We study transients in resonantly coupled three-level systems. Two of the levels are coupled by intense two-photon pumping, and the third one provides a probing level. Adiabatically eliminated levels appear in effective system parameters. Experimentally, this model is applicable, e.g., in resonantly enhanced parametric and harmonic generation in atomic vapors. A distinguishing feature in the system is the appearance of ac Stark shifts in the probe spectra when pumping at the two-photon resonance. The nutation signal is shown to give information on the effective two-photon Rabi frequency and on the decay rate of the dipole-forbidden two-photon coherence. Free-induction decay is strongly dominated by population-induced effects; Raman-like peaks introduced by Stark shifts may show large instantaneous gain. Gaussian pump pulses are investigated to investigate effects arising from the temporal sweeping of the two-photon Rabi flipping and the modulation of the Stark shifts. The results also provide relevant information on the gain dynamics of coherently pumped lasers.

Analytic solutions for a class of pulses that includes an infinite variety of amplitude and frequency modulations which we previously obtained are applied specifically to the square, Gaussian, Lorentzian, hyperbolic-secant, and the exponential pulses, among others. For all the different types of amplitude- and its corresponding frequency-modulated functions, the outcome of the atomic excitation is given by the same simple analytic formulas. Our analytic solutions apply equally to two-state collision problems.

Nondegenerate four-wave mixing in a single-mode optical fiber is proposed as a method of squeezed state generation. An analysis of the near-degenerate mixing process for forward propagation in realistic fibers is presented along with the theory of an experimentally feasible detection strategy. The effects of the quantum nature of the optical nonlinearity and absorption are modeled by treating the fiber medium as a collection of anharmonic oscillators. Methods of suppressing undesired effects such as stimulated Brillouin scattering are presented as is a technique for providing the phase-shifted local oscillator wave necessary for the detection of squeezing. Preliminary experiments on fiber characterization and the detection of four-wave parametric fluorescence are described.

This paper contains a description of the behavior of a multimode unidirectional ring laser with a homogeneously broadened active medium. Our formulation is based on the conventional Maxwell-Bloch (MB) equations, but is distinguished from other treatments by the inclusion of a finite mirror reflectivity and an arbitrary value of the gain parameter. We review the steady-state behavior of the system and analyze the longitudinal profile of the field and of the atomic variables. With an appropriate transformation of variables, we transform the boundary conditions of the ring cavity into standard periodicity type, even in the presence of a finite reflectivity, and derive an infinite hierarchy of coupled mode equations. We analyze exactly the linear stability of the system, and investigate the dependence of the instability domain on the reflectivity and gain parameters. A numerical study of the full MB equations for a parameter range of the type explored in the recent experiments by Hillman et al. [Phys. Rev. Lett. 52, 1605 (1984)] reveals similarities, but also considerable differences between the results of the theory and the main experimental signatures of their instability. However, the injection of numerical noise shows the presence of numerous coexisting basins of attraction which are likely to play a significant role in the dynamics of a noisy laser.

Under conditions that are properly detailed in the text, we demonstrate the existence of a deep and useful link between single-mode and multimode instabilities in lasers, and laser-related optical systems. We exhibit this connection explicitly for a homogeneously broadened single-mode and multimode laser model, with the possible inclusion of a driving external field; we also provide the necessary arguments to justify the validity of our conclusions for inhomogeneously broadened lasers, lasers with a nonuniform transverse intensity profile, lasers with saturable absorbers, laser systems in a Fabry-Perot cavity, and lasers whose dynamics is governed by the rate equations. Our main conclusion is that in all these systems, the existence of a single-mode instability implies necessarily a corresponding multimode instability in the ‘‘good-cavity’’ limit and, conversely, the existence of a multimode instability in the good-cavity limit implies, under an appropriate additional condition, the existence of a single-mode instability for a sufficiently ‘‘bad’’ cavity. We provide numerous examples to illustrate this correspondence, and provide evidence of its usefulness by making specific predictions on a new type of unstable behavior.

We discuss the steady-state and the linearized response of a multimode laser with an injected signal. The steady-state analysis is carried out for arbitrary values of the laser gain and resonator parameters, while the linearized stability calculation is limited to parameter ranges where the mean-field assumption is a reasonable approximation. For suitably large values of the polarization and population decay rates, we review the problem of the adiabatic elimination of the atomic variables and demonstrate explicitly the existence of possible pitfalls and how to avoid them.

Steady-state interactions of one, two, and three waves with two-photon two-level media are treated semiclassically. Dynamic Stark shifts as well as dynamic Stark splittings are included in the theory. The intermediate levels are assumed to be nonresonant, and one wave is allowed to have arbitrarily large intensity. The theory parallels the one-photon theory of multiwave mixing couched in terms of population pulsations. We find the one-, two-, and three-wave two-photon absorption coefficients and the three-wave coupling coefficients. We find similarities and significant differences between the one- and two-photon polarizations of the medium. The work treats two-photon saturation spectroscopy, laser- and optical-bistability instabilities, and phase conjugation with a unified formalism.

A generalized perturbation theory is developed for an inhomogeneously broadened two-level quantum system interacting with an optical field of arbitrary temporal shape. Solutions of the Liouville equation carried out to nth order in the optical field strength exhibit a rephasing behavior and therefore are interpreted as an n-pulse echo where each pulse corresponds to one power of the field strength. We conclude that at low fields any coherence effect can be interpreted as a generalized stimulated echo phenomenon. Several well-understood coherence effects are explained and a few new ones are predicted, including one example where the light source is incoherent.

We analyze the properties of phase-conjugate (PC) emission via resonant, Doppler-broadened, backward four-wave mixing in the saturation regime, when both counterpropagating pump waves are arbitrarily intense. One considers two atomic situations, either a four-level system modeled as a pair of uncoupled transitions, or a three-level system. The first case leads to an analytical expression of the PC field, for arbitrary pump intensities, in the Doppler limit. The second case, in general, necessitates a numerical solution, except in the asymptotic regime when one pump is very intense compared to the other one. One finds that both cases lead to quite similar predictions: (i) two-peaked or four-peaked emission line shape, depending on the forward to backward pump intensity ratio; (ii) the maximum of PC reflectivity is obtained for infinite backward saturation, but for a fi-p nite value of the forward pump intensity; (iii) for backward saturation, the emission line shape is practically independent of the forward pump intensity. Finally, the theoretical analysis is extended to the case of a saturating probe and its effect on emission line shape and PC reflectivity, as well as its application to the properties of emission processes involving higher-order optical susceptibilities (degenerate multiwave mixing).

Elastic and depolarizing collisions between excited ytterbium atoms (6s6p ${}^3$$P_1$ level) and noble gases (He, Ne, and Xe) are investigated using a stimulated-photon-echo technique. The method is sensitive to collisional velocity changes concerning both the total population ${\rho }^0$ and the alignment ${\rho }^2$ of the level. More specifically, it enables us to compare precisely the velocity changes associated with elastic scattering and with alignment-preserving scattering. This represents an improvement with regard to previous works. A detailed theoretical discussion of depolarizing collisions in laser spectroscopy is presented. A simplified density-matrix equation is derived under appropriate approximations. Stimulated photon-echo data for elastic scattering are interpreted within the limits of small-angle scattering in a long-range van der Waals potential; total elastic scattering cross sections are derived from comparison between experiment and calculation: ${\mathit{\sigma }}_{\mathrm{He}}^{\mathrm{el}}$=220(20) A${̊}^2$, ${\mathit{\sigma }}_{\mathrm{Ne}}^{\mathrm{el}}$=320(20) A${̊}^2$, ${\mathit{\sigma }}_{\mathrm{Xe}}^{\mathrm{el}}$=1240(60) A${̊}^2$. Total rates for destruction of alignment are measured in an auxiliary standard photon-echo experiment; the corresponding cross sections are ${\mathit{\sigma }}_{\mathrm{He}}^{\mathrm{}\left(2\right)\mathrm{}}$=94(3) A${̊}^2$, ${\mathit{\sigma }}_{\mathrm{Ne}}^{\mathrm{}\left(2\right)\mathrm{}}$=123(7) A${̊}^2$, ${\mathit{\sigma }}_{\mathrm{Xe}}^{\mathrm{}\left(2\right)\mathrm{}}$=300(20) A${̊}^2$. Stimulated photon-echo data for depolarizing collisions are successfully compared with a calculation that we develop starting from a long-range anisotropic model potential.

The quantum-mechanical features of radiation produced by the Hanle effect are examined. Squeezing characteristics of the field are calculated. The radiation field is found to exhibit considerable squeezing under a variety of externally controllable parameters such as the magnetic field strength, laser intensity, and pump polarization. The Zeeman coherences lead to squeezing, which is dependent on the direction of detection. Photon-counting measurements on the radiation from the forward Hanle effect are shown to provide a measure of the squeezing of the field.

The laser-induced associative ionization process $A^{\mathrm{*}}$+B+ħω→${\mathrm{AB}}^{+}$+$e^{\mathrm{-}}$ is investigated using a nonlocal scattering potential. It is found that for each vibrational level of the ion complex ${\mathrm{AB}}^{+}$ multiple resonances for association can occur as the laser frequency is varied, provided the laser intensity is beyond a certain critical value, estimated to be on the order of ${10}^7$ W/${\mathrm{cm}}^2$ for alkali diatomic systems. The locations of the resonances also depend crucially on the laser intensity. These results are contrary to the Franck-Condon assumption of localized electronic transitions, which predicts a single resonance for each vibrational level.

A high-current annular electron beam in an accelerator is subject to various instabilities. A general fluid-Maxwell theory of the diocotron instability is developed for an infinitely long and azimuthally symmetric annular electron beam propagating along an external magnetic field. In contrast with the treatment used in the conventional diocotron instability, the assumptions of tenuous electron beam and strong magnetic field have been eliminated. Furthermore, the restriction of infinite axial wavelength perturbation has been removed and the approximation of ω∼ckβ is no longer applied. Instead, we conduct full electromagnetic perturbation in the macroscopic cold-fluid description of plasma dynamics with the beam parameters of general interest. In the special case of a sharp-boundary density profile, the diocotron instability which dominates in the low-frequency region is investigated in a broad range of beam parameters and geometries. The results are significantly different from that obtained from the conventional diocotron instability; the kink mode can be destabilized and the growth rates are much larger for every azimuthal mode.

In processes of excitation–deexcitation and of ionization–recombination of ions immersed in dense plasmas, multistep processes through various intermediate states are important. In the present paper we deal with the excitation and deexcitation that have doubly excited, or autoionizing, states as intermediate states. We call these the dielectronic-capture ladderlike (DL) processes. Hydrogenlike 1s⇆2s or 1s⇆2p transitions are considered for the purpose of illustration. The DL excitation rate coefficient is obtained as a function of electron density with an approximation that is based on the picture of dielectronic capture of the 1s ion into the doubly excited states followed by the collisional ladderlike excitation-ionization chain. The DL deexcitation rate coefficient results from autoionization of the doubly excited level ions that are in local thermal equilibrium with respect to the 2l-level populations (l is s or p). Both of the rate coefficients are interpreted as an extrapolation of the excitation cross section due to lowering of the threshold energy of the 1s→2l excitation and are found to obey the principle of detailed balance. Thus, the DL processes may be regarded as enhancements of the direct excitation and deexcitation. A detailed collisional-radiative-model calculation, which includes 60 doubly excited levels and relevant collisional and radiative transitions, is performed, and the above approximations are found to be consistent with the results.

The authors generalize the Golden-Kalman one-component-plasma (OCP) nonlinear-response-function approach to the formulation of a dynamical theory for binary-ionic-mixture plasmas. The principal result of the new dynamical theory is a self-consistent approximation scheme for the calculation of linear ionic polarizabilities and collective-mode structure at long wavelengths and arbitrary coupling strengths. The approximation scheme is constructed from the dynamical nonlinear fluctuation-dissipation theorem and the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) kinetic equation prepared in the velocity-average approximation (VAA). Equilibrium three-point correlations, quadratic response functions, and the dynamical superposition approximation are all central elements of the theory. The theory is exact at zero frequency and exactly reproduces the coefficients of the high-frequency-moment-sum-rule expansion through order 1/${\omega }^4$. Collective-mode calculations based on the new approximation scheme indicate that the (positive) shift in the plasma frequency is temperature dependent at weak coupling and temperature independent at very strong coupling. These calculations, moreover, reproduce the qualitative features of the Hansen-McDonald-Vieillefosse molecular-dynamics data for the dispersion of the optical mode in the strong-coupling regime, while at the same time very nearly reproducing the weak-coupling frequency shift predicted by Baus’s microscopic theory. The authors conclude that the temperature-dependent broadening and shifting of the plasma made at weak coupling is controlled primarily by ionic interdiffusion transport. At very strong coupling, the dispersion of the optical mode is almost entirely controlled by the static-correlational parts of the third-frequency-moment-sum-rule coefficient. Finally, new OCP-like formulas are presented for the dispersion and damping of the plasma mode in the special ‘‘symmetric’’ ($e_A$/$m_A$=$e_B$/$m_B$) ionic mixtures.

Results are presented from a numerical calculation for the bremsstrahlung spectrum and Gaunt factors of Al, Cs, and Au atoms in high-temperature (-T), high-density (-ρ) plasmas. Plasma temperatures kT=0.1 and 1.0 keV and plasma densities ρ=${\rho }_0$ (the normal solid density) and ρ=100${\rho }_0$ are considered. This allows us to determine the generality and identify the origins of features which we had previously identified in calculations for Cs. We also now present results for the total energy loss of an electron in such a plasma. We use a relativistic multipole code which treats the bremsstrahlung process as a single-electron transition in a static screened central potential. We take for the static potential corresponding to an atom in a hot dense plasma the finite-temperature, finite-density Thomas-Fermi model. This approach corresponds to an average atom in local thermodynamic equilibrium. In comparison to isolated-neutral-atom results we observe general suppression of cross sections and a particular suppression in the tip region of the spectrum. Within this model, both superscreening and shape resonances are found in the circumstances of extreme density. At more normal densities and except for the soft-photon end, the spectrum at these energies for an atom in a hot plasma (characterized by an average degree of ionization) can be well represented by the spectrum of the corresponding isolated ion, which has a similar potential shape at the distances which characterize the process.

Model equations for circular symmetric Taylor-Couette flow are derived in the narrow-gap limit by a mode truncation of the full Navier-Stokes equations. For static Taylor numbers these model equations can be transformed into the Lorenz equations for Rayleigh-Bénard convection. Linear growth rates of the most unstable modes and the torque on the cylinders evaluated within this model reproduce well the known results. The response to periodic modulation of the forcing is different from that of the convective Lorenz model.

A formal derivation of the wave kinetic equation governing the wave-action density for electromagnetic waves propagating in a weakly inhomogeneous and nonstationary medium is presented. The method is based on the Weyl representation of a general vector wave equation (including local sources and dissipation) governing the evolution of the field spectral tensor in the phase space of the (geometric-optics) rays. This equation is systematically approximated with ordering assumptions consistent with conventional eikonal methods, leading to a natural definition of the wave-action density.

With use of a recent variational formulation of the Maxwell-Vlasov and guiding-center theories [D. Pfirsch, Z. Naturforsch. A 39, 1 (1984)], the energy-momentum and angular momentum tensors for such theories are derived and the corresponding local conservation laws are proven. The energy-momentum tensor is shown to be symmetric in its spatial components while the angular momentum density is naturally antisymmetric.

For a double Yukawa interparticle potential which well approximates the Lennard-Jones form, two modified hypernetted-chain equations, corresponding to two chosen model bridge functions, are solved numerically near their respective critical points. For the first, the use of a hard-sphere bridge function yields an isothermal compressibility $K_T$ that deviates from power-law behavior. In contrast to this, if the bridge function is chosen to cross over from a hard-sphere to mean-spherical form, then power-law behavior in $K_T$ is recovered with the mean-spherical result γ=2. This striking difference is traced to the presence of correspondingly long-ranged behavior in the crossover bridge function itself.