Stimulated Brillouin scattering in a micrometer-sized liquid droplet is treated theoretically using recently developed techniques, with emphasis on the doubly resonant case, in which the frequencies of both the laser field and the scattered Brillouin field fall within a morphology-dependent resonance, leading to input and output enhancement. An important difference from a bulk medium is the replacement of the selection rules based on momentum conservation by those based on angular momentum conservation, with the latter most conveniently expressed through the spherical wave modes. Special attention is paid to the eigenvalue equation defining the gains and Brillouin shifts, in particular to the difference between small and large droplets. For large droplets, and for given angular momenta of the laser field and the scattered field, there is only one allowed shift with a positive gain. Numerical results for gain and threshold are shown for a droplet of size parameter about 30, and a simple approximate analytic formula for the gain is presented.

We examine the dynamical behavior of the cryogenic hydrogen maser. Studying the coupled field-matter equations, which have been reduced to the complex Lorenz equations, we obtain two operating domains, one in which steady-state oscillation takes place and a time-dependent domain that is characterized by a pulsed output power. For the latter we obtain bifurcation diagrams, both with and without detuning, that display both periodic and chaotic attractors. Finally, we study the influence of thermal noise on this time-dependent domain and show that for reasonable experimental conditions the pulse triggering will be stochastic, but the pulse buildup and decay can be deterministic.

By an adiabatic elimination of the fundamental mode, the equation of motion for the density operator describing the model of Drummond, McNeil, and Walls [Opt. Acta 28, 211 (1981)] of the quantum parametric oscillator can be reduced to an equation of motion for the subharmonic field for large damping constants of the second-harmonic field. Introducing the quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882 (1969)], it is shown next that the equation of motion for the density operator is reduced to an equation of motion of the quasiprobability distributions. Because of symmetry relations the eigenfunctions can be divided into four classes according to whether the eigenfunctions are symmetric or antisymmetric in the real or imaginary part of the complex field variable. By using intensity and phase variables, the quasiprobability distributions are then expanded into Laguerre functions with respect to the intensity and into a Fourier series with respect to the phase. With a proper notation the equation of motion for the expansion coefficients can be cast into a tridiagonal recurrence relation, which is then solved by the matrix continued-fraction method. The results are compared with one-dimensional approximations.

A recently developed theoretical approach to degenerate four-wave mixing (DFWM) in the Raman-Nath regime is extended to allow the analysis of pulsed DFWM experiments in laser-excited semiconductors. The full time-dependent carrier-density grating equation is solved numerically to allow the calculation of time-integrated diffraction efficiency spectra. The calculations are compared with the results of pulsed experiments performed on low-temperature CdS for a variety of excitation intensities. Qualitative agreement between experiment and theory is obtained, yielding insights into the dynamics of the nonlinear-optical properties underlying the excitation-dependent behavior of the scattering spectra.

We present an investigation of the stability of the cylindrically symmetric higher-bound states that can be formed in a self-focusing medium with saturation. The higher-bound states are found to display transverse instabilities that break the azimuthal symmetry of the system. An approximate analytic theory is presented that correctly describes the qualitative variations of the numerically calculated instability growth rates.

The quantum theory of the Borrmann effect proves that the extinction of the β beam through the crystal is not originated by ordinary absorption processes but is due to a coherent scattering of photons into the α beam; in this paper the extinction equations for the α and β beams inside a crystal will be derived by taking into account both ordinary Compton and photoelectric absorption, and coherent scattering between the two beams. Such equations will not have an analytical solution in the general case, but it will be shown that it is possible to find approximate solutions in the cases of very thin or very thick samples; it will turn out that the x-ray extinction is no longer exponential and that the penetration depth depends strongly on the quotient between the initial incident intensity and the normal absorption coefficient of the crystal. It will be shown that, in the case of a thin transparent crystal, the transmission and reflection coefficients are not exactly periodic with respect to the crystal thickness and that they depend on the initial incident intensity.

We have derived an equation of motion for a Wigner operator in phase space, which is the phase-space analog of the Heisenberg equation of motion for a quantum-mechanical operator. An application of this operator equation to time-dependent systems possessing invariants is considered, and the solution for the corresponding Wigner phase-space distribution function is obtained.

A metal-clad optical waveguide with a semiconductor microcavity structure is proposed to increase the coupling efficiency of spontaneous emission into a lasing mode (spontaneous emission coefficient β) and to increase a total spontaneous emission rate simultaneously. Such a microcavity semiconductor laser with enhanced spontaneous emission has novel characteristics, including high quantum efficiency, low threshold pump rate, broad modulation bandwidth, and intensity noise reduced to below the shot-noise limit (amplitude squeezing).

The spontaneous emission rate and radiation pattern for a thin quantum well sheet enclosed by a one-dimensional dielectric microcavity have been calculated. By placing the sheet in the node (antinode) position of the cavity standing wave, the spontaneous emission in the direction normal to the sheet will be decreased (enhanced). In the former case the theory predicts that the spontaneous lifetime can be increased more than a factor of 10. In the latter case both theory and experiments confirm that such a simple structure can couple a substantial amount (30–90 %) of the spontaneous emission into the cavity resonant mode. In both cases, however, theory predicts that the spontaneous emission lifetime will increase for structures without guided modes.

Although the positive P representation (PPR) is widely used in the literature, there are still many open questions concerning its use as a general tool for solving problems in quantum optics. Recently, there has even been doubt as to whether it gives correct results at all. We present two nonlinear examples in which a comparison with independent methods shows the validity of the PPR. Then we show that, in general, the PPR is not restricted to a lower-dimensional subspace. Finally, we address the problem of initial conditions, which have to be chosen carefully to avoid incorrect results. More specifically, we show that the explicit form of the PPR that was given in the original existence proof leads to unphysical behavior when used as an initial distribution.

A general model for the laser with an intracavity saturable absorber (LSA), with relaxation processes represented by a set of auxiliary variables simply coupled to the field equation, is proposed. Within this framework, a popular model for LSA is discussed through a systematical analysis of the parameter ranges for which chaotic behavior is present. The origin of the instabilities is traced back to the presence of a homoclinic orbit biasymptotic to a periodic unstable solution of the system. The relevant influence of the spontaneous emission in enhancing the underlying deterministic instability is pointed out.

The concept of a traveling-wave free-electron laser (TWFEL) is presented. This hybrid device consists of both a periodic waveguide and a planar wiggler. It combines the interaction mechanisms of both the traveling-wave tube (TWT) and the free-electron laser. This combination produces a synergistic interaction. A linear model of the TWFEL is derived in this paper. It results in a general dispersion equation for the TWFEL interaction. Coupling coefficients are derived for various ratios between the wiggler period ${\lambda }_{\mathit{W}}$ and the periodic waveguide period ${\lambda }_{\mathit{p}}$. It is shown that when ${\lambda }_{\mathit{W}}$=${\lambda }_{\mathit{p}}$ the parametric interaction is composed of a double FEL interaction, a TWT interaction, and a hybrid interaction. All these are in resonance with three different spatial harmonics. The coupling coefficient for this scheme is a complex sum of the known FEL and TWT terms, and of complex terms for their cross coupling. It is shown that the coupling coefficient of the synergistic TWFEL interaction (and consequently its gain) can be larger than the sum of the two separate interactions. Simpler TWFEL schemes in which ${\lambda }_{\mathit{W}}$≠${\lambda }_{\mathit{p}}$ (single-harmonic interaction) and ${\lambda }_{\mathit{W}}$=2${\lambda }_{\mathit{p}}$ (two-harmonic interaction) are presented first as an introduction for the analysis of the ${\lambda }_{\mathit{W}}$=${\lambda }_{\mathit{p}}$ TWFEL interaction. A compact TWFEL based on a miniature wiggler, which functions also as a periodic waveguide, is proposed for operation in the millimeter-wave range with a tenuous low-energy e beam.

The violation of Bell’s inequality in collective resonance fluorescence of two strongly driven two-level atoms is discussed. Our proposal and calculations are essentially based on the two-mode source experiment of Reid and Walls [Phys. Rev. A 34, 1260 (1986)]. The two modes in our case consist of the highly correlated sidebands of the Mollow triplet in the resonance-fluorescence spectrum.

The autodetachment of 1s2s2p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ in ${\mathrm{He}}^{\mathrm{-}}$ and ${\mathit{nsnp}}^2$ ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ in ${\mathrm{Be}}^{\mathrm{-}}$ (n=2), ${\mathrm{Mg}}^{\mathrm{-}}$ (n=3), and ${\mathrm{Ca}}^{\mathrm{-}}$ (n=4) is calculated using an extension to continuum processes of the multiconfiguration Hartree-Fock method. The main interest is to investigate the processes giving rise to long-lived, metastable states in negative ions. In ${\mathrm{He}}^{\mathrm{-}}$ and ${\mathrm{Be}}^{\mathrm{-}}$ our results agree with earlier experimental and theoretical ones, and do predict a long-lived component. In ${\mathrm{Mg}}^{\mathrm{-}}$ and ${\mathrm{Ca}}^{\mathrm{-}}$, however, we do not find any corresponding long-lived state. The processes behind the decay of these states are investigated, and a comparison of the different systems is made.

One- and two-photon ionization of atomic hydrogen by an ultrashort hyperbolic secant laser pulse is analyzed in detail by means of the essential-states method. We consider two frequency regimes. For photon energies close to the ionization potential, we show that the excitation of atomic hydrogen, initially in its ground state, leads, at low and moderate laser intensities, to an np-state population distribution that, for ultrashort pulses, is strongly shifted down to low-lying Rydberg states. At very high intensities in this frequency regime, we show that the time evolution of the Rydberg-state population follows adiabatically the pulse shape and does not lead to population trapping in the Rydberg states. This contrasts with the results obtained in the low-frequency regime. We demonstrate that, when hydrogen is excited from the 2s state, a substantial inhibition of ionization occurs at high field intensities. The stabilization is caused by the creation of a spatially extended wave packet that results from the Raman mixing of intermediate Rydberg states.

Second-harmonic generation in rubidium vapor has been studied in the absence of external symmetry-breaking dc fields. It is shown that binary collisions between atoms in the presence of the fundamental laser beam leads to the generation of a coherent second-harmonic beam in accordance with a recent theoretical proposal [A. Elçi and D. Depatie, Phys. Rev. Lett. 60, 688 (1988)].

The decay of the active atoms in micromasers is theoretically analyzed. The equations of motion for the diagonal elements of the micromaser field, which include an atomic-decay effect, have been obtained. The relation between the photon statistics and the micromaser field on the atomic decay has been studied. The effect of atomic-decay rates and average photon numbers, photon-number variances, and the photon-number distribution has been discussed. It has been shown that generation of approximate trapping states or number states requires very small atomic-decay rates and very large field-atom coupling constants.

A multimode photodetection theory is developed that includes both the presence of radiation sources and the damping of the field due to the measurement. Making use of Green’s-function techniques and the rotating-wave approximation, the counting statistics is calculated in terms of input field quantities. The treatment of the detector-field interaction yields expressions that essentially differ from the results of nonperturbative single-mode theories but are very similar to those of the well-known perturbative photodetection theories. The field damping due to the detection of photons is found to lead to a renormalized detector response function that approaches a maximum value if the number of detector atoms tends to infinity. It is worth noting that our result may be closely related to those of Mandel’s heuristic description of photodetection based on the concept of configuration-space photon number operators.

The recently proposed Harbola-Sahni potential [Phys. Rev. Lett. 62, 489 (1989)] is shown to give Hartree-Fock quality values of static dipole and quadrupole antishielding factor ${\mathrm{F}}^{\mathrm{-}}$ and ${\mathrm{Cl}}^{\mathrm{-}}$, respectively.

Relativistic many-body results (in MHz) for the magnetic dipole coupling constants of ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$, ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$ are -1682, 14 446, 21 349, -48 407, and 39 637. Experimental results for Ag and Cd are -1712.56 and -14 700.