We investigate the electromagnetic properties of three-dimensional (3D) arbitrarily-shaped invisible cloaks based on the analytical field transformation theory instead of the complicated numerical simulations. Very simple closed-form expressions for fields and energy flows have been derived for arbitrarily-shaped 3D cloak, which could help us to investigate the electromagnetic properties of the 3D cloaks rapidly and efficiently. The difference between 2D and 3D cloaks have been compared in detail. Distributions of the fields, power flows and wave polarizations for the 3D case have been discussed inside the cloak. Numerical results have been presented at the cutplanes of cloaks to valid the theoretical analysis, which shows clearly how the incident waves are bent at the inner boundary. In order to further reveal the physical essence of the cloaks, both 3D spherical and ellipsoidal cloaks have been considered based on the analytical method. The common features and the differences for the two structures have been also illustrated in this paper.
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