Abstract
We generalize Kupisewska method to the three-dimensionalsystem and another derivation of the Casimireffect between two dielectric plates is presentedbased on the explicit quantization of the electromagnetic field in thepresence of dielectrics, where the physical meaning of ``evanescent mode''is discussed. The Lifshitz's formula is rederived using all the vacuum modefunctions, which include the contribution of the `evanescent modes'. Only inthe case of the perfect metallic plates will the evanescent modes become unimportant.
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