A method for the analysis of pulse statistics in one-dimensional dynamical systems with random modulation of the control parameter is developed. The stationary properties of pulses are obtained via the solution of an integral equation for the probability density of the passage time by a reference level. The method is applied to a complex Landau-type model with random on-off modulation. In some cases analytical expressions are derived for the passage time distribution. This distribution is shown to be multimodal due to memory effects. An excellent agreement is obtained in all situations between theoretical results and numerical simulations. © 1996 The American Physical Society.

A comprehensive analytical approach to scalar and vectorial interaction in cascaded quadratic nonlinearities is presented. Exact formulas for the intensity as well as the phase modulation in dependence on all conceivable control parameters are derived, provided that group-velocity dispersion, diffraction, and pulse walk off can be neglected. The first two constraints are uncritical as far as channel waveguides and thin bulk crystals are concerned. Particular emphasis is paid to a detailed study of the phase evolution in order to identify optimum conditions for an almost homogeneous phase shift across an entire pulse which is in contrast to the generation of a large chirp in cubic nonlinear materials. Moreover, the general results are simplified to relevant limiting cases where simple analytical formulas emerge for the amplitude and phase modulation. The analytical results are used for a classification of all-optical effects based on cascading. Optimum conditions for picosecond modulation processes are discussed. © 1996 The American Physical Society.

We report experimental evidence of a series of transitions over different classes of two-dimensional patterns (hexagons, horizontal rolls, vertical rolls, zigzags) observed in a nonlinear optical system in which nonlocal interactions have been introduced by a lateral wave-front shift. At variance with similar scenarios of transitions observed in fluid dynamics, here the pattern selection is operated by the nonlocality mechanism, and a simple theoretical analysis yields predictions in good agreement with the experiment. © 1996 The American Physical Society.

We present a simple structure that can be readily fabricated through standard nanofabrication technology and can permit the control of spontaneous emission. Its emission control properties are based on the photonic bandgap displayed by a planar Fabry-Pérot cavity for an in-plane polarization. Coplanar juxtaposition of Fabry-Pérot cavities with different photonic band gaps produces confinement of the field in the narrow-gap part of the structure and gives rise to a ‘‘photonic well’’ in which spontaneous emission can be enhanced. Semiconductor microcavities with metallic mirrors and strained-layer quantum well emitters are promising candidates for relatively efficient photonic-well structures. © 1996 The American Physical Society.

The transition probabilities of a quantum system introduced between parallel conducting walls approaching or receding from each other with arbitrary constant relative speed are evaluated in the dipole approximation. The interaction with the vacuum fluctuations of the quantum electromagnetic field inside the box induces modifications in the spontaneous emission probabilities. While the transition probabilities in free space are recovered in the ultrarelativistic limit, an enhancement or inhibition of the spontaneous emission in the nonrelativistic limit is expected according to the dipole moment orientation of the detector. These results are discussed in the context of photon generation by the moving walls. © 1996 The American Physical Society.

The transverse spatial properties of the twin light beams of the down-conversion have been recently investigated in experiments using double-slit and coincidence measurements. Fringes are obtained, with a controlled degree of visibility, placing the slits in the signal beam and scanning the signal detector [direct interference—Phys. Rev. A 49, 4176 (1994)] and also, for the degenerated type II down-conversion, with slits in the signal beam and scanning the idler detector [ghost interference—Phys. Rev. Lett. 74, 3600 (1995)]. The idea of a ghost source is used to discuss the direct interference experiment. Using a nondegenerated type I down-conversion, experimental results are obtained showing that the visibility of the ghost interference patterns can be controlled by the ghost source size, analogously as it can be done for a real light source. © 1996 The American Physical Society.

We propose a mechanism for achieving optical bistability in semiconductor heterostructures. In contrast to the well-known refractive shift of the Fabry-Perot mode in macroscopic resonators, we consider the bleaching of the exciton Rabi splitting in strong-coupling microcavities and prove that this nonlinear process leads to an optically bistable behavior. Through a model based on the transfer-matrix formalism, we predict the dependence of this effect on specific material parameters and on the nature of the cavity. Numerical calculations are carried out for quantum well embedded cavities and the possibility of room-temperature bistable operation is also discussed. © 1996 The American Physical Society.

We have examined the temporal evolution of a two-level atom in response to stochastic phase-fluctuating fields by applying perturbation theory to the optical Bloch equations written in the instantaneous frame. Our results show that the general nature of the atomic population variations is relatively simple, being composed of adiabatic and nonadiabatic components. The adiabatic response results from Fourier components of the phase variation below the system’s Rabi frequency and is proportional to the product of the relatively slow phase variation and its first derivative. The nonadiabatic response has its maximum amplitude at the system’s Rabi frequency, for which the atom behaves like a simple harmonic oscillator whose resonance frequency is the Rabi frequency. In this sense the atom acts as a tunable narrow-band filter. © 1996 The American Physical Society.

We use a quantum-mechanical linear-response formalism in the dipole approximation to calculate the decay-rate change and the energy-level shift of an atom between two parallel dielectric surfaces. Our results can be applied to various problems such as two conductor plates, one conductor and one dielectric, and two different dielectrics. In particular, we calculate the decay rate and the level shift in the case of two identical dielectric plates. The dependences of the transition rate on the atomic position in the gap and on the dielectric constant of the surfaces are investigated in detail. In the case of the level shift, we are able to obtain analytic expressions for two limiting cases (the short-range instantaneous van der Waals interaction energy and the long-range Casimir-Polder retarded interaction energy). © 1996 The American Physical Society.

I derive a simple model for the propagation of a smooth pulse detuned outside a gain line. The pulse moves superluminally and with little distortion provided the medium is not longer than the saturation length. If the medium is longer than this, two effects occur: amplified spontaneous emission interferes with the pulse (although this interference averages to zero over many experiments) and the magnitude of the group delay increases only logarithmically with the length. I argue that both of these effects are inherent to any optical system with gain. Numerical simulations of the superluminal pulse agree with the model presented. © 1996 The American Physical Society.

We report experimental observations of modulational instability of copropagating waves in a highly birefringent fiber for the normal dispersion regime. We first investigate carefully the system behavior by means of nonlinear Schrödinger equations and phase-matching conditions, and then, experimentally, we use two distinct techniques for observing MI (modulational instability) in the fiber; namely, the single-frequency copropagation, where two pump waves of identical frequency copropagate with orthogonal polarizations parallel to the two birefringence axes of the fiber, and the two-frequency copropagation, where the two polarized waves copropagate with different frequencies. In both cases the GVM (group-velocity mismatch) of the two copropagating waves appears as the particularly important parameter which governs the system behavior. For the single-frequency copropagation, the GVM is simply proportional to the intrinsic birefringence of the fiber and therefore varies only very slightly versus the wavelength, and there exists a nonzero critical power for the input wave above which MI vanishes [Phys. Rev. A 42, 682 (1990)]. In the two-frequency-copropagation regime, however, the GVM becomes a variable parameter, that is, a real control parameter for MI, whose value can be easily tuned over a wide range by just changing the wavelength separation between the two pump waves. For several values of the GVM we show that the two-frequency-copropagation regime provides a richer spectrum of behavior than the single-frequency copropagation. Most of the richness comes from the existence of particular values of pump wavelengths for which MI disappears for all input-wave power, that is, the existence of a critical regime in which the critical power becomes zero. This behavior is drastically different from what was previously observed in the single-frequency configuration. © 1996 The American Physical Society.

A mechanism for controlling arbitrary quantum-field states in a cavity is proposed. It is based on a single conditional measurement of the state of a two-level atom, following a periodic sequence of field-atom couplings with alternating near-resonant and off-resonant detunings. The resulting field state is controlled by the arbitrarily large number of parameters that characterize the sequence of detunings. © 1996 The American Physical Society.

We present an analytical theory of propagation of electromagnetic pulses through a Doppler-broadened medium in the adiabatic population transfer regime. We show that thermal motion of atoms causes a strong asymmetric distortion of the pulse shape. Two different kinds of pulse distortions are found to be relevant for cases of (a) nondegenerate and (b) degenerate atomic states between which the population is transferred adiabatically. In case (a) the forward front of the nonlinear electromagnetic wave becomes steeper; otherwise, in case (b) a trailing front sharpening takes place. To increase the effect in the degenerate atomic level configuration to an experimentally significant value, the ratio of the Doppler profile width to the Rabi frequency must be much higher than in case (a). © 1996 The American Physical Society.

A theoretical rate-equation analysis is presented to investigate the molecular properties that are important for achieving high-fluence optical limiting. Critical conditions for achieving induced absorption are derived in terms of the material and laser parameters by employing a range of hierarchical energy-level models. The influences of stimulated emission and saturation of the excited-state absorption are seen to induce the regime of optical limiting to one of increasing transmittance. This is in direct agreement with recent experimental measurements. © 1996 The American Physical Society.

In the literature two different simplified expressions exist for the spontaneous emission factor β, being the fraction of spontaneous emission radiated into a specific optical mode. These expressions are valid in two mutually exclusive regimes. By treating the coupling between one discrete cavity mode and the outside optical continuum quasi one dimensionally in the spirit of Fano [Phys. Rev. 124, 1866 (1961)], we extend the validity range of both expressions and show that they lead to essentially the same result. The relevance and limitation of this result are discussed. © 1996 The American Physical Society.

In dense media, the Lorentz local-field condition results in a generalization of the usual semiclassical Maxwell-Bloch formulation for two-level atoms in which the optical Bloch equations are recast in terms of macroscopic spatially averaged atomic variables. We derive an adiabaticlike, or stationary, approximation for the generalized Bloch equations in the ultratransient limit and establish validity criteria. The significance of this quasiadiabatic approximation is that a point response solution of the generalized Bloch equations is obtained in terms of the field strength, thereby allowing the atomic response to be expressed as a nonlinear susceptibility that can be used to predict and analyze propagation effects in dense media. The quasiadiabatic approximation is quite general, allowing for a combination of detuning, chirping, and a variety of local-field and mean-field effects. It spans the range from cases for which local-field effects can be neglected, as in the usual adiabatic approximation, to cases in which local-field effects cause a large inversion-dependent frequency renormalization. The approximation is used to interpret previous numerical results for the resonant interaction of ultrashort pulses with dense media and it is shown that dense media can exhibit behavior analogous to adiabatic following and adiabatic inversion. The nonlinear index of refraction in the quasiadiabatic limit is purely real for large detunings. However, at and near resonance, the nonlinear index is purely imaginary. The imaginary index relates to coherent reflectivity arising from the reaction field of the cooperating atoms, rather than absorption, and transmission and reflection coefficients for thin films are derived. In the intermediate range of detunings, the intensity-dependent index of refraction can undergo a phase transition due solely to the variation of the field intensity during excitation by an ultrashort pulse. Propagation effects are investigated using a finite-difference time-domain method to integrate the generalized Bloch-Maxwell equations and the results of the numerical simulations are analyzed in the context of the nonlinear index of refraction obtained using the quasiadiabatic approximation.

We establish a quantum theory of gap solitons in a one-dimensional periodic dielectric structure [distributed Bragg reflector (DBR)] of a Kerr nonlinearity. The electromagnetic field in the structure is quantized within the two-band approximation. The basic idea for this quantization is that incident photons with frequencies in the band gap of the DBR are scattered into the upper ‘‘conduction’’ and lower ‘‘valence’’ bands by the nonlinearity. The effective Hamiltonian of quantum gap solitons is derived within the effective-mass regime. The eigenstates of the Hamiltonian are constructed exactly by Bethe’s ansatz method. We find that in certain band gaps of the DBR these eigenstates can be bound, consisting of one or more photon pairs from the conduction and valence bands. These bound multiphoton states are optical analogs of exciton molecules [optical multiexcitons (OMEs)]. Their existence should be manifested by the discrete spectrum of band-gap transmission as a function of the transmitted photon number and by the multiexponential falloff of intensity-intensity correlations on a 0.1-mm scale. Quantum gap solitons are shown to arise as superpositions of OMEs whenever the nonlinear binding exceeds phonon scattering. © 1996 The American Physical Society.

The coupling of an atom to its environment can be strongly dependent on frequency when that atom is placed in, for example, a cavity. We consider here the exact dynamics of a three-level atom for a resonant form of the atom-environment coupling of the type found in a cavity. The three-level atom forms a quantum-beat V system in the general model that we consider. Without the use of perturbation theory, we derive a set of three coupled differential equations that describe the system. Results are compared to quantum beats in free space and an interpretation is provided in terms of the coupling of the three-level system to a pseudomode. The pseudomode is defined by the differential equations involving its amplitude and possesses the properties of a finite-Q cavity mode. The signal from a detector is formulated in terms of a resonant coupling between the detector and the cavity modes. Limits for a broadband and a narrow-band detector are considered. © 1996 The American Physical Society.

In lasers with strong atom-field coupling, Rabi-type oscillation effects are apparent not only in the atomic inversion and the photon number, but also in the field correlation function. Whereas the former play an important role in the standard micromaser with Poissonian injection, the latter are particularly relevant in lasers with non-Poissonian atomic injection. In such lasers, there is generally no steady state in the usual sense, and the field correlation function is really a two-point correlation. We analyze the field correlation function and the spectrum under these circumstances. Our analysis uses a stochastic simulation as well as an approximate analytical description. For lasers with a regular injection, this analysis explains the occurrence of a multipeak spectrum in simple terms. In the more general situation, the spectrum is related to the counting statistics of the atoms. Conditions for an experimental realization are discussed. © 1996 The American Physical Society.

Quantum electrodynamics of a single two-level atom placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied. Despite a nonlocal effective polariton-polariton coupling, the system is proven to be integrable and is diagonalized exactly by means of the Bethe-ansatz technique. Its spectrum consists of bound many-polariton complexes (quantum solitons) and exhibits some unusual features due to the existence of the polaritonic gap. Only solitons containing an even number of polaritons propagate within the gap, while a soliton with an odd number of polaritons is pinned to the atom and forms a many-polariton-atom bound state, in which the radiation and the medium polarization are localized in the vicinity of the atom. The model under consideration has a quite general structure and can also be applied to the case of photonic-band-gap materials. © 1996 The American Physical Society.