Non-linear optical properties of (Pb<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)TiO<Subscript>3</Subscript> thin films

Thin films of (Pb_1−x Sr _x )TiO₃, x=0,0.5,1.0 have been prepared on glass substrates by the chemical-solution method using the spin-coating technique. The optical nonlinearity in the visible spectral region is investigated using short (5 ns) laser pulses at the off-resonant wavelength of 532 nm employing the open aperture z-scan technique. It is found that the third order nonlinear absorption is dependent on the lead content of the films, with the compositions x=0, 0.5 exhibiting large values (β∼10⁻⁷ m/W), thereby suggesting the possible use of these materials as optical limiters. No optical nonlinearity is observed for the composition with x=1.0.     

Second-order nonlinear optical susceptibility in chalcone-group crystalline molecular compounds

A study is reported of the second-order nonlinear optical susceptibility in polycrystalline molecular materials of the chalcone group made by second-harmonic generation at a wavelength of 1.06 μm. Some of the compounds studied exhibit a high nonlinear activity and are transparent in the blue region of the spectrum. The measured macroscopic nonlinear polarizability χ ² was compared with the calculated values of β, the second-order molecular polarizability tensor. The high nonlinear optical polarizability observed in some chalcone compounds is shown to be related to crystal symmetry type. Fiz. Tverd. Tela (St. Petersburg) 41, 2084–2087 (November 1999)     

Chaotic dynamics in the electroconvection system of a nematic liquid crystal

The transition from a steady domain structure to turbulence in the electroconvection system of a nematic under the action of a constant electric field is studied using the methods of optical and acoustic responses. The chaotic dynamics is investigated both by conventional methods (Fourier signal spectrum) and by methods of nonlinear dynamics. From the quantitative estimates of basic characteristics of the chaotic behavior (namely, the correlation dimension, leading Lyapunov exponent, K-entropy, and embedding dimension), one can conclude that temporal chaos arises in the system, giving rise to a strange attractor, as the control parameter increases at ɛ ≥ ɛ _c ≈ 0.5. The fact that the distribution of laminar domains in the liquid-crystal layer depends on their length under the conditions of developed turbulence indicates that the dynamics of the nematic demonstrates the intermittent behavior.     

Two-photon absorption of high-power picosecond pulses in PbWO<Subscript>4</Subscript>, ZnWO<Subscript>4</Subscript>, PbMoO<Subscript>4</Subscript>, and CaMoO<Subscript>4</Subscript> crystals

The nonlinear process of two-photon interband absorption is studied in tungstate and molybdate oxide crystals excited by a sequence of high-power picosecond pulses with a wavelength of 523.5 nm. The transmission of the crystals is measured for the excitation pulse intensity up to 100 GW/cm². The pulse intensity in the crystals initially transparent at a wavelength of 523.5 nm is strongly limited due to two-photon absorption (TPA), and the reciprocal transmission in PbWO₄ and ZnWO₄ crystals reaches 50–60. In all crystals, TPA induces long-lived one-photon absorption, which affects the nonlinear process dynamics and leads to a hysteresis in the dependence of the transmission on the laser excitation intensity. Absorption dichroism manifests itself in a significant difference in the transmission intensities when the principal orthogonal optical axes of the crystals are excited. The TPA coefficients are determined during the excitation of two optical axes of the crystals. TPA coefficients β for the crystals vary over a wide range, namely, from β = 2.4 cm/GW for PbMoO₄ to β = 0.14 cm/GW for CaMoO₄, and the values of β can differ almost threefold when different optical axes of a crystal are excited. Good agreement is achieved between the measured intensities limited by TPA and the estimates calculated from the measured nonlinear coefficients. Stimulated Raman scattering (SRS) upon excitation at a wavelength of 523.5 nm is only detected in two of the four crystals under study. The experimental results make it possible to explain the suppression of SRS by its competition with TPA, and the measured nonlinear coefficients are used to estimate this suppression.     

Orientational distribution function in nematic liquid crystals by x-rays: Fourier method

The existing methods for the determination of the orientational distribution functionf(β) in the nematic liquid crystals using X-rays have been reviewed. A simple Fourier method which givesf(β) in terms of the measured intensity is analysed. Using this distribution function, the accuracy with which the order parameters could be evaluated is discussed and the results show the elegance of the Fourier method used here.     

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.     

Nonlinear optical absorption and refraction in Ru, Pd, and Au nanoparticle suspensions

We present the results of studies of the nonlinear optical properties of Pd, Ru, and Au nanoparticles. We studied the nonlinear refraction and nonlinear absorption of suspensions of these nanoparticles at 1064-nm wavelength. A relatively strong nonlinear absorption of the Pd nanoparticles was observed in the case of 1064-nm, 50-ps pulses (β=2×10⁻⁹ m W⁻¹). The Ru and Pd nanoparticles showed weak negative nonlinear refraction (γ∼−(6–8)×10⁻¹⁶ m² W⁻¹) in this spectral range. In the case of the Au nanoparticles, a saturated absorption at 532 nm dominated over other nonlinear optical processes.     

Charge transport properties of undoped congruent lithium niobate crystals

Time-resolved light-induced birefringence measurements based on a phase compensation technique are used to determine the charge transport properties of congruent, nominally-undoped lithium niobate crystals (LiNbO₃). Some of the crystals are conventionally oxidized. The steady-state space-charge field E _pv, the bulk photovoltaic coefficient β, and the photoconductivity σ _ph are determined in the intensity range (30–30 000) W/cm². The photovoltaic coefficient β increases by one order of magnitude over this intensity range, the space-charge field E _pv even by two orders of magnitude. We discuss the results in the context of the known one- and two-center charge transport models for LiNbO₃. The experimental findings presented here are of relevance for the long-standing problem of optical damage in such crystals, which inhibits their use in high-intensity applications like nonlinear optics.     

Phase transitions in the framework of complete version of IMB-1

The classical energy functional of complete IBM-1 model version is studied in terms of nuclear shape variables (β, γ), employing two essential control parameters (r ₂, r ₁) used in catastrophe theory formalism. The dependence of energy surface equilibrium values from deformation parameter β is analyzed in the case when γ = 0. The results, obtained for critical points and phase transition lines between spherical (β = 0) and two deformed (β > 0, β < 0) shapes, are compared with the ones, following from the studies, in which the simplified extended Casten triangle version of interacting boson model was used. Original Russian Text ? J. Proskurins, A. Andrejevs, T. Krasta, J. Tambergs, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 241–244. The article is published in the original.     

Low frequency fluctuations of laser beam intensity run through the system of cavitation water clusters

Experiments on water cavitation in ultrasonic field have been carried out. Low frequency fluctuations of the intensity of laser beam run through the cavitation area have been studied. Experiments have proved presence of low-frequency random fluctuations with frequency dependence of power spectra, S ∼ 1/f ^α where the exponent α ranged within 0.8 ≤ α ≤ 1.2. From experimental realizations, large-scale low frequency pulsations characterized by scale invariance, which duration is distributed according to the power law, have been distinguished. The results are explained on the basis of mathematical model for the rise of scale invariant fluctuations with 1/f ^α power spectrum in the system of two nonlinear stochastic differential equations describing interaction of heterogeneous phase transitions. Distribution of extreme low frequency emissions obtained from numerical solutions to stochastic equations takes the power series form. Correlations of dynamic scaling between critical indicators determining frequency dependence of pulsations power spectra α and distribution functions of extreme low frequency pulsation amplitudes β have been determined. It is shown that both in the experiments on acoustic cavitation of water and in the theoretical model of interacting phase transitions critical indicators are bound with the correlation α + β = 2. Spectra of fluctuation power are determined in the experiments simpler and more accurately than the function of extreme amplitudes distribution. In case when only one frequency dependence of fluctuation capacity spectra is known correlations between indicators serve to obtain information on the distribution of large scale emissions and to estimate critical amplitudes.     

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density Λ. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion θ in the model is assumed to be proportional to the shear σ. This condition leads to A = βB ^m , where A and B are the metric coefficients, m is a constant and β is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

Nonlinear optical characterization of LaEr(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> thin films using the <Emphasis Type="BoldItalic">Z</Emphasis> -scan technique

The nonlinear optical properties of thin films of LaEr(MoO₄)₃ were studied using a ∼30 ps Nd:YAG laser at 532 nm with a repetition rate of 250 Hz. Closed aperture Z-scan measurement revealed a negative nonlinearity in the LaEr(MoO₄)₃. The nonlinear refractive index γ=1.38×10^-10 cm²/W and nonlinear absorption coefficient β=16.8×10^-6 cm/W were calculated from the Z-scan data. The fluorescent upconversion spectra were recorded with 980 nm excitation. An optical switching mechanism based on nonlinear absorption is also presented experimentally. PACS 81.15.Fg; 77.84.Bw; 33.50.Dq; 42.70.Mp     

Nonlinear optical absorption in Bi3TiNbO9 thin films using Z-scan?technique

Bi₃TiNbO₉ (BTN) thin films with layered perovskite structure were fabricated on fused silica by pulsed laser deposition. The XRD pattern revealed that the films are single-phase perovskite and highly (00l) textured. Their fundamental optical constants, such as band gap, linear refractive index, and linear absorption coefficient, were obtained by optical transmittance measurements. The dispersion relation of the refractive index vs. wavelength follows the single electronic oscillator model. The nonlinear optical absorption of the films was investigated by single beam Z-scan method at a wavelength of 800 nm with laser duration of 80 fs. We obtained the nonlinear absorption coefficient β=1.44×10⁻⁷ m/W. The results show that the BTN thin films are promising for applications in absorbing-type optical devices.     

Influence of quenched nonmagnetic impurities on phase transitions in a three-dimensional diluted Potts model with spin state number q = 4

The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure (p = 1.00) and weakly diluted (p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.     

Calculation of the phase diagram of the TiZr alloy and investigation of the tendency toward separation of the ω phase

The electronic, structural, and thermodynamic properties of the TiZr equiatomic alloy have been calculated in terms of the electron density functional theory and Debye-Grüneisen model. The calculated lattice parameters a and c/a agree well with experimental data for the α, ω, and β phases. It has been shown that the ω phase is stable at atmospheric pressure and low temperatures, and it remains energetically more favorable up to T = 600 K. In the temperature range 600 K < T < 900 K, the α phase becomes stable, and above 900 K, the β phase of the TiZr alloy is stable. The phase diagram constructed in this study agrees qualitatively with the available experimental data. A tendency toward separation of the TiZr equiatomic alloy in the ω phase has been analyzed. It has been demonstrated that, in the ground state, the TiZr equiatomic alloy in the ω phase exhibits a tendency toward ordering rather than toward phase separation.     

Absorption spectrum and excitons in thin films of the solid electrolyte RbCu4Cl3I2

We have investigated the absorption spectrum of thin films of the superionic conductor RbCu₄Cl₃I₂ synthesized on NaCl crystalline substrates. It is shown that the electron and exciton excitations in the energy interval 3–6 eV are associated with optical transitions in the CuHal sublattice, and the edge of the fundamental band is controlled by optical transitions in the Cu(II)Hal sublattice. It is found that the large band gap of this compound (E _g =3.86 eV) in comparison with those of CuCl and CuI is a result of the small number of Cu ions in the second coordination sphere. The temperature dependence of the spectral position and half-width of the low-temperature exciton band reveals features associated with the phase transitions γ→β (T _c1=170 K) and β→α (T _c2=220 K) and with disordering of the cation sublattice attendant to the transition to the superionic state. Fiz. Tverd. Tela (St. Petersburg) 40, 1022–1026 (June 1998)     

Enhancement of the Nonlinear Optical Absorption of the E7 Liquid Crystal at the Nematic–Isotropic Transition

We present an experimental study of the nonlinear optical absorption of the eutectic mixture E7 at the nematic?Cisotropic phase transition by the Z-scan technique, under continuous-wave excitation at 532?nm. In the nematic region, the effective nonlinear optical coefficient ??, which vanishes in the isotropic phase, is negative for the extraordinary beam and positive for an ordinary beam. The parameter $S_\textrm{NL}$ , whose definition in terms of the nonlinear absorption coefficient follows the definition of the optical-order parameter in terms of the linear dichroic ratio, behaves like an order parameter with critical exponent 0.22 ±0.05, in good agreement with the tricritical hypothesis for the nematic?Cisotropic transition.     

Low-frequency fluctuations in stochastic processes with a 1/<Emphasis Type="Italic">f</Emphasis><Superscript>α</Superscript> spectrum

The results of numerical analysis of the Brownian movement of a particle in the force field of the potential corresponding to interacting subcritical and supercritical phase transitions are considered. If the white noise intensity corresponds to the critical intensity of the noise-induced transition, the system of stochastic differential equations describes random steady-state processes with fluctuation power spectra inversely proportional to frequency f, S(f) ∼ 1/f ^α, where exponent α varies in the interval 0.8 ≤ α ≤ 1.8. Exponent β of distribution function P(τ) ∼ τ^−β for the duration of low-frequency extremal fluctuations, which are analogous to avalanches considered in the models of self-organized criticality in many respects, varies between the same limits. It is shown that exponents α and β are connected through the relation α + β = 2.     

Azimuthal dependence of the two-photon absorption coefficient for CdP2 crystals with tetragonal syngony

We studied the two-photon absorption coefficient (β) for cadmium diphosphide (CdP₂) single crystals in the tetragonal modification vs. the polarization azimuth (φ) of the incident light for intensities close to the optical breakdown (or optical damage) threshold for the crystal (11 MW/cm²). We have established that the value of β_max = 0.16 cm/MW is reached for φ = 0, i.e., for the ordinary wave. At the lasing frequency of a ruby laser, β_⊥/β_|| = 2.13, which suggests anisotropy of the two-photon absorption in the studied crystals. These dependences are needed for design and fabrication of quantum electronics and nonlinear optics elements whose operation is based on the use of the two-photon absorption effect for high radiation fluxes. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 117–121, January–February, 2009.     

Residual impurity effects on the magnetic ordering in α-Mn observed by hyperfine interaction

We report on the lattice location of indium in and the magnetic ordering of manganese in its α- and β-phases, as seen by perturbed angular correlation. Quadrupole interaction spectra show that indium prefers to replace Mn atoms of type I in α-Mn, but replaces type II atoms in the β-Mn structure. The interaction strength equalseQV _zz /h=3.6 (6) MHz in α-Mn and 172.3 (3) MHz with ν=0.13 (1) in β-Mn. No magnetic ordering down to 4.2 K was observed in β-Mn, while belowT _N =95 K in the α-Mn phase, a magnetic hyperfine interaction appears indicating two distinct magnetic probe environments. The hyperfine field, when measured atT=4.2 K, equals for 70% of the probes 6.33 (1) T, while the remaining fraction senses a 3.10 (4) T field. The magnitudes of the hyperfine fields are essentially unaffected by a variety of conditions in the sample preparation. The ordering temperature, on the contrary, turns out to be rather sensitive to residual impurities especially any oxygen contamination.