Based on composite optical transformation, we propose a rotatable illusion media with positive permittivity and permeability to manipulate terahertz waves, and a new way to realize singular parameterindependent cloaks when the incident wave with a certain width propagates from specific incident directions. The fundamental mechanism of this kind of cloak is that the illusion media can be able to avoid the incident wave interacting with the objects. Comparing with traditional

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... ate-based cloaks such as cylindrical-shaped cloaks, our cloaks are independent of singular material parameters. Furthermore, this type of rotatable illusion media can be applied to design tunable miniaturized highdirectivity antenna (a small antenna array covered with the rotatable illusion media appears like a large one and meanwhile, the radiation directions of the small antenna array is tunable via this rotatable illusion media). Full wave simulations are performed to confirm these points.