Variational study of a model for near-perfect transmission through lossy media with acoustic sources

Abstract

Complementary acoustic metamaterials have been proposed as a means of compensating for the high impedance mismatches of aberrating layers that disrupt the acoustic field and hence distort acoustic images. Recently, a complementary acoustic metamaterial featuring active components was shown in principle to compensate for both the impedance mismatch and energy attenuation of lossy materials, but a physical realization of the concept has not yet been implemented. Here, we present results from a one-dimensional acoustic model showing how a plane wave incident on a lossy material can be augmented by point monopole and dipole sources to allow for near-perfect transmission, thus rendering the lossy medium acoustically transparent. We present general expressions for source magnitudes that are dimensionless with respect to frequency, material thickness, and the background medium. We explore the sensitivity of the performance to variations in each of the model parameters, considering both theoretical and practical limitations to the proposed method. We show that these findings are consistent with three-dimensional finite element simulations.