Fisher information flow in wave scattering

Abstract

The information-theoretical concept of Fisher information has recently delivered promising results when applied to coherent scattering measurements. Its most remarkable feature is that it allows the identification of the optimal wave front for probing any parameter that is hidden within an arbitrary complex scattering medium.To understand Fisher information in wave scattering on a more fundamental level, we introduce a quantity that describes its behavior locally within the scattering medium: the Fisher information flow. The latter constitutes an information flux density that complements the widely-used energy flux density commonly known as the Poynting vector.In this work, we investigate the Fisher information flow and the corresponding source term for stationary scalar waves. We demonstrate the properties of these novel quantities using numerical simulations, thereby gaining an intuition for the information-transport characteristics of electromagnetic waves. Moreover, we measure the Fisher information flow using microwave technology to show that the latter is not just a theoretical concept but plays a vital role in practical applications.