We employ the known in photonic crystals phenomenon of self-collimation (SC) for modifying the performance of invisibility cloaks composed of dielectric rod arrays. Incorporation in the cloak design two circular sections, supporting SC, allows for refusing from Transformation Optics (TO) based prescriptions for the cloak medium, which request too challenging material parameters. In addition to SC sections, unidirectional cloak contains two TO-based transition sections with easily realizable parameters of rod arrays. These sections control wave paths between cloak input and output and SC sections. At plane wave incidence, the designed cloak was found to provide as restoration of initial flat wavefront behind the hidden object, so significant reduction of wave scattering by the object.
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