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At the third order of the order parameter expansion, the system under study is variational, and for some range of parameters, a two-mode structure may occur. Both a square pattern and a 48\ifmmode^\circ\else\textdegree\fi{} rhombic pattern are shown to minimize the free energy, while the numerical simulations of the full equations display only the squares. The expansion at the nontrivial fifth order removes the degeneracy between the two different patterns and predicts squares.

The plane-wave dynamics of 3*omega => (2*omega, omega) subharmonic optical parametric oscillators containing a second harmonic generator of the idler wave omega is analyzed analytically by using the meanfield approximation and numerically by taking into account the field propagation inside the media. The resonant Chi(2):Chi(2) cascaded second-order nonlinearities induce a mutual injection-locking of the signal and idler waves that leads to coherent self phase-locking of the pump and subharmonic waves, freezing the phase diffusion noise. In case of signal-and-idler resonant devices, largely detuned sub-threshold states occur due to a subcritical bifurcation, broadening out the self-locking frequency range to a few cavity linewidths., RevTeX file + 11 figures (.jpg format) Accepted in Phys. Rev. A (oct 2000)

The degenerate optical parametric oscillator may generate very high-intensity two-dimensional localized structures. A quantitative comparison of the propagation and the mean-field models is presented for different mistunings, corresponding to monostable and bistable homogeneous solutions. In both models, we study the circular domain walls as an example of localized structures. The peak intensities are comparable; the difference lies mainly in their domain of existence as a function of the pump amplitude parameter.

We investigate properties of the cooperative emission of radiation from $N$ identical two-level atoms by using, for the collective atomic operators, the Holstein-Primakoff transformation to boson operators. In the basis of the Glauber states, a weight function is associated with the atomic density operator. The equation of motion for the weight function is derived from the master equation and approximate solutions are given in the two limit cases of superradiance and diffusion. The moments of the radiation intensity are calculated and are found to be in close agreement with previous works.

A single pass of an intense cw light beam through a strongly absorbing medium can be characterized by two parameters, the input on-axis intensity normalized to the saturation value ${I}_{0,0}$, and the Fresnel number $F$ for an absorption length ${\ensuremath{\alpha}}^{\ensuremath{-}1}$. For both large ${I}_{0,0}$ and $F$, propagation can be divided in two parts: At the very beginning, the transverse profile of the beam experiences an encoding. For a beam tuned exactly on resonance, encoding reduces to a stripping of the profile from the wings to the center, progressively, as the light beam goes further into the cell. For $Fgg1$ and ${I}_{0,0}gg1$, and both of the same order of magnitude, this stripping can be modeled by a circular aperture placed at the end of the encoding region. Afterwards, the beam is assumed to propagate in free space, its profile exhibits Fresnel interferences and on-axis enhancement. Using a perturbative treatment, the width and the location of the aperture are analytically estimated, and the model is successfully compared with numerical predictions of on-resonance self-focusing. For ${I}_{0,0}\ensuremath{\lesssim}F$, the stripping and free-space propagation cannot be separated because near-axis stripping coexists with large diffraction effects on the wings. This case, the best for observing cw on-resonance enhancement, would gain in a more sophisticated model, taking into account diffraction by successive apertures.

A theory is presented of the near-resonant interaction of two-level atom with strong Gaussian fields. Analytical expressions are given for the fluorescence intensity and for the two-time first- and second-order correlation functions of the intensity in both cases of a chaotic field and a real Gaussian field. The usual three-peak structure in the fluorescence spectrum is found to disappear because the amplitude fluctuations of the driving light prevent the nutation process. The scattered intensity is shown no longer to present a Markovian character when the atom is driven by a Gaussian field. The atom gains a sort of memory because of the intensity fluctuations in the driving field.

In order to study the cooperative emission of radiation from an extended system of $N$ two-level atoms, we use the master-equation approach within the Born and Markov approximations. All the properties of the emission of radiation can be deduced from the diagonalization of the coupling matrix $\ensuremath{\Gamma}$, where an element ${\ensuremath{\Gamma}}_{\mathrm{jk}}$ gives the coupling between the atoms labeled $j$ and $k$ via the electromagnetic field. We choose a pencil-shaped volume and study analytically the coupling matrix in the limit for small and large Fresnel numbers. For Fresnel numbers of order unity numerical methods are used. Thus we prove that, for the pencil-shaped geometry, any elaborated model must take into account the interaction of the atoms with the infinity of electromagnetic field modes lying inside two small solid angles about the axis of the largest linear dimension, which we label the $z$ axis. In other words, the intensity of radiation emitted by any atom of the system depends on its position with respect to the others and this "propagation effect" cannot be neglected when interpreting superradiance experiments. For small Fresnel numbers the $z$ dependence predominates, in the opposite case the ($x, y$) dependence does, while for Fresnel numbers of order unity the dependence of all three components must be taken into account. Preliminary calculations are given for which only the $z$ dependence is considered; for Fresnel numbers of magnitude of order unity or smaller, the effect of propagation along the $z$ axis displays large delays for the appearance of superradiance with respect to the time at which the superradiant pulse is maximum when the "propagation effects" are neglected (one-mode model).

The normalized two-time intensity-fluctuation functions are calculated for the spontaneous-emission radiation from a system of $N$ two-level atoms. The radiated field, when the system decays from the excited state to the ground state, does not look like a Gaussian or a coherent field.

We investigate the statistical properties of the intensity of radiation emitted by $N$ two-level systems, for which the cooperation number is constant. The $l$-fold moments of the intensity are shown to obey a closed set of equations. For long times, the normalized moments are found to go up to infinity. But, taking into account the experimental limitations, large fluctuations will be seen only for almost completely excited systems.