Suppression of the Resonant Scattering in Imperfect Acoustic Cloaking with a Lossy Medium in ?³

It has been realized that resonance frequencies of imperfect acoustic cloaking based on a small perturbation of the transformation acoustics in ?² are located near Dirichlet eigenvalues of the cloaked region Chin. Phys. Lett. 26 (2009) 014301; 29 (2012) 124301. In this work, we study the performance of the three-dimensional approximate cloaking system based on the transformation acoustics and show that the cloaking effect may be deteriorated at zeroth order Neumann eigenvalues of the concealed region. In particular, transmitted fields into the concealed region can be extremely resonated at frequencies corresponding to the zeroth-order Neumann eigenvalues while scattered fields are suppressed well for any frequency. To enhance the cloaking effect at resonance frequencies, we introduce a lossy medium inside the cloaked region and show that the new proposal can reduce the intensity of transmitted fields significantly due to the lossy medium.