The quantum-defect-orbital method has been reformulated in order to include a major part of the relativistic effects. The resulting quasirelativistic approach retains the simplicity of the original formulation but leads to more reliable results, particularly for the highly ionized atoms. The theory is illustrated by a series of calculations of oscillator strengths for the resonance transitions in atoms of lithium, sodium, and copper isoelectronic sequences.

Doppler-free two-photon spectroscopy has been applied to investigate the hyperfine structures and the isotope shifts of 27 fine-structure levels of ${}_{}{}^{151,153}{}_{}{}^{}\mathrm{Eu}$ in the energy region between 34 400 and 36700 ${\mathrm{cm}}^{\mathrm{-}1}$. With the experimental data the fine-structure calculations of Wyart have been widely confirmed, and two levels of the ${}_{}{}^8{}_{}{}^{}$D term of the configuration 4${\mathit{f}}^7$6s6d have been identified as e ${}_{}{}^8{}_{}{}^{}$${\mathit{D}}_{3/2}$ (35 282.22 ${\mathrm{cm}}^{\mathrm{-}1}$) and e ${}_{}{}^8{}_{}{}^{}$${\mathit{D}}_{7/2}$ (35 377.94 ${\mathrm{cm}}^{\mathrm{-}1}$).

With effective one-electron parameters ${\mathit{a}}^{\mathit{k}\mathit{l}}$ and ${\mathit{b}}^{\mathit{k}\mathit{l}}$ an analysis of the magnetic and electric hyperfine structure for the terms ${\mathit{e}}^6$D, ${\mathit{e}}^{10}$D, and ${}_{}{}^8{}_{}{}^{}\mathrm{D}$ of the configuration 4${\mathit{f}}^7$6s6d was performed: ${\mathit{a}}_{4\mathit{f}}^{10}$=-50(13) MHz, ${\mathit{a}}_{6\mathit{s}}^{10}$=12 590 (90) MHz, ${\mathit{a}}_{6\mathit{d}}^{12}$=25(20) MHz, ${\mathit{b}}_{4\mathit{f}}^{11}$=0(2) MHz, ${\mathit{b}}_{6\mathit{d}}^{11}$=-4(2) MHz, ${\mathit{b}}_{6\mathit{d}}^{13}$=-30(20) MHz, and ${\mathit{b}}_{6\mathit{d}}^{02}$=+81(5) MHz. From the quadrupole moment ${}_{}{}^{151}{}_{}{}^{}$Q(6d)=2.07(30) barn a Sternheimer quadrupole shielding factor was found to be ${}_{}{}^{151}{}_{}{}^{}$R(6d)=-1.29(35). In addition, higher-order effects of the isotope shift could be explained in the same terms of 4${\mathit{f}}^7$6s6d with the use of a parametric description. We obtained the following parameters: ${\mathit{d}}_{6\mathit{s}6\mathit{d}}$=-3140(80) MHz, ${\mathit{d}}_{5\mathit{d}}^2$=-5270(130) MHz, ${\mathit{g}}_1$(4f,6d)=+1(3) MHz, ${\mathit{g}}_2$(6d,6s)=-290(50) MHz, ${\mathit{g}}_3$(4f,6s)=-36(2) MHz, and ${\mathit{z}}_{6\mathit{d}}$=6(4) MHz.

Calculations are reported of the dynamic second hyperpolarizabilities (γ) of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ which are relevant to three different nonlinear optical processes. They have been carried out using an expanded basis set for the Δ states that occur in the sum-over-states formula. There is extremely good agreement with recent electric-field-induced second-harmonic-generation experiments; e.g., the experimentally derived static, averaged, γ${\mathrm{¯}}_{\mathrm{?}}$ (electronic) for ${\mathrm{H}}_2$ is 686±4 ${\mathit{e}}^4$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{h}}^{\mathrm{-}3}$, whereas our value is 683 ${\mathit{e}}^4$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{h}}^{\mathrm{-}3}$. Values of the dynamic B and C polarizabilities are also given.

A detailed analysis of the resonant radiative capture process by F ii is carried out in the low-energy region. Contributions from the intrashell excitation modes with Δn=0 and Δl=1 are estimated. In addition, several peaks in the cross sections are found near the elastic threshold ${}_{}{}^3{}_{}{}^{}$P that correspond to the excitation transitions among the ground-state multiplets, with Δn=0, Δl=0. They are important for temperatures below 0.1 Ry. The Δn=0, Δl=1 contribution is large at higher temperatures, in the region of 1 Ry, where the Δn≠0 mode is also present. Cross sections for the direct radiative recombination are estimated to be very large for temperatures below 0.2 Ry.

We present measurements and calculations of the evolution of the ion-charge-state distributions in an electron-beam ion trap. Direct measurements of the charge-state distributions are made with an ion extraction system. The data are used to test our computer model, which solves the set of coupled nonlinear differential equations for the energy and charge balance for all ionic species. The model is used to assess the importance of various processes in establishing the charge-state distribution.

The mechanism of evaporative cooling of highly charged ions in an electron-beam ion trap (EBIT) is discussed. Computer simulations of evaporative cooling in superEBIT indicate that with the use of neon, nitrogen, or helium coolants, significant amounts of bare and hydrogenlike dysprosium ions can be trapped indefinitely for the observation of bound-state β decay.

Calculations of the limitations imposed by radiation trapping on the polarization of an alkali-metal atomic beam by optical pumping are presented. In an atomic beam radiation trapping limits the density of alkali-metal atoms that can be highly polarized by optical pumping. This density is about 1/3 the density of an alkali-metal vapor that can be highly polarized by optical pumping. In a low magnetic field the maximum intensity of an atomic beam that can be optically pumped is a few particle milliamperes.

A quantum theory of a Λ-type three-level single-mode quantum-beat laser with injected atomic coherences and with an external microwave field, which coherently drives the lower two nearly degenerate levels, is studied. A master equation for the field-density operator and the photon statistics is derived. The laser operation is analyzed in terms of the coefficients of the Fokker-Planck equation of the laser field. Noninversion lasing is found in both cases: without and with injected atomic coherences. At the same time, in the latter case large quantum-noise reduction is found, and for particular initial parameter choices the laser field is very near to a coherent state with exactly Poissonian photon-number distribution and near-Poissonian phase distribution.

Excitation of a three-level atom irradiated by a sequence of two fluctuating pulses is discussed. The pulses have bandwidth ${\mathrm{\tau }}_{\mathit{c}}^{\mathrm{-}1}$, relative delay time ${\mathit{t}}_{12}$, and can be correlated with one another. It is shown that, for strong excitation pulses, the level populations and atomic coherence as functions of ${\mathit{t}}_{12}$ can vary on a time scale much smaller than ${\mathrm{\tau }}_{\mathit{c}}$. This effect may lead to a means for obtaining high temporal and spatial resolution.

Effects of a small violation of Bose statistics are investigated by treating the photon as a q boson, i.e., the commutation relation of creation and annihilation operators is replaced by ${\mathit{aa}}^{\mathrm{°}}$-${\mathit{qa}}^{\mathrm{°}}$a=1 with -1≤q≤1, so that q=1 is a Bose particle and q=-1 is a Fermi particle. A theory of q-boson emission is modeled on the usual theory of photon emission, and the physical consequences of a small deviation of q from unity are determined. The fact that a and ${\mathit{a}}^{\mathrm{°}}$ are bounded operators for all q<1 implies that stimulated emission ceases when the intensity is sufficiently large in any simple model. The specific relationship between q and the maximum attainable intensity depends on the model, although rather insensitively. Two simple models are examined in detail. In both we find that stimulated emission saturates when there are approximately 4/(1-q${)}^2$ quanta per mode. This implies a maximum attainable intensity for 1-eV lasers of ≊3/(1-q${)}^2$ MW/${\mathrm{cm}}^2$ so that a deviation of q from unity as large as ${10}^{\mathrm{-}6}$ is quite consistent with the existence of current high-intensity lasers. One of the two models constructed, which appears very natural in the mathematical formalism of the generalized commutator algebra, is found to give a q extension of the exclusion principle. Specifically it predicts that the growth of the occupation number in time will drop from quadratic to logarithmic when the occupation number reaches a value of ≊[2/(1-q)${]}^2$. Peculiarities in the large-t behavior near q=0 and -1 are examined briefly.

The squeezing properties of a model of a degenerate parametric amplifier with absorption losses and an added fourth-order nonlinearity have been analyzed. The approach used consists of obtaining the Langevin equation for the optical field from the Heisenberg equation provided that a linearization procedure is valid. The steady states of the deterministic equations have been obtained and their local stability has been analyzed. The stationary covariance matrix has been calculated below and above threshold. Below threshold, a squeezed vacuum state is obtained and the nonlinear effects in the fluctuations have been taken into account by a Gaussian decoupling. In the case above threshold, a phase-squeezed coherent state is obtained and numerical simulations allowed to compute the time interval, depending on the loss parameter, on which the system jumps from one stable state to the other. Finally, the variances numerically determined have been compared with those obtained from the linearized theory and the limits of validity of the linear theory have been analyzed. It has become clear that the nonlinear contribution may perhaps be profitably used for the construction of above-threshold squeezing devices.

Perturbation theory is applied to the evaluation of the multiphoton-detachment cross sections of ${\mathrm{H}}^{\mathrm{-}}$ in a number of approximations. The zero-range plane-wave approximation is the simplest, as its effective dipole matrix element is reducible to a recursive differentiation, and it is applied to the one- to seven-photon-detachment processes. Improvements on this are made in the bound state by means of a short-range potential model and a dynamic screening representation, and in the continuum wave functions with the use of the best previously calculated e-H(1s) singlet scattering phase shifts. The dynamic screening parameters are adjusted to give a good fit of the resulting one-photon cross section to its correct well-known value, and the accurate phase shifts effectively include all the important correlation effects in the free-free amplitudes. These improved wave functions are used for the evaluation of the two- and three-photon generalized detachment cross sections by explicitly carrying out all intermediate state sums. Our best σ${\mathrm{^}}_2$ and σ${\mathrm{^}}_3$ are estimated to be accurate to order 5%. The present theoretical results are compared with other calculations and recent measurements, revealing areas of agreement as well as certain discrepancies.

Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell’s equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.

We study a two-mode squeezed state of the electromagnetic field, in which each mode is degenerate in frequency, but they have orthogonal polarizations. We use a degenerate four-wave-mixing geometry and two-photon transitions for these squeezed states. The modes are treated in a mean-field approximation that includes the effects of vacuum fluctuations. Material parameters of sodium vapor and the semiconductor CuCl are used to illustrate the results.

We analyze the phase and squeezing properties of the cotangent states of the electromagnetic field. We calculate the phase distribution, phase variance, and number-phase uncertainty product for these states. Under appropriate conditions, the phase distribution develops oscillations resulting from the formation of states, reminiscent of macroscopic superpositions. In other cases the cotangent states are nearly minimum number-phase uncertainty states, emulating the coherent states. We also study the quadrature squeezing properties of the cotangent states and find that under a wide range of conditions they are highly squeezed.

We study the nonlinear optical response of an electromagnetically aligned shaped-microparticle suspension, and focus on the physical characteristics of static, microparticle index gratings. Theory suggests that the physical properties of shaped-microparticle index gratings can be considerably altered by aligning the suspension with either an electric field or polarized radiation. Specifically, the medium response times are reduced, the grating polarization characteristics are altered, and depending upon the specific situation, the index grating depth can be either increased or decreased.

A two-photon optical bistability equation is derived for a three-level V-type atom in a cavity. We consider the bistable states of the purely absorptive type and investigate the influence of the phase difference of the two cavity field modes on bistability characteristics due to the nonlinear coupling between atomic transitions and fields. Very different results are found for the three cases of phase difference we considered. The bistability is found to diminish when the two modes are in phase, in contrast to the two-level case. In addition, we also discuss the effect of longitudinal and transverse relaxation times on the bistability and how the bistability operation characteristics of one mode can be controlled by adjusting the other.

Multiple four-wave mixing processes in an optical fiber are investigated both theoretically and experimentally. The propagation equations for the complex amplitudes of two pump waves (angular frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$) and four sidebands (${\mathrm{\omega }}_3$=2${\mathrm{\omega }}_1$-${\mathrm{\omega }}_2$, ${\mathrm{\omega }}_4$=2${\mathrm{\omega }}_2$-${\mathrm{\omega }}_1$, ${\mathrm{\omega }}_5$=2${\mathrm{\omega }}_3$-${\mathrm{\omega }}_1$, and ${\mathrm{\omega }}_6$=2${\mathrm{\omega }}_4$-${\mathrm{\omega }}_2$) are derived. These six waves interact through seven partially degenerate and nondegenerate four-wave mixing processes. Conservation relations for the wave amplitudes are obtained. Numerical integration of these equations reveals both periodic and chaotic energy exchange between the pump waves and sidebands. Predictions from the model are tested directly by experimental measurements on a single-mode optical fiber.

We present an experimental and theoretical study of the dynamics of a ${\mathrm{CO}}_2$ laser with delayed feedback. Working with a delay time such that its product with the bandwidth of the feedback loop yields a number close to unity (so-called short-delay regime), we show evidence of a low-dimensional chaos, reached by the destabilization of a two-dimensional torus (Curry-Yorke route to chaos). A suitable model provides numerical solutions in agreement with the experiment. We discuss under which conditions our system reduces to an Ikeda-type delayed dynamics.

The resonance-radiation-pressure effect induced by a broadband long-cavity dye laser has been observed on sodium vapor confined in a capillary cell. The diffusion of the vapor has been studied as a function of laser intensity and vapor density, and the induced drift velocity has been measured. The time evolution of the vapor density is in agreement with the theoretical model under the hypothesis of optimized laser-vapor coupling. The drift velocity and the diffusion coefficient are shown instead to be larger than predicted, indicating an incomplete thermalization of the atoms at the cell walls.