  Perfect, broadband and asymmetric sound absorption is theoretically,
numerically and experimentally reported by using subwavelength thickness panels
in a transmission problem. The panels are composed of a periodic array of
varying cross-section waveguides, each of them being loaded by an array of
Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of
the absorption band is fixed by the resonance frequency of the deepest HR, that
reduces drastically the transmission. The preceding HR is designed with a
slightly higher resonance frequency with a geometry that allows the impedance
matching to the surrounding medium. Therefore, reflection vanishes and the
structure is critically coupled. This results in perfect sound absorption at a
single frequency. We report perfect absorption at 300 Hz for a structure whose
thickness is 40 times smaller than the wavelength. Moreover, this process is
repeated by adding HRs to the waveguide, each of them with a higher resonance
frequency than the preceding one. Using this frequency cascade effect, we
report quasi-perfect sound absorption over almost two frequency octaves ranging
from 300 to 1000 Hz for a panel composed of 9 resonators with a total thickness
of 11 cm, i.e., 10 times smaller than the wavelength at 300 Hz.
