The nonlinear optical susceptibility and electro-optic tensor of ferroelectrics: first-principle study

The nonlinear optical properties of some ABO₃ materials (BaTiO₃, KNbO₃, LiTaO₃ and LiNbO₃) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO₃ structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X _ijk ⁽²⁾ (−2ω, ω, ω) over a large frequency range for ABO₃ crystals. The electronic linear EO susceptibility X _ijk ⁽²⁾ (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X _ijk ⁽²⁾ (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.     

First-principles study of the optical properties of PbFX (X = Cl,Br, I) compounds in its matlockite-type structure

We present the results of the ab initio theoretical study of the optical properties for PbFX (X = Cl, Br, I) compounds in its matlockite-type structure using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Z resulting in a direct energy gap. We present calculations of the frequency-dependent complex dielectric function ε( ω) and its zero-frequency limit ε₁ ( 0 ). We find that the values of ε₁ ( 0 ) increases with decreasing the energy gap. The reflectivity spectra and absorption coefficient has been calculated and compared with the available experimental data. The optical properties are analyzed and the origin of some of the peaks in the spectra is discussed in terms of the calculated electronic structure.     

High-frequency asymptotic behavior of T-odd optical effects

It is shown that the contribution of low-frequency excitations with characteristic energy ℏω _l to T-odd (nonreciprocal) optical effects, including spatial dispersion effects, at optical frequencies ω≫ω _l can be calculated in the zeroth-order approximation with respect to the parameter ω _l/ω. This greatly simplifies their analysis. Some of these effects are found to be frequency independent in the spectral regions where the refractive index n(ω)≈ const. It is shown that frequency-independent Faraday rotation can be observed in media with zero magnetization, including in media with zero microscopic magnetic moment density. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 510–513 (10 April 1999)     

Nonlinear optical properties of nanometer-size silver coated polydiacetylene composite vesicles and resulting Langmuir–Blodgett films

Noble metal-coated PDA composite vesicles were expected to increase the effective third-order nonlinear optical susceptibility χ ⁽³⁾(ω), due to the enhancement of the optical electric field induced by localized surface plasmon resonance. Different size (20, 50 and 80 nm) Ag colloidal nanoparticles were coated on the outer surface of polydiacetylene (PDA) vesicles to form PDA/Ag nanocomposite vesicles and the size-dependent effect of Ag colloidal nanoparticles on NLO properties enhancement has been explored. The explanation based on the competition of a size-dependent light-confinement effect and a size-dependent dielectric constant of Ag particles had been presented. Furthermore, these PDA/Ag composite vesicles were successfully immobilized onto the solid substrate by the Langmuir–Blodgett (LB) method and their linear and nonlinear optical properties were characterized, respectively. Obviously, PDA/Ag composite vesicles Langmuir–Blodgett (LB) films promoted the enhancement of the third-order NLO properties.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

On the supraluminal group velocity and the transmission of information

The calculations are reported indicating that the transmission of information through a medium with the frequency dispersion of the refractive index n(ω), where the group velocity is higher than the speed of light in vacuum, always occurs exactly with the speed of light in vacuum. This result is valid for any functional dependence n(ω).     

Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Contribution of nonequilibrium optical phonons to the Peltier and Seebeck effects in polar semiconductors

Additive contributions to the Seebeck and Peltier coefficients made by nonequilibrium longitudinal optical phonons have been calculated. The results obtained are valid for any temperature and applicable to polar nondegenerate semiconductors with low carrier concentrations. The calculated components of the thermoelectric coefficients are exponentially small in the low-temperature domain and reach a maximum at k _BT∼ħω ₀. In materials with a large carrier mass and strong electron-phonon coupling the contribution of optical phonons to the Seebeck coefficient can exceed 1 mV/K. Fiz. Tverd. Tela (St. Petersburg) 40, 1209–1215 (July 1998)     

Transport and dielectric properties of thin polycrystalline CoO films

Transport and dielectric properties of polycrystalline CoO films were studied as functions of the applied field, frequency and temperature. TheI–V plots showed that the Poole-Frenkel field emission mechanism is responsible for conduction at fields>10⁵ V/cm. The ac conductivity σ(ω), the imaginary part of the dielectric constantε ₂, and tan δ plots as functions of frequency revealed three dispersion regions. The σ(ω) andε ₂ frequency dependence indicates a non-adiabatic hopping of charge carriers at low frequencies and adiabatic hopping at high frequencies. The activation energy of a dielectric oscillator is 0.15 eV. Work supported by the Office of Naval Research.     

Microwave dielectric characterization of binary mixture of formamide with <Emphasis Type="Italic">N,N</Emphasis>-dimethylaminoethanol

Dielectric relaxation measurements of formamide (FMD)-N,N-dimethylaminoethanol (DMAE) solvent mixtures have been carried out over the entire concentration range using time domain reflectometry technique at 25, 35 and 45°C in the frequency range of 10 MHz to 20 GHz. The mixtures exhibit a principle dispersion of the Davidson-Cole relaxation type at microwave frequencies. Bilinear calibration method is used to obtain complex permittivity ɛ*(ω) from complex reflection coefficient ρ*(ω) over the frequency range of 10 MHz to 10 GHz. The excess permittivity (ɛ ^E), excess inverse relaxation time (1/τ)^E, Kirkwood correlation factor (g ^eff), activation energy and Bruggeman factor (f _B) are also calculated to study the solute-solvent interaction.      

The Probability of Entanglement

We show that states on tensor products of matrix algebras whose ranks are relatively small are almost surely entangled, but that states of maximum rank are not. More precisely, let and be full matrix algebras with m ≥  n, fix an arbitrary state ω of N, and let E(ω) be the set of all states of that extend ω. The space E(ω) contains states of rank r for every r = 1, 2, . . . , m · rank ω, and it has a filtration into compact subspaces

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Biexcitonic absorption in a disk-shaped GaN quantum dot

The present work investigates the nonlinear optical properties of a GaN quantum dot in the disk limit via the exciton and biexciton states using the compact density matrix formalism. Based on this model, we calculate the ground state energy of the exciton and biexciton states by the variation method, within envelope function and effective mass approximations. Linear and nonlinear optical absorption (α ⁽¹⁾, α ⁽³⁾) and oscillator strengths attributed to the optical transitions are obtained. The details of the behaviour of α ⁽¹⁾ and α ⁽³⁾ around the resonance frequencies and for different quantum dot geometries are presented. It is found that the size of quantum dot and the optical intensity have a remarkable effect on the optical absorption, and the biexcitonic two-photon absorption coefficient(K ₂) has also been calculated in this system. The results show that this parameter is strongly affected by the size of the quantum dot.     

ρ(ω) → π0π0γ, ρ(ω) → ηπ0γ decays in the local quark Nambu-Jona-Lasinio model

The branching ratios and photon spectra of the rare processes ρ(ω) → π ⁰ π ⁰ γ, ρ(ω) → ηπ ⁰ γ are calculated in the framework of the standard local quark Nambu-Jona-Lasinio model. Three types of diagrams are considered: the quark box and the pole diagrams with scalar (σ, α ₀(980)) and vector (ρ, ω) mesons. The obtained estimates for the widths of the processes ρ(ω) → π ⁰ π ⁰ γ are in satisfactory agreement with existing experimental data. Predictions are made for the widths of the processes ρ(ω) → ηπ ⁰ γ. The text was submitted by the authors in English.     

Studies of the second-order nonlinear optical properties of cubic boron nitride

Cubic boron nitride (cBN) is a kind of artificial wide-energy-gap semiconductor crystal, which has zinc blende structure with Td symmetry. The second-order nonlinear optical properties of cBN single crystal were investigated for the first time. Using a Q-switching Nd:YAG laser, the optical rectification and the second-harmonic generation at 532 nm from cBN single crystal were observed. In order to determine the nonlinear optical coefficient of a minute-size cBN sample, a simple method based on modified transverse linear electro-optic modulation was also introduced. This approach is convenient because it is unnecessary to know the absolute intensity of a probing beam for measuring the half-wave voltage of a cBN sample. Finally, cBN’s linear electro-optic coefficient γ₄₁=1.07×10^-14 m/V and nonlinear optical coefficient d₁₄(0,ω,-ω)=1.07×10^-13 m/V were obtained. PACS 42.65.An; 42.65.Ky; 78.20.Jq     

First principles calculations of structural,electronic and optical properties of various phases of CaS

First principles calculations have been performed within the framework of density functional theory to investigate the structural, electronic and optical properties of all four possible B1, B2, B3 and B4 phases of CaS. Apart from the standard local density approximation (LDA) and GGA (PBE), a more accurate nonempirical density functional generalized gradient approximation (GGA), as proposed by Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] for the exchange-correlation energy, E_XC, has been attempted in these calculations. Calculated electronic structure and the density of states are analyzed in terms of the contribution of Ca d states and S s and p states in determining the nature of the fundamental band gap in various phases. Reflectivity, R (ω), the real and imaginary part of the dielectric functions, ε(ω), have been calculated for all the phases and the results have been discussed and compared with the existing experimental data.     

Transmission spectra of thin CdS and CdSe crystals near higher-order isotropic points

Summary For photon energies below the absorption edge in CdS, CdSe and other II–VI crystals the polariton dispersion curves forE⊥c andE‖c (c-axis in a wurtzite crystal) corss at some points called isotropic points (IP). The occurrence of isotropic points provides the possibility of mode coupling between ordinary and extraordinary waves. Since the consequences of mode coupling on the optical properties for photon energies near the lowest IP lying much below the first excitonic state were widely discussed in recent years, more attention is now paid to isotropic points lying near the band gap and related to then=2,3, … excitonic states (?higher isotropic points?). Making use of Stahl's real density matrix approach we derive the polariton dispersion relationsk _⊥ (ω), andk _‖ (ω), for CdS and CdSe bulk crystals and determine the positions of IP's due to the crossing of theB-polariton with higherA-excitonic resonances. By the method of multiple internal reflection we calculate the transmission spectra for various crystal thicknesses (between 3 μm and 0.5 mm) and coupling mechanisms. The calculated transmission shows sharply peaked structures centred at the isotropic points.