Magneto-optical Kerr effect enhancement at the Wood's anomaly in magnetoplasmonic crystals

Magneto-optical Kerr effect enhancement in longitudinal and transversal configurations is systematically studied in one- and two-dimensional magnetoplasmonic crystals based on the nanostructured nickel films. Spectral dependences of magneto-optical effects demonstrate resonant features with the Fano-type lineshape in the spectral vicinity of the Wood's anomaly associated with excitation of surface magnetoplasmons in Voigt and Faraday configurations, respectively.     

Magneto-optical effects for detection of in-plane magnetization in plasmonic crystals

Methods for magneto-optical detection of the in-plane magnetization in a magnetic film due to the deposition of a one-dimensional metallic diffraction grating on the film have been considered. This structure is a magnetoplasmonic crystal, in which the excitation of the waveguide and plasmon modes leads to the appearance of five resonant magneto-optical effects that consist in a change of the intensity, the polarization, and the phase of the transmitted and reflected waves. The conditions responsible for the origin of these effects and their magnitude are determined by the configuration of the incident light, the parameters of the metallic grating, and the chemical composition of the magnetic layer. It has been found that the magnetophotonic intensity effects are the most optimal for the detection of the in-plane magnetization. The influence of the parameters of the metallic grating on the magneto-optical effects has been analyzed and the most optimal conditions for the observation of these effects have been determined. It has also been found that an increase in the concentration of bismuth in a magnetic dielectric material can lead to a weakening of the optical and magneto-optical responses.     

Magneto-optical permittivity tensor in crystals

The number of independent components of the permittivity tensor in a crystal displaying ferromagnetic order depends on the point group of the crystal. The paper gives the form of the magneto-optical permittivity tensor for all crystal classes in terms of the linear and quadratic magneto-optic tensors assuming an arbitrary orientation of magnetization.     

Magneto-optical defects in two-dimensional photonic crystals

We analyze the properties of magneto-optical defect states in two-dimensional photonic crystals. With out-of-plane magnetization, the magneto-optical coupling splits doubly-degenerate TE states into two counter-rotating modes at different frequencies. The strength of magneto-optical coupling strongly depends on the spatial overlap of the cavity domain structures and the cross product of the modal fields. The transport property of the resultant nonreciprocal states is demonstrated in a junction circulator structure with a magneto-optical cavity coupled to three waveguides. By a proper matching of the magneto-optical frequency splitting with the cavity decay rate into the waveguide, ideal three-port circulator characteristics with complete isolation and transmission can be achieved, with an operational bandwidth proportional to the magneto-optical constant. The proposed optical circulator in a bismuth-iron-garnet/air photonic crystal is demonstrated with finite-difference time-domain calculations and is compared to an alternative implementation of silicon/air crystal infiltrated with a single bismuth-iron-garnet domain.     

Magneto-optical effects in ultrathin structures at transversal magnetization

Procedures based on the Yeh’s 4 × 4 matrix formalism for the treatment of the electromagnetic interactions in multilayers at transversal magnetization and at an arbitrary angle of incidence are described. With the restriction to the magneto-optical effects linear in the magnetization the characteristic matrix for magnetic layer is derived. The reflection and transmission coefficients are obtained in the case of magnetic ultrathin film on substrate. The magneto-optical thin film waveguides at transversal magnetization are analysed in details and the dispersion relations for guided modes in a single layer, a bilayer, a sandwich and the approach to expand this way for waveguiding conditions in multilayers are presented. Work partially sponsored by Grant Agency of the Czech Republic, reg. No. 202/98/0235 and Ministry of Education in the frame of KONTAKT program, reg. No. ME 175/1998.     

Magneto-optical Faraday effects in dispersive properties for three-dimensional magnetized plasma photonic crystals

The dispersive properties of three-dimensional magnetized plasma photonic crystals composed of homogeneous magnetized plasma spheres immersed in isotropic dielectric host with face-centered-cubic lattices are theoretically studied based on plane wave expansion method, as the magneto-optical Faraday effects of magnetized plasma are considered. The equations for calculating the band structures are theoretically deduced. The photonic band gap and a flatbands region can be obtained. The influences of host dielectric constant, plasma collision frequency, filling factor, external magnetic field and plasma frequency on the dispersive properties are investigated in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the photonic band gap can be manipulated by the plasma frequency, filling factor, external magnetic field and host dielectric constant, respectively. However, the plasma collision frequency has no effects on photonic band gap. The location of flatbands region cannot be tuned by any parameters except for the plasma frequency and external magnetic field.     

Magneto-optical effects in Eu chalcogenides

To discuss the Faraday and Voigt effects in the Eu chalcogenides we derive a general expression for the polarizability of a system in which the important electronic transitions are from localized to itinerant orbitals. This expression is applied to a model system in which the electronic transitions take place from a 4f orbital to a 5dt_2g Wannier orbital centered at the same cell. We treat in detail the matrix elements of the electric dipole operator taking into account the many-body character of the 4f shell. The Coulomb potential of the intermediate state localized hole is included explicitely within a simple approximation. We present a numerical calculation of the frequency dependent Verdet constant and Voigt phase shift for the paramagnetic and ferromagnetic phases of EuSe. The fitting of the Verdet constant to the experimental results is fairly good and allows us to estimate the value of the integral (4f|r|5d) ? 4 × 10^?9 cm.     

Magneto-optical properties of one-dimensional conjugated magnetophotonic crystals heterojunctions

The 4 × 4 transfer matrix for the magneto-optical layer at oblique incidence is derived. With the help of the transfer matrix, the magneto-optical properties of one-dimensional conjugated magnetophotonic crystals (MPC) heterojunctions are studied. The results show that there exists a Tamm state localized at the interface between conjugated MPC. By coupling the Tamm states, high transmittance and large Faraday rotation angle can be obtained simultaneously in conjugated MPC multiple heterojunctions structure. It can be used to make novel mageto-optical device, promised to further application in optical information process.     

Magneto-optical effects of the antiferromagnetic semiconductor EuTe

The Faraday rotation and the absorption of EuTe have been measured on thin films in the fundamental absorption region from 2·0 to 4·3 eV. Above the Néel temperature,T _N =9·6 °K, we observe in the energy range of the 4f ⁷–4f ⁶ 5dt _2g transition, one minimum and two main maxima of rotation. The temperature dependence of the maxima is found to be different: for one extremum the rotation resembles the magnetization curve of an antiferromagnet with a maximum at the Néel temperature; for the second, however, the rotation shows a ferromagnetic dependence on temperature with a point of inflexion at the Néel temperature and saturation for lower temperatures.This ferromagnetic behaviour within the antiferromagnetic structure of EuTe can be explained by assuming a ferromagnetic superlattice which gives rise to a magnetic Brillouin zone. Thus the ferromagnetic peak is attributed to transitions from the localized 4f ground state to the new zone boundaries.We wish to thank Mr. H. P. Staub for technical assistance, Dr. E. Kaldis for supplying the substances and Dr. J. Muheim for the mass spectroscopic analysis. Financial support by the Schweizerische Nationalfonds zur Förderung der wissenschaftlichen Forschung is gratefully acknowledged.     

Graphs for the design of laser mirrors at normal incidence

The results of computer calculations concerning the reflectivity in the stop-band at normal incidence are given for periodic multilayer systems made out of layers of ZnS and MgF₂ of equal optical thickness. General formulae are derived to distinguish between the maxima and minima of the reflectivity at the centre of the stop-bands and for the calculation of the width of the stop-band of higher order mirrors as a function of the wavelength.The bandwidth of higher order mirrors and the reflectivity at the centre of the stop-band are presented in a number of graphs for systems with up to 18 layers on substrates with varying refractive index. Quarter-wave layer anti-reflection coatings are treated as special cases. The process of designing laser mirrors can be simplified using the graphs. They may also be useful during the evaporation process when thickness monitoring is done by optical methods. An example of a partially reflecting mirror is given. This uses a flat minimum of reflectivity at the centre of the stop-band to obtain an almost constant reflectivity over the total width of the stop-band.     

Wave reflection from inhomogeneous media at normal incidence

Wave reflection from a medium with continuously varying refractive index is examined. A differential equation is developed, the solution of which yields the back-reflected part of a wave of unity amplitude incident on a non-homogeneous medium at normal incidence.     

Magneto-optical activity of Ag at the plasma frequency

Kerr activity is observed in pure Ag films in the vicinity of the plasma resonance (3.85 eV) when subjected to a strong external magnetic field. This inherent magneto-optical behaviour of Ag in a narrow wavelength range (0.12 eV) around the plasma resonance is explained utilizing the classical Lorentz-Drude model for the off-diagonal elements of the dielectric function. This activity is a consequence of a combined effect of the weakly damped free electron system and the sharp onset ofd-band transitions. The possibility of enhancing the Kerr activity of amorphous TbFeCo alloys by Ag overlayers is also investigated.     

Magneto-optical study of the superconducting gap of MgB(2) single crystals

We present magneto-optical reflectivity results in the basal plane of the hexagonal MgB(2). The data were collected on a mosaic of MgB(2) single crystals with T(c)=38 K from the ultraviolet down to the far infrared as a function of temperature and magnetic field oriented along the c axis. In the far infrared, there is a clear signature of the superconducting gap with a gap ratio 2 Delta/k(B)T(c) approximately 1.2, well below the weak-coupling value. The gap is suppressed in an external magnetic field, which is a function of temperature. We extract the upper critical field H(c2) along the c axis. The temperature dependence of H(c2) is compatible with the Helfand-Werthamer behavior.     

Quantum reflection from a solid surface at normal incidence

We observed quantum reflection of ultracold atoms from the attractive potential of a solid surface. Extremely dilute Bose-Einstein condensates of 23Na, with peak density 10(11)-10(12) atoms/cm(3), confined in a weak gravitomagnetic trap were normally incident on a silicon surface. Reflection probabilities of up to 20% were observed for incident velocities of 1-8 mm/s. The velocity dependence agrees qualitatively with the prediction for quantum reflection from the attractive Casimir-Polder potential. Atoms confined in a harmonic trap divided in half by a solid surface exhibited extended lifetime due to quantum reflection from the surface, implying a reflection probability above 50%.     

Reflection refractometry for nearly normal incidence and at the Brewster angle

We consider and experimentally study two reflection refractometry methods involving reflection of light from the optical surface of a material for nearly normal incidence and for incidence at the Brewster angle. We analyze the sources of error in the methods, and show that it is possible to use laser radiation to measure the refractive index of materials to four decimal places. We note the advantages of the methods in preparing samples for measurements in the case of solid, liquid, film, and weakly absorbing materials.     

Dual-negative-refraction and imaging effects in normal two-dimensional photonic crystals with hexagonal lattices

A novel dual-negative-refraction (DNR) effect is studied in two types of normal two-dimensional photonic crystals (2DPCs) with hexagonal lattices. Systematical analyses of the band structures and equifrequency surfaces indicate that the DNR may be realized when the overlapping second and third bands with relatively flat shapes and only a slight separation are available at some frequencies close to the band's peak of 2DPCs. Further simulations have not only confirmed the DNR and corresponding dual-imaging effects in normal 2DPCs with hexagonal lattices but also revealed some relative rules to the dual images. In particular, the thickness as well the cutoff value at terminations of PCs can strongly influence the performance of dual images and even determine whether the dual images would appear. Moreover, a relatively low working frequency is recommended to minimize the distortion degree of dual images.     

Energy distribution of reflected ions at normal incidence on the target surface

Summary The energy distribution of reflected ions at normal incidence of the primary beam on the target surface is obtained as a result of approximate solution of the Boltzmann equation by the method of discrete streams. This method gives the opportunity to avoid the problem of negative distribution function, arising in the generally applied method of spherical harmonics, and to present the final result in analytical form. The analysis is performed for a power scattering cross-section and the theoretical energy distribution demonstrates one maximum when the ion mass is equal to the mass of a target atom, and two maxima when the ion mass is much less than the mass of a target atom.