‘‘First-order’’ exact solutions of the nonlinear Schrödinger equation (NLSE) with positive group-velocity dispersion are obtained. We find a three-parameter family of solutions that are finite everywhere; particular cases include periodic solutions expressed in terms of elliptic Jacobi functions, stationary periodic solutions, and solutions describing the collision or excitation of two dark solitons with equal amplitudes. A classification of solutions using the plane of their parameters, a geometrical description on the complex plane, and physical interpretations of the solutions obtained are given. A simple relation, which permits transformation of the solutions of the NLSE in the anomalous-dispersion regime into solutions of the NLSE in the normal-dispersion regime, is also discussed.

In ultrashort (femtosecond) pump-probe spectroscopy, the pump pulse creates a nonstationary medium while the probe pulse propagates in such a medium. The analysis of this situation is performed in the framework of linear nonstationary optics. Constitutive equations and electrodynamics of the nonstationary media are analyzed. The propagation of the probe-pulse energy is characterized by the coarse-grained susceptibility introduced in the previous works of the authors [S. H. Lin and B. Fain, Chem. Phys. Lett. 157, 233 (1989); B. Fain, S. H. Lin, and N. Hamer, J. Chem. Phys. 91, 4485 (1989); B. Fain and S. H. Lin, Chem. Phys. 161, 515 (1992)]. The main objective of the paper is the derivation and analysis of the delay-time-dependent absorption and dispersion line shapes of the probe pulse. This line shape has a very specific form corresponding to phase-dependent Raman absorption (emission). The latter phenomenon is introduced and described in the present paper.

We describe the collisions of an electron with a target atom in the presence of a strong, linearly polarized, monochromatic, oscillating electric field in the Kramers-Henneberger gauge. We show that the resulting set of coupled-channel equations, originally derived by Gavrila and Kaminski [Phys. Rev. Lett. 52, 613 (1984)], represents electron scattering by a vibrating charge initially in a highly excited state. This formulation leads to a mechanical model of the atom-field interaction from which we can draw better insights into the nature of the process. We solve these coupled equations numerically in the close-coupling approximation by a combination of the linear algebraic and R-matrix propagator approaches. We specifically treat electron-proton collisions in an intense field and investigate the capture-escape resonances over a range of intensities and frequencies. We also investigate multiphoton ionization of atomic hydrogen in various intensity regimes. We extend our calculations for single-photon ionization into the superintense regime (>${10}^{16}$ W/${\mathrm{cm}}^2$) and compare our results with results from time-dependent solutions of the Schrödinger equation.

We study the phase properties of two quantized modes within the model of a two-mode coupler with intensity-dependent coupling. The dynamics of the system is solved numerically as an approximate analytical solution is available only for the initial moments of the time evolution. The phase properties are discussed on the basis of the joint phase distribution. Other quantities of the particular modes (measure of entropy and photon-number distribution) are presented to support the conclusions reached on the basis of the joint phase distribution. The obtained results are compared with the known results for the closely related model of an ordinary linear coupler.

Second-harmonic generation in multimode laser beams is studied experimentally. A multimode laser beam derived from a laser oscillating simultaneously in many longitudinal modes that have the same transverse profile (${\mathrm{TEM}}_{00}$) is focused into a nonlinear crystal. Noncritical phase matching is utilized to generate the second harmonic. The number of longitudinal modes is systematically varied from 1 to 7 and the dependence of the efficiency of second-harmonic generation on the number of modes in the fundamental beam is studied. Experimental results clearly demonstrate the increasing degree of photon bunching in the fundamental beam as the number of modes increases. Experimental results are discussed and compared with the predictions of theoretical models.

We construct an extension of the spectral transform theory that allows us to build nonlinear systems of coupled waves that are integrable for arbitrary boundary values. The related time evolution of the spectral transform is in general nonlinear. This result has many important applications in physics, and we apply the procedure to plasma waves (laser-plasma interaction), to quantum electronics [self-induced transparency (SIT) and laser-pulse amplification], and to nonlinear optics (stimulated Raman scattering). In the case of laser-plasma interaction, we obtain an exact model for the description of the total reflexivity due to stimulated Brillouin scattering. For SIT, we show that the presence in the initial state of the medium of some atoms in an excited state drastically modifies the related time evolution of the spectral data, possibly making the problem unsolvable. In the case of laser-pulse amplification, we prove that the presence of background noise in the firing laser pulse drastically modifies the long-distance behavior of the solitons. Finally, for the general process of stimulated Raman scattering, we give the correct evolution of the spectral transform and show that the Stokes wave becomes rapidly totally localized; in other words, the system naturally evolves into a pure soliton state, whatever may be the initial profile of the acoustic wave. In the same context, another quite interesting example is studied: it is the first instance of an integrable system which develops a singularity in a finite time (for which the solution blows up). The physical application is under study.

We demonstrate the possibility of stabilizing unstable stationary states (unstable focus) in an experiment by applying feedback on a control parameter. The technique also allows the characterization of these unstable states. It has been checked experimentally on the spontaneous instability appearing in a Nd-doped optical-fiber laser.

Compared to two-particle states, entangled states of three or four particles can lead to a much stronger test of local realism than is possible with Bell inequalities. It is the purpose of this paper to mention an exactly soluble quantum model in which entanglement of atomic states with cavity photon states leads to a perfectly correlated three-particle state. We demonstrate how to realize this model atom-field system and to create and observe such states, in the context of cavity quantum electrodynamics.

By using a direct method for obtaining exact solutions of the nonlinear Schrödinger equation that describes the evolution of spatial or temporal optical solitons, a two-parameter family of solutions is given. These exact solutions describe the periodic wave patterns that are generated by the spatial or temporal modulational instability, the periodic evolution of the bright solitons superimposed onto a continuous-wave background, and the breakup of a single pulse into two dark waves which move apart with equal and opposite transverse components of the velocities.

We investigate the nonlocal effects of dispersion and loss on entangled photon pairs. These effects modify the coincidence properties in fourth-order interference. Absorption can increase or decrease the width of coincidence-count distributions. It can also wash out fourth-order interference by providing ‘‘which-way’’ information.

We study how a strong semi-infinite laser pulse affects an electron confined by a potential whose parameters mimic an AlAs-GaAs-AlAs double quantum well. Interesting phenomena take place for special values of laser frequency, intensity, and pulse rise time. There are values of these parameters for which the dipole moment of the system has a low-frequency Fourier component whose magnitude is higher than that of the fundamental (i.e., the component having the same frequency as the laser). For other parameter values, the low-frequency component disappears and the Fourier transform of the dipole moment has a large zero-frequency component and intense even-harmonic components (i.e., with frequency 2nω, where n is an integer and ω is the laser frequency). The presence of the even harmonics is intriguing: The system has inversion symmetry and even harmonics are forbidden by symmetry rules valid to all orders in perturbation theory. Finally, a laser pulse with well-chosen parameters can drive an electron that was initially in a delocalized eigenstate, to a state in which it is almost completely localized in one well. These processes are systematically investigated by numerical calculations and are rationalized with the help of a simple model which predicts the qualitative behavior observed numerically. The model suggests that these phenomena occur at those values of the parameters for which two Floquet states having different generalized parities become degenerate or nearly degenerate. This condition is rather general and we see no reason why it will not be fulfilled in systems other than double quantum wells (e.g., atoms or molecules).

We present the complete analytical solution of the cavity QED of a two-level atom and a field mode at zero temperature. It includes both dissipation of the field due to a finite Q value of the cavity and incoherent decay mechanisms for the atom. This analytical solution is provided by a powerful method for treating general master equations that appear in quantum optics. As distinct from the usual approaches we first deal with that part of the master equation which describes the dissipative coupling of the field and the atom to their reservoirs. Rather than using number-state or dressed-state bases we expand the density operator into the eigenstates of the nonunitary parts of the master equation which model the dissipative part of the dynamics. The set of these eigenstates is the damping basis. With the aid of this expansion we find the eigenvalues and eigenstates of the total Liouville operator. The evolution of an arbitrary initial state is then known. We employ these results to give an exact solution of the dynamics of the photon field in realistic experiments with one-atom masers at very low temperatures. It includes detuning, cavity leakage effects, spontaneous decay mechanisms for the atoms, a Fizeau-type velocity distribution for the atomic beam, and a statistical parameter for the probability of the excitation of incoming atoms, covering the limits of Poissonian pumping and of regular pumping. On the same grounds one can treat the one-atom laser, consisting of a single atom which stays in permanent interaction with the field mode and which is continuously pumped by external heat baths.

We consider two-photon bound states which may be excited in a planar waveguide filled with a self-focusing Kerr material. These bound states are the quantum analogs of the classical light bullets which form under the combined effects of self-focusing, diffraction, self-phase-modulation, and anomalous group-velocity dispersion. A variational approach is used to establish a threshold condition on the strength of the nonlinearity for the existence of the bound state, and a gedanken experiment is proposed to outline the principles for creation and detection of this quasiparticle.

The Wigner distribution functions for the output of a linear amplifier are investigated. The input light field of the ampliflier is assumed to be a squeezed and displaced vacuum state. The in-phase and quadrature-phase field amplitudes, the contours of Wigner distribution functions, and the three-dimensional picture of the Wigner distribution functions at the output fields are plotted as a function of the interaction time.

We use a continuous-mode quantization scheme to derive relations between the output- and input-field operators for traveling-wave propagation along attenuating and amplifying optical fibers. These relations provide complete information on the temporal and longitudinal spatial developments of the signal field. They are used here to obtain the effects of propagation on the first and second moments of the photocount in direct detection and of the signal field measured in balanced homodyne detection. Some of the results are similar to those obtained for attenuation or amplification of standing waves in cavities, and, for example, the survival of any input squeezing still limits the maximum gain to twofold. There are, however, additional propagation effects for the traveling-wave system. Thus, in direct detection, it is necessary to take account of the changes in gain profile with propagation distance, and in homodyne detection there are fundamental quantum-mechanical restrictions on the minimum field uncertainties that can be achieved in measurements at separated space-time points. These uncertainty properties are derived in detail and illustrated by the example of a squeezed input signal.

The susceptibility of a quantum coherent gas is derived near resonance and the effect of dipole-dipole interactions are assessed for a three-level system using mean-field theory. It is shown that the gas exhibits an ultralarge index effect with no absorption with the dipole effects included, but that for large N (number of atoms per unit volume) the dipole interactions have a marked effect. These results imply that the dipole interactions of a coherent gas near resonance do not destroy the ultralarge absorption-free index effect.

Squeezed states have been described in optics with the mathematics of quantum mechanics. Yet, electromagnetic fields of a single color obey the Helmholtz equation, of which the Schrödinger equation is but the paraxial (parabolic) approximation. We extend the ordinary squeezed states to solutions of the Helmholtz equation that contain them as their paraxial approximation. Third-order aberration expansion and asymptotic analyses are performed on these states.

The self-induced transparency in the Kerr host medium has been studied beyond the slowly-varying-envelope approximation. An analytic solution is obtained. There exists a hyperbolic-secant soliton whose power, pulse width, group velocity, and propagation constant are uniquely determined for given parameters of the medium. The reductions of the group velocities of the solitons by the self-induced-transparency effect in the resonant medium with homogeneous and inhomogeneous broadening are also studied. It is found that there is negative dispersion induced by the self-induced transparency, which is not predicted by the theory with the slowly-varying-envelope approximation. The amount of the induced dispersion is determined by the total dispersion of the system required to be compensated by the Kerr effect. Numerical examples of the self-induced transparency in an erbium-doped fiber are shown. In a typical erbium-doped fiber, the soliton solution has not been found because the inhomogeneous-broadening linewidth of the medium is too large.

We consider the process of spontaneous emission of a two-level atom embedded into a periodic layered dielectric structure. When the resonant atomic frequency lies within the photon-density-of-states gap, of width Γ, the atom emits light during a time interval tΓ≪1 until the spontaneous emission becomes fully inhibited. We discuss the enhancing of spontaneous emission by tuning the atomic resonance with a one-mode microcavity. In the λ/4-shifted distributed feedback microcavities which possess the δ-function-like density of states, in the middle of the gap, the process of spontaneous emission has damped Rabi oscillation behavior; the damping depends on the width of the gap and the height of its walls. A profile of the density-of-states gap can be determined from the experimental data on the temporal behavior of the atomic spontaneous decay.

We study light-induced mechanical forces that act on atoms interacting with colored photon reservoirs. An exact treatment to calculate the forces, based on the numerical computation of a hierarchy of correlation functions, is presented. We show that such forces may be significantly larger than that in free space. Our numerical results confirm and extend a previously existing simplified model to describe such forces.