Focusing Vacuum Fluctuations

L.H. Ford and N.F. Svaiter

Physics Department
Tufts University
Medford, MA 02155


The quantization of the electromagnetic field in the presence of a parabolic mirror is discussed in the context of a geometric optics approximation. We calculate the mean squared electric field near the focal line of a parabolic cylindrical mirror. This quantity is found to grow as an inverse power of the distance from the focus. We give a combination of analytic and numerical results for the mean squared field. 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.