This article explores, theoretically and experimentally, asymmetric absorbers made of detuned and folded quarter wavelength resonators filled with air or porous materials. When used as acoustic lining in ducts, their thickness can be sub-wavelength and they can be designed for perfect absorption in broad target frequency bandwidth. The considered filling porous material can be easily 3D printed and is formed of a structured micro-lattice with variable lattice constant, allowing precise control of its acoustic properties. The underlying physics of asymmetric absorbers is discussed through a simplified analysis by means of the transfer matrix method. The behavior of the porous absorbers is also predicted by a mode-matching technique accounting for the possible couplings between the resonators. An absorber made of folded quarter-wavelength resonators is optimized, 3D printed and experimentally tested. The experimental results are in good agreement with the theory and show a mean absorption coefficient of 99% over almost an octave and below the quarter-wavelength frequency corresponding to the height of the absorber.