Calculation Of The Casimir Effect Between Dielectric Plates

Casimir effect is the vacuum attractive force between two neutral conducting plates. Physicists have developed many methods to calculate the Casimir effect,but only few of them have turned out to be capable of dealing with realistic dielectric plates,main They all used Maxwell stress tensor to calculate but invoked statistical thermodynamics, mode functions, Green functions to write down the field correlation functions in Maxwell stress tensor respectively. However, the second approach has restricted to one dimensional system so far. Physicists have also studied some aspects of Casimir effect between anisotropic dielectric plates, but only obtained approximate analytic results in non-retarded limit and numerical results in retarded limit. This paper mainly deals with the calculation of Casimir effect between dielectric plates. We first generalized Kupisewaka method from one dimensional system to the three dimensional one and another derivation of the Casimir effect between two dielectric plates was presented based on the quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of the 'evanescent mode'was discussed. The Lifshitz's formula was rederived using all the vacuum mode functions, which include the contribution of the 'evanescent modes'. Only in the case of perfect metallic plates, the 'evanescent modes'will become unimportant. We also calculated the Casimir effect between two anisotropic dielectric plates using the surface mode technique and 4 ×4 matrix formula. We obtain the approximate analytic results in the retarded limit and found that the correction to the Casimir force in the Lifshitz result is proportional to δwhile the torque due to the anisotropic dielectric is proportional to the square of δ,and the torque varies as sin(2φ), reaching its maximum at φ=π/4 and φ=3π/4, with φthe angle between the two optical axes and δthe relative difference between two elements of the dielectric tensor along the optical axis and along the plane orthogonal to the optical axis. This work was partially supported by National Basic Research Program of China (2003CB716300) and the National Natural Science Foundation of China (NSFC:10121503).