Inverse Design of Phononic Crystal with Desired Transmission via a Gradient-Descent Approach

We propose a general approach based on the gradient descent method to study the inverse problem,making it possible to reversely engineer the microscopic configurations of materials that exhibit desired macroscopic properties.Particularly,we demonstrate its application by identifying the microscopic configurations within any given frequency range to achieve transparent phonon transport through one-dimensional harmonic lattices.Furthermore,we obtain the phonon transmission in terms of normal modes and find that the key to achieving phonon transparency or phonon blocking state lies in the ratio of the mode amplitudes at ends.