In our previous work, we estimated the mass of an Abrikosov vortex in a nearly optimally doped YBaCuO film at 45 K using circular dichroism at terahertz (THz) frequencies. In this paper, we want to underline the relevance of our method, propose improvements of our experimental approach, provide a detailed description of the calculations leading to the evaluation of the vortex mass, and present an explanation of its variation with frequency. We also partially study the case of a slightly underdoped film deposited on a different substrate.

We demonstrate an experimental method of determining the mass of Abrikosov vortices in a superconductor. For a nearly optimally doped thin $\mathrm{YBa}_2\mathrm{Cu}_3\mathrm{O}_{7-\delta}$ film, we found the value of a diagonal mass amounting to $2.2\times 10^{8}$ electron masses per centimeter $(\mathrm{m}_{\mathrm{e}}/\mathrm{cm})$ at $45\mathrm{~K}$ and in the zero-frequency limit, and an even larger off-diagonal mass of $4.9\times 10^{8}\mathrm{~m}_{\mathrm{e}}/\mathrm{cm}$.

Mass of Abrikosov vortices defied experimental observation for more than four decades. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBaCuO film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of 2.2 x 10^8 electron masses per centimeter at 45 K and zero-frequency limit and even larger off-diagonal mass of 4.9 x 10^8 electron masses per centimeter.

Soft magnetic wires and microwires are currently used for the cores of magnetic sensors. Due to their low demagnetization, they contribute to the high sensitivity and the high spatial resolution of fluxgates, Giant Magnetoimpedance (GMI), and inductive sensors. The arrays of nanowires can be prepared by electrodeposition into predefined pores of a nanoporous polycarbonate membrane. While high coercivity arrays with square loops are convenient for information storage and for bistable sensors such as proximity switches, low coercivity cores are needed for linear sensors. We show that coercivity can be controlled by the geometry of the array: increasing the diameter of nanowires (20 µm in length) from 30 nm to 200 nm reduced the coercivity by a factor of 10, while the corresponding decrease in the apparent permeability was only 5-fold. Finite element simulation of nanowire arrays is important for sensor development, but it is computationally demanding. While an array of 2000 wires can be still modelled in 3D, this is impossible for real arrays containing millions of wires. We have developed an equivalent 2D model, which allows us to solve these large arrays with acceptable accuracy. Using this tool, we have shown that as a core of magnetic sensors, nanowires are efficiently employed only together with microcoils with diameter comparable to the nanowire length.

We report the design, construction, and testing of a broadband-tunable terahertz circular polarizer, which we developed for our magneto-optical measurements using the far-infrared/THz laser source in the range of 0.25-7.5 THz. We present a thorough analysis of the lock-in amplifier signal generated by using a rotating analyzer with regard to setting the desired state of polarization. The phase-sensitive detection method is applied to a combination of a wire-grid polarizer and a parallel translation mirror providing a tunable retardance. The proposed technique is appropriate not only to free-standing grids but also to those deposited on transparent substrates which may introduce additional non-linear effects. The method is preferred when the distance between the mirror and the grid cannot be exactly determined, but the relative displacements are measured. The device enables switching between left- and right-handed polarization states on a time scale of a few seconds. Practical use of the circular polarizer is demonstrated by directly probing the far infra-red magneto-optical properties of the two-dimensional electron gas on the 458 μm laser line.

Transmission of terahertz waves through a thin layer of the superconductor NbN deposited on an anisotropic R-cut sapphire substrate is studied as a function of temperature in a magnetic field oriented parallel with the sample. A significant difference is found between transmitted intensities of beams linearly polarized parallel with and perpendicular to the direction of applied magnetic field.

We studied a thin superconducting NbN film in magnetic fields up to 8 T above the zero- temperature limit by means of time-domain terahertz and scanning tunneling spectroscopies in order to understand the vortex response. Scanning tunneling spectroscopy was used to determine the optical gap and the upper critical field of the sample. The obtained values were subsequently used to fit the terahertz complex conductivity spectra in the magnetic field in the Faraday geometry above the zero temperature limit. These spectra are best described in terms of the Coffey-Clem self-consistent solution of a modified London equation in the flux creep regime.

We provide a thorough analysis of THz properties of BCS-like superconducting thin films. Temperature and frequency dependence of complex conductivity in zero magnetic field is discussed by utilizing the Zimmerman et al. explicit BCS based formula [Physica C 183 (1991) 99]. We extend this approach by employing the effective medium theory and develop a phenomenological model capable of accounting for the influence of external magnetic field. Using Yeh powerful formalism [Surface Sci. 96 (1980) 41] we calculate optical transmission of linearly polarized laser beam normally incident to a multilayered sample consisting of a thin NbN film grown on birefringent sapphire substrate, entirely covering ranges of interest in temperature and frequency. A proposal to exploit linear polarization of the incident beam parallel with principal axes of conductivity tensor is explained and theoretical predictions for a realistic NbN sample are computed and discussed.

We report far-infrared optical properties of a NbN superconductor. Transmission through a high-quality NbN film grown on a birefringent sapphire substrate above and below its superconducting transition down to the zero-temperature limit is measured at six different frequencies from 0.4 to 2.5 THz both above and below its optical gap. The experimental results agree with theoretical calculations developed based on utilization and extension of the BCS model of Zimmermann et al. [Physica C 183, 99 (1991)] applied for the NbN film. Full quantitative agreement over the entire ranges of temperature and frequencies is found based solely on the physical properties of this NbN film sample and on the parameters of an identical sapphire substrate as measured in time-domain spectroscopy experiments, without use of any additional fitting parameters.

We report far-infrared optical properties of a thin NbN superconductor in magnetic field, B, up to 10 T. Transmission, Tr (T,B), of monochromatic linearly polarized laser beam with frequency below and above an optical gap is measured both below and above T-c. Tr(T,B=0) is well described by the BCS-based model that approximates the sample as a mixture of superconductors with different T-c. T-r(T,B not equal 0) appears qualitatively different for Voigt and Faraday geometry. To calculate optical properties, we use Bruggeman's approach and present a phenomenological model accounting for both field orientations. The model captures all observed features of the Tr(T,B) data.

Transmission of terahertz waves through a thin layer of the NbN superconductor deposited on a sapphire substrate was studied as a function of temperature in zero field as well as in magnetic field perpendicular to the sample. For photon energies lower than optical gap, detailed temperature measurements in zero field provide BCS-like curves with a pronounced peak below the critical temperature. In accordance with the BCS model, the temperature peak disappears as the energy of incident radiation is increased above the gap. In non-zero field, the temperature behavior of transmission is modified because the gap is suppressed and vanishes at upper critical field. In addition, the presence of quantized vortices in the superconducting film substantially changes shape of the temperature curves.

An optical equipment has been developed, which is originated with two mirrors shaped like an ellipsoid of revolution. Firstly it is found that the pseudo Brewster angle for an absorbing substrate becomes small with increasing a nonabsorbing film thickness. The thickness of a dielectric thin film can be measured on a metal substrate in the visible region. Secondly a plane-parallel plate serves as an interferometer and the coefficient of finesse for an S-polarized plane wave increases with increasing an incident angle. Thus the refractive index of a thin film on the plate can be measured in the millimeter wave region.

Temperature dependence of far-infrared transmission of NbN thin films deposited on MgO and Si substrates was measured at several frequencies from 0.4 to 4.3 THz. Activated exponential increase of relative penetration depth at low temperatures and a peak in transmission near Tc were observed for frequencies below the optical gap. On the other hand, the transmission measured at frequencies above the gap exhibits only flat, almost linear temperature dependence. This behaviour is consistent with the BCS theory of superconductivity. Similar measurements were performed also on YBa2Cu3O7−δ thin films deposited on MgO and sapphire substrates. Low-temperature variation of transmission indicates the d-wave symmetry. The peak below Tc predicted by the BCS theory is not observed. Flat temperature dependence of transmission at higher frequencies shows that the photon energy was sufficient for excitation over the optical gap. The s-wave BCS theory is adequate for NbN films but not for the YBa2Cu3O7−δ materials. Using the theoretical BCS model we show that the transmission peak is not correlated to the coherence peak in real conductivity at given frequency and other parameters relevant to experiment.

Measurements of the far-infrared magnetotransmission of YBa2(ZnxCu1−x)3O7−δ thin film (x∼0.025) deposited on a wedged MgO substrate are reported. The application of magnetic field perpendicular to the ab plane produces at low temperature a linear increase of transmission for frequencies below ∼30cm−1. We present a model of high-frequency vortex dynamics which qualitatively explains these results.

Optical absorption and Faraday rotation of vacancy-defective spinel Mn-ferrite thin films Mn1.18Fe1.82O4+δ were studied in the visible and near-infrared regions. To introduce cation vacancies the films were oxidised between 150 C and 475°C. The resulting decrease of the absorption brought about the figure of merit of oxidised samples below 480 nm superior to that of the original Mn-ferrite films.

The Faraday rotation and optical absorption of the Co- and Ti-substituted barium hexaferrite thin films measured in the 500–2000 nm wavelength range at room temperature are presented together with the results of the Faraday rotation measurements carried out on selected samples at 80 K. The spectral dependences of the Faraday coefficient are described and interpreted using a set of optical electron transitions belonging to either cobalt or iron cations occupying the tetrahedral and/or octahedral positions in the spinel blocks of hexagonal ferrite crystal lattice.

Optical and magneto-optical properties of several single and layered Co-, Ti- and Al-substituted hexaferrite thin films prepared by the sol-gel method were investigated. The Faraday coefficient exhibits pronounced extrema in the infrared and visible part of the spectra. Broad maxima of the figure of merit at 700 to 900 and 1400 to 1800 nm regions show that some of the materials could be considered as the candidates for magneto-optical recording materials at interesting laser wavelngths of 800 and 1500 nm.

To study the crystal field (CF) at praseodymium sites in praseodymium gallium garnet (PrGG) we investigated experimentally and theoretically its Raman scattering, magnetization, and far infrared magnetotransmission. The experimental data can be described by a set of CF parameters which are rather close to those available for analogous neodymium-doped rare earth gallium garnets.

Faraday rotations of the BaCoxTixFe12-2xO19 (0 ≤ x ≤ 0.8) hexagonal ferrite films, prepared by the dip-coating method, were measured in the range from 500 to 2500 nm at room temperature. Spectra of cobalt and titanium doped ferrite films showed local extrema at 625, 750, 1475 and 1725 nm which are due to the presence of Co2+ in tetrahedral positions.