Elimination of optical self-focusing by population trapping.

It is well known that intense laser beams, when tuned near to a resonance, will often break up into an unpredictable distribution of hot spots and filaments. This beam breakup and filament formation is initiated by self-focusing, which, in turn, is caused by the intensitydependent refractive index [1]. In this Letter we show experimental results that demonstrate, at least for the near-ideal conditions described here, how optical self-focusing, defocusing, and filament formation may be eliminated. Our method is based on the use of two copropagating lasers to nearly instantaneously prepare an off-resonance population trapped state [2]. Once the atoms are in this state, then, irrespective of the relative intensity of the laser beams, there is no dipole moment and therefore no beam distortion at either laser wavelength. The essence of the theoretical problem is therefore to establish the necessary conditions and time scale for off-resonance trapped state preparation. We apply two laser beams to a detuned three-state system (inset, Fig. 1). We assume that the common detuning, Dv3, from state j3l is large as compared to both the strongest Rabi frequency and the linewidth of state j3l, but still sufficiently small that the rotating wave approximation is valid. With these assumptions, the three-state Hamiltonian may be replaced by an effective two-state Hamiltonian [2,3]. With the envelopes of the fields denoted by Vpfstd and Vcgstd, this two-state Hamiltonian is