Role of the gouy phase in the coherent phase control of the photoionization and photodissociation of vinyl chloride

Contribution of the Gouy phase to two-pathway coherent control of the photoionization and photodissociation of vinyl chloride

The electric field of a light wave accumulates a pi phase shift as it passes through a focus. We show here how this effect, known as the Gouy phase, may be used to control the branching ratio of a unimolecular reaction when the products are formed with different numbers of photons. We demonstrate this control method for the ionization and dissociation of vinyl chloride, using absorption of 177 and 532 nm photons to induce a pair of interfering paths. Excellent agreement between the observed and calculated phase shift as a function of the axial coordinate of the laser focus indicates that fragmentation occurs via a ladder switching mechanism. The axial dependence of the modulation depth is evidence of loss of coherence at higher internal temperatures of the molecule.

Fractional Gouy phase

In general, the total Gouy phase shift has the form n pi, where n need not be an integer. As a result of the Fourier transforming property of a lens, the Gouy phase is found to be related to the types of discontinuities at the upper or lower range of the pupil function Q(c) resulting from the asymptotic order of the Fourier transform. The sign of the Gouy phase is also related to the slope of the pupil function. The oscillations of the Gouy phase shift arise from the strength of the nondominant discontinuity.

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.