EXACT SOLUTION FOR THE REFLECTION AND DIFFRACTION OF ATOMIC DE-BROGLIE WAVES BY A TRAVELING EVANESCENT LASER WAVE

The exact solution to the problem of reflection and diffraction of ato mic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, th e tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Ra bi frequencies, thus generalizing previous approximate methods. Furthe rmore, we give the limiting cases of the amplitudes in the uniform sem iclassical limit, which is valid in all regions including near the cla ssical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel fu nctions. We find our uniform semiclassical limit to be closer to the e xact result over the full range of parameter values than the previousl y reported calculations.