The details of the time-dependent output from a hybrid optical bistable device are investigated in the regime where the delay time of the feedback signal is much larger than the response time of the device (determined by electrical bandwidth of the feedback loop). The delayed feedback is produced by placing a computer equipped with fast $A-D$ and $D-A$ converters in the feedback loop. This bistable system exhibits periodic and chaotic instabilities as predicted by Ikeda. In particular, as the input intensity is increased, the device output goes through a series of bifurcations (second-order nonequilibrium phase transitions). First, the initially stable output changes to a periodic output (a square wave) followed by a second periodic region whose period is twice that of the previous region. Up to this point, the system behavior is in agreement with the period-doubling scheme of Feigenbaum. However, the period doubling which is predicted next is only rarely observed. Instead the system usually goes over into chaotic behavior. Within the chaotic region, the device largely follows the reverse bifurcation scheme of Lorenz. In addition, there is a small domain of frequency-locked behavior that exists within the chaotic domain. These bifurcations are not only of fundamental interest but may find applications in practical optical devices.

The general formalism of transient four-wave mixing is developed using the diagrammatic technique of Yee and Gustafson, and applied systematically to two-, three-, and four-level systems. The results predict all possible photon-echo phenomena including free-induction decay in the low-intensity limit. Connections to transient saturation spectroscopy and other coherent transient effects can also be made. The treatment can be readily extended to the more general problem of coherent transient optical effects with $n$ waves.

A fully quantized theory of the free-electron laser in the small-signal regime is presented which allows for a calculation of the photon statistics. For an initial vacuum, we find photon antibunching if the electron momentum is below resonance. We conjecture that, in general, the free-electron laser preserves coherent states only in the absence of gain.

We propose and analyze an experiment designed to probe the extent to which information accessible to an observer and the "eraser" of this information affects measured results. The proposed experiment could also be operated in a "delayed-choice" mode.

This is the first of three papers dealing with the effects of quantum noise on the mean beat frequency and the spectrum of the beat signal produced by a ring-laser gyro. The behavior of a noise-free ring laser is analyzed from a novel point of view, and the characteristic response curve, demonstrating the existence of the well-known locked region, is derived. The noise-free spectrum is calculated in both the locked and unlocked regions, and the existence of higher harmonics in the unlocked region is demonstrated. The general eqution for the phase of the beat signal is then derived from a quantum-noise perspective and the general approach to the problem of calculating the spectrum in the presence of noise is presented from a Fokker-Planck point of view. Approximate analytic expressions for the spectrum are derived in the locked region and well into the unlocked region. In the latter case, the usual laser spectrum is obtained, while in the former case, the spectrum is shown to separate into two parts: a "coherent" part consisting of a $\delta$ function centered at zero frequency which represents the continued effect of locking even in the presence of noise, and a weak background "incoherent" part representing the effects of noise.

This is the second of three papers dealing with the effects of quantum noise on the operation of a ring-laser gyro. Exact expressions for the spectrum and the mean beat frequency of the beat signal are obtained in terms of infinite continued fractions. The spectrum is found to be always separable into a "coherent" $\delta$-function contribution at zero frequency, representing the effects of locking, and an "incoherent" part of nonzero band-width. Computed forms for the spectrum and the frequency response curve are presented for parameter values appropriate to the ring-laser gyro. The results obtained show that for laser rotation rates corresponding to the locked zone in the absence of noise, the tendency for locking as measured by the strength of the coherent contribution continues to dominate, but this effect rapidly becomes negligibly small outside this zone. In addition, the transition in beat frequency between the locked and unlocked zones which is discontinuous in the noise-free case ceases to be well defined in the presence of noise. Finally, the higher harmonics predicted to occur in the unlocked zone in the absence of noise are found to reoccur in the presence of noise except that the individual harmonics are now found to be broadened.

Oscillatory free-induction decay (FID) theoretically predicted by Schenzle, Wong, and Brewer was observed by using NMR in an inhomogeneously broadened proton system. Oscillatory behaviors were also observed, in the same system, in two-pulse echoes generated by large-area pulses. These phenomena appear in a highly inhomogeneous-broadened atomic or spin two-level system driven by resonant laser or rf pulses with areas equal to or larger than $2\pi$. Detailed studies were made for spin-locked and notched echoes. Behaviors of the oscillatory FID and the oscillatory echoes were theoretically examined by solving the Bloch equations and numerically integrating the solution over the inhomogeneous broadening. Excellent agreement between experiment and theory was obtained. Analytic expressions for the shapes of the locked- and notched-type echoes are obtained, which interpret the main characteristics of these echoes, when the infinite linewidth of the inhomogeneous broadening and the $\delta$-function-type excitation for one of the pulses are assumed.

A resolvent superoperator approach is described for the evaluation of the dynamic conductivity of a strongly interacting electron-phonon system, starting from a current-correlation integral formula. The conductivity is expressed in terms of a self-energy superoperator and a self-consistent expression is obtained for this temperature-dependent quantity.

High-resolution ac specific-heat measurements of the smectic-$F$—smectic-$H$ transition of $\mathrm{N}-(4-n-\mathrm{heptyloxybenzylidene})-4-n-\mathrm{hexylaniline}$ (HBHA) are reported. A hysteresis of 160 mK in the transition temperature is measured for the first time for transformations in thermotropic liquid crystals. The specific heat, obtained during heating, is larger and changes more rapidly at the transition than during the cooling cycle. This behavior of the specific heat may be explained by assuming that dislocations and defects play an important role at this transition. High-resolution x-ray measurements of the smectic layer thickness were made with an accuracy of better than 250 ppm. The temperature dependence of the smectic-$F$ layer thickness of HBHA is qualitatively different from that of TB5A and its homologs.

We report the measurement of the principal indices of refraction, and the density as a function of temperature for five liquid crystals from two homologous series. These data are used to calculate the corresponding polarizabilities after first examining published models for calculating the internal fields. The Neugebauer model, which allows for anisotropic internal fields, was chosen as the basis for interpreting data. The biaxiality of the smectic-$C$ phase is shown to be small, and possible interpretations using the Straley order parameters are discussed. The effects of varying the amount of smectic order at the $A-C$ transition are also discussed. Finally the indices of refraction in the smectic-$C$ phase are used to obtain the value of the optic angle versus temperature. Crudely, this temperature dependence goes as ${(T_{\mathrm{AC}}-T)}^{0.27}$ which seems to favor theoretical models in which the molecule rotates freely in the smectic-$C$ phase.

Morphological evidence is presented showing that the high-temperature cholesteric "blue" phase (BP II) has a simple-cubic point group, while the low-temperature phase (BP I) is probably body-centered cubic. This evidence was gathered through optical microscopy on platelets oriented with their shortest reflecting wave vector along the direction of observation. The "crosshatch" markings commonly observed during the BP I-II transition are explained in terms of the relationship between the unit cell of the BP II product and that of the BP I from which it arose.

The wavelength and angle dependence of the Bragg reflection from the cholesteric "blue" phase is studied as a function of temperature. Dynamical "Darwin flat-top" behavior is found, and the width in energy and angle of the reflection are used to estimate the ratio of the order parameters in the cholesteric and both blue phases. For both blue phases, the order parameter is about $\frac{1}{3}$ that in the cholestric, and shows a distinctive temperature dependence, part of which may be associated with the presence of a blue-phase-isotropic two-phase region in the phase diagram of one of the mixtures studied. The resemblance of the reflection curve to its ideal form indicates that the blue phase's ordering is correlated over at least 50 lattice spacings, or 10 μm.

The static dielectric permittivity of a nitrobenzene-isooctane mixture shows, along its critical isochore, a 0.3% deviation from normal behavior at a temperature of 5×${10}^{-3\mathrm{}}$ K above $T_c$. Near the consolute point, no gravity effects resulting from composition gradients are detected. A free fit of the critical exponent $\theta$ yields a value of 0.855±0.035, in good agreement with the theoretical values.

The intermittent behavior of area-preserving maps of the plane just before the appearance of cycles is investigated. Analysis of a differential-equation version of a prototypical map predicts two new scaling laws. Numerical experiments confirm these predictions in the case of three cycles.

A number of spectrum lines of highly ionized copper, nickel, iron, chromium, and germanium have been observed and the corresponding transitions identified. The element under study is introduced into the discharge of the Princeton Large Torus tokamak by means of rapid ablation by a laser pulse. The ionization state is generally distinguishable from the time behavior of the emitted light. New identifications of transitions are based on predicted wavelengths (from isoelectronic extrapolations and other data) and on approximate expected intensities. All the transitions pertain to the ground-state configurations of the respective ions, which are the only states strongly populated at tokamak plasma conditions. These lines are expected to be useful for spectroscopic plasma diagnostics in the 1 - 3-keV temperature range, and they provide direct measurement of intersystem energy separations from chromium through copper in the oxygen, nitrogen, and carbon isoelectronic sequences.

An ionization model, partly time dependent, is presented. It is convenient for modeling laser-created plasmas and simple enough to be used in short computer simulations. This model, called the mixed model (MM), is built by gathering excited bound levels and free levels of a same-charge state into one superlevel and by assuming partial local-thermodynamic equilibrium over those levels. Transition rates between two superlevels can then be computed. Its structure allows the development of the MM for inner-shell excitation and ionization, ionization-potential lowering, and Fermi statistics of bound electrons. Mean electron number, spectroscopic ratios, and radiative losses are calculated in the steady-state case. Comparison with other ionization models are made and MM calculations give better agreement with experiments. Furthermore, simple approximation formulas are given for specific energy and mean electron number of high-atomic-number materials.

We derive a variational principle for the eigenvalues of the Fokker-Planck equation in detailed balance, which holds for additive as well as multiplicative stochastic processes and which is not restricted to one dimension. An intermediate theorem for the Fokker-Planck equation is presented for the first time from which lower bounds for the eigenvalues can be extracted. The same theorem can be applied to the master equation in detailed balance. We discuss as a first application the lower and upper bounds for the lowest eigenvalue of a quartic potential in one dimension. To show the applicability of our procedure to more complicated problems we give lower and upper bounds for the linewidth factor and the second eigenvalue of the Fokker-Planck equation for the single-mode laser. In addition, we discuss three models of multiplicative stochastic processes which represent three different classes of behavior. For each model we give stationary results, namely, the probability distribution and the first two nontrivial moments. To characterize the long-time behavior of the relaxation processes involved we calculate lower and upper bounds for the lowest eigenvalue. It is pointed out that, at least in the models presented, there does not exist critical slowing down as a function of the strength of the fluctuations. We conclude that one should be cautious when using the term noise-induced phase transition in connection with multiplicative stochastic processes.

${}_{}{}^1{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ NMR measurements are reported for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ dissolved in various nematic phases. The main results are the following: Signs of order parameters are liquid-crystal dependent; the molecules with larger average bond lengths show smaller order parameters; the order parameters for ortho- and para-deuterium are equal within experimental error; the ratios of quadrupolar to dipolar couplings in HD and ${\mathrm{D}}_2$ are about seven percent lower than in the gas phase. These results are rationalized in terms of environmental effects of the liquid-crystal field on the dissolved molecules. This field decreases the quadrupolar coupling in HD and ${\mathrm{D}}_2$ and causes extensive mixing of different rotational states of the hydrogens in the liquid phase. The observed isotope dependence of the average orientation is a quantum-mechanical effect which can be explained by the influence of a simple one-parameter mean liquid-crystal field on the rotational energies and rotational wave functions of the hydrogens.

The effect of suprathermal electron drive on symmetry and uniformity of compression is studied for directly irradiated, thick-wall laser-fusion targets. In these experiments, in which suprathermal electron range is comparable to target-wall thickness, two-dimensional multispectral x-ray images (2.5, 4.5, 6, and 17 keV) support the conclusion that suprathermal electrons dominate target drive. Although symmetry is improved by the suprathermals, drive nonuniformities persist through the implosion process, compromising the ultimate symmetry and uniformity of compression. These experiments explicitly demonstrate the need to moderate suprathermal electron production and improve drive symmetrization.

This paper presents an investigation of the nonlinear interaction of a Gaussian electromagnetic (EM) beam with an electrostatic upper hybrid wave in a collisionless magnetoplasma. The EM beam is assumed to be propagating in the ordinary mode, having a nonuniform intensity distribution (along its wave front) in a plane transverse to the direction of propagation. Because of the Gaussian intensity distribution of the EM beam, a time-independent component of the ponderomotive force becomes finite and this leads to a coupling between the pump EM beam and the electrostatic upper hybrid wave. This coupling is so strong that the weak electrostatic upper hybrid wave gets excited. The excited electrostatic upper hybrid wave may again interact with the pump EM beam and lead to the generation of an electrostatic lower hybrid wave of significant power.