Wave-based motion sensors, such as radar and sonar, are designed to detect objects within a direct line-of-sight of the sensor. As a result, surveillance of a cavity with multiple internal partitions generally demands use of a network of sensors. In the first part of the dissertation, we propose and test a new paradigm of sensing that can work in such cavities using a single sensor. The sensor utilizes the time reversal invariance and spatial reciprocity properties of the wave equation, and the ray chaotic nature of most real world cavities. Specifically, classical analogs of the quantum fidelity and the Loschmidt echo are developed. The sensor was used to detect perturbations to local boundary conditions of an acoustic cavity, and the medium of wave propagation. This result opens up various real world sensing applications in which a false negative cannot be tolerated.

The sensor is also shown to quantitatively measure perturbations that change the volume of a wave chaotic cavity while leaving its shape intact. Volume changes that are as small as 54 parts in a million were measured using microwaves with 5cm wavelength inside a one cubic meter wave chaotic cavity. These results open up interesting applications such as monitoring the spatial uniformity of the temperature of a homogeneous cavity during heating up / cooling down procedures, etc.

The second part of the dissertation is dedicated to improving the performance of time reversal (TR) mirrors, which suffer from dissipation. TR mirrors can, under ideal circumstances, precisely reconstruct a wave disturbance which happened at an earlier time, at any given later time. TR mirrors have found applications in imaging, communication, targeted energy focusing, sensing, etc. Two techniques are proposed and tested to overcome the effects of dissipation on TR mirrors. First, a tunable iterative technique is used to improve the temporal focusing of a TR mirror. Second, the technique of exponential amplification is proposed to overcome the effect of dissipation on TR mirrors. The applicability of these techniques is tested experimentally using an electromagnetic TR mirror, and numerically using a model of the star graph.