Arbitrary polygonal cloaks with multiple invisible regions

Arbitrary polygonal cloaks with multiple invisible regions are achieved by transformation optics. The original total space is divided into several layers. Choosing proper spatial mappings for these layers, a few empty layers in which objects can be hidden without bringing any scattering are available as extended invisible regions. Compared with the original polygonal cloaks the proposed one can provide multiple interior and/or exterior invisible regions simultaneously, and the objects can thus be hidden in the interior cavity and/or in the exterior space, or even be embedded into the gap between the cloaking shells.