Electromagnetic field near focus as seen by a moving particle*

Abstract

In a number of recent experiments, moving atoms are allowed to interact with the focused light from a resonant-dye laser. In such cases the frequency content of the light seen by the atom depends on its trajectory. The electromagnetic field produced by a laser beam near the focus of an ideal aplanatic lens has been calculated in the frame of a nonrelativistic particle moving at right angles to the optic axis. The frequency content of this field can be approached in two different ways—via its power spectrum, and via an envelope representation that yields the instantaneous frequency as a function of time. Both quantities have been evaluated for a number of different trajectories, and are found to be entirely different, in general. Whereas the power spectrum falls to zero for frequency deviations in excess of the maximum Doppler shift associated with the converging cone of light, there is no corresponding limit to the excursions of the instantaneous frequency.