A Feasible Method for Temporal Modulation of Phononic Crystals
Discipline: Physics
Subcategory: Physics (not Nanoscience)
Session: 3
Room: Woodley Park
Matthew Li - University of North Texas
Co-Author(s): Dmitrii Shymkiv, University of North Texas, Denton, Texas; Arkadii Krokhin, University of North Texas, Denton, Texas
Phononic crystals are spatially periodic materials with the ability to manipulate sound waves. One unique effect of this periodicity is the creation of band gaps (ω-gaps), which are frequency ranges where sound wave propagation is prohibited within the crystal. The present work extrapolates from the time-space symmetry of the wave equation in order to realize analogous wave vector gaps (k-gaps) within the band structure of the system. By using the plane wave expansion method (PWE) to model a time and space dependent phononic crystal, we show that k-gaps appear in tandem with strong non-reciprocal effects. Experimentally, these gaps can be tuned to generate large non-reciprocal effects, allowing for the creation of a one-way acoustical diode. Theoretically, these gaps draw important insight into the topology of the band structure. Recently, it has been demonstrated that spatiotemporal photonic crystals are able to powerfully manipulate light waves [1]. However, the analogous temporal modulation of elastic structures has been limited due to the insensitivity of the mechanical properties of elastic materials to time-dependent external perturbations, e.g., external electric and magnetic fields. In this project, we propose the synchronous mechanical rotation of heterogenous solid (Cu-Al) cylinders as a resolution. Period size and filling fraction remain the degrees of freedom that allow for the continuous tuning of ω and k gaps and other important characteristics of an acoustic device containing this space-time phononic crystal as basic element. To model this system, developments upon the standard acoustic wave equation were made to account for terms originating from the active rotation of scatterers. Physically, these terms can be attributed to the centripetal and Coriolis forces that must be considered within the dynamical equation [2]. To maneuver around the difficulty of imposing boundary conditions upon an infinite system, the problem was transformed into Fourier representation. As a result, we obtain a quadratic eigenvalue problem whose solutions outline the band structure of the system. The eigenvalues were numerically determined using python. Notably, parallelization techniques and the computational strength of the Texas Lonestar6 Supercomputer were leveraged in order to make the convergence of our model possible.It was found that both ω and k gaps appear in the frequency spectrum of our system which is periodic in both space and time. Because we observe these gaps at frequencies as low as the first band, it is shown that mechanical modulation offers a rather deep control of sound waves. Breaking the phase of rotation, it is found that the band-structure becomes non-reciprocal with respect to forwards and backwards transmission through the crystal. Frequencies at which a pass band exists in one direction while a band gap exists in the other have been found, theorizing the existence of a one-way acoustic diode. In the future, we plan to adjust the spatial and material parameters of the system and manufacture the system in order to realize our theoretical results experimentally.References:1.Yonatan Sharabi, Alex Dikopoltsev, Eran Lustig, Yaakov Lumer, and Mordechai Segev, “Spatiotemporal photonic crystals,” Optica 9, 585-592 (2022)2.D. Censor, J. Aboudi, “Scattering of sound waves by rotating cylinders and spheres,” Journal of Sound and Vibration, Volume 19, Issue 4, 437-444 (1971)
Funder Acknowledgement(s): This work was supported by EFRI Grant No. 1741677 from the National Science Foundation.
Faculty Advisor: Dr. Arkadii Krokhin, arkady@unt.edu
Role: I took the form of the wave equation with terms relating to the Coriolis and centrifugal force and made the Fourier transforms. Additionally, I built all of the Python models to numerically determine solutions to our mathematical framework. I implemented computational algorithms to lower the runtime of the model to a feasible time. I also proposed the linearization method to make our mathematical calculations approachable in Python. I produced and analyzed images and derived a condition to check the validity of our solutions by taking the curl of the dynamical equation.