Abstract
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.
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