Tuning of the photonic band gaps and the reflection spectra of a one-dimensional photonic crystal based on silicon and a liquid crystal

The reflection spectra and the photonic band gaps of a one-dimensional composite photonic crystal are calculated for different filling factors (the ratio of the thickness of a silicon layer to the lattice constant A). A change in the refractive index of the filler in a photonic crystal leads to the shift of both edges for certain side photonic bands. It is shown that, with a change in the refractive index from 1.49 to 1.69, the shift of the edges (the tuning effect) can reach the value A/λ = 0.04 for the main photonic band and 0.08 for a side band. An additional criterion for designing a photonic crystal is the estimation of the sharpness of the edges of photonic bands in the reflection spectra.     

Resonant tunneling effect in one-dimensional twinned lattice photonic crystal under total reflection conditions

Under total reflection conditions, it typically seems as though light waves will be reflected completely on the interface; in actuality, the waves can penetrate the medium as evanescent waves. In this paper, we present a twinned lattice photonic crystal with a unit cell composed of AB layers and their mirror. We assume that the refractive index n ₀ of the input and output end is equal to n _B and larger than n _A . We first demonstrate the dependence of band structure on the incidence angle and normalized wavelength, in which the resonant tunneling bands are exposed. We then draw a comparison of bands between ABBA and AB. To conclude, we discuss the resonant tunneling effect in the twinned lattice photonic crystal under the total reflection conditions. As incidence angle increases, the resonant tunneling band ultimately vanishes completely.     

Electromagnetic-field amplification in finite one-dimensional photonic crystals

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

Computation of the electronic structure and direct-gap absorption spectra in Ge-rich Si<Subscript>1−x</Subscript> Ge<Subscript>x</Subscript>/Ge/Si<Subscript>1−x</Subscript>Ge<Subscript>x</Subscript> type-I quantum wells

This paper presents the results of conduction band discontinuities calculation for strained/relaxed Si_1?x Ge _x /Si_1?y Ge _y heterointerfaces in Γ _15C , Γ _2′C and L upper bands minima, as well as the room-temperature strained (vs. relaxed) band gaps deduced from the classical model-solid theory. Based upon the obtained data, we propose a type-I W-like Si_1?y Ge _y /Si_1?x Ge _x /Ge/Si_1?x Ge _x /Si_1?y Ge _y quantum wells heterostructure optimized in terms of compositions and thicknesses. Electronic states and wave functions are found by solving Schrödinger equation without and under applied bias voltage. An accurate investigation of the optical properties of this heterostructure is done by calculating the energies of the interband transitions and their oscillator strengths. Moreover, a detailed computation of the bias-voltage evolution of the absorption spectra is presented. These calculations prove the existence of type-I band alignment at Γ _2′C point in compressively strained Ge quantum wells grown on relaxed Ge-rich Si_1?y Ge _y buffers. The strong absorption coefficient (> 8 × 10³ cm^-1) and the large Stark effect (0.1 eV @ 2 V) of the Γ _2′C transitions thresholds open up perspectives for application of these heterostructures for near-infrared optical modulators.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Photonic crystals with a specified bandgap width

A new method is proposed for the production of photonic crystals with a thoroughly controlled photonic bandgap. The method is based on the synthesis of an A_1?x B _x photonic crystal with controlled parameter x based on two isostructural A and B photonic crystals such that the photonic bandgap of the A crystal is smaller and that of the B crystal is greater than the required bandgap. The method is exemplified in a (100 ? x) mol % SiO₂?x mol % ZnO inverse opal, in which the relative stop-band width monotonically increases with parameter x.     

Dielectric photonic crystal with a near-zero effective refractive index in the microwave range

The microwave propagation in a 3D dielectric photonic crystal at the frequency range from 8.5 to 12GHz has been investigated. A frequency range where effective refractive index n _ef of the crystal approaches zero is found. In the frequency range where n _ef <0.2, themicrowave beam becomes collimated, sharpened, and free of diffraction noise. An excitation of a surface wave, propagating along the external surface of the structure, is revealed in same frequency range. This property of the photonic crystal structure can be used to screen and mask objects scanned by external radiation.     

Spin observables in <Emphasis Type="Italic">np</Emphasis> elastic scattering in the energy range 200–600 MeV. Complete experiment

A survey of available experimental data on the measurement of spin observables in neutron-proton (np) elastic scattering in the neutron energy range 200–600 MeV is presented. Sixteen spin observables (the polarization of recoil particles P _0n00, the analyzing power A _00n0, the spin correlation parameters A _00nn , A _00ss , A _00sk , and A _00kk , the spin transfer parameters K _0nn0, K _0ss0, and K _0sk0, the depolarization parameters D _0n0n , D _0s0s , and D _0s0k , and the three-spin parameters N _0nkk , N _0skn , N _0ssn , and N _0sns for energies of 200–590 MeV and scattering angles in the center of mass system of 60°–164°) were studied in experiments using polarized neutron beams and polarized proton targets at the Paul Scherrer Institute. The results of these investigations present a complete set of precision data on np elastic scattering which, along with the complete set of data for proton-proton (pp) elastic scattering obtained earlier, provides a basis for unambiguous determination of the amplitudes of the scattering matrix for nucleon-nucleon (NN) elastic scattering for the channel with the isotopic spin I = 0 and makes it possible to describe NN interaction in a model-independent way.     

Investigation of the conditions of efficient I*<Subscript>2</Subscript> (342 nm) luminescence in a barrier discharge in a Kr-I<Subscript>2</Subscript> mixture

The energy and spectral characteristics of a barrier discharge in a mixture of iodine vapor with krypton have been investigated theoretically and experimentally. The emission spectrum consists of the single I*₂ molecular band D′ → A′ peaking at 342 nm, the iodine resonance line at 206.2 nm, and the group of bands corresponding to iodine emission. The highest intensity of the I*₂ (342 nm) band was obtained at a mixture pressure near 450 Torr. A mean output power and an efficiency of 550 mW and 1.6%, respectively, have been achieved. It is shown that, for the I₂ barrier-discharge excilamp, the homogeneous, rather than filamentary form of discharge glow is optimal from the viewpoint of the highest mean output power. The maximal calculated value of the emission efficiency for the 342-nm band was 5%. The main processes determining energy losses in plasma have been found, and ways to increase the efficiency of emission in the D′ → A′ band of the I*₂ molecule have been proposed.     

Topological Scenario for High-Temperature Superconductivity in Cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity ρ(T), including the observed crossover from the linear temperature behavior ρ(T, x) = A₁(x)T at doping levels x below the critical value x _c ^h corresponding to the boundary of the superconducting region to the quadratic temperature behavior at x > x _c ^h , which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient A₁(x) is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the D-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, leads to high-temperature superconductivity in the D channel.     

Luminescence of Tl<Superscript>+</Superscript> ions in a KZnF<Subscript>3</Subscript> crystal

The luminescence spectra of a KZnF₃: Tl⁺ crystal are investigated in the energy range from 4.75 to 5.9 eV at temperatures of 10–300 K upon excitation into the A absorption band (5.7–6.3 eV). At T=300 K, the luminescence spectra exhibit an intense band with a maximum at 5.45 eV, which is attributed to single Tl⁺ ions substituted for K⁺ ions. The 5.723-eV intense narrow band observed at T<20 K is assigned to the ³Γ_1u-¹Γ_1g zero-phonon transition, which is weakly allowed by the hyperfine interaction. The luminescence decay is studied as a function of temperature. The main characteristics of the luminescence spectra are adequately described in terms of the semiclassical theory based on the Franck-Condon principle and the Jahn-Teller effect for an excited sp configuration of the Tl⁺ ion with the use of the parameters obtained earlier from analyzing the absorption spectra of the system under investigation.     

Low-temperature heat capacity upon the transition from paramagnetic to ferromagnetic Heusler alloys Fe<Subscript>2</Subscript> <Emphasis Type="Italic">Me</Emphasis>Al (<Emphasis Type="Italic">Me</Emphasis> = Ti,V, Cr,Mn, Fe,Co, Ni)

The heat capacity of band magnets Fe₂MeAl (Me = Ti, V, Cr, Mn, Fe, Co, Ni) ordered in crystal structure L2₁ has been measured in the range 2 K ≤ T ≤ 50 K. The dependences of the Debye temperature Θ_D, the Sommerfeld coefficient γ, and the temperature-independent contribution to heat capacity C₀ on the number of valence electrons z in the alloys have been determined.     

Raman spectroscopy of SrB<Subscript>4</Subscript>O<Subscript>7</Subscript> single crystals in the temperature range 300–1273 K

The polarized Raman spectra of SrB₄O₇ (SBO) single crystals are studied in detail in the temperature range of 300–1273 K. The TO, LO, and IO phonon lines of A₁, A₂, B₁, and B₂ symmetries of rhombic SBO at 300 K are identified. The behavior of the Raman spectra of SBO crystals is studied upon heating up to their melting. The relation of Raman spectra with the structure of boron–oxygen fragments, as well as the transformation of spectra in the process of melting of SBO crystals, is discussed.     

Variation in the energy spectra of primary cosmic rays for 2007–2015, according to data from the URAGAN muon hodoscope

Simulations of how secondary components of cosmic rays are generated and pass through the atmosphere are performed using the CORSIKA software package. The relationship between the vertical projection of the local anisotropy vector A _Z and the index of primary particle spectrum γ is calculated. The time series of A _Z for 2007–2015 are obtained using data from the URAGAN muon hodoscope. Matrix data corrected for barometric and temperature effects are used to estimate A _Z . Using the A _Z time series, the average annual daily variations Δγ are estimated. Annual and daily variations in the slope of the energy spectrum of primary protons are observed.     

The electronic structure and optical and magnetooptical properties of the CaCo<Subscript>2</Subscript> compound synthesized at a high pressure: Experiment and theory

The optical properties (the real ε₁ and imaginary ε₂ permittivity parts, optical conductivity σ, and reflectivity R) of the new ferromagnetic compound CaCo₂ in the Laves cubic phase (C15) synthesized at a pressure of 8.0 GPa were studied over the spectral range ?ω = 0.2–9 eV. The field and spectral (?ω = 0.5–4.2 eV) dependences of the equatorial Kerr effect were determined. The electronic structure and optical characteristics of CaCo₂ were calculated using the electron density functional theory by the linearized augmented-plane-wave method. The main band structure parameters of the compound were determined. The experimental and theoretical σ(ω) and R(ω) dependences were in satisfactory agreement with each other. The formation of the main absorption bands was found to be caused by the (p,d → d,p)-type electronic transitions related to the cobalt and calcium atoms. The exchange splitting of the 3d band of CaCo₂ was estimated, 2Δ_exc ～ (1–1.3) eV.     

Electronic structure and energies of interatomic bonds in the TiSi<Subscript>2</Subscript> compound with a <Emphasis Type="Italic">C</Emphasis>49 crystal structure

Full-electron calculations of the electronic structure of the TiSi₂ compound in the structural modification C49 are performed using the augmented-plane-wave method. The total energy, the electronic band structure, and the density of states are calculated for an extended translational unit cell Ti₄Si₈, which is formed during the growth of a silicon nanowire on a p-Si substrate. Calculations are also carried out for two orthorhombic unit cells of the nonstoichiometric compositions Ti₃Si₉ and Ti₅Si₇. The energies of the interatomic bonds are determined to be E _Si-Si = 1.8 eV, E _Ti-Ti = 2.29 eV, and E _Ti-Si = 4.47 eV. The dependence of the total energy of the unit cell E _tot(V) on the unit cell volume V is obtained by optimizing the unit cell volume. The bulk modulus B ₀ = 132 GPa is determined from the Murnaghan equation of state for solids and the dependence E _tot (V). This value of the bulk modulus is used to estimate the activation energy for interstitial diffusion of silicon atoms Q _i(Si) ≈ 0.8 eV.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).