  Causal nature of the acoustic response, for any materials or structures,
dictates an inequality that relates the absorption spectrum of the sample to
its thickness. We present a general recipe for constructing sound-absorbing
structures that can attain near-equality for the causal relation with very high
absorption performance; such structures are denoted optimal. Our strategy
involves using carefully designed acoustic metamaterials as backing to a thin
layer of conventional sound absorbing material, e.g., acoustic sponge. By using
this design approach, we have realized a 12 cm-thick structure that exhibits
broadband, near-perfect flat absorption spectrum starting at around 400 Hz.
From the causal relation, the calculated minimum sample thickness is 11.5 cm
for the observed absorption spectrum. We present the theory that underlies such
absorption performance, involving the evanescent waves and their interaction
with a dissipative medium, and show the excellent agreement with the
experiment.
