The Eikonal-SVEAS analytic closed forms for single-photon superradiance

Emission from a slab of resonant two-level atoms induced by a delta-pulse excitation

“…For much larger values of u, the memory required to store and manipulate the values of the different eigen values may become a limiting factor for using this method. In those cases, and as was shown in [9] and in [11] the eikonal approximation gives accurate results for the forward emission. Finally, I point out that the above theoretical pre dictions for the spectral distributions) can be experi mentally observed as they are all of the same order of magnitude or larger than the pressure broadened line width of the gas absorption line (≈C).…”

“…The mode analysis formalism proved in the past a most powerful tool for studying in samples with sizes not exceeding 10 3 λ 0 , the coherence effects and the dynamical cooperative effects due to excitation exchange between the similar atoms in the ensemble. For example, in the calcula tion for single photon superradiance from a sphere [10,11], this method allowed us to study the time dependence of both the decay rate, the instantaneous emitting frequency and the emission amplitude from a weakly excited sphere. For the slab geometry, this method was used to compute the emission instanta neous frequency and lead to the discovery of we called the "Dynamical Cooperative Lamb Shift" [12].…”

The Purcell-Dicke effect in the emission from a coated small sphere of resonant atoms placed inside a matrix cavity

“…This work expands on recent research on superra diance of atoms [6][7][8][9] in that it explores a solvable model, which represents a potentially realizable phys ical system where in addition to the cooperative effects resulting from the close proximity of identical atoms, I am also exploring the effects of the cavity on the sys tem's cooperative decay, a feature which so far has not been explored except in spin superradiance [10][11][12][13][14][15][16][17]. Yukalov and collaborators have shown that the pres ence of a resonator is crucial to spin superradiance.…”

Initial cooperative decay rate and cooperative Lamb shift of resonant atoms in an infinite cylindrical geometry

“…The cooperative Lamb shift (CLS) [2] is an analog of the Lamb shift, where the virtual photon emitted by one atom is reabsorbed by another. These quantities have been discussed for various geometries in the literature, primarily for the "slab" [2,3,9,10,27] and the sphere [2,7,8,[11][12][13][14][15][16][18][19][20]23,25,26,30]. More recently, similar discussions have appeared [5,24,28,29] for a cylindrical geometry.…”

“…In [1] and many papers since, it was supposed that this state would remain spatially unchanged in the course of decay; it is now evident, however, that significant change takes place [5,10,12,[14][15][16][17][18]20,25,26,[28][29][30]. This change can be explored by various methods, notably by finding the eigenmodes of the system [5,8-11,13,15,16,19,20,24-26, 28,29].…”