Directivity analysis of time-reversal arrays in a simple ocean waveguide

This paper analyses the directivity of time-reversal arrays of arbitrary shape in a range-independent homogeneous ocean waveguide. Through feedback, these devices have the ability to focus waves in unknown media, which makes them potentially useful in many applications. The analysis is based on the image method, which expands the array into a series of reflected virtual replicas that interfere to create a strong focal spot. This setup allows the acoustic field to be approximately expressed as the product of two terms, one of which depends on the free-space directivity of the array, and the other one on the environmental properties. The former dictates the gross distribution of acoustic energy in the water column, while the latter defines the fine-scale variations and the effective size of the focus.