Theoretical study of van der Waals dispersion force between macroscopic bodies with a periodic material distribution

A method has been developed for calculating the van der Waals dispersion force between a macroscopic body consisting of a uniform material and a macroscopic body with a spatially periodic material distribution. The periodic material distribution is one dimensional in the x-direction. The periodically distributed material property function is expanded as a Fourier series. The van der Waals forces for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The effects of parameters such as the duty ratio of the material distribution, the refractive index ratio of the two materials, and the length of the uniform body on the van der Waals force were shown.