Elastic Wave Eigenmode Solver for Acoustic Waveguides

A numerical solver for the elastic wave eigenmodes in acoustic waveguides of inhomogeneous cross-section is presented. Operating under the assumptions of linear, isotropic materials, it utilizes a finite-difference method on a staggered grid to solve for the acoustic eigenmodes of the vector-field elastic wave equation. Free, fixed, symmetry, and anti-symmetry boundary conditions are implemented, enabling efficient simulation of acoustic structures with geometrical symmetries and terminations. Perfectly matched layers are also implemented, allowing for the simulation of radiative (leaky) modes. The method is analogous to eigenmode solvers ubiquitously employed in electromagnetics to find waveguide modes, and enables design of acoustic waveguides as well as seamless integration with electromagnetic solvers for optomechanical device design. The accuracy of the solver is demonstrated by calculating eigenfrequencies and mode shapes for common acoustic modes in several simple geometries and comparing the results to analytical solutions where available or to numerical solvers based on more computationally expensive methods

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937-940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix's radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.Comment: 13 figure

Twin-waves propagation phenomena in magnetically-coupled structures

The use of magnetic dipoles embedding in an elastic support introduces long-range interaction forces. This is a completely new paradigm in structural mechanics, classically based on local short-range particle interaction. The features of long-range forces produce very new mechanical coupling effects. This paper examines the case in which two identical rod-like structures, each with a dipole distribution embedded, vibrate side by side. Waves generated in one of the rods propagate also in the second and vice versa creating a new effect we name twin-waves. The present investigation unveils the existence of an infinite number of propagation modes even in one-dimensional infinite structures, a new and unus al behaviour in classical waveguides. The physics behind this phenomenon is further investigated also by numerical simulations