Using the semiclassical approach the simulation of the light pulse generation by a thin layer of quantum two-level dipoles has been performed. The state of each dipole is governed by Bloch equations for individual density matrix elements under condition of phase relaxation absence. Identical dipoles are located at the nodes of 2-D grating with corresponding sizes Lx, Ly and are considered as pointlike sources of classical field. At the initial moment all the dipoles are in an inverted state Initiation of the pulse was carried out by either incoherent spontaneous decay (superfluorescence mode simulated by setting of small random polarisation with *-correlation) or coherent initial state. Based on the numerical solution the kinetics of dipoles characteristics and evolution of the radiation directivity pattern have been calculated. The influence of the initial state and short-range Coulomb dipole-dipole interaction on the pulse characteristics have been analysed. Tending of axis X to be a direction of primary amplification of pulse with increasing of inequality Lx > Ly has been traced. The comparison of the results obtained with the results of paraxial approximation that uses the concept of slowly varying along axis X amplitudes of the electric field and medium polarisation has been done.
We give a general nonperturbative treatment of cooperative emission in systems of
N two-level atoms, starting from first principles and including inhomogeneous broadening. In particular, we study superfluorescence, which is defined as the cooperative spontaneous emission, i.e., radiation rate proportional to
N2, from an atomic system initially excited with zero macroscopic dipole moment and a uniform population difference between the excited and the fundamental states. The atomic system is described by means of collective dipole operators. A fundamental justification is given for the existence of damped "quasimodes" of the mirrorless active volume. The damping of such modes is simply due to the propagation of the Maxwell field, which escapes from the active volume. A general atom-field master equation is derived for the system atoms plus field inside the active volume, described, respectively, in terms of collective dipole operators and quasimode operators. An important feature of this equation is that inhomogeneous broadening simply appears via a time-dependent atom-field coupling constant. In this paper we give a semiclassical treatment of such a master equation. For a pencil-shaped geometry of the active volume, generalized Maxwell-Bloch equations are derived for the envelopes of the radiation inside the active volume and polarization. Such equations take into account the two directions of propagation of the radiation and the inhomogeneous broadening. Suitably phrasing our initial condition in semiclassical terms, we find that propagation effects can be neglected at all times and the generalized Maxwell-Bloch equations reduce to a simple pendulum equation. On the basis of the discussion of the pendulum equation, we conclude that superfluorescence occurs when (i) the length
L of the active volume is much larger than a suitable threshold length
LT (this condition ensures that the dephasing atomic processes occur on a time scale much larger than the times characteristic of the cooperative emission); (ii) the length
L is smaller or of the same order of a suitable cooperation length
Lc (this condition ensures that cooperative spontaneous emission dominates stimulated processes, which give radiation proportional to
N). For $L\ensuremath{\ll}{L}_{c}$, one has a hyperbolic-secant superfluorescent pulse; for $L\ensuremath{\approx}{L}_{c}$, as one has in the recent experiments of Skribanowitz et al., one finds oscillations in the cooperative decay and in the radiation emission. Such oscillations are due to the contribution of stimulated processes. For $L\ensuremath{\gg}{L}_{c}$, this contribution increases. As a consequence one gets more oscillations in the radiated intensity, which becomes proportional to
N, so that superfluorescence effects disappear.
We present the results of a theoretical study of XUV superfluorescence from doubly excited states of helium resonantly pumped by free-electron laser (FEL) pulses. Our model allows us to predict both the spectrum and angular distribution of emitted XUV radiation in a wide range of experimentally accessible parameters. This is achieved by going beyond two key deficiencies of most previous models: The one-dimensional treatment in space is upgraded to three dimensions with electromagnetic fields treated in the paraxial approximation and spontaneous emission is modeled by a recently developed approach that avoids the unrealistic delayed response but preserves the expected characteristics of the emitted field in the spontaneous emission limit. The case study of
3a1Po resonance in helium with
63.66eV excitation energy is presented for realistic parameters of seeded light pulses from the FERMI FEL facility and a recently developed high-pressure gas cell. Results of numerical simulations show that both the spectral width and angular divergence of emitted radiation vary with gas pressure and pump pulse intensity in a complex way.
We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ensuremath{\ge} 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.