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 σ axis and the mapping of the τ axis of bipolar coordinates. The permittivity and permeability tensors for the cloaking devices are obtained from an effective medium approach in general relativity. The σ-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 τ-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.

Full-wave finite-difference time-domain (FDTD)analysis of an invisibility cloak with the cloaking shell, not necessarily enclosing the cloaking region completely, is presented for bipolar cylindrical geometry. The permittivity and the permeability tensors for the cloaking shell are obtained from an effective medium approach in general relativity. The cloak contains the complementary region adjacent to the cloaking shell. The role of the complementary medium is to cancel the phase vectors of the illuminated electromagnetic waves across the boundaries of the line-segment. By intelligent design of a cloaking shell and a complementary media, it is shown that the same cloaking performance as the conventional cloak can be achieved by using only the half of the cloaking shell required for the conventional invisibility cloak.