With a partial-wave interpolation method we calculated the positron energy spectra of pair production in the field of atoms with atomic number Z=82 for photons of energies k=10 and 15 ${\mathit{m}}_{\mathit{e}}$${\mathit{c}}^2$. Our results show that the screening effect is less than about 2%. Our results also indicate that the approximate treatment of screening through energy-shift screening theory becomes inadequate for photons of energy k≳10${\mathit{m}}_{\mathit{e}}$${\mathit{c}}^2$.

The quantum theory of a magnetic electron lens with rotational symmetry about its straight optic axis has recently been studied entirely on the basis of the Dirac equation [R. Jagannathan, R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Lett. A 134, 457 (1989)]. Following the same type of algebraic approach, the present paper elaborates on the quantum mechanics of beam transport through a general electron-lens system with a straight axis. The basic theory is developed in a general framework, and examples of applications are treated under the paraxial approximation and thin-lens assumption. Extension of the theory to systems with curved optic axes is dealt with very briefly. The present formalism based on a ‘‘beam-optical’’ representation of the Dirac equation goes over directly to the Hamiltonian formalism of geometrical electron optics upon classicalization.

We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.

Exact results for the photon statistics of a two-photon micromaser are presented, including the effect of finite detuning of the intermediate level. A periodic dependence on interaction times is shown to arise for large detunings, when sufficiently long interaction times are considered. Some typical photon-number distributions are shown, including some exhibiting sub-Poissonian fluctuations and multiple peaks. Previous treatments and the validity of some usual approximations are discussed. By direct comparison with the exact results, it is shown that the effective-Hamiltonian approximation yields incorrect equations for the off-diagonal elements of the field density matrix.

We extend the theory of the Hermitian optical phase operator to analyze the quantum phase properties of pairs of electromagnetic field modes. The operators representing the sum and difference of the two single-mode phases are simply the sum and difference of the two single-mode phase operators. The eigenvalue spectra of the sum and difference operators have widths of 4π, but phases differing by 2π are physically indistinguishable. This means that the phase sum and difference probability distributions must be cast into a 2π range. We obtain mod(2π) probability distributions for the phase sum and difference that unambiguously reveal the signatures of randomness, phase correlations, and phase locking. We use our approach to investigate the phase sum and difference properties for uncorrelated modes in random and partial phase states and the phase-locked properties of the two-mode squeezed vacuum states. We reveal the fundamental property of two-mode squeezed states that the phase sum is locked to the argument of the squeezing parameter. The variance of the phase sum depends dilogarithmically on 1+tanhr, where r is the magnitude of the squeezing parameter, vanishing in the large squeezing limit.

The calculation of the oscillation frequency of a single-mode laser oscillator is examined systematically. Mode-pulling formulas are developed for a variety of laser systems, and the limitations of a standard approximation are explored.

The symmetry principles governing the nonlinear interaction of intense laser radiation with molecular ensembles show that dynamical interaction phenomena exist in the ensemble even though the induced frequency-dependent polarization could be purely imaginary and unobservable in the static limit. An example is computer simulated in the S enantiomer of bromochlorofluoromethane, showing clear effects on the orientational and rotational velocity correlation functions and by Fourier transforming these functions, the dielectric and far-infrared spectra. Conditions are suggested for its experimental observation and orders of magnitude calculated for the appropriate mediating tensors.

Optical guiding in the free-electron laser is studied for a configuration in which a relativistic electron beam propagates through a rectangular waveguide in the presence of a planar wiggler. The wiggler model includes the effect of parabolically tapered pole faces for enhanced focusing of the electron beam. A set of coupled nonlinear differential equations is solved in three dimensions, which governs the evolution of the fields in a loss-free rectangular waveguide as well as the trajectories of an ensemble of electrons that are integrated using the complete Lorentz force equations. The interaction in a free-electron laser arises from the beating of the wiggler and radiation fields, which produces both upper and lower beat waves. The upper beat wave results in a slowly varying ponderomotive wave, while the lower beat wave introduces an oscillation at half the wiggler period. The lower beat wave cancels out entirely for a helical wiggler, but is present in planar configurations and causes the power and phase of the wave to oscillate at half the wiggler period. This effect also results in an oscillation in the guiding of the signal. The three-dimensional, multimode waveguide code WIGGLIN has been adapted to treat the short-wavelength regime and is capable of examining the effect of the lower beat wave because the orbit equations are not averaged over a wiggler period. The analysis assumes the injection of a Gaussian mode from a master oscillator into the wiggler in synchronism with the electron beam. The Gaussian mode is assumed to be focused down to the minimum spot size upon entry to the wiggler and is then decomposed into the modes of the rectangular waveguide, which satisfy the boundary conditions. Results indicate that the optical guiding of the signal (i) is oscillatory at one half of the wiggler period, and (ii) is more marked in the direction of the wiggle motion rather than transverse to it. In addition, side lobes about the principal radiation signal are observed to grow, which may adversely affect the bulk guiding of the wave and could result in increased wall loading. Implications of these results upon future free-electron laser designs are discussed.

In this paper we have constructed the continuum eigenfunctions and eigenvalue spectra for the squeeze operators of both single mode and two modes. Our analyses also show explicitly that proper eigenstates of both single-mode and two-mode squeeze operators do not exist, which implies that the squeeze operators do not have a discrete spectrum.

A quantum theory of a two-photon laser is developed by making use of the antinormal-ordering Q function. Starting from the microscopic atom-field interaction Hamiltonian for cascade three-level atoms and including saturable absorbers, we first present a master equation for the field-density operator, and then transform the master equation into a Fokker-Planck equation for the Q function. The Q-function approach enables us to study the two-photon laser analytically, obtaining simple expressions for nonlinear gain, mean photon number, frequency pulling, natural linewidth, and photon-number variance in a unified method. We find that the field in a two-photon laser will build up from a vacuum without triggering if its linear gain is larger than the cavity loss. Also hysteresis can occur in the two-photon laser even without triggering. With an overall two-photon resonance, the normalized photon-number variance approaches a common value 11/8 well above ‘‘threshold,’’ independent of the one-photon detuning. We compare these results with previous results obtained from an effective interaction Hamiltonian. We find that the domain of validity of the effective Hamiltonian for the photon-number variance is much smaller than that for the mean photon number. Well above ‘‘threshold’’ the effective Hamiltonian overestimates both the natural linewidth and the photon-number variance.

We present a simple quantum model for intracavity four-wave mixing above threshold. A reduction of quantum noise below the shot-noise level is predicted not only for the intensity difference of the signal and idler beams, but for the signal and idler intensity sum and also for the individual signal and idler intensities. The noise spectrum for the signal and idler phase variables is also calculated.

Recent studies have shown that single-shot spectra in stimulated Raman scattering can be much narrower than the quantum-mechanical gain-narrowed linewidth. However, shot-to-shot fluctuations in the single-shot spectra are such that the ensemble average gives the gain-narrowed linewidth. This happens because the mean frequencies of the single-shot spectra fluctuate from shot to shot under the gain-narrowed linewidth, and because some ‘‘noisy’’ shots are broadened or display multipeaked spectra. The nature of these quantum-noise-initiated fluctuations will be discussed in this paper, with both numerical and experimental results presented. Noisy, multipeaked, single-shot spectra will be shown to have a broader distribution of mean frequencies than the distribution of near-Fourier-transform-limited spectra.

A model of bichromatic (or two-frequency) above-threshold ionization is extended to include dipole coupling between an infinite number of continua, each having specific angular momentum. The continuum-continuum matrix elements depend on the energy of each continuum state and have a singularity, as expected of a hydrogenic atom. This model is analytically soluble without recourse to the rotating-wave approximation. The ionization rate is independent of the intensity of the low-frequency laser. We examine the angular distribution of the photoelectrons under different circumstances of bound-state parity and ionization laser polarization. Qualitative differences between the models are also illustrated using the photoelectron spectra.

For continuous-wave (cw) squeezed light that has a monochromatic mean field and a rectangular squeezing spectrum covering bandwidth B, we calculate the photocount distribution for a counting time T. The nonclassical oscillations in the photon-number distribution of single-mode squeezed light have reduced visibility in the cw photostatics and often disappear entirely. The even-odd oscillations associated a with single-mode squeezed vacuum are absent for BT≪1, but for BT≳1 they appear in the cw photocount distribution with reduced visibility under appropriate conditions. The oscillations associated with a single-mode squeezed state that has a mean complex amplitude disappear from the cw photostatistics for all counting times.

We describe the dynamics of an exactly solvable Raman coupled model interacting with two modes of a quantized cavity electromagnetic field. The model consists of a three-level atom in the Λ configuration whose excited state is considered to be far off resonance and is adiabatically eliminated. The effective Hamiltonian for this system contains products of the transition operators between the two ground-state levels and a field annihilation operator from one mode and a creation operator from the other. This Hamiltonian provides an example of a zero-photon process. We study the atomic inversion and investigate the production of nonclassical effects such as antibunched light, violations of the Cauchy-Schwartz inequality, and squeezing.

Nonisotropic scattering patterns showing a minimum for small and almost transparent core-shell particles are discussed. It is shown that the Rayleigh-Gans theory will not predict accurately the scattering by such particles. A law of corresponding patterns is established for small core-shell particles with an effective index of refraction as close as possible to that of the medium. Based on this nonisotropic scattering phenomenon, a method for determining the thickness itself and its distribution of very thin coatings on small colloidal particles is proposed.

Predictions for dye-laser intensity correlation functions of a stochastic model incorporating colored gain-noise fluctuations are discussed and compared with the predictions of the model incorporating loss-noise fluctuations. It is shown that differences between the two models are generally masked by the finite correlation time of the noise. Important differences are shown to exist well above threshold when the correlation time of the colored noise is of the same order or smaller than the cavity decay time. A new algorithm for the simulation of stochastic equations with colored noise is used and discussed.

Time-dependent Schrödinger (TDS) equations can be solved efficiently by expanding the solution on a finite basis set. For strongly time-dependent regimes, a set of complex static vectors is proposed as a natural basis. Proofs of completeness and optimization prescriptions are given in a general way, suggesting that this technique can be used to solve a broad class of TDS equations. As an illustration, we use this optimal basis-set expansion to solve a simplified two-dimensional free-electron laser model that can be formulated in terms of a TDS equation. This physical application allows us to prove the accuracy of this basis-set technique by comparison with a standard mesh technique.

A technique of canonical quantization in a general dispersive nonlinear dielectric medium is presented. The medium can be inhomogeneous and anisotropic. The fields are expanded in a slowly varying envelope approximation to allow quantization. An arbitrary number of envelopes is included, assuming lossless propagation in each relevant frequency band. The resulting Lagrangian and Hamiltonian agree with known propagation equations and expressions for the dispersive energy. The central result of the theory is an expansion of the quantum Hamiltonian in terms of annihilation and creation operators corresponding to group-velocity photon-polariton excitations in the dielectric.

This paper is a natural extension of a previous paper [Guedes, Penaforte, and Baseia, Phys. Rev. A 40, 2463 (1989)], where a quantum theory of laser transmission loss was developed to give the solutions for the laser field, inside and outside an optical cavity. Here we calculate in the linear and nonlinear analysis the coherence functions and spectral distributions for the internal and external fields, for a laser operating below and above threshold. The comparison of our results with those found in the current literature shows that with the use of a more realistic model of optical cavity, together with the assumption that the field is initially in a random-phase state, we are able to avoid the use of the ‘‘fictitious’’ heat bath of the conventional treatments.