolated and non-percolated semiconducting nanomaterials is solved. This theory is used to investigate charge transport in samples of nanoporous-Si-derived nanocrystals and in epitaxial Si nanocrystal superlattices. The experimental spectra are successfully modeled with the use of Monte Carlo calculations of charge carrier mobility in nanocrystals of corresponding sizes and degrees of percolation within the VBD approximation. It is found that nanocrystals from different regions of the nanocrystal size distribution of the sample dominate the signal in THz and...

Optical response of materials strongly depends on their magnetic properties. This phenomenon is also used in materials in the form of thin layers and multi- layers. Using cited literature we summarize theory needed to calculate magneto- optical response of multilayers. The calculation is based on Maxwell equations and magnetic materials are described with effective permittivity tensor. Jones formalism is used to describe polarised light and Yeh formalism is used to de- scribe multilayer response. A program using presented theory was developed and calculations for concrete structure were made. Multilayer parameters were cho- sen to correspond with those of a sample whose magneto-optical response was measured at the Department of Chemical Physics and Optics, MFF UK. 1

David Wagenknecht: Abstract of a diploma thesis Optical response of magnetic materials, 2014 Magnetooptical properties of anisotropic semiconductors are studied to describe asymmetry of Ga1−xMnxAs, because theoretical calculations predict extraordinary behaviour of reflectivity. Analytical formulae to describe materials with non-diagonal permittivity are derived and they are used for the numerical calculations to describe the optical response of the samples available for the measurement. The transversal Kerr effect is calculated and it exhibits asymmetry in both rotation of the plane of polarization and ellipticity of circularly polarized light due to asymmetry in reflectivity. Moreover, longitudinal and polar magnetization are studied because of the influence on the observability of the phenomena. Results are not only used to discuss conditions, which must be satisfied to prove the asymmetry, but also the actual experimental setup is designed to prepare the measurement. 1

In the presented thesis the topic of femtosecond pulse dispersion and methods of characterizing pulse profile are briefly introduced. Then, a functionality of a spatial light modulator is described. The spatial light modulator was used in an experimental scheme called the pulse shaper, which allowed independent amplitude and phase modulation of pulses. Duration and dispersion of pulses was measured by two methods called MIIPS and PICASO. MIIPS was also used for a reconstruction of a spectral phase of pulses. The autocorrelator was constructed on a design of the Mach-Zehnder interferometer. The duration of the shortest measured pulse (13.3 ± 0.5) fs was retrieved from measured interferometric autocorrelations by PICASO. Furthermore, theoretical dependence of pulse duration on the group delay dispersion was confirmed for pulses shorter than 120 fs. The group velocity dispersion was measured for fused silica windows and for a pair of diffraction gratings in the pulse shaper. Both values confirmed theoretical expectations.

Transparent magnetic materials, among the others semiconductors, have recently come to the focus of interest in both basic and applied research because they have great potential in optical applications and they can be used in optical spectroscopy to investigate fundamental physical phenomena. The theoretical calculations introduce that these materials have some extraordinary properties like asymmetric reflectance when light impact the sample from the opposite angles. In this bachelor thesis, transfer matrix formalism is derived based on Maxwell equations, taking into account special form of effective permittivity. The reflection coefficient for one layer demonstrates, that the asymmetric reflectance appears for transversal- magnetic polarization of light and transversal magnetization in the studied material. The derived formulae are used to calculate the difference in reflectivities for the waves impacting the structure from opposite angles. Ga1−xMnxAs with different concentrations of manganese is assumed to be the essential transparent magnetic layer in the sample. 1