Components Of Susceptibility Tensor Research Articles

A density functional study of second-order susceptibilities in calcium samarium oxyborate Ca4SmO(BO3)3

We report calculations of the linear and nonlinear optical susceptibilities (second harmonic generation) for calcium samarium oxyborate Ca4SmO(BO3)3 using the full-potential linear augmented plane wave method. Our calculations show that this compound is metallic-like with density of states at the Fermi energy EF, N(EF) = 421.6 states/Ry-cell or a bare electronic specific heat coefficient of 73.14 mJ mole−1 K−2. We find that the metallic behaviour is due to the strong overlap of the Sm and O states around EF. We have performed calculations for the two contributions to ε(ω), namely, intra-band and inter-band transitions. The effect of the intra-band term is significant for energies less than 1 eV. We have calculated the various components of the second-order susceptibility tensor and find that is the dominant component. We find opposite signs for the contributions of 2ω and 1ω inter-/intra-band to the real and imaginary parts of the dominant component throughout the wide optical frequency range.

Difference in the nonlinear optical response of epitaxial Si on Ge(100) grown from SiH4 at 500 °C and from Si3H8 at 350 °C due to segregation of Ge

The properties of epitaxial strained Si on Ge (001) grown from SiH4 at 500 °C and from Si3H8 at 350 °C have been investigated as a function of film thickness using second harmonic generation (SHG). A clear difference in the corresponding signal amplitude, for both the interface and the “bulk” contributions, is observed. After analysis of the nonlinear susceptibility tensor components, this difference is attributed to the segregation of Ge to the SiO2/Si interface. It is demonstrated that when employed in combination with more standard experimental techniques, SHG can be a valuable tool for probing and characterizing the SiO2/Si/Ge interfaces.

Nonlinear optical properties of lithium sulfate monohydrate

AbstractIn this paper, all eight tensor components of the nonlinear optical susceptibility tensor for second harmonic generation were determined for monoclinic non‐centrosymmetric lithium sulfate monohydrate, Li2SO4·H2O, using the Maker fringe technique at the wavelength λ=1064 nm. The largest component of the nonlinear optical susceptibility tensor was 0.34 pm/V. This crystal has the maximum effective value 0.13 pm/V along the phase matching directions at type I and 0.10 pm/V at type II. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Chiral Specificity of Doubly Resonant Sum-Frequency Generation in An Anisotropic Thin Film

The chiral specificity of infrared-visible sum-frequency generation (SFG) is investigated under doubly resonant (DR) conditions. An anisotropic thin film made of stacks of chiral supramolecular assemblies is investigated as a function of incoming and outgoing light polarizations. SFG experiments, crossed with in situ polarized absorption measurements, show that the double resonance process leads to a selection of the nonvanishing components of the chiral second-order susceptibility tensor. Specifically, it is demonstrated that a chiral component overcomes the achiral ones. This result is linked to the model for DR-SFG and to the selection rules of the vibration modes and electronic transition involved in the process.

Nonlinear optical response from periodic molecular structures

The explicit expressions of all independent components of the molecular crystal nonlinear susceptibility (NS) tensor (of any order) are given through the independent components of hyperpolarizability (HP) tensors of the constituting molecules. This expression has a polynomial form of convolutions of HP components and includes local field tensor components; each product contains from 1 to k−1 HP cofactors of all preceding ranks, and k is NS rank. The Bloembergen-Armstrong formula for the first NS and Hurst-Munn for the second NS are particular cases of this expression. The reciprocal equation for molecular HP in terms of crystal NS is also presented. The Lorentz formula of the phenomenological reaction field theory is derived from the microscopic crystal Hartree-Fock HP equations with the Madelung polarization potential included. The derivation is based on the expansion of the Madelung polarization interaction over the inter-ion distances. The second order term of this expansion is expressed through the Lorentz tensor components. The expansion is obtained due to a convenient method of calculation of the Madelung crystal sums. This technique enabled to reformulate for a molecular crystal the existing computational quantum methods for lone molecules. In particular, Hartree-Fock equations for HP of molecules are adjusted for the optical properties of molecular crystals and layers. The illustrative examples, demonstrating various aspects of the mentioned techniques, are presented.

Field-induced non-linear optical features of p-aminoazobenzene crystals

Using ethanol as a solvent p -aminoazobenzene ( p -AAZB), an organic nonlinear optical crystal having good optical quality was grown by slow evaporation solution technique. Structural and optical properties were studied by applying XRD and UV-Vis spectroscopy. The measurement of the second harmonic generation was performed using the fundamental Nd:YAG 10 ns laser beam with wavelength 1.064 μ m. Dependence of the second order susceptibilities for the two principal second order susceptibility tensor components d 14 and d 25 with the simultaneously applied dc- and UV-laser fields were investigated and discussed.

Magnetic second harmonic generation at the Co2MnSi∕AlOx interface

We have studied magnetic second harmonic generation (MSHG) at the Co2MnSi∕AlOx interface. The variation of the MSHG intensity was consistent with the nonvanishing components of the nonlinear susceptibility tensor expected for the (001) cubic surface. The difference in the MSHG asymmetry, the MSHG anisotropy, is found to have maximum value at an annealing temperature of 450°C, for which similar samples have previously been found to show optimum L21 site ordering and maximum tunnel magnetoresistance.

Nonlinear Optical and Structural Properties of Langmuir−Blodgett Films of Thiohelicenebisquinones

We provide a detailed investigation of the second-order nonlinear optical and structural properties of Langmuir-Blodgett (LB) films of nonracemic thiohelicenebisquinone (THBQ). We prepare both X- and Y-type films of different thicknesses and characterize them using optical second-harmonic generation and atomic-force microscopy (AFM). We find that the overall nonlinear properties of the samples are essentially independent of the film thickness and the deposition type and arise from susceptibility tensor components associated with chirality. Both X- and Y-type films can be described by D2 symmetry, which is a higher symmetry than the previously assumed C2 of LB films of THBQ and a similar helicenebisquinone (HBQ). However, the two types of films are shown to differ significantly with respect to the orientation of the in-plane axis. For Y type, the axis follows the direction of vertical sample deposition, but for X type, the direction of the axis varies randomly and significantly between different samples. The Y-type samples are therefore more ordered than the X-type samples. This was confirmed by AFM measurements in which the Y type exhibits uniform ordering into columnar structures. Similar structures in X type, on the other hand, are shorter and more randomly oriented, like those earlier observed for racemic samples of HBQ [Verbiest, T., et al. Science 1998, 282, 913]. The common nonlinear properties and different high-level ordering observed here for two different types of nonracemic samples reinforces that the nonlinearity of THBQ (and probably HBQ, as well) originates from the low-level columnar aggregation of the molecules with the higher-level structures playing a lesser role. In addition, within the columns, the molecules likely assume fairly random azimuthal orientations so that the columns themselves exhibit approximate Dinfinity symmetry.

Domain microstructures and ferroelectric phase transition in Pb0.35Sr0.65TiO3 films studied by second harmonic generation in reflection geometry

Second harmonic generation (SHG) measurements were performed in the reflection geometry using the femtosecond Ti:sapphire laser at the wavelength of 810nm for Pb0.35Sr0.65TiO3 films, which were epitaxially deposited on (001) MgO substrates by pulsed laser ablation under different oxygen pressures. We formulated the procedures to measure the ratios of the compensated fractions of both c domains and in-plane domains and the ratios of the components of the nonlinear susceptibility tensor under only a non-normal incidence of the fundamental beam. We applied this technique to characterize the domain microstructures of the Pb0.35Sr0.65TiO3 films at three typical temperatures (78, 150, and 300K) and found these films to exhibit a larger compensated fraction of c domains. The ratios of the components of the nonlinear susceptibility tensor were calculated to be relatively constant regardless of the temperature and the oxygen pressure. On the other hand, their SHG intensities were found to increase as the oxygen pressure goes lower, which is attributed to the higher density of the oxygen vacancies in the films. These films also exhibit the diffuselike phase transition in a very wide temperature range, which is attributed to the structural inhomogeneity and the nonuniform distribution of Pb2+ and Sr2+ in the Pb0.35Sr0.65TiO3 films.

Spin-flop transition in uniaxial antiferromagnets: Magnetic phases, reorientation effects, and multidomain states

The classical spin-flop is the field-driven first-order reorientation transition in easy-axis antiferromagnets. A comprehensive phenomenological theory of easy-axis antiferromagnets displaying spin-flops is developed. It is shown how the hierarchy of magnetic coupling strengths in these antiferromagnets causes a strongly pronounced two-scale character in their magnetic phase structure. In contrast to the major part of the magnetic phase diagram, these antiferromagnets near the spin-flop region are described by an effective model akin to uniaxial ferromagnets. For a consistent theoretical description both higher-order anisotropy contributions and dipolar stray-fields have to be taken into account near the spin-flop. In particular, thermodynamically stable multidomain states exist in the spin-flop region, owing to the phase coexistence at this first-order transition. For this region, equilibrium spin-configurations and parameters of the multidomain states are derived as functions of the external magnetic field. The components of the magnetic susceptibility tensor are calculated for homogeneous and multidomain states in the vicinity of the spin-flop. The remarkable anomalies in these measurable quantities provide an efficient method to investigate magnetic states and to determine materials parameters in bulk and confined antiferromagnets, as well as in nanoscale synthetic antiferromagnets. The method is demonstrated for experimental data on the magnetic properties near the spin-flop region in the orthorhombic layered antiferromagnet (C_2H_5NH_3)_2CuCl_4.

Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures

We study the second-harmonic (SH) parametric processes in unpoled crystals of Strontium Barium Niobate (SBN) with disordered structures of ferroelectric domains. Such crystals allow for the simultaneous phase matching of several second-order nonlinear processes. We analyze the polarization properties of these parametric processes using two types of generation schemes: quasi-collinear SH generation and transverse SH generation. From our experimental data we determine the ratio of d(32) and d(33) components of the second order susceptibility tensor and also the statistical properties of the random structure of the SBN crystal.

Second harmonic surface response of a composite

Abstract We calculate the nonlinear dipole and quadrupole moments induced at the second harmonic (SH) frequency 2 ω in a dielectric nanosphere by an inhomogeneous monochromatic electric field of frequency ω . We neglect finite size effects and assume that the surface region of the nanosphere is thin enough so that the surface may be considered locally flat. Then, we calculate the nonlinear optical response of a centrosymmetric semiinfinite composite made by the nanospheres. Within the dipole approximation, SH is forbidden in the centrosymmetric bulk, but allowed at the surface of the composite where the symmetry is broken. Therefore, the components of the surface susceptibility tensor, χ ijk , different from zero are calculated. As an application, we evaluate χ ijk for a composite made of Si nanospheres.

Harmonic generation in thin films and multilayers

A general method for computing harmonic generation in reflection and transmission from planar nonmagnetic multilayer structures is described. The method assumes plane waves and treats harmonic generation in the parametric approximation. The method is applied in studying the second- and third-harmonic generation properties of thin crystal silicon layers surrounded by thermal oxide. Most independent components of the nonlinear susceptibility tensor have unique signatures with silicon layer thickness $d$, allowing their strength to be determined in principle by measuring harmonic generation as a function of $d$. Surface and bulk contributions to third-harmonic generation are cleanly distinguished, with the bulk signal dominating. Four of six nonvanishing components of ${\ensuremath{\chi}}^{(2)}$ are independent. An approximate value for the bulk susceptibility component ${\ensuremath{\delta}}^{\ensuremath{'}}$, which is accessible only in multibeam experiments and has not previously been measured, is obtained.

Fractional rotational diffusion of rigid dipoles in an asymmetrical double-well potential

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar molecules rotating in an asymmetric double-well potential are evaluated using a fractional rotational diffusion equation (based on the diffusion limit of a fractal time random walk) for the distribution function of orientations of the molecules on the surface of the unit sphere. The calculation is the fractional analog of the Debye theory of orientational relaxation in the presence of external and mean field potentials (excluding inertial effects). Exact and approximate (based on the exponential separation for normal diffusion of the time scales of the intrawell and overbarrier relaxation processes associated with the bistable potential) solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the characteristic relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. The model explains the anomalous (Cole-Cole-like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times (e.g., in glass-forming liquids).

Modification of cubic susceptibility tensor in birefringent porous silicon

AbstractPolarization‐sensitive third‐harmonic generation in birefringent (110) porous silicon layers reveals a modification in the cubic susceptibility tensor of silicon caused by strongly anisotropic pores. The ratio $ (\chi _{1111} ^{(3)} + \chi _{1122} ^{(3)} / \chi _{3333} ^{(3)}) $ of cubic susceptibility tensor components for the porous layers is shown to be 40% higher than this ratio for crystalline silicon. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ultrafast third-order optical nonlinearity of noble and transition metal thin films

We present transient ellipsometry measurements made upon Au, Cu, Ag, Ni, Pd, Ti, Zr, and Hf thin films under identical experimental conditions. Using an elliptically polarized pump beam, we have simultaneously observed the specular inverse Faraday effect (SIFE) and specular optical Kerr effect (SOKE) contributions to the optical polarization response, in order to extract the real and imaginary parts of the non-vanishing components of the third-order optical susceptibility tensor. The signal magnitudes and the extracted tensor components show a systematic variation that reflects the underlying band structure of the different metals. A time delay observed between the SIFE and SOKE signals is interpreted in terms of lifetimes for the transient polarization that may be of comparable magnitude to the pulse width. This suggests that formulae derived in the continuous wave limit may not be applicable in the description of ultrafast nonlinearities in metallic samples. The implications of our results for different areas of applied optics are discussed.

Fractional rotational Brownian motion in a uniform dc external field

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar particles subjected to a dc bias field are evaluated in the context of a fractional noninertial rotational diffusion model. Exact and approximate solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the effective relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. Simple equations for the characteristic frequencies of the dielectric loss spectra are obtained in terms of the physical model parameters (dimensionless field and fractional exponent). The model explains the anomalous (Cole-Cole like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times.

Components of the third-order nonlinear susceptibility tensors in KDP, DKDP and LiNbO3 nonlinear optical crystals

The ratio of the components of the third order nonlinear susceptibility tensors (which are responsible for the self-action effects) in KDP, DKDP and LiNbO3 crystals is measured at the 1064-nm wavelength of a Nd:YAG laser. Measurements were made on the basis of analysis of polarisation dependences of the focused radiation transmission by the z-scan method. The obtained polarisation dependences of the effective Kerr nonlinearity correspond to a tensor of the fourth rank that is symmetric in all its indices. The measured values of the Kerr nonlinearities that are responsible for the self-action of o-polarised radiation were found to be (1.75 ± 0.55) × 10-14 and (2.4 ± 0.8) × 10-13 esu for KDP and LiNbO3 crystals, respectively.

Transient optical polarization response of aluminium at an interband transition

Femtosecond optical pump–probe measurements have been performed upon a500 Å polycrystalline Al film at an interband transition at a wavelength of 800 nm.The dependence of the intensity and polarization of the reflected probe pulseupon the polarization of the pump pulse has been determined. A sharp peak wasobserved in the polarization signal at zero time delay that contains contributionsfrom both the specular inverse Faraday effect (SIFE) and the specular opticalKerr effect (SOKE). The SIFE and SOKE are associated with the opticalorientation of angular and linear momentum, respectively. The dependence ofthe peak height upon the pump polarization has allowed us to deduce values ofχxxyy = (1+0.6i) × 10−8 rad cm3 erg−1 and χxyyx = (0.5−0.1i) × 10−8 rad cm3 erg−1 for the non-vanishing components of the local cubic susceptibility tensor. A distortion ofthe peak was observed when the pump was elliptically polarized. Its detailed shape showsthat the characteristic relaxation time for the SOKE is about 30 fs longer than that for theSIFE in measurements of ellipticity. This suggests a similar difference in the relaxationtimes for the angular and linear momentum of the optically excited hot electrons. Theinitial peak was generally followed by a tail that decayed with a time constant of severalpicoseconds, which we attribute to an ultrafast anisotropic excitation of the lattice.

Investigation of ultrafast demagnetization and cubic optical nonlinearity of Ni in the polar geometry

Femtosecond optical pump-probe experiments were performed upon a Ni(720 Å)/Si(100) sample in the polar geometry with the pump beam close to normal incidence. A signal due to the ultrafast demagnetization effect was observed when the pump pulse was linearly polarized. When the pump was elliptically polarized, additional peaks were observed at zero time delay, resulting from the specular inverse Faraday effect (SIFE) and the specular optical Kerr effect (SOKE). By comparing measurements made with different pump helicities, the SIFE and SOKE peaks and the demagnetization signal were found to superpose in a linear fashion. From the dependence of the peak height upon the pump polarization, values of χxxyy=(1−3i)×10−10 rad cm3 erg−1 and χxyyx=(−9+2i)×10−12 rad cm3 erg−1 were deduced for the nonvanishing components of the local cubic susceptibility tensor. For applied fields less than the saturation value, the sudden reduction of the thin film demagnetizing field leads to an imbalance of the torques acting upon the magnetization, causing it to precess.