Alexander Lvovsky, Sven Hartmann

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In his classic paper on superradiance [1], R. H. Dicke has considered a case when a large number of dipoles oscillating in phase are concentrated in a very small (<l³ ) volume. In experimental practice this situation is quite uncommon, and in later works on superradiance (see, for example, [2]) Dicke's analysis has been modified to account for larger excited volume. Modern treatment usually regards the excited volume as cylindrical, with all the elementary dipoles equally excited. But this assumption is not, generally speaking, correct either. The macroscopic dipole moment induced in a sample by a highly energetic excitation pulse of nonuniform (e.g. Gaussian) profile forms a ring pattern, where highly excited areas alternate with regions where the Rabi area of the excitation field is a multiple of 2p and the excitation is weak (Fig. 1).

The superradiant beam, generated by the macroscopic dipole moment of such complicated structure, undergoes self-diffraction, resulting in high beam divergence and complex pattern of the far field radiation (Fig. 2). We have performed a detailed theoretical analysis of superradiant self-diffraction patterns and found a number of interesting properties they possess. We have also proven a theorem stating that for sufficiently smooth excitation profiles in an optically thin sample, the total power of superradiant emission is proportional to the integral, over the excited volume, of the macroscopic dipole moment squared. A curious consequence is that for such nonuniformly excited samples, the total power of cooperative emission is given by the same function of excitation pulse area a₀ as the total power of noncoherent fluorescent emission as a function of  a₀/2.

This existence of superradiant self-difraction is made manifest by a two-pulse photon echo experiment where the second pulse is spatially much broader than the first and has a small Rabi area. As a function of the intensity of the first excitation pulse, we measure the on-axis and off-axis echo intensity and find, in agreement with our calculations, that the two behave differently.

1. R. H. Dicke, Phys. Rev. 93, 99 (1954)
2. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966)