Effect of the Gouy phase on the coherent phase control of chemical reactions

We show how the spatial phase of a focused laser beam may be used as a tool for controlling the branching ratio of a chemical reaction. Guoy discovered [Acad. Sci., Paris, C. R. 110, 1250 (1890)] that when an electromagnetic wave passes through a focus its phase increases by pi. In a coherent control scheme involving the absorption of n photons of frequency omega(m) and m photons of frequency omega(n), the overall phase shift produced by the Gouy phase is (n-m)pi. At any given point in space, this phase shift is identical for all reaction products. Nevertheless, if the yields for different reaction channels have different intensity dependencies, the Gouy phase produces a net phase lag between the products that varies with the axial coordinate of the laser focus. We obtain here analytical and numerical values of this phase as the laser focus is scanned across the diameter of the molecular beam, taking into account the Rayleigh range and astigmatism of the laser beam and saturation of the transition. We also show that the modulation depth of the interference pattern may be increased by optimizing the relative intensities of the two fields.