Fig. 1: Wave scattering setups.

a The monopole scattering with symmetrical pressure fields. b The dipole scattering with anti-symmetrical pressure fields. The sound fields in either half of the spaces in a, b can be applied to the causality constraints as per Eqs. (1) and (2) (equivalent to the 1-port setup). c The effective medium description of a monopole-dipole resonator, with generalized 2-port setup allowing both reflection and transmission.