Wide-Stopband Aperiodic Phononic Filters K Rostem 1,2 , D T Chuss 3 , K L Denis 2 and E J Wollack 2 1 Department of Physics & Astronomy, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218 2 NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 3 Department of Physics, Villanova University, 800 E. Lancaster Avenue, Villanova, PA 19085 E-mail: krostem1@jhu.edu 16 July 2018 Abstract. We demonstrate that a phonon stopband can be synthesized from an aperiodic structure comprising a discrete set of phononic filter stages. Each element of the set has a dispersion relation that defines a complete bandgap when calculated under a Bloch boundary condition. Hence, the effective stopband width in an aperiodic phononic filter (PnF) may readily exceed that of a phononic crystal with a single lattice constant or a coherence scale. With simulations of multi-moded phononic waveguides, we discuss the effects of finite geometry and mode-converting junctions on the phonon transmission in PnFs. The principles described may be utilized to form a wide stopband in acoustic and surface wave media. Relative to the quantum of thermal conductance for a uniform mesoscopic beam, a PnF with a stopband covering 1.6-10.4 GHz is estimated to reduce the thermal conductance by an order of magnitude at 75mK. Keywords: Phononic Meta-material, Phonon Filter, Thermal Conductance arXiv:1509.03923v2 [cond-mat.mes-hall] 14 Mar 2016