s-Polarized nonlinear surface polaritons

An exact solution of Maxwell's equations is found, corresponding to ans-polarized nonlinear surface polarition, at the planar interface between two dielectric media, one of which is optically unaxial and is characterized by a diagonal dielectric tensor whose elements depend on the amplitude of the electric field according to ₁₁=₂₂=₀()+a() (|E ₁|²+|E ₂|²), ₃₃=(). Such modes have no counterpart in the corresponding linear system.     

Band-gap structure of the spectrum of periodic Maxwell operators

We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR ³, is considered. The medium is assumed to consist of two components: the background, where (x) = _b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = _a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = _b / _a are chosen in such a way thatL ^–2, and quantities ^-1-3/2 and ² are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(^3/2)^-1 of the set {² L ^-2 k ²:kZ³}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.     

Reflection and Absorption Spectra of Fluorite in the UV Spectral Region

We have calculated the R(E) and ₁(E) spectra from the theoretical ₂(E) spectra of five models in the region 8–27 eV and the ₂(E) and ₁(E) spectra from the experimental R(E) spectrum in the region 6–35 eV. The results are compared with the known theoretical ₂(E) spectra of five models. The basic features of all of the R(E), ₂(E), and ₁(E) spectra have been revealed. It is established that the experimental R(E) spectrum and the ₂(E) and ₁(E) spectra calculated with the use of experimental data are in good agreement with the results of theoretical calculations for the models of ₂(E). On the basis of the known theoretical calculations of the fluorite zones, a scheme of the nature of the principal maxima of R(E) and ₂(E) is suggested.     

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions _AA , _AB , _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rate _A , B-atoms with jump rate _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special case _A = _B on a square lattice, considering three different choices of interactions with the same = _AB – ( _AA + _BB )/2: (i) _AB =, _AA = _BB = 0; (ii) _AA = 0, _AA = _BB ; = ; (iii) _AB = _BB = 0, _AA = –2. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V 0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.     

TM-polarized nonlinear waves guided by asymmetric dielectric layered structures

We found the field structure, exact dispersion relations and power flow ofp-polarized nonlinear guided and surface waves travelling along a three-component layered structure consisting of a film of thicknessd with dielectric constant _b bounded at the negativez-side by a linear medium with dielectric constant _a and at the positivez-side by a nonlinear uniaxial substrate characterized by the diagonal dielectric tensor ₁₁ = ₂₂ = + (|E ₁|² + |E ₂|²), ₃₃ = , <0 (self-defocusing medium),E ₁ andE ₂ being the components of the electric field in thex andy-direction, respectively. It is shown that for sufficiently smalld/ (: wavelength) the nonlinear wave may exist only at power flows exceeding some certain minimum values. For sufficiently larged/ to some values of the power flow there correspond two distinct values of the propagation constant. In this case with increasing of the power flow the number of waveguide modes is decreasing and for higher-order modes the film-waveguide exhibits an optical-power limiter from the above behaviour.     

Study of the ferroelectric phase transition of TlGaSe2 by dielectric,calorimetric, infrared and X-ray diffraction measurements

The real part of the dielectric constant , the heat capacityc _p, the infrared reflectivity, and the X-ray diffraction of TlGaSe₂ have been measured in the temperature range from 12 K (30K) to 300 K. Both andc _p show two anomalies at about 110 K and 120 K. A study of the hysteresis loop as well as an investigation of the dielectric dispersion in the microwave region show that the phase below 110 K is ferroelectric. The crystal structure remains nearly unchanged in the course of the phase transition. The loss of the symmetry (C2/cCc) results from small positional shifts of the T1 atoms in the ab plane accompanied by a discontinuity in the axial ratios. We suggest, that the ferroelectricity is caused by the stereochemically active electron lone pair configuration of the Tl⁺ ion. Thus TlGaSe₂ may provide the first example for ferroelectricity caused by this mechanism.     

Frequency Dependence of the Components of Dielectric Permeability and Characteristic Losses of Fluorite

The ₁(E), –Im^–1, and Re^–1 spectra of the fluorite crystal are calculated on the basis of the experimental (10–35 eV) and theoretical spectra ₂(E) (10–27 and 8–20 eV). They were employed to decompose the ₂(E) and –Im^–1 spectra into elementary components. The most intense transverse and longitudinal components of transitions and their parameters have been determined. The correlation between two types of components of transitions and their distinguishing features have been established.     

P-Polarized nonlinear surface polaritons in layered structures

We found an exact solution of Maxwell's equations, which describes the propagation ofp-polarized nonlinear surface polaritons and ofp-polarized nonlinear guided wave polaritons in two cases:i) in a film of a surface active material placed on a substrate described by a diagonal dielectric tensor whose elements depend on the amplitude of the electric field according to _{1 1}=_{2 2}= + (|E ₁|² + |E ₂|²), _{3 3}=, andii) in a film described by the same dielectric tensor (optically uniaxial nonlinear crystal) placed on a substrate with dielectric constant ₃ (optically linear medium). The power carried in the surface waves has also been exactly calculated.     

Photonic pseudogaps for periodic dielectric structures

We consider the problems of existence and structure of gaps (pseudogaps) in the spectra associated with Maxwell equations and equations that govern the propagation of acoustic waves in periodic two-component media. The dielectric constant is assumed to be real and positive, and the value of = _b on the background is supposed to be essentially larger than the value of = _a on the embedded component. We prove the existence of pseudogaps in the spectra of the relevant operators. In particular, we give an accurate treatment of the term pseudogap. We also show that if the contrast _b / _a approaches infinity, then the bands of the spectrum shrink to a discrete set which can be identified with the set of eigenvalues of a Neumann-type boundary value problem and thus can be effectively calculated.     

Two singular integrals containing a partial wave of the two-body coulomb T-matrix

The operatorsT _C,l E+i0)[–G ₀(E+i0)]^1–i andT _C,l(E+i)G ₀[–iG ₀(E+i)]ⁱ acting on spaces of Hölder continuous, differentiable and analytic functions are investigated. The results of their action are expressed in terms of explicit singular factors and terms and Hölder (differentiable, analytic) functions. The most singular part of these operators is shown to be determined by a simple functional.     

A generalized Kubo-Toyabe formula for muon spin relaxation in crystals with uniaxial symmetry

The Kubo-Toyabe semiclassical formula, describing the time development of the polarization of a particle in zero external field at a lattice site with cubic local environment, is generalized for uniaxial site symmetry. The relaxation function and, in particular, its first moments and long time asymptotics obtained in a closed form depend on the angle between polarization and the crystalc-axis and are shown to vary sensitively with the asymmetry of the field distribution at the particular muon site. Besides the exact uniaxial variant of the Kubo-Toyabe relaxation function, an approximate simple interpolation formula is also derived, which is correct for both short times and in its long time asymptotics. The two parameters (, ₁) in the uniaxial formulae can be determined by using the observed values of the second momentM ₂ for two different crystal orientations.     

Dielectric constant characterization of large-area substrates in millimeter wave band

A possibility of the dielectric constant measurement for substrates with permittivity=+i without an essential restriction on their area has been shown experimentally. The method uses frequency measurement of quasioptical dielectric resonator (QDR) with two slots oriented along the QDR radius with a dielectric substrate in one of them. Taking QDR of teflon in 8mm waveband as an example it is found that measurable values of can ran up 15 _q , where _q is the QDR material permittivity. Absolute error of the measurements is determined by an accuracy with which the permittivity of calibrated (standard) samples is known. The relative measuring error is determined by the accuracy of the QDR frequency measurement and can be quite a small. As an example the method is demonstrated forLaAlO ₃ single crystals.     

Fine Structures of the Permittivity and Characteristic Losses of Electrons in Fluorite

Experimental-computational spectra of the permittivity and characteristic losses –Im^–1 for energies in the range 5–21 eV at a temperature of 4.2 K and theoretical spectra of and –Im^–1 of a fluorite crystal are resolved into elementary transition bands. The parameters of transition bands (energies of their maxima E _i, band halfwidths H _i and areas S _i, and oscillator forces f _i) are determined. A correlation of the spectral bands of and –Im^–1is established, and their specific features are elucidated.     

Relationship between low frequency dielectric dispersion and ferroelectric phase transition in pulsed-laser-deposited Bi<Subscript>4-x</Subscript>La<Subscript>x</Subscript>Ti<Subscript>3</Subscript>O<Subscript>12</Subscript> thin film

The frequency and temperature dependence of the complex dielectric constant of Bi_4-xLa_xTi₃O₁₂ (BLT, x=0.9) ferroelectric thin film was studied in the frequency range of 10^-110⁶ Hz and the temperature range of 298673 K. A low frequency dielectric dispersion (LFDD) was found. A model was proposed to account for this observed phenomena. The complex dielectric constant data obtained in the measured frequency and temperature ranges have been found to fit very well to the dielectric dispersion relation: ^*=+i/₀+[B(i)^n-1]/₀. The knee in the log of the electrical conductivity versus the reciprocal temperature curve occurs at T_c. The activation energies associated with charge conduction are E_a,II=0.73 eV below T_c and E_a,I=0.95 eV above T_c. The occurrence of an anomaly in both the n and parameters near T_c indicates a coupling between charge carries and phonons. PACS 77.55.+f; 77.80.-e; 77.22.Jp     

Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

A derivation of the Broadwell equation

We consider a stochastic system of particles in a two dimensional lattice and prove that, under a suitable limit (i.e.N, 0,N²const, whereN is the number of particles and is the mesh of the lattice) the one-particle distribution function converges to a solution of the two-dimensional Broadwell equation for all times for which the solution (of this equation) exists. Propagation of chaos is also proven.Research partially supported by CNR-PS-MMAIT     

On the theory of electroabsorption in amorphous semiconductors

The coefficient of electroabsorption between localized states of an amorphous semiconductor in the weak electric field is evaluated. The decrease in the relative EA ₂/ ₂ F ₂ with increasing energy deficitE _g- is found to be caused by the linear decrease in the density of thermally unstable localized states in the external electric field with the absolute value of the energy inside the gap. If we take into account exciton effects in the EA the qualitative picture does not change, only the slope and the position of the turnover of the relative change in the EA depends on the exciton binding energy.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.The authors are indebted to T. F. Mazets (A. I. Ioffe PTI, Leningrad) for directing our attention to these problems and for useful discussions during the stay of one of us (E. M.) in the A. F. Ioffe Physico-Technical Institute. We thank also Ing. . Barta for useful discusions.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

Singular perturbations of piecewise monotonic maps of the interval

Let t: [0, 1] [0, 1] be a piecewise monotonic, C₂, and expanding map. In computing an orbit { ⁱ (x ₀)} _i=0 , we model the roundoff error at each iteration by a singular perturbation; i.e.,X _n+1=(X _n )+W , whereW is a random variable taking on discrete values in an interval (-&#x03B5;, ). The main result proves that this process admits an absolutely continuous invariant measure which approaches the absolutely continuous measure invariant under the deterministic map t as the precision of computation 0.