Well-resolved Ramsey fringes have been demonstrated using laser Stark spectroscopy of ${\mathrm{CH}}_3$F in a molecular beam with two interaction regions. Fringe separations as low as 155 kHz were obtained. The interaction regions were produced by masks containing slits placed in the Gaussian-profile beam of a cw ${\mathrm{CO}}_2$ laser. Population inversion resulting from a frequency sweep associated with the curvature of the slit-diffracted wave fronts has limited the observations at high laser-power values. An imaging system has been shown to eliminate this effect. Experiments with three and five laser-molecular beam crossings were also conducted to demonstrate the feasibility of using multiple interaction regions as a tool for high-resolution spectroscopy. The results have been modeled using the optical Bloch equation for a two-level system. Good agreement with the experiment has been obtained.

A three-dimensional free-electron-laser theory in the small-signal regime is presented. In the first part, we derive an energy theorem which relates the gain and the loss of an optical beam of arbitrary shape, driven by an electron beam of arbitrary profile. We show how this theorem can be applied for gain calculation and optimum resonator design. In the second part, we introduce a generalized description of a Gaussian optical beam. This includes four real parameters: the on-axis intensity and phase, the beam waist, and its radius of curvature. These quantities are made to evolve self-consistently and are governed by a set of ordinary differential equations which are readily integrated numerically. The solution of these equations provides an easy and intuitive means for the understanding of transverse effects induced by the interaction with the electron beam in a way which is considerably simpler than the more accurate large-scale simulation techniques.

The problem of pulse amplification in the small-signal regime of a laser amplifier is investigated theoretically. Analytical solutions to the Maxwell-Bloch equations are obtained. These reconcile the concept of laser gain needed to describe free-electron lasers (and synchronously pumped lasers in general) with earlier concepts that describe pulsed laser amplifiers. We find the latter to be a transient of our solution while the former depends on its asymptotic features.

Multiphoton absorption at a crossed-laser-beam interference pattern followed by nonradiative relaxation of the excited molecules creates a thermal Bragg grating containing harmonics of the spatial frequencies present in the interference pattern. The linearized hydrodynamic equations describing the evolution of the density and temperature modulations induced by electrostriction and multiphoton absorption at a two-beam intersection are solved. The solutions display an isobaric component arising from purely electrostrictive coupling to the liquid. Forced Rayleigh scattering from the anharmonic density modulations provides a zero-background technique for determining the highest order of an n-photon absorption process. Third-order diffraction is observed from Bragg gratings created in benzene and chlorobenzene providing the first observation of three-photon absorption into a state above the lowest excited electronic state in these liquids. The measured three-photon cross sections are ${\sigma }_3$(λ=532 nm)=(7.9±2)×${10}^{\mathrm{-}79}$ ${\mathrm{cm}}^6$ ${\sec }^2$ for benzene and ${\sigma }_3$(λ=532 nm)=(2.6±0.6)×${10}^{\mathrm{-}78}$ ${\mathrm{cm}}^6$ ${\sec }^2$ for chlorobenzene. The three diffraction orders observed are well fit to the theory developed for relative intensity, angular sensitivity, and transient decay rate.

A harmonic-generation mechanism that relies on the coupling modulation between an electron orbit and an electromagnetic mode is proposed. Applications of this mechanism to harmonic generation in linearly polarized free-electron lasers predicts the emission of even-harmonic radiation in the forward direction primarily in the ${\mathrm{TEM}}_{01}$ mode.

Propagation of a Gaussian wave packet in an absorbing medium is examined in order to shed light on the physical basis of group velocity which exhibits a singular behavior. It is found that the velocity of the wave packet, defined as the traveling distance of the peak amplitude divided by its flight time, decreases in the absorption range of frequency, although the group velocity becomes infinite in the same range. Fast pulse propagation, which was observed by Chu and Wong and is characterized by a packet velocity faster than the light velocity, turns out to be a characteristic in the early stage of the flight and is understood in terms of packet distortion due to damping of Fourier-component waves in an anomalous dispersion region. It also turns out that slow pulse propagation characterized by a packet velocity less than the light velocity appears for long traveling distance. The results provided a unified picture of wave-packet propagation in an absorbing medium.

We represent two groups of excited atoms which radiate at slightly different frequencies by means of a pair of inverted harmonic oscillators coupled to the radiation field. The radiation emitted spontaneously by these oscillators is amplified exponentially and the field generated by each exerts a strong dynamical influence on the other. For the regime in which the amplification rate is large compared to the frequency difference of the uncoupled oscillators, the indirect coupling via the field tends to lock the two systems in phase so that they radiate in unison. When the amplification rate is small compared to the frequency difference, however, each oscillator undergoes, in addition to its own spontaneous oscillation, a partially coherent oscillation forced at the frequency of the other oscillator. These mutually induced oscillations give rise to intensity beats in the radiated field. Such beats have predetermined phases which are independent of the random initial phases of the oscillator amplitudes. The beats can be present and detectable in statistical terms even before a single photon has been emitted on the average.

The Holstein-Primakoff transformation is used to transform the model of N (>1) two-level atoms collectively interacting with multiphotons of a single quantized mode of the field (the Tavis-Cummings model) into a boson-boson model. Formal solutions are obtained in the strong-coupling limit and/or the large-number-of-atoms limit. The analogy is drawn with a simple model of frequency conversion. The characteristic function in the p representation for the transformed model is calculated.

The free-electron laser can be described by solving the Lorentz-Maxwell equations self-consistently in weak optical fields. The field evolution is determined by an integral equation that allows the inclusion of an arbitrary electron distribution function in a simple way. Contour maps are used to show the gain degradation due to an electron-beam energy spread and an electron-beam angular spread. In the limit of low gain, the gain spectrum is related to the spontaneous emission line shape through successively higher derivatives. In the limit of high gain, it is shown that the growth rate becomes less susceptible to degradation from the electron-beam quality.

The energy-level shifts for a multilevel atom interacting with a squeezed vacuum are calculated. The level shifts are made up of two contributions: (i) the ordinary Lamb shift and (ii) a shift due to the squeezed-vacuum intensity spectrum (similar to the blackbody-radiation shifts).

Short, bright pulses of x-ray line emission are needed for flash radiography of laser-fusion targets. The experiments described here were carried out with the nominal laser pulse lengths of 60 and 120 ps. The M→L spectra were for Y (2.00–2.35 keV), Pd (2.95–3.46 keV), and Cs (4.43–5.15 keV), and the L→K spectra were for Cl (2.790 keV), Ti (4.749 keV), Mn (6.180 keV), and Ni (7.804 keV). The L→K energies are for the 1s2p thinsp${;}^1$$P_1$→1$s^2$ ${}^1$$S_0$ transition. Both the duration and the absolute brightness of the x-ray line emission were measured. Even at 60 ps, the x-ray flashes from Y, Pd, and Ti were all bright and of duration comparable to or shorter than the laser pulse length. In particular, the Pd M→L lines were as bright as 2×${10}^{12}$ photons/j? and the Ti L→K lines as bright as 5×${10}^{10}$ photons/j?.

A model of a coupled atom—quantum-field system is presented, consisting of a time-independent Hamiltonian and a realistic dynamical initial condition. The Hamiltonian describes a fixed bound atom coupled to the complete electromagnetic field. The initial condition is a consistent quantum-mechanical description of an atom in the exact ground state of the coupled atom-field system, on which is superimposed an approaching quasiclassical excitation of the field which will cause the interesting dynamical processes later on. Tools are presented for the manipulation of this model, with emphasis towards series expansions of all relevant quantities suitable for small strength $\lambda$ of the atom-field coupling and (potentially) large magnitude $\alpha$ of the coherent field excitation, such that the "influence of the coherent excitation on the atom" (i.e., the product $\lambda \alpha$) remains constant as $\lambda$ tends to zero. The following results are obtained, at the lowest nontrivial order in $\lambda$, in an approximation suitable for times much shorter than any radiative lifetime of the atom: (a) The change in free-field energy due to the interaction with the atom is exactly compensated at all times by the change in bare-atom energy plus the atom-field coupling energy. This checks the consistency of the proposed scheme. (b) The frequency distribution of this change in free-field energy has a (somewhat unexpected) component, with a smooth spectrum, spreading over the whole width of the spectrum of the exciting pulse, in addition to $\delta$ and dispersive singularities centered on the atomic transition frequencies. This frequency distribution is discussed in detail and its features are illustrated by a number of figures, in a simple case, numerically tractable. (c) The heterodyne detection of the radiation emitted by the atom is investigated, with emphasis on the issue of causality and propagation of light. Strict causality is obtained, without further approximation, in a model with an atom-field coupling involving the field at a single point and a detector similarly sensitive to properties of the field at a single point. This result breaks down if one uses nonlocal approximations such as the rotating-wave approximation or a detection observable ${\mathbf{E}}^{-}\left(\mathbf{r}\right)·{\mathbf{E}}^{+}\left(\mathbf{r}\right)$. Finally, an appendix is devoted to the use, in quantum mechanics, of bases moving with respect to each other.

A fully quantum-mechanical theory of nondegenerate four-wave mixing in a system of two-level atoms is presented. The squeezing in the output field from an intracavity four-wave-mixing experiment is calculated. The theory is compared with the recent experimental results of Slusher, Hollberg, Yurke, Mertz, and Valley and strategies to improve the squeezing are suggested.

We present experimental results for the location of the Eckhaus stability boundary in rotating Couette-Taylor flow between concentric cylinders of radius ratios 0.892 and 0.747. Generally, they agree well with recent calculations by Riecke and Paap. However, for wave numbers q larger than the critical $q_c$, the experimental stability boundary lies significantly above the theoretical calculation. We also present experimental results for the wave-number selection by a gentle spatial variation (ramp) of the Reynolds number R from above to below the critical value $R_c$ for the onset of Taylor-vortex flow. For a sufficiently small ramp angle α, the data suggest that a unique, R-dependent value of q is selected, regardless of the aspect ratio (supercritical system length) L. For finite α, a band of wave numbers is accessible, and for a given L the system can select one or more discrete values of q within that band. The selected q(L) has a period close to λ=2π/qapeq22. The bandwidth initially decreases as R exceeds $R_c$, and then increases again. The initial band near $R_c$ is quantitatively consistent with an explanation offered by Cross. The wave number at high R, although it also has a period of about 2, is phase shifted relative to that near $R_c$ by half a period. The corresponding stability band and selected q for vanishing α have not yet been explained in detail from theory. They are, however, generally consistent with the theoretical considerations of Kramer et al. We also discuss the use of the Ginzburg-Landau equation for estimating $R_c$ of the infinite system from measurements of the apparent ‘‘onset’’ of Taylor-vortex flow in finite systems.

We analyze in detail an algorithm for computing Liapunov exponents from an experimental time series. As an application, a hydrodynamic experiment is investigated.

We study the growth of dendritic crystals from a supersaturated solution in a channel geometry. This model provides a continuous interpolation between the Saffman-Taylor problem and the (two-dimensional) free-space dendrite. We derive an integral equation for the shape of steady-state propagating fingers, which we treat by discretizing the curve and solving the resulting set of nonlinear algebraic equations by Newton’s method. For general Peclet numbers, in the absence of anisotropy the finger widths are always greater than half the channel width, but with anisotropy all widths are obtained. The numerical results are in rough agreement with an approximate WKB treatment for small anisotropy and zero Peclet number. Finally, we speculate on the emergence of sidebranches in this system.

Solutions of tetramethoxysilicon are reacted until very near the sol-gel transition. At this point the sol is diluted and elastic and quasielastic light scattering measurements are made at intermediate momentum transfer. The static scattering exponent for the diluted sol is found to be in good agreement with the percolation prediction of 1.6, and the quasielastic scattering measurements demonstrate the flexibility of the sol clusters.

The stress-relaxation function σ(t) in a stabilized glass is described by a potential-barrier model which is based on separating geometric packing considerations from thermal excitations in the dynamical evolution of a many-body system. The analysis proceeds in stages: (1) The configuration space is uniquely divided into cells, each associated with a minimum on the potential energy φ hypersurface. (2) ‘‘Crystal-free’’ particle packings are isolated. (3) Since the φ hypersurface in the amorphous manifold is topographically rough over a wide range of length scales, a coarse graining is carried out to suppress small-scale roughness. (4) Stress relaxation is connected with transition between cells which involve localized particle motions. A master equation describes the time-dependent residence probabilities in the cells. The basic physical assumption is that the slowest structural rearrangements in a dense, highly viscous supercooled fluid occur on a molecular length scale via self-diffusion. We find that σ(t)=${\phi }_0$exp[-(t/τ${)}^{\alpha }$]; for t≪τ, α=(1/3); for t∼τ, α=(1/2); for t≫τ, α=1. The temperature dependence of τ is governed by the self-diffusion of the viscous fluid.

We treat the effect of parametric modulation on the onset of instability in Rayleigh-Bénard and Taylor-Couette geometries. Closed-form solutions are obtained for the case of realistic rigid-boundary conditions. The high-frequency limit of the effect in the Taylor-Couette flow differs from that of Hall.

A model, recently introduced to describe diffusion-limited aggregation without branching (i.e., in the limit of extreme anisotropy), is studied in the deterministic continuum limit. An exact solution of the resulting nonlinear mean-field equations, describing deposition onto a (d-1)-dimensional surface from a d-dimensional semi-infinite space, is found.