Field transformation in a multimode optical waveguide with random irregularities of the film surface

A self-consistent mathematical model for the transformation of the average intensity of the mode spectrum I(z) of a waveguide field in a multimode planar optical waveguide with a step profile and rough surface is developed. This model is based on the matrix model for multiple scattering of modes in an optical waveguide. The elements of the intermode scattering matrix are found, which describe the process of mutual transfer of the energy of modes along a waveguide and their transformation into radiation modes. The transformation of the I(z) modes in waveguides with large-and small-scale inhomogeneities is investigated. It is shown that the largest qualitative differences in the noted dependences manifest themselves only in the initial portions of the optical waveguide. The length z of these portions is much smaller than the characteristic scale length L _k at which the fundamental energy of the kth mode excited in the optical waveguide is renewed. The effect of self-filtration of the mode spectrum I(z) is described, as a result of which a stable (normalized), independent of distance z, distribution I* is formed. It is established that irregularities of the optical waveguide boundaries exert a depolarizing effect on a guided light beam. The specific features of the normalization of the radiative dissipation of a group of modes I_i(z) in an optical waveguide are investigated. It is ascertained that, in the case of small-scale irregularities, the attenuation coefficient is described by a nonlinear monotonic dependence α(z), which asymptotically converges to the value α*, characteristic of the normalized field I*. When the optical-waveguide film has large irregularities, the dependence α(z) is characterized by a pronounced maximum due to the formation of alternative channels of radiative dissipation of the energy of waveguide modes.     

Behavior of dirty superconductors in high magnetic fields

This paper discusses some properties of homogeneous, dirty superconductors, where the motion of electrons in the normal state can be described as a diffusion process. It is shown that at the nucleation field (H _e2 orH _e3) corresponding to the onset of superconductivity, the order parameterΔ(r) satisfies a linearised equation which has the Landau-Ginsburg form atall temperatures. This considerably extends the validity of the existing calculations ofH _e2 andH _e3; it is possible to show in particular that the ratioH _e3/H _e2 and the form of the angular dependence ofH _e3 are independent of temperature. It is also possible to compute explicitely the local density of statesN(r,ω), at any pointr and energyω, for fields slightly belowH _e2 (orH _e3), when the order parameter is stronglyr-dependent. Due to some remarkable sum rule propertiesN (r,ω) depends only on the local value of the order parameterΔ(r). These results may be of use in the interpretation of tunneling experiments on the mixed state and on surface superconductivity.     

Minimization of losses and calculation of the optical properties of Bragg fiber waveguides with a hollow core

A numerical method for solving the inverse problem of determining the geometry of the multilayer shell of a Bragg waveguide that has the lowest waveguide losses for a given mode has been developed with the use of the genetic algorithm. For the calculated designs of waveguides, the distribution of the coordinates of the boundaries of shell layers has been found to be aperiodic under the condition r ₁ ≤ λ due to the axial symmetry of the problem. Waveguide losses for the TE ₀₁, TM ₀₁, and HE ₁₁ modes satisfy the conditions \(\alpha _{TM_{01} } > \alpha _{HE_{11} } > \alpha _{TE_{01} } \). It follows from the dependence of n _eff obtained for these modes on the core radius and number of shell layers that any change in the structure of the waveguide leads to the violation of the optimal propagation regime for these modes. A Bragg fiber waveguide with a hollow core that is designed for the TE ₀₁ mode and directs light in the single-mode regime is presented. The main fraction of losses in this waveguide is attributed to material absorption.     

A spectroscopic prism coupler for measuring the refractive indices and thicknesses of dielectric films

A spectroscopic prism coupler is created for measuring refractive indices n_f and thicknesses H_f of dielectric films. The operating principle of the device is based on the simultaneous resonance excitation of several waveguide modes in a film by a focused TE or TM polarized light beam in the geometry of frustrated total internal reflection. Calculations of n_f and H_f are performed using measured angular positions θ_m of dark m-lines in the cross section of the specularly reflected beam. Using obtained angles θ_m, we can calculate effective refractive indices β_m of modes. By solving a set of nonlinear dispersion equations for the modes of a planar waveguide, we can calculate refractive index n_f and thickness H_f of a film. The proposed prism coupler has no moving parts and allows us to measure the optical parameters of films 0.5–10 μm thick in the 400–1100 nm range of wavelengths. The device can also be used as a spectroscopic refractometer for measuring the refractive indices of bulk media. The device is used to measure refractive index and thickness of a SiO film and the refractive index of TF4 glass.     

Sound attenuation in a random waveguide when using a radiating system with different patterns of directivity

Using numerical simulations of sound propagation on Russia’s shallow Arctic shelf, low frequency sound attenuation is analyzed for acoustic sources with different patterns of directivity, i.e., vertical discrete radiating arrays of different length. It is shown that sound attenuation depends largely on the parameters of patterns of directivity and the intensity of surface waves even at short ranges r from a source (r < 250H, where H is the waveguide depth).     

Planar anisotropic Mikaelian lens on the basis of EBG-structure

The problem on the synthesis of a planar Mikaelian lens in the form of layered metal?dielectric waveguide with a nonuniform anisotropic dielectric layer is solved. The problem is reduced to solution of the dispersion equations for E and H modes of a homogeneous layered waveguide. As an example of implementation of the solution obtained, the synthesis and analysis of the Mikaelian lens is carried out on the basis of the EBG structure in the form of a planar corrugated open and closed layered metal?dielectric waveguide. For a special case of the closed waveguide, the solution of the problem of synthesis for both polarizations is obtained explicitly.     

The effects of the composition,temperature and geometry on the hysteretic properties of the Ising-type barcode nanowire

In the present study, a theoretical approach to investigate the magnetic hysteresisproperties in barcode nanowire are used and applied to study Ising system on hexagonalstructure. The hysteresis behaviors of Ising-type barcode nanowire (IBN) are studiedwithin the effective-field theory with correlations. The effects of the composition(p),temperature (T) and geometry (interlayer length (d), shell length(s), andwire length (r)) on the hysteresis behaviors are examined indetail. The phase diagrams are presented in the five different planes, namely(p,T),(d,r),(d, T), (r, T) and (s, T) as function of coercive field (H _C ) and remanence(M _r ), and investigatedsoft/hard the magnetic characteristics of the system. We find that the hysteresis loopsareas decrease case as the temperature, wire and lengths increase. Moreover, whenp increasesthe hysteresis loop areas increase. Moreover, H _C exhibits an increasein around d =1 value, then H _C does not change withthe increasing d values. Theoretical results have qualitativelycompatible with some experimental works of multilayer nanowire.     

High-frequency susceptibility and ferromagnetic resonance in multidomain thin films of the yttrium-iron garnet type

The field dependence of the high-frequency susceptibility and the ferromagnetic resonance were experimentally studied in a thin (d≈0.1 µm) (111)-oriented single-crystal film of substituted yttrium-iron garnet with the factor q?1. It was shown that the anomaly in the high-frequency susceptibility observed in a magnetic field H parallel to the normal to the film surface in the magnetization saturation region (H≈H_s) has a dual nature; more specifically, this anomaly is associated with an abrupt collapse of the stripe domain structure and a ferromagnetic resonance in the experimental configuration H ∥ [111] and h ⊥ H. In this case, the film transition from the inhomogeneous multidomain state to the homogeneous (single-domain) state at the point H≈H_s has no indications of a second-order phase transition. The experimental frequency-field dependence of ferromagnetic resonance (FMR) in the sample under study, having a characteristic minimum at the point ω₀=5 MHz and H_FMR=H_s, agrees qualitatively and quantitatively with calculations. The influence of the cubic magnetic anisotropy and the film thickness on the FMR spectrum and the orientation of the spontaneous magnetization in domains with respect to the film plane in the zero field H was theoretically studied.     

Magnetization behavior and metamagnetic transitions in electron-doped manganites induced by a strong magnetic field

The behavior of magnetization M of the R_xA_1?xMnO₃ manganites (R=La, Pr, Nd, Sm, etc., A=Ca, Sr, Ba) in the electron doping region (x<0.4) is studied as a function of external magnetic field H. The M(H) relations for homogeneous magnetic structures are obtained by performing band calculations in the double-exchange model. Three different types of magnetization behavior corresponding to three electron concentration ranges (x<0.14, 0.14<x<0.27, x>0.27) are revealed. The M(H) relations are interpreted in terms of the phase diagram for the homogeneous ground state of the manganites calculated for H=0, and the results agree qualitatively with experimental data on the magnetization of Sm_xCa_1?xMnO₃.     

Asymmetric planar luminescent waveguide based on amorphous silicon carbide with polarized radiation in leaky modes

Plasma-enhanced chemical vapor deposition is used to fabricate asymmetric planar luminescent waveguides (APWs) based on amorphous silicon-carbide films with submicron thickness on quartz substrates. Narrow peaks of linearly (P and S) polarized radiation related to the emission in the APW leaky modes are detected in the APW emission spectra from the end surface of a substrate under excitation of photoluminescence. The dependence of the spectral positions of peaks on the angle at which the radiation is emitted from the end surface and the film thickness is analyzed. At grazing angles of emission, the radiation wavelength is almost independent of the angle. It is demonstrated that the difference between the wavelengths of the P- and S-polarized peaks in the PL spectra decreases with an increase in the waveguide thickness. The waveguide works as an optical microcavity for leaky modes. The amplitude of the S-polarized peak is higher than the amplitude of the P-polarized peak due to the fact that the Q factor for the S-polarized leaky modes is greater than the Q factor for the P-polarized leaky mode. The luminescent APWs can be used to generate optical beams with radial and azimuthal polarizations.     

Intrinsic Localized Modes in Quantum Ferromagnetic XXZ Chains in an Oblique Magnetic Field

A semiclassical study of intrinsic localized spin-wave modes in a one-dimensional quantum ferromagnetic XXZ chain in an oblique magnetic field is presented in this paper. We quantize the model Hamiltonian by introducing the Dyson-Maleev transformation, and adopt the coherent state representation as the basic representation of the system. By means of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude can be reduced to the standard nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, when θ < θ _c a bright intrinsic localized spin-wave mode appears below the bottom of the magnon frequency band and when θ > θ _c a dark intrinsic localized spin-wave resonance mode can occur above the bottom of the magnon frequency band. In other words, the switch between the bright and dark intrinsic localized spin-wave modes can be controlled via varying the angle of the magnetic field. This result has potential applications in quantum information storage. In addition, we find that, at the boundary of the Brillouin zone, the system can only produce a dark intrinsic localized spin-wave mode, whose eigenfrequency is above the upper of the magnon frequency band.     

Magnetic properties of Fe<Subscript>3</Subscript>C ferromagnetic nanoparticles encapsulated in carbon nanotubes

The low-temperature dependences of magnetic characteristics (namely, the coercive force H _c , the remanent magnetization M _r , local magnetic anisotropy fields H _a, and the saturation magnetization M _s ) determined from the irreversible and reversible parts of the magnetization curves for Fe₃C ferromagnetic nanoparticles encapsulated in carbon nanotubes are investigated experimentally. The behavior of the temperature dependences of the coercive force H _c (T) and the remanent magnetization M _r (T) indicates a single-domain structure of the particles under study and makes it possible to estimate their blocking temperature T _B = 420–450 K. It is found that the saturation magnetization M _s and the local magnetic anisotropy field H _a vary with temperature as ～T ^5/2.     

On the theory of the resonant interaction of electrons with a high-frequency electric field in one-dimensional two-barrier nanostructures with symmetric barriers of finite height and width

The theory of the interaction of electrons with a high-frequency electric field in one-dimensional two-barrier nanostructures with symmetric barriers of finite height and widths was developed. An exact solution to the Schrödinger equation was found for electrons in this nanostructure in the absence of high-frequency electric field. An analytical expression for the direct current I ₀ induced in this structure by an incident electron flux with energy ε differing slightly from the resonant level energy ε _r (|ε ? ε _r | << ε _r ) was derived. In the small-signal approximation, the active (field-phased) component I _c of the alternating electric current was calculated. At ε > ε _r , the current I _c is negative in the entire frequency range, which suggests the possibility of ac electric field amplification and generation in the two-barrier resonant-tunneling structure with the barriers of finite height and width. Within the applicability of the theory (?ω << ε _r ), the frequency at which amplification and generation of the ac electric field are possible reaches ω ? 10¹³ s ^?1; the power transferred by electrons to the field is ～1 W/cm².     

Reconditioning in Discrete Quantum Field Theory

We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x ₀,r) where x ₀ and r are positive integers representing time and maximal total energy, respectively. The operator S(x ₀,r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x ₀,r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each (x ₀,r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter.     

Field dependence of the superconducting properties induced by proximity effects: Breakdown fields

It has been shown that the proximity-effect induced superconductivity in the normal partN of a superconductor-normal metal binary layer (such asIn Bi/Zn) can screen a magnetic field up to a critical fieldH _b. AtH _b, a sharp penetration of flux intoN occurs. However, the breakdown fieldH _b can only be observed for certain values of the thickness ofN and of temperature. We study here the domain of existence ofH _b as a function of these two parameters. We also show that studies onH _b yield some information on the properties of the pair potential inN. Thus measurements onH _b performed at the critical temperature ofN confirm the theoretical predictions concerning the remarkable behavior of the order parameter inN at this temperature.     

Antiferromagnetic Resonance in GdB<Subscript>6</Subscript>

The electron spin resonance has been measured for the first time both in the paramagnetic phase of the metallic GdB₆ antiferromagnet (T_N = 15.5K) and in the antiferromagnetic state (T < T_N). In the paramagnetic phase below T* ~ 70 K, the material is found to exhibit a pronounced increase in the resonance linewidth and a shift in the g-factor, which is proportional to the linewidth Δg(T) ~ ΔH(T). Such behavior is not characteristic of antiferromagnetic metals and seems to be due to the effects related to displacements of Gd³⁺ ions from the centrosymmetric positions in the boron cage. The transition to the antiferromagnetic phase is accompanied by an abrupt change in the position of resonance (from μ₀H₀ ≈ 1.9 T to μ₀H₀ ≈ 3.9 T at ν = 60 GHz), after which a smooth evolution of the spectrum occurs, resulting eventually in the formation of the spectrum consisting of four resonance lines. The magnetic field dependence of the frequency of the resonant modes ω₀(H₀) obtained in the range of 28–69 GHz is well interpreted within the model of ESR in an antiferromagnet with the easy anisotropy axis ω/γ = (H ₀ ² +2H_AH_E)^1/2, where H_E is the exchange field and H_A is the anisotropy field. This provides an estimate for the anisotropy field, H_A ≈ 800 Oe. This value can result from the dipole?dipole interaction related to the mutual displacement of Gd³⁺ ions, which occurs at the antiferromagnetic transition.     

Nonergodic state of relaxation ferroelectric Cd<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>7</Subscript> in a constant electric field

The temperature dependence of the residual polarization of the nonergodic relaxation state (NERS) obtained from the measurements of pyroelectric current during zero-field heating (ZFH) in the temperature interval from 10 to 295 K is investigated for the Cd₂Nb₂O₇ relaxation system in two cases: (1) after sample cooling in a constant electric field E (FC) from T = 295 K to a preset temperature, which is much lower than the “freezing” temperature of the relaxation state (T _f ≈ 182 K), field removal, and subsequent cooling in zero field (ZFC) to T = 10 K and (2) after ZFC from T = 295 K to the same temperature below T _f , application of the same field, and FC to T = 10 K. The behavior of the P _r ^FC (T) and P _r ^ZFC (T) dependences is analyzed. In the field E < 2 kV/cm, the P _r ^ZFC curves as functions of 1/T have a broad low-intensity peak in the region T ≈ T _f , which vanishes in stronger fields, when the P _r ^FC (1/T) curves intersect at T ≈ T _f and have no anomalies. The difference in the behavior of P _r ^ZFC (T) and P _r ^FC (T) indicates the difference in the nature of NERS formed during ZFC and FC of the system upon a transition through T _f . In the ZFC mode, NERS exhibits glasslike behavior; in the FC regime, features of the ferroelectric behavior even in the weak field. Analogous variations of P _r ^ZFC (T) and P _r ^FC (T) in a classical ferroelectric KDP are also given for comparison.     

Temperature dependence of the surface upper critical field of superconducting alloys

The temperature dependence of the surface upper critical field,H _c3, nearT _c is calculated for arbitrary values of the mean free pathl by taking into account the fourthorder term of the generalized Ginzburg-Landau theory. For finitel the boundary condition is modified such that the normal derivative of the energy gap at the surface becomes positive. The slope of the curveH _c3/H _c2 versust=T/T _c att=1 is found to decrease monotoneously from zero to ?1.040 as one goes from the “dirty” to the “clean” limit.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

Controlling depinning and propagation of single domain-walls in magnetic microwires

The magnetization reversal in magnetostrictive amorphous microwires takes place by depinning and propagation of a single domain wall. This is a consequence of the particular domain structure determined by the strong uniaxial anisotropy from the reinforcement of magnetoelastic and shape contributions. In the present study, after an overview on the current state-of-the art on the topic, we introduce the general behaviour of single walls in 30 to 40 cm long Fe-base microwires propagating under homogeneous field. Depending on the way the walls are generated, we distinguish among three different walls namely, standard wall, DW _st , depinned and propagating from the wire’s end under homogeneous field which motion is the first one to switch on; reverse wall, DW _rev , propagating from the opposite end under non-homogeneous field, and defect wall, DW _def , nucleated around local defect. Both, DW _rev and DW _def are observed only under large enough applied field. In the subsequent section, we study the propagation of a wall under applied field smaller than the switching field. There, we conclude that a minimum field, H _dep,0, is needed to depin the DW _st , as well as that a minimum field, H _prop,0, is required for the wall to propagate long distances. In the last section, we analyse the shape of induced signals in the pickup coils upon the crossing of the walls and its correlation to the domain walls shape. We conclude that length and shape of the wall are significantly distorted by the fact that the wall is typically as long as the measuring coils.