We study the phase dynamics of a single-mode ring laser described by the complex Maxwell-Bloch equations. We identify three reference-frame frequencies and determine the properties of the field dynamics observed in these frames. In one of these reference frames, the phase jumps are always equal to π, irrespective of the detuning, while in another reference frame quasiperiodic field portraits reduce to periodic field portraits. We also apply the recent theory of Ning and Haken [Phys. Rev. Lett. 68, 2109 (1992)] to prove that the laser phase can be decomposed into a geometrical component that is frame invariant and a dynamical component that is frame dependent.

We show that the phenomena of soliton trapping and daughter wave (‘‘shadow’’) formation in optical fibers are already contained in the Manakov model [Sov. Phys. JETP 38, 248 (1974)].

Two generalized rate equations describing single-mode ${\mathrm{CO}}_2$-laser dynamics are derived by applying the center-manifold theory to an improved four-level scheme. The model is studied in the case of periodic modulations of the losses and compared with the outcome of an experiment, revealing an excellent agreement.

We present an experimental study of strong self-focusing in nematic liquid crystals. In a planar geometry, a linear dependence of the focal power on the input intensity for 100-μm-thick samples turns into an exponential one when thicker samples are used. A transverse visualization of the beam structure is performed in a cylindrical geometry. We observe an undulation and a filamentary structure of the laser beam for large intensities. Also, multiple focal points appear along the beam axis in this configuration. Undulation and filamentation of the beam are also observed in a spherical geometry.

We present the results of exact wave-function calculations that are equivalent to numerical experiments on a two-electron quantum system. We show that Rabi oscillations of the core electron can modify the photoelectron spectrum of the outer electron by efficient coherence transfer via e-e correlation, even in the absence of an autoionizing level or other continuum structure. We compare a simplified analytically soluble two-electron theory with our numerical results.

Starting with the ${\mathrm{H}}^{\mathrm{-}}$ 2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$P excited bound state, we have studied the problem of direct versus sequential two-photon, two-electron ionization with linearly polarized laser light of λ=5320 Å and intensity I=1.4×${10}^9$ W/${\mathrm{cm}}^2$. The theory is nonperturbative and electronic-structure oriented. It allows for the multiconfigurational zero-order representation of bound and autoionizing states, for electron correlation, and for the effects of nonorthonormality which cause multielectron excitation even without correlation corrections. The one- and two-electron multichannel continua are represented by square-integrable complex exponential functions. The results show that the sequential process is dominant, even though there exists the ${\mathrm{H}}^{\mathrm{-}}$ 4s4p ${}_{}{}^3{}_{}{}^{}$P° autoionizing state, which is near resonance. However, the direct process would dominate if the autoionization width, which is computed to be 1.16×${10}^{\mathrm{-}3}$ a.u., happened to be smaller by about a factor of 100, which is a realistic possibility for other systems.

The space-time field evolution in a Kerr slice with single feedback mirror is considered. A full symmetry analysis of the governing equations reveals profound differences between plane-wave and Gaussian-beam excitation. For Gaussian-beam pumping primary bifurcations to a succession of polygonal figures are predicted and confirmed in numerical simulations. Secondary bifurcations are complicated by competition between local and global bifurcations. Chaotic itinerancy and intermittency are among the phenomena observed in the simulations. For broad pump beams, multispot polygons with fivefold symmetry are observed to coexist with sixfold quasilattice patterns, in excellent agreement with the theoretical predictions based on symmetry considerations only.

We demonstrate that the generalization of the two-level Jaynes-Cummings model to an N-level atom leads to the creation of up to N macroscopically distinct field states. These field states are Schmidt-orthogonalized superpositions of Fock states. They correspond to macroscopic states of the field, attainable with large mean photon numbers. Unlike the situation with a two-level atom and a coherent-state field, which evolves into a macroscopic coherent superposition state (a Schrödinger cat), we find that when the additional levels participate strongly in the excitation (e.g., all transitions are resonant with equal dipole moments) then the system does not evolve into a pure state.

The operator algebra of the quantum harmonic oscillator is applied to the description of Gaussian modes of a laser beam. Higher-order modes of the Hermite-Gaussian or the Laguerre-Gaussian form are generated from the fundamental mode by ladder operators. This approach allows the description of both free propagation and refraction by ideal astigmatic lenses. The paraxial optics analog of a coherent state is shown to be a light beam with a displaced beam axis which is refracted by lenses according to geometric optics. The expectation value of the orbital angular momentum of a paraxial beam of light is found to be expressible in terms of a contribution analogous to the angular momentum of the oscillator plus contributions which arise from the ellipticity of the wave fronts and of the light spot. This clarifies the process by which a transfer of orbital angular momentum between a light beam and astigmatic lenses or diaphragms occurs.

The spectrum of scattered radiation was computed for an electron, bound initially in the 2s state of a hydrogen atom and driven resonantly by the sinusoidal field of a moderately intense (∼${10}^{13}$ W/${\mathrm{cm}}^2$) linearly polarized laser. A numerical solution of the time-dependent Schrödinger equation was performed for the duration of a 20–30-fs laser pulse. The radiation which emerges from this transient state was characterized by the autocorrelation function of the electronic acceleration defined as ${\mathit{C}}_{\mathit{a}}$(t) =${\mathcal{F}}_{\mathrm{-}\mathrm{\infty }}^{\mathrm{\infty }}$dt’〈1s‖a(t’)⋅a(t’-t)‖1s〉, as previously described [K. LaGattuta, J. Mod. Opt. 39, 1181 (1992)]. Then the energy spectrum of the radiation was determined from S(Ω) =(${\mathrm{\alpha }}^3$/3π)${\mathcal{F}}_{\mathrm{-}\mathrm{\infty }}^{\mathrm{\infty }}$dt ${\mathrm{e}}^{\mathit{i}\mathrm{\Omega }\mathit{t}}$${\mathit{C}}_{\mathit{a}}$(t). Copious radiation, near the second harmonic, was emitted from this metastable excited state, prior to ionization.

We study analytically the properties of second-harmonic generation in a laser cavity. We determine the general criterion of stability for stable steady-state multimode operation. When this condition is not verified we construct analytically the emerging periodic solutions and show that they display antiphase dynamics. When the steady state is stable, we prove that there are four internal frequencies irrespective of the mode number. We show that in this case antiphase dynamics occurs in the transient relaxation to the stable steady state and in the response to noise. Transient antiphase dynamics is shown to imply the disappearance of low-frequency features in the total intensity whose power and noise spectra display a single maximum.

A theoretical study is presented of the gain and the noise spectra of laser amplifiers at pumping rates both above and below the oscillation threshold. The theory is valid for both class-A and class-B laser systems, where the decay rate of the collective atomic dipole moment greatly exceeds the decay rates of the atomic population inversion and the laser cavity. The gain and the noise properties are shown to be strongly influenced by a four-wave mixing of the signal and image frequencies via a modulation of the population inversion. Particular attention is paid to the residual noise flux that persists in the laser output above threshold and to the typical characteristics of a second-order phase transition displayed by the gain in the threshold region. The results for the above-threshold laser amplifier are compared with experimental measurements of both gain and noise for the argon-ion (class-A) and ${\mathrm{CO}}_2$ (class-B) lasers. The signal-to-noise ratios for both heterodyne and direct-detection measurements are evaluated, and the conditions are determined under which optical amplification can lead to an enhancement of sensitivity.

The quantum Zeno effect is known as the inhibition of a system’s reversible dynamics by frequent measurements. Aharonov and Vardi [Phys. Rev. D 21, 2235 (1980)] proposed a scheme intimately related to the quantum Zeno effect. They showed that, by performing a dense sequence of measurements along a presumed path, the system is found to follow this—arbitrarily chosen—trajectory. The proof was based on the von Neumann projection hypothesis. In this paper we investigate whether this effect still holds if we model a realistic measurement process instead of the artificial instantaneous von Neumann collapse. We test the orientation of the Bloch vector of a two-level system using a third level and resonance fluorescence as the measuring apparatus. Therefore we are able to use a dynamical collapse governed by the three-level master equations. We show that a sequence of orientation measurements designed to monitor a particular trajectory indeed induces a dynamics exactly along this trajectory.

We use a density-matrix formalism to illustrate the possibilities of detecting quantum-beat phenomena in the frequency domain. In a pump-probe absorption-saturation experiment, the differential-transmission spectrum is shown to have features at frequencies that are separated from the laser frequency by the quantum-beat frequency. We show the conditions under which these features are observable.

The non-Hermitian character of a gain-guided amplifier leads naturally to a description of the amplified field in terms of a nonorthogonal mode basis. We present a theoretical analysis, based on a nonorthogonal mode expansion, for the output of an amplifier with focused gain. The theory predicts that the gain-guided nature of the amplification process can lead to excess noise in the output of the amplifier. We then report the results of two experiments in which the output from a focused-gain Raman amplifier was measured. The experimental results are found to be in reasonable agreement with the nonorthogonal mode theory.

This paper gives a simple plane-wave multimode semiconductor-laser theory valid near threshold under the quasiequilibrium assumption that the total field envelope varies little in the intraband scattering times. Subject to these limitations, the theory is able to describe the full many-body effects in the semiconductor medium for a variety of field configurations including unidirectional, bidirectional, and two-mirror standing-wave lasers with nonuniform gain distributions. The theory predicts that spatial-hole burning can lead to multimode operation and that bidirectional ring-laser operation cannot occur. Generalization to larger field intensities is discussed within the framework of the quasiequilibrium assumption.

Classical-like, Wehrl’s entropies of various quantum states of light are calculated and investigated as functions of the average value of the photon-number operator. Qualitatively similar behavior of the Wehrl entropies, corresponding to quantum states with quite different properties, is observed. A type of damping of the Wehrl entropies for states with high coherent components is pointed out and discussed.

We present a detailed numerical study of the one-atom laser, that is, a single two-level atom interacting with one lasing mode, whereby both the atom and the photon field are coupled to reservoirs. The stationary as well as the dynamical properties of the model are calculated directly from the quantum master equation with the help of two numerical methods. These numerical methods do not need any quasi-probability representation and they do not require approximations. We find that the one-atom laser exhibits most of the typical features of a normal laser. In the region far below threshold some aspects, among them the linewidth, are changed due to eigenvalues of the master equation with imaginary parts. In this regime the complexity of the eigenvalues prominently enters the dynamical behavior.

A unified colored-noise approximation is applied to calculate the stationary intensity probabilities of colored-gain-noise and colored-loss-noise models for dye lasers with saturation effects. We compare the results of the unified colored-noise approximation with the predictions of the best Fokker-Planck equation for the stationary intensity probability of a colored-gain-noise model, and find that the results of the unified colored-noise approximation agree better with simulation results than the results of the best Fokker-Planck equation. The first-order-like transition of colored-gain-noise and colored-loss-noise models with saturation effects is discussed and compared. It is found that the emergence of the first-order-like transition is related to the saturation element in the fluctuation term of the dye-laser model for white pump noise, and the occurrence of the first-order-like transition is only due to the existence of colored pump noise in the loss-noise models for dye lasers with saturation effects.

With the help of phase-space pictures we consider the dynamics of a hydrogen atom driven by a high-frequency periodic electromagnetic field. We show that the stabilization phenomenon, widely discussed in the literature, has quantum and classical appearances, which correspond to different physical situations. Classical stabilization relies on the dynamics of the electron in the laser-induced effective potential: the electron repeatedly crosses the separatrix of the Coulomb potential moving along the trajectories of the effective potential. Quantum stabilization results from the decrease of matrix elements of multiphoton transitions, which implies a decrease of the net cross section of multiphoton photoeffect from the new stationary states of the effective potential.