When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a ${\mathrm{Tm}}^{169}$ vapor.

The nonclassical phenomenon of ‘‘induced coherence without simulated emission’’ is analyzed under the condition where two nonlinear ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ crystals are aligned in such a way that their idler emissions are collinear and inside a ringlike cavity with loss. This forced indistinguishability of the idler photons produces an interference between the free traveling conjugated signal beams when they are superposed. This interference is independent of the cavity loss, within the limits of a single-mode theory, and highly dependent on the position of the crystals inside the cavity. The maximum obtainable visibility of 100% reflects an induced coherence in the two crystals by the cavity field.

A set of integrable four-wave-mixing models arising in a medium with a resonant transition is presented. A suitable modification of the inverse scattering transform is constructed and used to find a common one-phase perioidic solution of the evolution equations. The Whitham equations describing the dynamics of slowly changing parameters are found. Their solution is used for a description of the evolution of light pulses with sharp leading edges. The possible application of the results for the analysis of the evolution of dense packets of solitons is discussed.

Semiclassical theory is used to study the effect of excitation-field bandwidth on the gain exhibited by driven, three-level, ssV-type, atomic systems. Gain, which may or may not be inversionless in the atomic-state basis, is produced through strong monochromatic driving of one atomic transition and weaker pumping of a coupled transition. It is found that monochromatic pumping frequently yields a greater optical gain than incoherent (wide-bandwidth) pumping. This is particularly true when the system gain can be attributed to hidden inversion among the eigenstates (semiclassical dressed states) of the coupled-atom plus driving-field quantum system.

A transformation of the linear second-order Fokker-Planck equations occurring in quantum optics is presented which overcomes difficulties connected with negative definiteness of the diffusion matrices. This transformation is based on a dynamical ordering of quantum quasiprobability distribution functions. The ordering depends on the parameters of the dynamical problem under consideration. An algorithm leading to exact solutions of the dynamically ordered Fokker-Planck equations with arbitrary initial conditions is given, and simple criteria, how to recognize squeezed light in arbitrary ordering, are presented. The problem of Fokker-Planck equations with time-dependent diffusion is also investigated.

We study a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We derive a master equation governing the evolution of such a system, and show that the stationary state can be described by Bose-Einstein or Fermi-Dirac distributions. The quantum-statistical character of the atoms exhibits itself in the dynamical behavior of the system and in the statistical properties of fluorescence photons emitted in the stationary state.

We construct, according to Glauber’s definition, the coherent states in a univocally specified finite-dimensional Hilbert space. Their analytical form is obtained as an analytical solution of the problem raised by Bužek et al. [Phys. Rev. A 45, 8079 (1992)]. The phase properties of the coherent states are studied within the Pegg-Barnett formalism.

A model for a laser with modulated signal and noise in the semiclassical approach allows the characterization of a Hopf bifurcation point and correspondingly of its spectrum. By means of the normal-form theory we have been able to give explicit normal-form equations that describe the system’s dynamic in the vicinity of the bifurcation point. At first order we determine the system’s behavior for the case when the signal modulation is coincident with the Hopf frequency and when it does not. In both cases, a characterization of the unfolding parameter is possible. We also consider an injected laser the Hopf frequency of which is an integer multiple of order n of the frequency modulated signal. In this case a perturbative theory of order n is necessary. We present also an example of noise for which this system does not present cooperative amplification. Numerical analysis is consistent with this prediction.

We present the results from simulations of harmonic generation using intense ultrashort laser pulses, both for single atoms and in an extended gaseous medium. Using a windowing technique on the single-atom spectrum, we show that the highest-order harmonics are generated simultaneously with rapid ionization, and that these harmonics have a phase dependence which is consistent with a quasiclassical tunneling model. By solving the atomic dynamics simultaneously with the propagation equations, we have obtained spectra that directly show the effects of phase mismatching and blueshifting produced by an ionizing medium. At experimental pressures, the plasma-induced phase mismatch is only important for the highest-order harmonics near the plateau cutoff. All harmonic orders, however, are seen to be blueshifted, by an amount consistent with a blueshifting of the fundamental as it propagates through the ionizing medium.

We consider the problem of optical pulse compression by cross-phase modulation in Bragg gratings—the ‘‘optical pushbroom’’ effect. Interpreting the effect of the moving pump as inducing Doppler shifts on the weak probe pulse, we find a simple approximation equation of motion that yields very general conditions for an observation of the compression effect.

We consider the integrability problem for a quantum version of the perturbed nonlinear Schrödinger (NS) equation, including a higher spatial dispersion and nonlinear dispersion of the group velocity (the corresponding classical equations are well known in the nonlinear fiber optics and in other applications). Employing the Bethe ansatz (BA) technique, which is known to yield a complete spectrum including the so-called quantum solitons (multiparticle bound states) of the unperturbed NS system, we find that the particular cases of the model which correspond to integrable classical equations, viz., the derivative NS and Hirota equations, are also fully integrable at the quantum level. In the generic (nonintegrable) case, the model remains integrable in the two-particle sector. In the three-particle sector, the BA produces unphysical states with complex energy. It turns out that the Hamiltonian in this case becomes non-Hermitian. We propose a procedure for finding the physical eigenstates of the system. We build an example of such a state and we show that it describes inelastic scattering.

Two ${\mathrm{CO}}_2$ lasers with ${\mathrm{SF}}_6$ as an intracavity saturable absorber were optically coupled, and their passive Q-switching dynamics were investigated. The amount of coupling used induced transitions from two unsynchronized periodic oscillating lasers into two synchronized chaotic ones. Conversely, the uncoupled lasers set in the chaotic regime could be made synchronized with a periodic pulsation after their coupling. Numerical solutions for the laser equations agree with the observations.

Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.

Spin-correlated interferometry of the fourth order for independent polarized as well as unpolarized photons arriving simultaneously at a beam splitter and exhibiting spin correlation while leaving it is formulated and discussed in the quantum approach. The beam splitter is recognized as a source of genuine singlet photon states. Also, typical nonclassical beating between photons taking part in the interference of the fourth order is given a polarization-dependent explanation.

We show that in the k-photon down-conversion a fundamental limit on the energy transfer does exist providing the signal mode is initially in the vacuum state and the pump mode is excited. In particular, in the two-photon down-conversion less than 2/3 of the pump energy can be transferred from the pump to the signal mode. With the increase of the order of the nonlinear process under consideration the efficiency is even smaller. On the contrary, we show that no restriction on the efficiency of the energy transfer in the kth harmonic generation does exist, i.e., in this process the total energy from the initially excited mode can be transferred into the mode which initially was in the vacuum state. We study restrictions implied by the fundamental limit on the energy transfer in the k-photon down-conversion on nonclassical effects which can be observed in the signal mode in the process.

We consider a two-level atom driven by modulated light and find that complete population inversion can be induced by light without any resonant frequency component. This is in contrast to the familiar case of monochromatic driving in which complete population inversion is only possible with resonant light. Our results concern experimentally realizable systems, and hence the effect of spontaneous emission is considered. We relate our results to recent work on double quantum wells and hence extend the parameter regime for low-frequency radiation generation

A phase space for the single-mode light field is constructed by using optical phase variables. This phase-space formalism is directly connected to optical-phase-related operators. The phase-state basis ‖θ〉 is used to represent various quantum operators and states. Properties of the density operator ρ^ phase-state matrix elements P(θ,θ’)=〈θ‖ρ^‖θ’〉 and their relations to phase-related quasiprobability distributions are discussed. By using the phase representation, different types of number-phase intelligent states are analyzed.

The expansion of the universal function in terms of the momentum transfer squared, ${\mathit{K}}^2$, has been investigated. We find that in the region of ${\mathit{K}}^2$≪1 a.u. both the Born approximation and the universal function yield a linear relationship between the generalized oscillator strength (GOS) and ${\mathit{K}}^2$, thus establishing the validity of the universal function for use in extrapolating the GOS through the unphysical region to the optical oscillator strength. As an illustration, the GOS for the inner-shell transition 2p-3s of sodium has been calculated using Hartree-Fock atomic orbitals and the universal function, and compared with measurement at 1000 eV. For 0.0<${\mathit{K}}^2$<0.01 a.u. the universal function merges with the Born approximation, and shows a correct asymptotic behavior. At 0.1<${\mathit{K}}^2$<0.4 a.u., the Born approximation fails to reproduce the measurement, while the universal function agrees excellently with the experimental data.

Coupled differential equations resulting from an application of the hyperspherical-harmonic expansion method to a number of two-electron atoms have been solved by an exact numerical method (renormalized Numerov method). Calculations are feasible (for the available computer facility) for the inclusion of up to 20 (K=20) partial waves. Although the convergence trend is discernible, the binding energies for K=20 are far from the converged values. An application of a convergence theorem by Schneider [Phys. Lett. 40B, 439 (1972)] permits extrapolation of the results to large K values. Such converged results agree closely with an accurate multiparameter variational calculation by Pekeris [Phys. Rev. 126, 1471 (1962)]. Even though the hyperspherical-harmonic expansion is notoriously slow for the long-range Coulomb interaction, the present prescription is a highly economical and accurate method for few-electron atoms. We have applied this method to the ground states of ${\mathrm{H}}^{\mathrm{-}}$, He, ${\mathrm{Li}}^{+}$, and ${\mathrm{Be}}^{2+}$, as well as to the first excited singlet state of He.

If the Dirac-Coulomb problem is solved by expanding the large and small components of the wave function in certain finite bases, spurious solutions are found for the lowest states with j=l-1/2. This paper shows that these must arise in any so-called kinetically balanced basis.