A ‘‘missing-state’’ analysis is introduced and used to identify excited states and dynamics important for ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ and ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$. This method is applied to the Pariser-Pople-Parr self-consistent-field configuration-interaction transition moments and energies that are used to calculate the second-harmonic susceptibility ${\chi }_{2\omega }^{\mathrm{}\left(2\right)\mathrm{}}$ and the third-harmonic susceptibility ${\chi }_{3\omega }^{\mathrm{}\left(3\right)\mathrm{}}$ for a group of organic molecules. Examination of charge and bond-order distributions for the relevant states reveals the nature of the states that contribute to the nonlinear optical processes. Results are presented for benzene, nitrobenzene, p-dinitrobenzene, and p-nitroaniline.

Optical phase conjugation by stimulated Brillouin scattering, excited by an inhomogeneous light field with a self-focusing strong component, has been investigated. The conjugation fraction η depends on the intensity ratio σ of the strong component to the total pump light, attaining a maximum at a certain value of σ. Theoretical analysis shows that a four-wave-mixing process is involved in its physical mechanism. By taking into account the effect of self-focusing, a fair agreement with experiments is obtained.

This paper gives a detailed description of the plane-wave Gaussian models of optical bistability and of the experimental investigations of the single-mode instability induced on a beam of sodium atoms in a cavity by an external driving field. Our goal is to provide a careful comparison of the theoretical and experimental results. We focus on the shape of the instability domain, the nature and behavior of the spontaneous output oscillations produced by the instability, and their frequency dependence on the control parameters. We carry out this comparison using both the plane-wave and Gaussian models. Our analysis shows that the latter is in good quantitative agreement with the experimental results. We investigate in detail the main assumption of the Gaussian model, namely, that the internal cavity field retains the same radial profile as the input field.

Petermann first predicted in 1979 the existence of an excess-spontaneous-emission factor in gain-guided semiconductor lasers. We show that an excess spontaneous emission of this type, and also a correlation between the spontaneous emission into different cavity modes, will in fact be present in all open-sided laser resonators or optical lens guides. These properties arise from the non-self-adjoint or non-power-orthogonal nature of the optical resonator modes. The spontaneous-emission rate is only slightly enhanced in stable-resonator or index-guided structures, but can become very much larger than normal in gain-guided or geometrically unstable structures. Optical resonators or lens guides that have an excess noise emission necessarily also exhibit an ‘‘excess initial-mode excitation factor’’ for externally injected signals. As a result, the excess spontaneous emission can be balanced out and the usual quantum-noise limit recovered in laser amplifiers and in injection-seeded laser oscillators, but not in free-running laser oscillators.

When the Petermann excess-spontaneous-emission factor described in the accompanying paper [Siegman, preceding paper, Phys. Rev. A 39, 1253 (1989)] is taken into account, we find that the quantum-noise fluctuations or Schawlow-Townes fluctuations in the output spectrum of a laser oscillator will be multiplied by this excess noise factor. The excess spontaneous emission in a laser oscillator cannot be canceled by adjoint-mode-excitation techniques as it can be in a laser amplifier. The resulting noise enhancement can be very sizable (100 to 1000 times or more) in gain-guided laser oscillators, and especially in laser oscillators using geometrically unstable cavities with moderate to high magnifications and Fresnel numbers.

The Lorentz group, which is the language of special relativity, is a useful theoretical tool in modern optics. Optics experiments can therefore serve as analog computers for special relativity. Possible optics experiments involving squeezed states are discussed in connection with the Thomas precession and the Wigner rotation.

We present a detailed analysis of the dynamical behavior of an optically pumped molecular laser. This study combines bifurcation and power spectral analysis with numerical investigation of the global features of attractor topology under control parameter variation. The special role of the pump laser in generating physically distinct periodic and chaotic dynamics is emphasized through the complementary use of laser gain and dispersion characteristics. Our main results are the following: (i) instabilities associated with the physically distinct mechanisms of relaxation and pump-induced Rabi sideband oscillations are readily generated; (ii) the topological characteristics of both periodic and chaotic attractors reflect these physically distinct mechanisms, making it possible to discriminate between both types of behavior in heterodyne power spectra; and (iii) the ratio of deenergization to dipole-dephasing rates is central to determining the operating characteristics of the laser.

A new model of the Fokker-Planck equation (FPE) without detailed balance is suggested. The potential of the FPE is solved explicitly in the weak-noise limit. A discontinuity of the first derivative of the potential is revealed. The approach of solving the model may be extended to solving general FPE’s lacking detailed balance, provided the drift of the FPE can be written in proper form.

The derivation and generalization of the Navier-Stokes equation is discussed from a group-theoretical point of view. The distinction between longitudinal and shear modes is a broken-symmetry effect, which arises when a direction is chosen for the wave vector. Other symmetry-breaking effects encountered in computer simulations are discussed. The results are used in an accompanying paper [Logan and Visscher, following paper, Phys. Rev. A 39, 1298 (1989)] to extract transport coefficients from simulation data.

In this paper we apply a new method to the calculation of transport coefficients by computer simulation of fluids. It differs from previous methods in two essential respects. Firstly, it involves the simultaneous fitting of all of the correlations among conserved hydrodynamic variables, rather than just the density or current autocorrelation function. This gives more detailed information on the hydrodynamics, and, in particular, makes it possible to separate some of the effects of viscoelasticity, which may seriously bias transport-coefficient estimates. Secondly, it is formulated in a simple way, which avoids certain complicating approximations traditionally made in computing fluid correlation functions. Results of pilot calculations for the soft-sphere viscosity agree with those of previous workers. The most conspicuous physical effect observed is a strong wave-vector dependence of the thermal diffusivity, in agreement with previous work.

A set of nonlinear Langevin equations for fluctuations of the local conserved densities in a fluid under shear is proposed. These equations are a model for the extension of hydrodynamics to very short wavelengths at liquid densities. The hydrodynamic modes associated with the linearized equations are studied as a function of wave vector and shear rate. The degeneracy of the viscous shear modes is lifted by the shear, and one of these modes combines with the heat mode to form a propagating pair. As an example of nonequilibrium fluctuations, the dynamic structure factor is calculated for several values of frequency and wave vector. At large shear rates one pair of propagating modes becomes unstable at a wavelength of the order of the particle size. This instability is suggested as a possible explanation for a shear-induced disorder-order transition seen in computer simulations. Nonlinear mode-coupling effects are studied elsewhere.

Measurements of viscoelastic properties near the sol-gel transition demonstrate that viscoelastic phenomena are described by power laws. To describe these phenomena, we derive the distribution of relaxation times for branched polymers, both in the reaction bath and in the dilute solution. From this spectrum we can compute viscoelastic properties such as the shear relaxation modulus G(t) and the complex shear modulus G(ω). Near the gel point we find G(t)∼$t^{\mathrm{-}\Delta }$, with Δ a universal exponent, for times that are small compared to a divergent time ${\tau }_z$: For longer times the decay is a stretched exponential. The exponent Δ is found to be sensitive to dilution. Likewise, the storage and loss parts of the complex shear modulus are found to scale as ${\omega }^{\Delta }$. These results for the dynamics lead to a theory for the critical growth of the equilibrium shear modulus E above the gel point, and the divergence of the steady-state creep compliance $J_e^0$ above the gel point. Finally, we discuss the concentration dependence of the viscosity of a solution of branched polymers.

Through Monte Carlo simulations of rapidly quenched one-component plasmas, we investigate microscopically the dynamic evolutions of local and extended bond-orientational symmetries in supercooled states and show that the resulting states are the Coulomb glasses. The glass states are characterized by random polycrystalline structures with long-range bond-orientational order; in these states the particles are virtually locked around their equilibrium positions. The inverse temperature at the glass transition is found between 200 and 300 in units of the average Coulomb energy. The polycrystalline structures of the resulting glasses depend sensitively on how the rapid quench is applied. Physical problems specific to the Coulombic systems are discussed.

Studies of the effects of laser intensity nonuniformities on the ablation pressure profile of irradiated Si disk targets were made by measurement of the velocity profile of the shock wave launched into the target. The results show significant lateral smoothing of laser nonuniformities which increases with intensity. Experimental data are matched in two-dimensional hydrocode calculations with classical lateral heat flux.

The frequency spectrum of the thermal fluctuations in the shape of fluid droplets is derived when the droplets are coated with a thin film such as a surfactant monolayer or lipid bilayer. The surface viscosity and compressibility and the inertia and viscosity of the bulk fluids interior and exterior to the droplet are taken into account, and their effects on the decay of the surface modes is discussed in detail.

The behavior of aggregates grown using random walkers is shown to be quantified by a unique equation for different variations of the original diffusion-limited aggregation model. Only four parameters (including the fractal dimension) are needed for describing this behavior, each of them having a clear physical significance. Two parameters correspond to two different length scales: the branch width, which is associated with asymptotic behavior, and the seed size, which determines the small-mass behavior.

High-resolution heat-capacity measurements have been made on mixtures of alkylphenyl-cyanobenzoyloxy benzoate (${\mathrm{DB}}_{\mathrm{n}}$CN) and cyanobenzoyloxypentyl stilbene (${\mathrm{C}}_5$stilbene). The mixtures ${\mathrm{DB}}_5$CN+${\mathrm{C}}_5$stilbene (with mole fraction of ${\mathrm{C}}_5$stilbene X=0.492) and ${\mathrm{DB}}_6$CN+${\mathrm{C}}_5$stilbene (X=0.505) both exhibit the phase sequence N–Sm-${\mathit{A}}_1$–Sm-ÖSm-${\mathit{A}}_{\mathrm{cren}}$–Sm--${\mathit{A}}_2$, where N and Sm denote nematic and smectic, respectively. The thermal behaviors of these two samples are in excellent agreement. The second-order N–Sm-$A_1$ transition can be well represented by the XY model. The Sm-$A_1$–Sm-à transition is weakly first order with a substantial and anomalous excess heat capacity over a considerable range above as well as below the transition. This thermal effect correlates well with the unusual viscosity behavior observed in ${\mathrm{DB}}_5$CN+${\mathrm{C}}_5$stilbene. The excess heat capacity associated with the Sm-ÖSm-$A_{\mathrm{cren}–}$Sm-$A_2$ transition sequence is similar to the inverted Landau behavior observed for the Sm-C̃–Sm-$C_2$ transition in other systems, but with the peak truncated due to the presence of the Sm-$A_{\mathrm{cren}}$ phase.

The fluctuation-spectrum theory aiming at the global characterization of temporal and spatial fluctuations, where the characteristic function ${\lambda }_q$ plays the central role, is reconsidered from the ensemble-processing viewpoint. The order-q ensemble processing is constructed so as to extract the statistical-aspect characteristic of the variable q. The quantity α(q) [≡d(q${\lambda }_{\mathit{q}}$)/dq] is shown to be the average of the fluctuations in the processed ensemble. The susceptibility ${\mathrm{\chi }}_{\mathit{q}}$ [≡dα(q)/dq] for the infinitesimal change of the degree of processing turns out to determine the asymptotic probability density of fluctuations in the processed ensemble.

A particular expression of the mutual coherence function of a wave is first derived for a system of random layers with rough boundaries, starting from the unified Bethe-Salpeter equation that involves the random medium and boundaries on exactly the same footing. An effective scattering matrix of the medium is then introduced, which is the only medium-dependent quantity involved in the expression and is obtained as a boundary-value solution of the diffusion equation. The diffusion approximation is based on an eigenfunction expansion by using a set of eigenfunctions of the medium scattering cross section that can be even rotationally variant, and the first term is good enough in the diffusion region. Here each expansion coefficient is obtained as the solution of an integral equation with terms of the boundaries, and, for the first term, the equation can be converted to a diffusion equation with a source term, subjected to boundary conditions determined by the boundary scattering cross sections. Here the condition at each boundary is valid even when the averaged refractive indices of the two media differ from each other by a large amount, as contrasted to the condition of no reflection used so far when obtaining boundary-value solutions of diffusion equations. Specific expressions are obtained for both backscattered and transmitted waves through a random layer, along with numerical examples. The boundary condition is finally generalized to meet the case of a rough boundary between two random media of different kinds, consistent with power conservation.

This paper is concerned with the onset of rigidity in randomly cross-linked macromolecules. We discuss in detail the possible partitionings of configuration space, which may accompany the spontaneous breaking of translational invariance, treating separately the cases of crystals, amorphous solids, and cross-linked macromolecules. We describe the order parameters for these systems, drawing the distinction between solids with discrete translational symmetry and solids with macroscopic translational invariance, such as randomly cross-linked macromolecular solids. We show that the latter may be described by a sequence of probability distributions for the overlaps of equilibrium states. In a cross-linked system of impenetrable linear chains, the configuration space of the solid state is partitioned into two categories of equilibrium states: those related by translational and rotational symmetry, and those unrelated by these symmetries. The latter are a consequence of the distinct topologies of the network, which are consistent with a given set of cross links. We show how the overlap-probability distributions may be calculated.