Analysis of Imperfect Acoustic Cloaking Resonances

We study the resonance phenomenon arising from imperfect acoustic cloaking in 2D based on a small perturbation of the transformation acoustics. It is shown that the resonant frequencies of imperfect cloaking appearing in the total scattering cross section converge to Dirichlet eigenvalues of the concealed region as a perturbation parameter approaches zero. This theory enables us to predict the location of the resonant frequencies of imperfect cloaking and to identify the corresponding resonance modes.