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Schematic illustration of the multiple-scattered waves that can lead to perfect absorption on a DMR, with a reflecting wall placed a small distance s behind it. (a) When the incoming wave energy has been totally absorbed, there should be no reflections, i.e., all the scatterings on the incident side cancel each other so that . Incoming wave generates only two net counter-propagating wave components and , in the air layer between the DMR (at z = 0) and the reflecting wall. Here the dot-dash lines stand for the location at which the periodic boundary condition is applied. (b) Due to the MCPA conservation, the three complex pressure amplitudes must form an isosceles triangle whose two equal sides are slanted toward each other with an angle given by 2δ = 2k0s.
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