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Theoretical model of lossy acoustic bipolar cylindrical cloak with negative index metamaterial

While, it was shown that for the lossless acoustic cloak the illumination direction independent cloaking can be achieved by employing the structure with compressed geometry and complementary media, the effect of the material loss have not been fully explored yet. Here, we show that realistic cloaking materials with moderate loss still works when complementary media is introduced but with the attenuated back scattering waves.