The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, and the approximate momentum relationship ${\mathrm{k}}_{3}={\mathrm{k}}_{1}+{\mathrm{k}}_{2}+\ensuremath{\Delta}\mathrm{k}$. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

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Interactions between Light Waves in a Nonlinear Dielectric

Thermal conductivity of solids and liquids under pressure is covered in this review. Experimental techniques are critically considered and compared, and an introduction to theory is provided. Results are presented and discussed for ionic crystals, normal molecular crystals, plastic crystal phases, clathrate hydrates, polymers and glass-formers, liquids, covalent and semiconducting crystals, rocks and metals. Special attention is given to isochoric conditions, change of crystal structure and molecular orientational disorder. Available reliable measurements at pressures up to a few GPa indicate the need for theoretical development, especially in connection with molecular crystals and ferromagnetic metals.

http://iopscience.iop.org/article/10.1088/0034-4885/47/10/002/pdf

Thermal conductivity of solids and liquids under pressure

NMR-NQR studies of structural phase transitions

The α-relaxation, involving local segmental motion, of poly(methyltolylsiloxane) (PMTS) was measured using dielectric spectroscopy, over a temperature range in excess of 100 deg at pressures up to 250 MPa. The data conformed to time−temperature−pressure superpositioning, although the Tg-normalized temperature dependence of the relaxation times exhibited a weak dependence on pressure. The combined temperature and pressure dependences could be accurately described using a generalized Vogel−Fulcher expression, with the Vogel temperature having the same pressure dependence as the glass temperature. In comparing the relaxation properties of PMTS to the structurally similar poly(methylphenylsiloxane) (PMPS), we found that while their ambient pressure behaviors were equivalent, the relaxation times, Tg-scaled temperature dependence, and Tg itself for PMTS were all more sensitive to pressure. These differences are consistent with a larger activation volume for PMTS, which is indeed comprised of proportionally lar...

Pressure and Temperature Dependence of the α-Relaxation in Poly(methyltolylsiloxane)

In some polymers, in addition to the usual structural α relaxation, a slower α′ relaxation is observed with a non-Arrhenius temperature dependence In order to understand better the molecular origin of this α′ relaxation in poly(methylphenylsiloxane) (PMPS) we have studied, for the first time, the pressure dependence of its relaxation time, together with the usual temperature dependence, by means of dynamic light scattering (DLS) For the same material the α relaxation was also studied by means of DLS and dielectric spectroscopy (DS) in broad temperature and pressure ranges We find that the temperature dependence of both α and α′ relaxation times, at all pressures studied, can be described by a double Vogel-Fulcher-Tammann (VFT) law The pressure dependence of the characteristic temperatures Tg (glass transition temperature) and T0 (Vogel temperature) as well as the activation volumes for both α and α′ processes are very similar, indicating, that both relaxation processes originate from similar local mol

Pressure effects on the α and α′ relaxations in polymethylphenylsiloxane

14N pure nuclear quadrupole resonance frequencies and inverse linewidth in s‐triazine were measured as functions of hydrostatic pressure to 6.2 kbar along two isotherms at 23.3 and −0.4 °C. The second order phase transition, previously studied at atmospheric pressure, was observed at high pressures. Above the transition pressure pc each resonance line splits into two. The line splittings were fitted to the equation Δν=B (p−pc)β, and the critical exponent β was found to be close to 0.5. The pressure dependence of the transition temperature Tc is described by the (linear) equation Tc(p) =198.8+18.2p, [Tc(°K);p (kbar)]. The present results along isotherms were compared with previous results along an isobar. In the low pressure region the inverse linewidth T2* is dominated by hindered rotations of the s‐triazine molecule. The activation volume for this motion is ΔV*=26 cm3/mole.

14N PNQR study of the effect of pressure on the phase transition and molecular reorientation in s‐triazine

14N nuclear quadrupole resonance frequencies and spin‐lattice relaxation time, T1, in hexamethylenetetramine (HMT) were measured as a function of hydrostatic pressure up to 6 katm at 257, 273, 294.5, 309, and 317°K. For the three higher isotherms T1 depends exponentially on pressure up to 3 katm. In this region T1 is determined mainly by molecular reorientation of the tetrahedral HMT molecule around its four threefold axes. This mechanism is discussed in terms of a simple activation process. The activation volume, ΔV*=23.6±1 cm3/mole, and activation enthalpy, ΔH*=17±1 kcal/mole were determined. From thermal expansion and compressibility data, the thermal pressure, Pt = T(∂p/∂T)v, of 6.2 katm and activation energy ΔE* = 12–15 kcal/mole were deduced. These values of ΔH*, ΔE*, and ΔV* are higher than the corresponding values reported by Anderson and Slichter for three other organic solids and might indicate the effect of the large number of hydrogen bonds in HMT.

Effect of pressure on 14N nuclear quadrupole relaxation in hexamethylenetetramine

The 14N pure nuclear quadrupole resonance frequencies in the molecular crystal malononitrile were measured as a function of hydrostatic pressure up to 5.6 kbar. Above T=21.55°C, the second order phase transition previously studied by Zussman and Alexander was observed at high pressures. Above the transition pressure pc, each resonance line splits into two. The splittings Δν along an isotherm at 23°C were fitted to the equation Δν=B (p−pc)β and the critical exponent β was found to be close to 0.5. The variation of Tc with pressure was measured to 2 kbar and the line of transition could be described by the linear equation Tc(p) = 21.51+16.5734p. The present results for the variation of Δν along an isotherm were compared with previous results obtained along an isobar.

14N PNQR investigation of the effect of pressure on phase transition in malononitrile

Periodically poled KTiOPO 4 (KTP) wafers with short period length are required for generation of green and blue coherent light Electric field poling processes developed for producing inverted micrometer scale domain structures in other ferro-electric materials cannot be directly applied to flux-grown KTP due to its relatively high (super ionic) conductivity at room temperature In this paper we describe the low temperature method developed by us for poling flux- grown KTP crystals without modifying their composition High voltage switching pulses were applied to KTP samples at a temperature below the superionic insulating transition and the switching charge was continuously monitored This way, high quality domain gratings of 38 - 10 micrometers periods were fabricated in 05 - 10 mm thick flux-grown KTP plates Second harmonic generation in the range of 400 - 530 nm light by these samples were tested with different types of IR lasers including diode, diode pumped solid state and fiber lasers The results demonstrate that the low temperature poling technique can provide high quality, short period periodically poled KTP for blue and green coherent light generation

Frequency doubling in periodically poled flux-grown KTP of short period length

A frequency-converted laser apparatus including a laser source (10) which generates primary radiation, a Bragg reflector (24) which reflects part of the primary radiation within a frequency range centered at a preselected fundamental frequency back along an optical path to the laser source (10) thereby to form an external laser cavity including the laser source (10) resonant at the preselected fundamental frequency, and a frequency converter (22) located within the external laser cavity on the optical path between the laser-source (10) and the Bragg reflector (24) and operative to convert part of the primary radiation into frequency-converted secondary radiation. There is also provided a method of forming on the surface of a crystal a frequency converting optical waveguide including a plurality of periodic segments comprising sections of a first kind, having a first electric polarity, and sections of a second kind, having a second electric polarity, including making a plurality of discrete regions on the surface of the crystal according to a preselected masking pattern, preparing an ion exchanging molten salt solution, controlling the concentration of oxides in the molten salt solution, immersing the masked surface ot the crystal in the molten salt solution for a preselected period of time and removing the masking material from the surface of the crystal.

Avigdor Zussman

Papers

14N PNQR study of the effect of pressure on the phase transition and molecular reorientation in s‐triazine

Effect of pressure on 14N nuclear quadrupole relaxation in hexamethylenetetramine

14N PNQR investigation of the effect of pressure on phase transition in malononitrile

Frequency doubling in periodically poled flux-grown KTP of short period length

Improved frequency multiplier and method of producing the same