Polarium model: Coherent radiation by a resonant medium
Sudhakar Prasad, Roy J. Glauber
In the absence of incoherent relaxation processes, the emission, absorption, and transport of resonant radiation by an extended medium are all cooperative processes in which the medium participates as a whole. Such radiative processes depend sensitively on the geometry of the source, on its size and density, and on the interplay of electric polarization resonances with the ambient electromagnetic field. By making a succession of simple approximations, we reduce the radiative interaction problem to one of solving a linear integral equation for the time-dependent polarization of the radiating medium. For the example of one-dimensional geometry, we show that the polarization possesses a sequence of exponentially decaying eigenmodes that oscillate at frequencies slightly shifted from that of the fundamental resonance. Only a few of these modes, for any radiating medium, are strongly coupled to the electromagnetic field, and thereby radiate efficiently. All of the other modes, infinitely many of them, are found to radiate quite slowly, or not at all. We consider in detail the radiation emitted by an arbitrary initial polarization distribution when the electromagnetic field is initially empty. Analytical and numerical results are presented for the time-dependent fields that follow from a wide variety of initial excitations. A locally oscillatory exchange of energy is found to take place between the electric and polarization fields, which gives rise to a ringing of the radiated intensity. The spectra of the emitted light are shown accordingly to be complex in structure, and to have a frequency gap which becomes independent of the size of the medium and its initial polarization distribution for media that are sufficiently large. The gap is caused by the interference and interaction of oppositely propagating excitations.
Physical Review A•May 17, 2000•53 citations