Focusing Vacuum Fluctuations with a Parabolic Mirror

The Casimir effect can be viewed as the reflection of vacuum fluctuations by mirrors. The presence of a reflecting boundary alters the modes of a quantized field, and results in shifts in the vacuum expectation values of quantities quadratic in the field, such as the energy density. Typically, Casimir effects for massless fields may be estimated by dimensional analysis. If r is the distance to the nearest boundary, then the Casimir energy density is typically of order r^-4 times a dimensionless constant. This constant is usually of order 10^-3 in four-dimensional spacetime...