Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in S${\mathrm{F}}_6$ using a pulsed C${\mathrm{O}}_2$ laser operated on the 10.4-μ m branch. A pulse width of 1.2 nsec was used to reduce effects of collisional relaxation. Data are also presented for pulse widths of 140 nsec. At high-energy fluences (∼0.1 J/${\mathrm{cm}}^2$) pulse breakup is observed and is believed to arise from multiple-photon effects. The data obtained with the short pulse width are compared to a four-level saturable-absorber model where excellent agreement is obtained when pump absorption is included. The qualitative behavior of DFWM due to dispersion is also demonstrated in the wings of the S${\mathrm{F}}_6$ absorption spectrum. Peak reflectivities of 38% were readily obtained. In addition contributions due to a coherent three-level nonlinearity are presented showing a contribution equal to the measured saturable contribution.

This paper considers the effect of stochastic variations in the polarization of a laser tuned to resonance with the transition between a $J=0\mathrm{}$ state and the $m=-1\mathrm{}$ magnetic sublevel, of a $J=1\mathrm{}$ state. The transition rate into the $M=1\mathrm{}$ sublevel, which is zero in the pure-polarization case, is calculated using two approximate methods, second-order perturbation theory and first-order Redfield theory.

The evolution of a light wave along an optical system, in paraxial approximation, can be described with the aid of a group of operators acting as canonical transformations in the framework of nonrelativistic quantum mechanics in two dimensions. This group is isomorphic to the ten-dimensional metaplectic group Mp(2). The homomorphism Mp(2)→Sp(2) (symplectic group) gives a description of the geometrical-optics approximation.

Magnetostatic wiggler fields $\hat{x}coskz+\hat{y}sin\mathrm{kz}$, commonly used to model the undulators of free-electron lasers, violate Maxwell's equations and are "unrealizable." Realizable wigglers that approximate the unrealizable ones near the axis have a radial variation and an axial field component, both of which affect electron motion. Exact helical equilibrium orbits are given for relativistic electrons in a combined uniform guide field and realizable wiggler, in cylindrical geometry. The parameter $\mathrm{ka}$ that measures the size of the helix also measures the imparted quiver motion, on which the gain of the laser depends. Hence, wigglers that impart substantial quiver motion necessarily have electrons far from the axis, for which the unrealizable wiggler model is not valid. A linearized stability analysis shows that the equilibrium helical orbits are either strongly unstable or else exhibit a secular growth, linear in time. The trajectory of an electron that starts from given position and velocity in combined guide field and wiggler is also found from the perturbation analysis, with corrections for realizability and for harmonics of practical wigglers, such as a bifilar winding. Although the helical orbits are either strongly or weakly unstable, a class of nonhelical bounded orbits is found when the secular behavior is suppressed.

A quantum-statistical theory of optical Hanle effect is developed for arbitrary intensities and bandwidths of the pump field. The excited- and ground-state level shifts, caused by another light field with appropriate polarization, are directly included in the theory by using the method of time averaging. The laser fluctuations are taken into account exactly by using the phase-diffusion model of the pump laser. The analytical and numerical results for the fluorescence signals are presented for a variety of excitations. Our results in the limiting case reduce to those of Kaftandjian, Klein, and Hanle. Finally, the case of a very broadband excitation under saturation conditions is analyzed and the results for signals in various directions and the polarizations are obtained.

A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized $P$ representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.

The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.

Owing to the large dipole associated with its nitrile bond, 8OCB (cyano-octyloxybiphenyl) tends to associate as antiparallel pairs. The number of pairs, $N$, increases with increasing mole fraction, $x_{6\mathrm{OCB}}$, of a shorter homolog, 6OCB (cyanohexyloxybiphenyl). The stability of the nematic and smectic-$A$ phase depends upon $N$: increasing $N$ favors the nematic and decreasing $N$, the smectic-$A$ phase. When $N$ saturates, the smectic-$A$ phase no longer exists and the nematic reenters. Experimental results which support the above are presented. (1) Density measurements of the 8OCB-6OCB system yield two main results. (a) The density $\rho$ is not linear in temperature at high temperatures but becomes so at low temperatures. (b) $\left(\frac{1}{\rho }\right)\propto x_{6\mathrm{OCB}}$. The first indicates saturation in the number of associations at low temperatures. The second implies that the volume of the mixture is simply the sum of the volumes of the two components. An investigation of the temperature dependence of (1b) indicates that the saturation effect of (1a) is associated with the reentrant nematic phase. (2) Using the results of (1b), we estimate $N$ from lattice-spacing measurements of the smectic-$A$ phase of the mixtures. Even though $N$ is large in 8OCB (∼95% of the molecules are paired at any one time) it increases with the addition of 6OCB. All the molecules are paired when $x_{6\mathrm{OCB}}\sim 37$%. (3) In the pressure-temperature phase diagram, the maximum pressure at which the smectic-$A$ phase is stable, $P_M$, decreases as $N$ increases. Since pressure tends to stabilize the nematic at the expense of the smectic-$A$ phase, this is consistent with an increase in $N$ with pressure. $P_M$ is found to decrease linearly in the 6OCB-8OCB scavenging parameter, $x_2=2\mathrm{}{x}_{6\mathrm{OCB}}{x}_{8\mathrm{OCB}}-{\left(x_{6\mathrm{OCB}}\right)}^2$. $x_2$ is proportional to the difference between the number of 6OCB-8OCB and 6OCB-6OCB pairs. These results, as well as others, are discussed in terms of a Landau theory which assumes that the nematic and smectic-$A$ order parameters are coupled, and that the coupling depends upon $N$, temperature, and pressure.

Radiation emission over a wide range (5-5000 Å) of wavelengths in a high-density aluminum plasma has been studied theoretically. The atomic model includes explicit treatment of a large number of states and transitions characterizing the line emission from the A1 III-A1 XIII ions. The state populations are calculated using a set of atomic rate equations describing a plasma in collisional-radiative equilibrium. The ionization state of the plasma is calculated self-consistently with line and continuum radiation transport using a one-dimensional multicell structure for the plasma. A new radiation transport scheme has been implemented in this model based on probability of escape for both line and continuum photons. The total $L$- and $K$-shell radiation emission is described as a function of plasma temperature, density, and source size, and is compared to predictions made from corona and local thermodynamic equilibrium models. It is shown that over a wide range of plasma parameters, neither of these two limiting models accurately describes the plasma emission characteristics. Several line intensity ratios from $L$-shell lines are studied and shown to be useful diagnostic indicators of the plasma temperature and density. Finally, theoretical spectra are calculated and discussed in the context of their comparability with experimental spectra in order to make contact with real plasma radiation signatures and exploit the predictive capabilities of the model.

We derive an expression for the wave-vector- and frequency-dependent shear-viscosity coefficient which involves equilibrium stress-stress time-correlation functions. Except at zero wave vector, the expression does not have the conventional Kubo form.

Calculations on the field-theoretic model of an interface, recently proposed by Wallace and Zia, are extended to three-loop order, in an expansion in $\epsilon =d-1\mathrm{}$, where $d$ is the bulk dimension. Extended to $d=2\mathrm{}$, we find a correlation-length exponent $\nu =1\mathrm{}$ near the critical point, in satisfying agreement with the two-dimensional Ising model. We also prove a Ward identity for the Gibbs free energy of the interface which allows a dramatic reduction of the calculational labor involved.

An approximation scheme is derived to calculate the velocity-autocorrelation function for the Lorentz model of overlapping hard discs and hard spheres. The theory describes a feedback between the particle-density correlations and the current relaxation rate, and is shown to give a percolation edge, a transition from the normal diffusion phase to nondiffusion phase characterized by a finite localization length $l_0$. Near the edge the low-frequency velocity spectrum for either phase is evaluated, thereby finding diffusivity to approach zero linearly with the separation parameter $\epsilon =\frac{(n-n_c)}{n_c}$, where $n_c$ is the critical density, while $l_0$ diverges like $\frac{1}{\sqrt{\epsilon }}$. A power-law long-time decay of the velocity-autocorrelation function is found for the diffusion phase. Upon approaching $n_c$ the hydrodynamic regime shrinks to zero, and a transition in the power-law exponent from its low-density value which is dependent on dimension to a value of $\frac{3}{2}$ for both dimensions is predicted.

The frequency of collision of a charged particle (electron or ion) with neutral particles in a strong magnetic field is rigorously calculated on the assumptions that both the charged and the neutral particles are composed of smooth elastic spheres on which no attraction operates at a distance, and that they have Maxwellian velocity distributions. The physics of the collision between a charged and a neutral particle is obtained by tracing the trajectory of the particle in the magnetic field. First the expression of the relative velocity of a charged particle to a neutral particle in a magnetic field is obtained, and after that, the equation of the collision frequency is derived. The collision frequency of the charged particles in the presence of the magnetic field is found to be smaller than that in the absence of the magnetic field.

We have obtained expressions including corrections to scaling terms for a number of thermodynamic properties of fluids near the critical point by specializing the appropriate derivatives of the logarithm of the grand partition function to trajectories of experimental interest. Our justification for applying Wegner's general predictions, for the functional form of the free energy, to this thermodynamic potential is that it is the potential for a fluid most closely analogous to the Helmholtz free energy for the Ising model. It is found that the average of the coexisting densities, the so-called rectilinear diameter, is a nonlinear function of the temperature with a temperature derivative which diverges like the constant volume specific heat, at the critical point, with a system-dependent coefficient. The second-temperature derivative of the chemical potential, along either the coexistence curve or the critical isochore, is found to be nondivergent at the critical point and its value is the same above and below $T_c$. The corrections due to the irrelevant scaling fields are found to be as important as those due to higher-order terms in the expansion of the scaling fields around the critical point. Using the parametric representation of the linear model, we have been able to obtain expressions for the elements of the matrix relating relevant scaling fields and physical variables in linear form, in terms of experimentally measurable quantities.

The diffusion coefficient $D$ and the Ostwald solubility $\alpha$ have been measured for ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}$ atoms in water-sucrose solutions ranging in viscosity $\eta$ from 1 to 289 cP, i.e., 0.68% sucrose by weight. In water $D\left(20\mathrm{}°\mathrm{C}\right)=(1.32\mathrm{}\pm 0.05)\times {10}^{-5\mathrm{}}$ ${\mathrm{cm}}^2$/sec, in agreement with the Stokes-Einstein (SE) law. Over the entire range studied the observed dependence is $D\propto {\eta }^{-0.63\mathrm{}\pm 0.02}$, significantly departing from the SE law. In water $\alpha \left(20\mathrm{}°\mathrm{C}\right)=0.108\mathrm{}\pm 0.005$. For water-sucrose solutions $\alpha$ is approximately proportional to the volume fraction of water in solution.

A compact path-diagram method has been introduced for the calculation of velocity moments of a probability function. This method is complementary to the approach developed earlier by Rechester and White. It is applied to the Chirikov-Taylor model. Analytic expressions for velocity-space diffusion have been derived and compared with numerical computations. A numerical method for path summations has been developed which is more efficient than directly advancing the model equations, and is applicable for small field-amplitude values, where the direct stepping method is impractical.

High-pass filtering of turbulent velocity signals is known to produce intermittent bursts. This is, as shown, a general property of dynamical systems governed by nonlinear equations with band-limited random forces or intrinsic stochasticity. It is shown that singularities for complex times determine the very-high-frequency behavior of the solution and show up in the high-pass filtered signal as bursts centered at the real part of the singularity and with overall amplitude decreasing exponentially with the imaginary part. Near a singularity, nonlinear interactions, however weak they may be on the real axis, acquire unbounded strength. Investigations of singularities by nonperturbative methods is thus essential for quantitative analysis of high-frequency or high-wave-number properties. In contrast to results based on two-point closures, the high-frequency dissipation-range spectrum is actually not universal with respect to the low-frequency forcing. Unlimited intermittency is demonstrated, i.e., the flatness of the high-pass filtered solution grows indefinitely with filter frequency. This gives strong support to a conjecture of Kraichnan [Phys. Fluids 10, 2080 (1967)] about intermittency in the dissipation range of turbulent flows. The analysis is carried out in great detail for the nonlinear Langevin equation $m\dot{v}=-\gamma v-v^3+f\left(t\right)\mathrm{}$. Lorenz's three mode system and Burgers's model are also discussed. Conjectures are made about Navier-Stokes turbulence which can be checked experimentally and numerically.

A perturbational method in the form of a power series in a "softness parameter" $\xi$ has been developed for determining the thermodynamic properties and the pair-correlation function of a real fluid using the thermodynamic quantities and distribution functions of a reference system. The method makes possible a simple treatment for the higher-order terms and enables us to take into account some parts of the higher-order terms in the usual density-dependent form of the thermodynamic quantities, in terms of lower-order terms, namely, those parts that can be expressed in terms of the derivatives of lower-order distribution functions with respect to the density. Thus we expect to achieve higher accuracy compared to the usual treatments in the case when we know, for example, only the pair-correlation function of the reference system, since the method makes full use of the information content of the pair function. Besides, new conditions have been proposed for the optimal choice of the reference system.

The thermodynamic properties and the radial distribution functions for systems with inverse-power potential and for a Lennard-Jones fluid at high temperature are calculated using a new perturbation method applied for a hard-sphere reference system. The results are compared to those obtained from the Andersen-Weeks-Chandler theory and to the Monte Carlo results.

The general conditions under which a system undergoing a first-order phase transition will exhibit hysteresis behavior, rather than simple jump behavior, are obtained. These are expressed in terms of the intrinsic time scales of the system and the time scale of variation of the control parameter. The size of the critical region is estimated. Estimates of the characteristic times are made for some equilibrium and nonequilibrium systems to show hysteresis behavior.