Nonlinear Electric Susceptibility Research Articles

Raman activity of the longitudinal optical phonons of the LiNbO3 crystal: Experimental determination and quantum mechanical simulation

AbstractIn this study, the and the two equivalent / polarized Raman spectra of a LiNbO3 single crystal have been recorded and used as a benchmark test for the density functional theory (DFT) calculation of the longitudinal modes and of their Raman activity. The theoretical approach, based on periodic boundary conditions and a linear combination of atomic orbitals (LCAO), provides excellent predictions of phonon wavenumbers and relative bands intensities for both A1 and E Longitudinal Optical (LO) modes and complements a previous paper limited to the study of Transverse Optical (TO) modes. Overall, the present investigation demonstrates that the LCAO approach, as implemented in the CRYSTAL software, gives results of similar accuracy for the TO and the LO phonons features. By means of a band deconvolution scheme applied to the experimental spectra, we present, for the first time, a quantitative comparison between experimental and theoretically predicted polarized Raman band intensities of LiNbO3 LO modes. This analysis highlights the role of the suitable determination of the static and high‐frequency dielectric matrices that are needed for the prediction of the TO/LO frequency split but also the first nonlinear electric susceptibility tensor for an accurate description of the Raman intensity pattern.

High sensitivity characterization of the nonlinear electric susceptibility of a glass ceramic in the microwave range

The nonlinear electric susceptibility of a glass ceramic is characterized in the microwave range by measuring intermodulation of two high-power signals. To achieve the necessary sensitivity for dielectric nonlinearities, the setup ensures that the measured intermodulation can be ascribed to the material under test while all other intermodulation sources are suppressed. This is achieved by coupling three dielectric resonators in a cut-off waveguide. The third order nonlinearity of the glass ceramic is found to be χ3/εr = (1.6 ± 0.8) × 10−15 m2/V2 at 950 MHz. The magnitude is comparable to the previously measured high-end sintered ceramics. The power of the intermodulation signal as a function of the input power deviates from the simple 3 dB/dB scaling and can be modeled by linear-nonlinear interaction.

Tuning Rashba spin-orbit coupling in homogeneous semiconductor nanowires

We use $\vec{k}\cdot\vec{p}$ theory to estimate the Rashba spin-orbit coupling (SOC) in large semiconductor nanowires. We specifically investigate GaAs- and InSb-based devices with different gate configurations to control symmetry and localization of the electron charge density. We explore gate-controlled SOC for wires of different size and doping, and we show that in high carrier density SOC has a non-linear electric field susceptibility, due to large reshaping of the quantum states. We analyze recent experiments with InSb nanowires in light of our calculations. Good agreement is found with SOC coefficients reported in Phys. Rev.B 91, 201413(R) (2015), but not with the much larger values reported in Nat Commun., 8, 478 (2017). We discuss possible origins of this discrepancy.

Second and third-order nonlinear optical properties of Er3+/Yb3+ doped PbO-GeO2-Ga2O3 glasses with Au nanoparticles

This paper reports the second- and third- order nonlinear properties of Er3+/Yb3+ -doped PbO-GeO2-Ga2O3 glasses with Au nanoparticles. The glasses were prepared by the melt-quenching technique, followed by annealing for the nucleation of gold nanoparticles. A 200kV high-resolution transmission electron microscope (HR-TEM) was used to verify the presence of Au nanoparticles and estimate their sizes. The role of annealing on the possible variation of the third-order nonlinear electric susceptibility is studied in details following the possible changes in the Au nanoparticle concentration. Two-photon absorption (TPA) coefficient (β) and nonlinear refractive index (n2) was measured by the conventional Z-scan method at 532nm wavelength. The highest values were obtained for the sample with gold nanoparticles annealed for 52h. Second harmonic generation (SHG) measurements were also performed and showed low conversion efficiency.

Electric field‐revealed precursor ferroelectric properties of low lithium ion‐doped KTaO3

The results of low‐temperature linear as well as nonlinear and electric susceptibility and polarization P measurements of the K1–xLixTaO3, x = 0.01 crystal are presented. A coexistence of two different phases within a temperature range where the glassy state sets in is proposed. In the current work, we have proved the existence of an electric field‐revealed precursor ferroelectric phase without low‐frequency relaxation. With decreasing temperature, the second‐order nonlinear electric susceptibility, , which is proportional to the polarization P, increases from zero at about 40 K to at 4.2 K. This behavior is independent of the frequency of the ac probing electric field, and thus discloses the existence of a newly observed polarization component.

Electrical control of second-harmonic generation in a WSe2 monolayer transistor.

Nonlinear optical frequency conversion, in which optical fields interact with a nonlinear medium to produce new field frequencies, is ubiquitous in modern photonic systems. However, the nonlinear electric susceptibilities that give rise to such phenomena are often challenging to tune in a given material and, so far, dynamical control of optical nonlinearities remains confined to research laboratories as a spectroscopic tool. Here, we report a mechanism to electrically control second-order optical nonlinearities in monolayer WSe₂, an atomically thin semiconductor. We show that the intensity of second-harmonic generation at the A-exciton resonance is tunable by over an order of magnitude at low temperature and nearly a factor of four at room temperature through electrostatic doping in a field-effect transistor. Such tunability arises from the strong exciton charging effects in monolayer semiconductors, which allow for exceptional control over the oscillator strengths at the exciton and trion resonances. The exciton-enhanced second-harmonic generation is counter-circularly polarized to the excitation laser due to the combination of the two-photon and one-photon valley selection rules, which have opposite helicity in the monolayer. Our study paves the way towards a new platform for chip-scale, electrically tunable nonlinear optical devices based on two-dimensional semiconductors.

Third-Order Nonlinear Optical Behavior of Novel Polythiophene Derivatives Functionalized with Disperse Red 19 Chromophore

Two copolymers of 3-alkylthiophene (alkyl = hexyl, octyl) and a thiophene functionalized with disperse red 19 (TDR19) as chromophore side chain were synthesized by oxidative polymerization. The synthetic procedure was easy to perform, cost-effective, and highly versatile. The molecular structure, molecular weight distribution, film morphology, and optical and thermal properties of these polythiophene derivatives were determined by NMR, FT-IR, UV-Vis GPC, DSC-TGA, and AFM. The third-order nonlinear optical response of these materials was performed with nanosecond and femtosecond laser pulses by using the third-harmonic generation (THG) andZ-scan techniques at infrared wavelengths of 1300 and 800 nm, respectively. From these experiments it was observed that although the TRD19 incorporation into the side chain of the copolymers was lower than 5%, it was sufficient to increase their nonlinear response in solid state. For instance, the third-order nonlinear electric susceptibility (χ3) of solid thin films made of these copolymers exhibited an increment of nearly 60% when TDR19 incorporation increased from 3% to 5%. In solution, the copolymers exhibited similar two-photon absorption cross sectionsσ2PAwith a maximum value of 8545 GM and 233 GM (1 GM = 10−50 cm4 s) per repeated monomeric unit.

Modeling of the optical properties of molecular crystals

In this contribution we present our current findings in the calculations of the linear and second-order nonlinear electric susceptibility tensor components of organic crystals. The methodology used for this purpose is based on a combination of the electrostatic interaction scheme developed by Hurst and Munn (Hurst & Munn, 1986) with electronic structure calculations for the isolated molecules. Our modification of the method consists in i) running periodic boundary condition (PBC) calculations for an adequate chromophore geometry (either experimental or optimized) to obtain atomic charges and in ii) performing the calculations of the molecular properties within a non-uniform embedding field generated by point charges located spherically around the reference molecule. Using this approach good accuracy is achieved on the electric susceptibility tensor components in comparison with the uniform dipole electric field (Seidler et al., 2013). We extend here the application of this method to other molecular crystals as well as we present the first attempt to predict the chi(1) and chi(2) components of two-component organic crystals (Gryl et al., 2014).

Proposed measurement of spin currents in a GaAs crystal using the electro-optical Pockels effect

A new method for measuring spin currents is proposed, based on the linear electro-optic (Pockels) effect caused by the additional second-order nonlinear electric susceptibility (electro-optic tensor) generated by the spin currents. The non-zero elements of electro-optic tensor induced by spin currents in GaAs crystal are calculated, and the wave coupling theory of linear electro-optic effect is used to analyze the polarization change of a probe beam. The numerical results show that, for a linearly polarized probe beam with a frequency close to the band gap of GaAs crystal, its polarization rotation can be as large as 14 μrad under an applied electric field of about 350 V/mm. This effect should offer an alternative detection method for spintronics.

Strain-Stable Nonlinear Dielectric Responses in Pyrochlore Bismuth Zinc Niobate Thin Films

The effect of film strain on the dielectric responses of pyrochlore Bi–Zn–Nb–O (BZN) thin films was investigated in (111)-oriented BZN thin films grown on various substrates. The bias-field dependence of dielectric constant revealed that both the linear and nonlinear electric susceptibilities of BZN thin films are stable against the film strain, unlike conventional tunable materials, such as (Ba,Sr)TiO3. The difference in dielectric nonlinearity between BZN and BST films is discussed on the basis of the phenomenological theory. The strain stability of linear and nonlinear dielectric responses of BZN is available for practical thin-film tunable applications.

Theoretical and experimental study of second harmonic generation from the surface of the topological insulator Bi2Se3

We develop a theoretical model that describes the second harmonic generation of light from the surface of the topological insulator Bi${}_{2}$Se${}_{3}$ and experimentally demonstrate that the technique is sensitive to the surface electrons. By performing a crystal symmetry analysis of Bi${}_{2}$Se${}_{3}$(111) we determine the nonlinear electric susceptibility tensor elements that give rise to second harmonic generation. Using these results, we present a phenomenological model that shows that the relative magnitudes of these tensor elements can be determined by measuring the polarization and intensity of the radiated second harmonic light as a function of the in-plane crystal orientation and incident laser polarization. We describe optical techniques capable of isolating second harmonic light and, using these techniques, we measure the first-order linear optical and second-order nonlinear optical responses as a function of crystal orientation and laser polarization on bulk single crystals of Bi${}_{2}$Se${}_{3}$(111). The experimental results are consistent with our theoretical description. By comparing the data to our theoretical model we determine that a portion of the measured second harmonic light originates from the accumulation region of Bi${}_{2}$Se${}_{3}$(111), which we confirm by performing surface doping-dependent studies. Our results show that second harmonic generation is a promising tool for spectroscopic studies of topological surfaces and buried interfaces.

Nonlinear dielectric response of AgNb1-xTaxO3in the vicinity of diffuse phase transitions

Linear and nonlinear dielectric studies of AgNb(1-x)Ta(x)O(3) (ATN) ceramics (x ≤ 0.6) were carried out in the temperature range of 80 to 673K. The temperature dependences of third-order nonlinear electric susceptibility X3'(T) exhibit two distinct maxima: at the temperature of the weak ferroelectric phase appearance, M(1)-M(2) transition, and at the temperature of the Nb/Ta ion dynamics freezing, Tf. For AgNbO3, they appear at 325K and 448K, respectively. With increasing Ta concentration, both maxima shift toward lower temperature: 4K/%Ta (M(1)-M(2)) and 5.6K/%Ta (T(f)). The X3' (T) maxima indicate changes of the Nb/Ta ion dynamics and their contribution to electric susceptibility. At T(f), a partial freezing of the Nb/Ta ion displacements to the disordered antipolar, antiferroelectric array takes place. At the M(1)-M(2) transition, further freezing of Nb/Ta displacements to polar weak relaxor ferroelectric or dipolar glass transition occurs. This polar state coexists with the ground antiferroelectric state. Studies of the aging process showed that below T(f) the aging influence on electric susceptibility is substantial, whereas above Tf it may be neglected. This means that for ATN ceramics in the concentration range used for applications, there is no aging process in the room temperature region, which is an additional advantage of this system.

Polarizability and hyperpolarizability of BN zigzag nanotubes calculated by the coupled perturbed Kohn-Sham scheme

Linear and nonlinear electric dipole susceptibilities are evaluated for infinite periodic zigzag BN nanotubes utilizing primarily the coupled perturbed Kohn-Sham scheme recently implemented in the crystal code. The effect of different functionals, basis set, and computational parameters is examined. Most of the calculations are done at the B3LYP/6-31G* level. For electronic linear polarizabilities, substantial differences compared to the uncoupled sum-over-states scheme are found. Much larger radii were considered than in earlier studies, thereby permitting accurate comparison with corresponding properties of the hexagonal monolayer. In addition, we confirmed the dielectric shell model for the linear polarizability, but with a significantly different shell thickness than previously thought. Vibrational (ionic) contributions to the nonlinear susceptibilities are calculated. In doing so, the finite-field--nuclear-relaxation (FF--NR) method was employed for the transverse components of the (6,0), (9,0), and (12,0) nanotubes. Aside from being computationally more efficient than other procedures, this method includes anharmonicity effects through first order and, as shown, is readily applied to key dynamic as well as static properties (and yields the static linear polarizability as well). Our calculated nonlinear vibrational susceptibilities sometimes exceed, or even greatly exceed, the corresponding static electronic susceptibility. In such cases, the relative magnitude of the vibrational contribution grows substantially with tube radius over the range considered. Future plans include extending these FF--NR calculations to large nanotubes and to the longitudinal (periodic) direction as well.

Second-Harmonic Generation Imaging of Membrane Potential with Retinal Analogues

Second-harmonic generation (SHG) by membrane-incorporated probes is a nonlinear optical signal that is voltage-sensitive and the basis of a sensitive method for imaging membrane potential. The voltage dependence of SHG by four different probes, three retinoids (all-trans retinal), and two new retinal analogs, 3-methyl-7-(4′-dimethylamino-phenyl)-2,4,6-heptatrienal (AR-3) and 3,7-dimethyl-9-(4′-dimethylamino-phenyl)-2,4,6,8-nonatetraenal (AR-4), and a styryl dye (FM4-64), were compared in HEK-293 cells. Results were analyzed by fitting data with an expression based on an electrooptic mechanism for SHG, which depends on the complex-valued first- and second-order nonlinear electric susceptibilities (χ2 and χ3) of the probe. This gave values for the voltage sensitivity at the cell's resting potential, the voltage where the SHG is minimal, and the amplitude of the signal at that voltage for each of the four compounds. These measures show that χ2 and χ3 are complex numbers for all compounds except all-trans retinal, consistent with the proximities of excitation and/or emission wavelengths to molecular resonances. Estimates of probe orientation and location in the membrane electric field show that, for the far-from-resonance case, the shot noise-limited signal/noise ratio depends on the location of the probe in the membrane, and on χ3 but not on χ2.

Contribution of molecular displacements to linear and nonlinear electric susceptibilities of molecular crystals

Expressions are derived for additional contributions to the linear, quadratic, and cubic electric susceptibilities of molecular crystals that arise when molecules are displaced by the applied electric field. The contributions depend on quantities related to the infrared intensity of lattice vibrations, to the Raman intensity of lattice vibrations, and to the intensity of hyper-Rayleigh scattering. Some nonlinear contributions are zero except for response to a static electric field applied directly or produced by optical rectification. There are also contributions from averaging the susceptibilities in the equilibrium structure over the lattice modes.

Calculation of the dielectric constant ϵ and first nonlinear susceptibility χ(2) of crystalline potassium dihydrogen phosphate by the coupled perturbed Hartree–Fock and coupled perturbed Kohn–Sham schemes as implemented in the CRYSTAL code

The high-frequency dielectric varepsilon and the first nonlinear electric susceptibility chi((2)) tensors of crystalline potassium dihydrogen phosphate (KH(2)PO(4)) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on varepsilon and chi((2)) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.

Kinetic Theory of the Langevin Saturation in Dilute Solution of Dipolar Symmetric-Top Molecules in Spherical Solvents

Assuming the low molecular reorientation approximation, the formulae for the third-order electric polarization induced in liquids composed of rigid noninteracting dipolar, symmetric-top molecules in spherical solvents were derived. Our medium is acted on by a strong external dc bias electric field superimposed on a weak ac electric field, and the classical Smoluchowski– Debye equation for rotational diffusion of the symmetric-top molecules is applied. In order to highlight the influence of the anisotropy of rotational diffusion tensor components and the orientation of permanent dipole moment of the molecule on the complex linear and nonlinear electric susceptibilities, we present three-dimensional plots of the linear and nonlinear dispersion and absorption spectra, for different values of the frequency of ac electric field.

Cole-Cole Plots for Linear and Nonlinear Dielectric Relaxation in Solutions of Rigid Highly Dipolar Symmetric-Top Molecules in Spherical Solvents

The graphical analysis of the in∞uence of the rotational difiusion tensor anisotropy and the orientation of the permanent dipole moment on the linear and nonlinear dielectric relaxation is shown. The solution of Smoluchowski{Debye rotational difiusion equation for rigid, and noninteracting polar, symmetric-top molecules, in the \weak molecular reorientation approximation, was used. In order to highlight the in∞uence of the symmetric shape of molecule, in comparison with classical, spherical-top Smoluchowski rotational difiusion, we present sets of Argand-type plots and three-dimensional Cole{Cole diagrams for linear and nonlinear electric susceptibilities. The results indicate that, in describing the nonlinear dielectric relaxation, the simplest spherical-top rotational difiusion model may be a su‐cient approximation in some special cases only. PACS numbers: 05.40.Jc, 77.22.id, 77.22.Gm

Linear and Nonlinear Electric Susceptibility in the Quantum Domain State of SrTi18O3

The complex dielectric susceptibility of SrTi18O3 has been measured at frequencies 10−3 ≤ f ≤ 105 Hz and temperatures 5 ≤ T ≤ 30 K with ac field amplitudes 0.01 ≤ E 0 ≤ 10 kV/m in order to inspect different mechanisms of the polarization reversal. This system displays a very strong nonlinear effect in its quantum domain (“ferroelectric”) state as evidenced by the field dependence of the susceptibility. Depending on the amplitude of the probing field partial or almost complete polarization reversal can be achieved at moderate values of E 0 being available in standard dielectric spectrometers.

Symmetry and phase-matching properties of third-harmonic generation under the photoelastic effect in Ge-As-Se chalcogenide glasses

We discuss the study of three chalcogenide glasses of high third-order nonlinear electric susceptibility, AsSe4,GeSe4, and GeAsSe8. We measured the strain optical coefficients, and we determined dispersion equations of the refractive index from previously published measurements. From these data, we performed a theoretical study of a new scheme for third-harmonic generation in a glass where phase matching is created by a photoelastic effect. A complete symmetry analysis based on Curie principle allowed us to define the configuration of polarization of the interacting waves, leading to a nonzero cubic effective coefficient. The generated third-harmonic intensity is then calculated.