A theory is presented that describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. The nonlinear wave packet representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton’s equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase portraits of the equivalent potential. Equilibria of the potential, or equivalently, critical points in the phase plane, represent stationary (stable or unstable) nonlinear surface waves. Stability of the latter follows immediately from a simple inspection of the potential. The shape of the equivalent potential changes with the power in the incident beam. Our theory provides the nonlinear analog of the well-known linear Snell’s laws of reflection and transmission. Conditions on the validity of the theory are established in parameter space by extensive numerical solution of the nonlinear partial differential equation describing beam propagation. One important conclusion of the paper is that the predictions of the equivalent-particle theory encompass a wide physical parameter space. As an illustration of an application of the theory, we show how to design an all-optical angle or power adjustable spatial scanning element. Contact is made with earlier numerical studies of beam propagation and nonlinear surface-wave stability at a linear-nonlinear interface.

The theory presented in the preceding paper is extended to account for incident optical beam breakup into multiple self-focused channels and to deal with multiple reflection and transmission at multiple interfaces. Beam breakup is explained by examining the decomposition of the channel in one medium, into its soliton and radiation components after it has crossed into the new medium. A formula is derived which gives the criterion for the number of channels appearing as a consequence of breakup. This formula also provides analytic expressions for the individual self-focused channel powers and the amount of radiation generated. An important observation here is that the amount of radiation generated at the interface shrinks rapidly as a function of increasing channel number N. Each new component generated can be treated as a separate equivalent particle moving in its own equivalent potential. The theory of the preceding paper [Aceves, Moloney, and Newell, Phys. Rev. A 39, 1809 (1989)] can therefore be applied directly to show that low-power channels generated in the breakup will suffer reflection while higher-power channels will undergo transmission. An added ingredient to allow for mutual-channel interaction is the soliton-collision formula. The multiple-interface extension of the single-interface problem results from patching individual single-interface equivalent potentials together. The theory is illustrated with two applications: (i) a nonlinear version of a directional coupler requiring just two interfaces and (ii) trapping of a channel at an interface by a ramped linear refractive index.

We present a fully quantum-mechanical theory of nondegenerate multiwave mixing processes in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong-pump intensities and tunings within the Rabi sidebands. We find good broadband squeezing for low-pump intensities and tunings outside a small region around central tuning. Both cases avoid regions of significant spontaneous emission.

The time evolution of the electron and field operators in stimulated Compton scattering is considered. The operators are described by equations of motion in which the coordinate and momentum operators of the electron appear separated. These equations are solved by applying a new integration method based on iteration techniques, so the rigorous solutions are obtained. The resultant operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals. Moreover, the functionals that describe the creation and annihilation operators are written in ordered form. Finally, applications of these results to particular cases are given.

We construct a large class of squeezed states realized in terms of density matrices. The moments of the canonical variable q^ and the number operator n^ distributions are analytically evaluated. The new states can be simultaneously squeezed in q^ and n^ to any desired amount and exhibit almost Gaussian shape in the former and strongly sub-Poisson distribution in the latter. The probability distributions can be synthetically characterized in terms of the fractional-photon index introduced by Katriel, Rassetti, and Solomon [Phys. Rev. D 35, 1248 (1987)].

The deleterious effects of nonlinear dispersion on squeezed light in two-photon devices when absorption losses are included have been analyzed making use of the variables called two-mode quadrature-phase amplitudes. The uncertainties in the quadrature amplitudes have been computed from a generalized Fokker-Planck equation. The dependence of squeezing on the nonlinear coupling, the modulation (including the case of high modulations), the pumping phase (where nonlinear dispersion causes an intensity-dependent shift in the minimum squeezing), and the absorption losses have been studied.

We present a statistical theory of forward and backward Raman amplification and spontaneous generation in dispersive media pumped by a phase-diffusion field of arbitrary bandwidth. It is shown that, unless the Stokes input is correlated with the pump, the Stokes output and the pump are statistically orthogonal, even if the Stokes field builds up spontaneously. The growth of the average Stokes field amplitude is not affected by dispersion. A general expression is given for the average Stokes intensity which is valid both above and below the critical pump intensity for overcoming the decorrelating effects of group-velocity dispersion. If the length of the medium is much greater than the coherence length associated with the dephasing of the two waves, then the average intensity of stimulated Raman scattering (SRS) depends on the pump bandwidth. For relatively short medium lengths the average intensity of spontaneously initiated SRS is essentially independent of the bandwidth of a phase-diffusion pump field.

A description of the electron-hole plasma of a semiconductor laser is developed that includes the many-body effects due to the Coulomb interactions. In particular, the plasma density-dependent band-gap renormalization, the broadening due to intraband scattering, and the Coulomb enhancement are included and evaluated for three- and two-dimensional semiconductor structures. Because of the short intraband scattering relaxation time one can eliminate the interband polarization adiabatically and at the same time introduce a hydrodynamic description of the intraband kinetics. From this general formulation a diffusion equation for the carrier density is derived. The resulting ambipolar diffusion coefficient decreases with the laser intensity due to the reduction of the electron drift. The present semiclassical theory is completed by the laser field equation and by the addition of Langevin fluctuations.

A systematic method for calculating nonlinear-optical susceptibilities in condensed phases, which incorporates intermolecular forces and spontaneous emission in a consistent way, is developed, using the multipolar (μ⋅D) Hamiltonian. Reduced equations of motion that couple the electromagnetic field and material variables are derived for a crystal of point dipoles. The Bloch equations in the local-field approximation, which were derived previously using macroscopic considerations, are obtained as a limiting case of the present microscopic theory. It is shown that correlations among the molecules and the radiation field are not treated rigorously in the local-field approximation, whereas they can be incorporated in a systematic way using the present formalism. An expression for the dielectric function ε(k,ω) is obtained, which is different from Hopfield’s exciton-polariton model. Our result does agree, however, with Hopfield’s expression, which is based on the minimal-coupling (p⋅A) Hamiltonian, in the long-wavelength and small-frequency limit (k,ω→0), provided spontaneous emission is neglected.

Two schemes to prepare pure number states in a high-Q micromaser with Rydberg atoms are proposed. In the first experiment the atoms are probed after the interaction with the cavity field and the number state is obtained via state reduction. In the second experiment the interaction time of ionic Rydberg atoms with the maser field can be controlled via an electric accelerating field. The velocity of the ions is adjusted in such a way that every ion emits a photon and the total number of photons is exactly known via the total number of passing ions. It is also shown how the photon statistics in the micromaser in general can be probed via the outgoing atoms.

A theoretical study of the nonlinear polarization in a molecular medium is presented. It enables us to stress the importance and to evaluate the contribution of the population and orientational gratings in four-wave mixing depending on the pump- and probe-beam polarizations. The medium is described as an ensemble of two-level systems and is subject to rotational diffusion. The model is valid far or near resonance, as well. It is only assumed that time variation of the field envelopes and rotational diffusion constant are much smaller than the transverse decay rate ${\Gamma }_2$. The nonlinear polarization is expressed as a function of the field polarizations. The results are applied to a four-wave-mixing experiment to discuss the influence of the rotational diffusion. Finally, by including propagation effects, we use this formalism to calculate a phase-conjugated signal. This enables us to stress the influence of rotational diffusion to achieve time reversal of the envelope of a light pulse.

We study the photon statistics in the interaction of a three-level atom with cavity fields of arbitrary detunings. A number of new features of photon-number distributions and fluctuations are found and discussed. The possibility of sub-Poissonian and antibunching effects is also discussed.

It is shown that squeezing will inevitably be generated in a harmonic oscillator with time-dependent frequency for any nonvanishing rate of frequency change, sudden or smooth. The general form of the time-dependent transition probabilities among the eigenstates of the initial Hamiltonian is obtained with an exact operator approach. Results for the case of a sudden frequency jump are explicitly given as an illustration. It is also pointed out that to generate squeezing in a harmonic oscillator, the Hamiltonian does not have to be a unitary squeeze transformation of the free Hamiltonian.

When an additive external signal is applied to an acousto-optic bistable device showing the Feigenbaum period-doubling route to chaos, various amplification phenomena are observed. We present these phenomena and show the importance of linearized modal and Floquet analyses in their explanation.

We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.

A diagrammatic technique is developed to account for the saturation effects which occur when optical coherent transients are generated by broad-bandwidth light pulses. The paper is focused on the calculation of the two-atom, single-time dipole correlation function which originates the signal. In addition to the single-excitation-field situation, we examine the coherent transient generation by overlapping time-delayed correlated pulses. Our approach requires that one of the two correlated pulses be weak. The calculation of the delay dependence of the signal intensity is thoroughly worked out in the case of two-pulse and three-pulse transients in an angled-beam configuration.

For several reasons, it is essential to have analytic descriptions of single-electron trajectories for wigglers and undulators. (a) They give a better insight into the complicated dependence of the electron motion on quantities like the injection conditions or the wiggler parameter K; (b) one can hope to calculate the radiation pattern from a particular wiggler or undulator only if at least the single-electron velocity is given in closed form; (c) analytic single-particle trajectories are an essential starting point for investigating advanced problems like stability analyses and free-electron laser performance. Therefore, single-electron motion was studied in wigglers with two-dimensional magnetic fields that are transverse and periodic but otherwise arbitrary on axis, and satisfy Maxwell’s equations off axis. In this class of fields, the energy and one component of the canonical momentum are conserved and can be used to reduce the trajectory problem to the integration of a single complicated second-order ordinary differential equation, which, for all realistic electron-beam emittances and for all realistic values of ${\delta }_w$=K/γ, is weakly nonlinear and lends itself to a two-level two-scale analysis, through which an accurate analytic description of the complete electron trajectory can be established. This analytic trajectory exhibits all the features that one expects to find in off-axis motion, such as small-amplitude rapid wiggler oscillations superimposed on large-amplitude slowly varying betatron oscillations. The accuracy of this analytic trajectory was tested for a sinusoidal on-axis field variation by comparison with a numerical trajectory, and it was found that even for far-off-axis electrons, the agreement was excellent, typically on the order of one part in a thousand. This high accuracy in the off-axis regime is an important feature, since in many devices real transverse beam dimensions, initial beam velocity spreads, lateral beam injection, and a small undulator period ${\lambda }_0$ lead to electrons traveling considerably off axis.

Considering a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a coherent state of the field, we show that the dynamics of the atom as well as the spectrum of the field are sensitive to the relative phase between the atomic dipole and the cavity field. It is shown that, for a certain choice of this phase, ‘‘coherent trapping’’ occurs in two-level atoms. In the case of spectra, for the same choice of the phase, instead of a three-peaked symmetric spectrum, we have an asymmetric two-peaked spectrum.

Novel electromagnetic directed-energy pulse train (EDEPT) solutions of Maxwell’s equations have been obtained. One particular solution, the modified-power-spectrum (MPS) pulse, will be described in detail. EDEPT’s such as the MPS pulses, can be tailored to give localized energy transmission along a specified direction in space that is significantly improved over conventional diffraction-limited beams. Moreover, they represent fields that recover their initial amplitudes along the direction of propagation at extremely large distances from their initial location. These EDEPT solutions are not physically pathological and can be reconstructed from causal Green’s functions. In fact, these fields appear to be launchable from finite-aperture antennas.

By means of the Wigner transformation procedure, we extract a generalized Fokker-Planck equation that represents the semiclassical version of the quantal master equation for Brownian harmonic motion. The Fokker-Planck equation and its solutions are investigated both in the Markovian and in the non-Markovian regimes. The relations between semiclassical and classical Brownian motion of harmonic oscillators are analyzed with special emphasis on the high-friction limit.