The discovery of Lax, Louisell, and Knight (LLK) [Phys. Rev. 9, 378 (1974)] that electromagnetic beams in vacuum do have a longitudinal component can be proved experimentally from the polarization independence of the energy of electrons from the focus of a laser. For this purpose we had to develop the LLK paraxial approximation to a Maxwellian exact solution for a Gaussian beam. Inserting the exact solutions into the Maxwellian stress tensor expression of the nonlinear force for the electron acceleration demonstrates a polarization dependence if only the transversal optical components are used. Including the exact longitudinal fields results in the experimentally proven polarization independence.

We study the effect of a static field on the stochastic layer of microwave-driven hydrogen using two approaches. We use the Chirikov overlap criterion on the Hamiltonian to estimate the critical field strength required for global chaos. We then derive the whisker and standard maps for this system valid for arbitrary field strengths and use the standard map to obtain a second estimate for the onset of global chaos. The standard-map estimate agrees well with both strobe plots and the whisker map plots for this system. Throughout, we use parameter values typically found in experiments.

A geometrical optics method for solving wave propagation in weakly nonlinear, weakly inhomogeneous media is presented and applied to the propagation of a two-dimensional Gaussian beam. A complex distorted phase φ is obtained. This complex phase is used to describe both the zeroth-order amplitude and the nonlinear rays along which the energy propagates. This approach recovers standard self-focusing and self-blooming effects in a quadratically nonlinear medium.

We have studied electric-field-induced rotational autoionization of ${\mathrm{Li}}_2$ Rydberg states converging to high, R>10, rotational limits of the ${\mathrm{Li}}_2^{+}$ ion. Although autoionization of such states lying above the lowest rotational level of ${\mathrm{Li}}_2^{+}$ is energetically allowed, the process is inhibited by the large transfer of angular momentum required from the ion core to the exiting electron, and it, in theory, does not occur in zero field. Nonetheless, autoionization requiring the transfer of ∼10 units of angular momentum is readily observed in fields of 10–330 V/cm. The application of a field allows autoionization to occur to the nearest continuum by allowing a series of quadrupole transitions, in each of which the molecular ion core loses two units of angular momentum while the Rydberg electron’s angular momentum is unchanged. We present a quantitative model based on this mechanism that is in satisfactory agreement with our experimental results.

We discuss macroscopic effects of broadband light on the transport properties of a single-component gas. We use the method of elimination of fast variables to calculate the slow evolution equations for the number density, the hydrodynamic velocity, and the temperature. Using a model for the Boltzmann collision terms, we find explicit expressions for the heat flux and the pressure tensor. We apply these results to some transport problems.

We report a measurement of the excitation spectrum of the laser-induced collisional energy transfer process for the Eu-Sr system in the weak-field regime. The measurement has been performed in a detuning range extending up to 85 ${\mathrm{cm}}^{\mathrm{-}1}$ in the static wing, providing a wider check of existing theoretical models. The frequency resolution of the measurement (0.1 ${\mathrm{cm}}^{\mathrm{-}1}$) was suitable for a quantitative study of the core of the line spectrum, where a comparison with the results of numerical calculations based on an effective three-level model gives complete evidence for a cooperative decay from the Sr(5${\mathit{p}}^2$${)}^1$${\mathit{D}}_2$ final level.

We have studied the electron-impact excitation of an atom, in the presence of a laser field whose photon energy is tuned close to the energy difference between two excited final states. Both the laser-projectile and the laser-target interactions are treated nonperturbatively, while the electron-atom interaction is treated within the first Born approximation. As an application, we have analyzed the resonant laser-assisted excitation of the $2^1$S and $2^1$P states of helium. The agreement between the present nonperturbative results and previous perturbative ones is excellent, except for very small detunings. The present nonperturbative treatment also shows that the results given by perturbation theory on both sides of the resonance, when plotted as a function of the laser frequency, correspond to the excitation of different Floquet pseudostates. This is related to the presence of avoided crossings in the diagram of the Floquet pseudoenergies, as a function of the laser frequency.

The problem of a two-dimensional anisotropic oscillator coupled through a complex parameter that oscillates at the frequency ω is considered. The treatment has been applied to the case when ω is not equal to the frequency difference of the oscillators. An exact solution for the Schrödinger wave function has been obtained. The Green’s function as well as the expectation value of the energy are calculated.

We consider the dynamics of a collection of atoms interacting with a coherent field and a broadband squeezed vacuum. We obtain an exact solution of the master equation and study in detail the types of nonequilibrium steady states that can be generated. We show that in the absence of coherent drive the atoms are in a state whose properties are similar to those of the squeezed vacuum for photons. We demonstrate that the steady state for certain discrete values of the external field strength and detuning is a pure state which is the eigenstate of the non-Hermitian operator cosh(‖ξ‖)${\mathit{S}}^{\mathrm{-}}$+sinh(‖ξ‖)${\mathit{S}}^{+}$, where ξ is the squeezing parameter associated with the input radiation field. These eigenstates play a very fundamental role in the theory and satisfy the equality sign in the Heisenberg uncertainty relation Δ${\mathit{S}}_{\mathit{x}}$ Δ${\mathit{S}}_{\mathit{y}}$≥1/2‖〈${\mathit{S}}_{\mathit{z}}$〉‖. We also present detailed numerical results for the characteristics of the field generated by the collective system.

In the framework of the ABCD ray matrix formalism, a theoretical model is proposed to describe the fundamental ${\mathrm{TEM}}_{00}$ elliptical Gaussian-mode size variations due to frequency-dependent lenslike effects in ring lasers. Two different mode size dynamics are predicted in the sagittal and tangential planes of the planar ring cavity, leading to the existence of different critical geometries in each plane, i.e., geometries for which the tangential or sagittal mode size at a given point becomes independent of the focal length. The frequency-dependent diffraction losses associated with these mode size variations predict rather complex asymmetries in the output power profiles in usual ring lasers, even in the case of a single-isotope gas mixture. Moreover, a ‘‘fully critical geometry’’ is predicted for which sagittal and tangential critical geometries occur simultaneously, making the two mode sizes independent of the lenses. A first type of experiment confirms the existence of the sagittal and tangential double dynamics and the role played by resonant diffraction thanks to the diffracted-light-spectroscopy technique. A second type of experiment proves the existence of the fully critical geometry. The theoretical predictions are in very good agreement with the experimental results.

The free-electron laser (FEL) is presented theoretically in this paper as an angularly directed radiation source. Features of phased-array antenna are incorporated in known FEL schemes to provide the angular steering of the FEL radiation in the far field. Various methods for FEL angular steering are proposed. These are classified in this paper as end-fire and broadside schemes. A unified two-dimensional linear model for the FEL angular steering is derived and implemented to demonstrate the performances of the various steering methods. It is shown that by using a miniature wiggler, a considerable angular steering range is feasible in the broadside FEL scheme in the millimeter wave range. Possible applications for the FEL angular steering features, considering their limitations, are proposed.

A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the evolution of the quantized radiation-matter system described by the multipolar (μ⋅${\mathbf{D}}^{\mathrm{\perp }}$) Hamiltonian. For a molecular system with localized electronic states we derive equations of motion in which the instantaneous intermolecular interactions are explicitly recovered and the interaction with the Maxwell electric field is of the μ⋅${\mathbf{E}}^{\mathrm{\perp }}$ type. It is shown that with total neglect of retardation, these equations lead to the usual expressions for nonlinear optical susceptibilities in terms of equilibrium correlation functions of the polarization field of the molecular system. A mean-field approximation for these equations of motion yields the commonly used local-field expression. Finally, a procedure is proposed for calculating the optical response that fully accounts for retardation, based on a hierarchy of equations of motion for polaritons.

We observe experimentally and explain theoretically second- and third-harmonic generation from a cell containing xenon gas using a tightly focused laser beam with intensities of up to 4×${10}^{13}$ W/${\mathrm{cm}}^2$. Both processes are forbidden according to standard lowest-order theories.

By a suitable variable transformation we show that detuned lasers can be described by complex Lorenz equations and establish a close analogy between detuned lasers and baroclinic instability. The analogy enables us to get all analytical and exact results for the second threshold of the detuned single-mode lasers. In order to discriminate sub- from supercritical Hopf bifurcations, we use a combined approach of elimination procedure and normal form techniques to make a systematic calculation of the criterion for both of the systems. The influence of the parameter variations on the nature of the bifurcation is discussed in detail. For detuned lasers it is shown that, if we restrict ourselves to the case of b≤1 (b=${\gamma }_{\mathrm{?}}$/${\gamma }_{\mathrm{\perp }}$, i.e., the ratio of the longitudinal to the transversal relaxation constant of the atoms) and not-too-small k (=κ/${\gamma }_{\mathrm{\perp }}$, with κ denoting the cavity relaxation constant) and Δ, for given b and Δ (Δ and k or k and b), there exists a ${\mathit{k}}_{\mathit{c}}$ (${\mathit{b}}_{\mathit{c}}$ or ${\mathrm{\Delta }}_{\mathit{c}}$) such that the Hopf bifurcation is subcritical if k<${\mathit{k}}_{\mathit{c}}$ (b>${\mathit{b}}_{\mathit{c}}$ or Δ<${\mathrm{\Delta }}_{\mathit{c}}$) and supercritical if k>${\mathit{k}}_{\mathit{c}}$ (b<${\mathit{b}}_{\mathit{c}}$ or Δ>${\mathrm{\Delta }}_{\mathit{c}}$). Numerical investigations show that period-doubling bifurcations to chaos exist not only for the subcritical but also for the supercritical case.

In this paper we derive a complete semiclassical description of Mössbauer spectroscopy with arbitrary external or internal perturbations of the active levels. The γ rays are taken to be weak enough to allow us to evaluate the linear Mössbauer response to lowest order in the intensity, in which case the γ-ray field can be treated classically. It induces transitions between level manifolds that can have arbitrary interactions inside themselves. The nuclear system is described by a density matrix. In principle, time-dependent perturbations can be handled by the formalism, but the equations are easier to solve for systems that display steady-state behavior. We consider, in particular, the case of magnetic radio-frequency modulation of the Mössbauer levels. Utilizing a matrix-continued-fraction technique, we solve for the absorption spectrum, and we choose numerical illustrations with parameters such that they describe the nucleus ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$. In this paper we treat mainly the case of magnetic modulation, but other experimental arrangements are discussed too. The calculations are able to treat both saturation and interference effects, which become important when the radio-frequency modulation is very strong. The new feature that emerges is the occurrence of resonances arising from the interference of different physical processes. The calculational method and its results are discussed and compared with other works.

Nonlinear problems in quantum optics can be described by an infinite hierarchy of ordinary differential equations for the moments. We discuss different truncation schemes involving cumulants. For illustration the method is applied to second-harmonic generation. We prove that all but second-order cumulants are equal for any quasiprobability distribution ${\mathit{P}}_{\mathit{s}}$, especially for the P, Q, and W functions.

Radiation at the harmonic frequencies in free-electron lasers is affected by several factors including misalignment of the electron beam and wiggler axes, and transverse gradients of the electron beam and wiggler field. These processes manifest themselves as changes in the harmonic power and transverse intensity profile. A transverse source function for the monochromatic radiation from a single electron in a plane-polarized wiggler magnetic field is derived that addresses these various effects. The resultant source is a composite of multiply peaked sources distributed over the local transverse wiggle range of each electron where the nth source has n peaks. For transverse-electron-beam density distributions that are slowly varying, an excellent description of the harmonic radiation can be obtained by including only the first few sources. Transverse averages of the distributed sources are taken to make comparisons with previous one-dimensional theories where they exist.

We consider a lossless micromaser in which a monoenergetic, low-density beam of two-level atoms in a coherent superposition of their upper and lower states is injected inside a single-mode high-Q cavity. This is a realization of a harmonic oscillator driven by a quantum current. We find that under appropriate conditions the field may evolve to pure states, which we call tangent and cotangent states, even for mixed-state initial conditions. In various limits, they exhibit nonclassical properties such as sub-Poissonian photon statistics, or even more interestingly acquire the characteristics of ‘‘macroscopic’’ quantum superpositions. The conditions under which these states are reached, as well as the dynamical approach of the system to steady state, are discussed in detail.

A nonequilibrium open-system theory for continuous photodetection processes is developed using a probability-density functional combined with the path-integral technique. Nonunitary time evolution of the system-environment density operator due to measurement back action and continuous measurement is exactly described for three familiar photodetection processes. New exact photocounting formulas are obtained for these three processes; in particular, Mollow’s photocounting formula is generalized for a nonequilibrium open system. Distinctive features between a closed system and an open system are presented; for example, the probability distribution for the number of counts is shown to contain complete information about photoelectron statistics for a closed system, whereas it does not for an open system. The obtained formulas are applied to photodetection of a single-mode photon field that interacts linearly with a pump source consisting of a single harmonic oscillator and a reservoir consisting of an infinite number of harmonic oscillators. In the former case, increasing the ratio of the source-field coupling constant to the field-detector coupling constant causes the photon field to cross over from a closed attenuating field to an open stationary field. In the latter case, a quantum-mechanical fluctuation-dissipation theorem in the continuous photodetection context is discussed.

We develop a quantum theory for continuous photodetection processes that describes nonunitary time development of the field under continuous measurement of photon number. Exact expressions are obtained for time evolutions of the photon-field density operator, average and variance of the photon number, and the Fano factor. These are applied to typical quantum states, i.e., number, coherent, thermal, and squeezed states. The continuous photodetection process is made up of two elementary processes in terms of the referring measurement process, that is, one-count and no-count processes. Just after the one-count process in which a photodetector registers one photoelectron, the average photon number 〈n(t)〉 of the remaining field is shown to increase for super-Poissonian states (e.g., thermal state) and decrease for sub-Poissonian states (e.g., number state); for the Poissonian state (e.g., coherent light), 〈n(t)〉 does not change. During the no-count process in which the photodetector registers no photoelectrons, on the other hand, 〈n(t)〉 decreases in time for all states except the number state. The physical origins for these results are clarified from the viewpoint of nonunitary state reduction by continuous measurement of photon number. Furthermore, we introduce a nonreferring measurement process in which the detector registers photocounts, but we discard all readout information. We discuss the difference in the way the photon field evolves in this process compared to the referring measurement process.