A dispersive full-wave finite-difference time-domain model is used to study the performance of bipolar cylindrical invisibility cloaking devices. We have considered two different cloaking structures generated by the mapping of the s axis and the mapping of the t axis of bipolar coordinates. The permittivity and permeability tensors for the cloaking devices are obtained from an effective medium approach in general relativity. The s-axis mapped bipolar cylindrical cloak is found to be imperfect, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of propagation of the waves, and the loss tangents of the metamaterial. Only the case of TM waves for the specific propagation direction shows good cloaking performance. On the other hand, the t-mapped cloaking device shows good cloaking performance for all polarizations and directions of propagation. However, this structure has a singular boundary at the inner radius. Realistic cloaking materials with loss still show a cloak that is working, but attenuated backscattering waves exist.
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