Frequency Dependent Generalized Polarization Tensors

Abstract

This chapter introduces the notion of higher-order frequency-dependent polarization tensors (FDPTs). Multipolar asymptotic expansions for wave scattered by a target of characteristic size smaller than the wavelength can be written in terms of high-order derivatives of the fundamental solution to the Helmholtz equation and high-order FDPTs. This key property is useful in imaging. It shows that the notion of FDPTs is the natural extension of the one of GPTs for wave propagation. We also introduce the notion of scattering coefficients which plays the same role as the notion of contracted generalized polarization tensors.