Asymptotic Behavior of the Casimir Force between Arrays of Planar Scatterers in the Large Separation Regime

Abstract

Using the dipole scattering theory, we study the dependence of the Casimir force on the separation between arrays of planar scatterers. The reflection amplitude near zero frequency is computed by taking into account the interaction between scatterers that are organized in an array. The absolute values of amplitude can be described as linearly increasing functions of frequency that cross the origin, with their slopes depending on the values of incidence angle and polarization. The argument value of the reflection amplitude is determined from the absolute value of the reflection amplitude, on the basis of the assumption that the reflection amplitude is analytical in the upper half of a complex frequency plane. The numerical results show that, for a large separation between the arrays, the strength of the Casimir force between arrays of metal disks is inversely proportional to the sixth power of the separation between the arrays.