Focusing Vacuum Fluctuations II

The quantization of the scalar and electromagnetic fields in the presence of a parabolic mirror is further developed in the context of a geometric optics approximation. We extend results in a previous paper to more general geometries, and also correct an error in one section of that paper. We calculate the mean squared scalar and electric fields near the focal line of a parabolic cylindrical mirror. These quantities are found to grow as inverse powers of the distance from the focus. We give a combination of analytic and numerical results for the mean squared fields. In particular, we find that the mean squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean squared electric field corresponds to a repulsive Van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.