In this contribution, we present and discuss the theoretical aspects, design and bandwidth limits of Doppler cloaking. Doppler cloaking is a new cloaking technique that allows moving scatterers to appear at rest for an external observer. It consists of a time-varying metamaterial whose refractive-index is properly modulated as a periodic function in both space and time, leading to a periodic profile of the refractive index that moves with a certain velocity. By properly choosing the modulation scheme and frequency, Doppler-cloaking results in a zero-apparent velocity for the moving object. Conversely, static scatterers can appear in motion creating an illusion effect. Here, we will focus on the analysis of the fields propagating in the Doppler cloak and derive the key formulas for the design of a Doppler cloak. Then, fundamental limits on the operational bandwidth are presented and discussed.

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