Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission

The theoretical investigation of sum and difference frequency generation in thin surface layers with rotational symmetry leads to formulas which connect the generated light intensities to the surface second order nonlinear susceptibility tensor. A maximum of seven tensor components can be determined in the case of lowest symmetry. Measurements in transmission should be especially useful since they allow easy variation of both polarization and angle of incidence. On the other hand, large signal enhancements are expected for total internal reflection geometries. A consistent set of ⁽²⁾ tensor components for a thin layer of rhodamine-6G adsorbed on fused silica is found based on data from reflection and transmission measurements.     

Second-Harmonic-generation studies of inclined thin films

The nonlinear surface susceptibility _S ⁽²⁾ is generally referred to the system of Cartesian coordinates of thesample. However, since actual measurements take place with respect to thelaboratory system of coordinates, appropriate transformation of _S ⁽²⁾ is necessary to deduce the underlying susceptibility-components. We demonstrate this by analyzing the second-harmonic signal generated by an inclined sample upon rotation around thes-axis of the laboratory system of coordinates. The sample consists of two Langmuir-Blodgett-type monolayers of rotational symmetry around the sample normal, the two layers being separated by a plane-parallel flat of 1 mm thickness. The occurrence of a symmetry-forbiddenI _SS ² -signal is discussed in detail.     

Die Magnetische SuszeptibilitÄt von Kristallinem n-CdGeAs2

The specific magnetic susceptibility of polycrystalline and powdered samples was measured between 77 °K and 570 °K. This dependence was interpreted in intrinsic range suggesting the susceptibility is given as a sum of contributions of the lattice ^G and of free carriers _L. The temperature dependence of the lattice susceptibility _G= _G ⁰ +T was checked: _G ⁰ =–2·35× ×10^–7, =4·5×10^–11. The contribution _L enabled to check the effective mass of holes m_h=0·25m₀ suggesting m_em_h.

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Herrn A. Hrubý gilt mein Dank für die Vorbereitung des polykristallinen Ingots von CdGeAs₂.     

Mechanism Study for Thermal/Electric Field Poling of Fused Silica

On the basis of the experimental reports, the mechanism of the second-order susceptibility ⁽²⁾ for the thermal/electric field poling of fused silica is analyzed, and expressions for ⁽²⁾ are detailedly derived and numerically calculated for the first time. By comparison the theoretical value of ⁽²⁾ with the experiment results, we propose that the effective ⁽²⁾ is created via both the interaction of the intense electric field with the third-order susceptibility ⁽³⁾ and the dipole orientation. The theoretical results show that, in the differently applied voltage, the dipole orientation and ⁽³⁾ play different role in the formation of ⁽²⁾. This theory successfully explains some experiment results.     

Effect of water of crystallization on magnetic properties of MgSO4

The object of this paper has been to determine the effect of water of crystallization on magnetic properties of MgSO₄. Changes in the magnetic properties of MgSO₄ in depenedence on the number of waters of crystallization have been established from the magnetic susceptibility changes. The value obtained by measurement differs from that calculated by the additivity law. This disagreement can be explained by the presence of the thermally independent Van Vleck's polarization paramagnetism _p .The paper brings forward calculations of _p values for the individual hydrates of MgSO₄.i H₂O fori=0, 1, ..., 7. Besides, it examines what portion of the polarization paramagnetism _pi of the overall values of _pci is due to the effect of water of crystallization. On the basis of this information the deviation from the spherical symmetry, caused by hydration of the MgSO₄ molecule, has been interpreted.     

Determination of the spatial profiles of all components of the quadratic susceptibility tensor \hat \chi ^{(2)} (z, 2ω; ω, ω) of a one-dimensionally inhomogeneous absorbing medium

For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor $\hat \chi ^{(2)} $ (z, 2??; ??, ?? responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of the wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.     

Two-photon absorption and resonant non-phase-matched second-harmonic generation in CdSe

Exciting a hexagonal CdSe crystal with picosecond Nd: glass laser pulses, two-photon absorption and resonant non-phase-matched second-harmonic generation occur simultaneously. Using different crystal orientations, all components of the secondharmonic susceptibility tensor (non-vanishing components ared ₃₁,d ₃₃ andd ₁₅) and some components of the two-photon absorption susceptibility tensor _ijkl ⁽³⁾ (–_L; _L, _L, –_L) are determined.     

Higher-order susceptibilities of the regular and the random Ising model on the Cayley tree. I

Explicit expressions for the fourth-order susceptibility (⁴), the fourth derivative of thebulk free energy with respect to the external field, are given for the regular and the random-bond Ising model on the Cayley tree in the thermodynamic limit, at zero external field. The fourth-order susceptibility for the regular system diverges at temperature T _c ⁽⁴⁾ = 2k _B ^–1 J/ln{1+2/[(z–1)^3/4–1]}, confirming a result obtained by Müller-Hartmann and Zittartz [Phys. Rev. Lett. 33:893 (1974)]; Herez is the coordination number of the lattice,J is the exchange integral, andk _B is the Boltzmann constant. The temperatures at which ⁽⁴⁾ and the ordinary susceptibility (²) diverge are given also for the random-bond and the random-site Ising model and for diluted Ising models.     

Gluonic transverse spin structure functions and their possible measurement inχ 2 production

Gluonic parton distributions in a transversely polarized proton are identified and their classification according to twist is discussed. We find that there are two twist-three transverse spin gluonic structure functions, called hereinH ₁(x, Q ²) andH ₂(x, Q ²). These are potentially measureable in ₂ production in hard polarizedp-p collisions. Crossection formulae are calculated for a variety of polarization states, assuming a simple effective interaction for ₂ production from gluon fusion.     

Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor _V depends on the shape of V, even in the thermodynamic V limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic V-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant =even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of _V predicted by macroscopic electrostatics and gives a finite-size correction term to _V.     

Third-order processes and their relation to structural symmetry

We have studied the various nonlinear optical processes that can be described by a fourth-rank ⁽³⁾-tensor: signals of frequency in degenerate four-wave mixing (DFWM), harmonics of frequency 2 and 3, and ⁽³⁾-type difference-frequency generation (DFG) with observation of anti-Stokes emission of a signal of frequency 2₁ — ₂. Structural information in terms of normalized anisotropies is derived in all frequency domains by analysis of the elements of the respective orientation-dependent susceptibility tensor. A novel laser-based technique for the remote orientation analysis of crystalline structures is introduced.     

Initial magnetic susceptibilities of iron and nickel aerosol powders

The dependence on angle is considered for the hysteresis-free initial susceptibilities _a and _ar together with the initial susceptibility _o for iron and nickel aerosol powders, as well as the effects on these characteristics from changes in powder packing density. Estimates are made of the negative-interaction fields, and a quantitative comparison is made between the observed _ar() and theoretical values by means of the pair model. The correlation between the experimental and theoretical relationships confirms the concepts used on the predominant effects from magnetostatic interaction in the mechanism for magnetization reversal in powders of materials with low anisotropy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, pp. 40–43, July, 1984.     

Temperaturabhängigkeit von Knight-shift und Suszeptibilität von Vanadium und Niob

Knight-shiftK and susceptibility have been investigated on single-crystals of vanadium and niobium between 4 K and 290 K.In the case ofV the changes ofK and are found to be of opposite sign and proportional toT ² with good approximation. This can be explained by theT-dependence of spin-paramagnetism of 3d-electrons. The hyperfine field due to oned-electron spin is found to be — 90 kG. Small deviations from theT ²-law are explained by minor changes in the orbital susceptibility, which gives the main constituents toK and. In the case of Nb only is found to be proportional toT ². TheT-dependence ofK is very small and shows a maximum at 140 K. This can be explained by theT-dependence of spinparamagnetism of 4d-electrons as well as 5s-electrons.     

Seventh and ninth order nonlinear susceptibility measurement in alkali metal vapour

We report the first experimental measurement and theoretical estimation of seventh _eff ⁽⁷⁾ and ninth _eff ⁽⁹⁾ order effective nonlinear susceptibilities. The correlation of ninth, seventh and fifth harmonic signal efficiencies in various phase-matched mixtures of Ar (or Xe) and sodium atoms, is experimentally investigated. Using direct and cascade processes of harmonic generation, the modulus ratio is measured for the higher nonlinearities, which allows an estimation of _eff ⁽⁷⁾ and _eff ⁽⁹⁾ from the lower order optical susceptibilities. Results from numerical calculations of atomic nonlinear susceptibilities up to the ninth order, accounting for the discrete spectrum and the continuum, are presented.     

Dependence of the magnetic susceptibility of the palladium silver alloy system on temperature and composition

Starting from thermodynamic considerations an analytical expression (T, x) is given for the variation of the magnetic susceptibility of the substitutional Pd_1–x Ag _x alloy series with both temperatureT and fractional silver contentx. The observed rapid decrease of the isothermal susceptibility (T=const,x) with increasingx and the disappearance of the maximum of the low temperature isopleths (T,x=const) forx0.1 can be specified by three fitting constants related to microscopic model parameters.     

On the magnetic susceptibility of Pd1−x Ag x in the range 0.5≦x≦1

The weak variation of the magnetic bulk susceptibility of Pd_1–x Ag _x with temperature T and silver mole fractionx within 0.5x1 has been investigated in the range 5KT400K. Experimental evidence can be given for an intersection point of the susceptibility isotherms (T=const,x) atx=0.55. The observed dependence of on T andx is interpreted by means of a semiphenomenological alloy susceptibility function (T,x).     

Magnetic moments and the high field susceptibilities of MnFe2O4

An extended version of the noncollinear spin model bySawatzky et al. is developed to derive a dependence of the differential high field susceptibility on the degree of inversion of the ferrite MnFe₂O₄. Using the available data on the main molecular field coefficients it is shown that the present model imposes restrictions on values of. Determination of from the measurements of the field dependence of the saturated moments at low temperatures on samples with varying degrees of inversion reveals good quantitative agreement with the present model.     

Anisotropy of the nonlinear optical susceptibility χ(3) in polydiacetylene single crystals

The anisotropy of ⁽³⁾ in Poly-bis(p-Toluene Sulfonate) of 2.4-hexadiyne-1.6-diol (PTS) PolyDiAcetylene (PDA) single crystals is investigated by Degenerate Four-Wave Mixing (DFWM) at a wavelength of 720 nm. The symmetries of ⁽³⁾(–;, –,) identify the non-vanishing and independent components of the tensor. For the calculation of the ⁽³⁾ elements from the measured values, the anisotropy of both the linear optical index of refraction and the absorption coefficient is included in the coupled wave approach. A magnitude of 10^–10 esu is measured for the ⁽³⁾ component if all beam polarizations are parallel to the polymer chains. The least upper bound for all other measurable components is estimated to be 10^–12 esu. The results for the intensity dependence of the DFWM signal are explained in terms of a thermooptic effect. Measurements on the orientational dependence of the DFWM signal in the samples are carried out, and the influence of the anisotropy of the linear optical parameters on the measured curves is discussed. A method for the preparation of thin layered polymer single crystals of poly-bis (4-ButoxyCarbonyle-Methylene-Urethane) of 4.6-decadiyne-1.1-diol (4-BCMU) and the first DFWM measurements on these samples are presented.     

Goldstone-mode induced susceptibility-singularity extending toT c of the Heisenberg ferromagnet EuS

At internal magnetic fields much smaller than the spontaneous magnetizationM _s (T) but large compared to the weak anisotropy field,H _A 20 Oe, the internal susceptibility measured parallel toM by NMR and low frequency ac-susceptibility is observed to diverge asH ^–1/2 for temperatures up to 0.998T _c . Numerous theoretical work predicted suchH ^–1/2-singularity to arise from massless Goldstone-modes associated with the perpendicular susceptibility of a Heisenberg system. The temperature variation of the amplitude, _z ·H ^–1/2, agrees with the results of the spin-wave and more general hydrodynamic theories, while the magnitude reveals the suppression of one Goldstone polarization by the dipoledipole interaction. In contrast to a previous renormalization-group estimate, a crossover to thermal critical behavior nearT _c is not observed.