This article is devoted to the construction and investigation of a class of polarization-invariant directional cloaks by concatenation of cloaking medium components via transformation optics. It improves the construction of the first polarization-invariant directional cloak, introduced by Agarwal et al. . The main ingredient is to construct a capsuloid transformed metamaterial consisting of an lp-cylindrical transformation map and two half lp--spherical transformation maps. Numerical investigation is carried out to test the performances of the cloaks under different polarized incoming waves. A salient feature of our cloaks is compact-sizedness, namely the geometrical size is no longer dependent on the regularization parameter ρ under the non-uniform map. In particular, we study the cloaking effect with respect to the regularization parameter ρ and the incident direction.
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