The Elastic Spiral Phase Pipe

Abstract

We design a device for the passive mode conversion of guided, axisymmetric, ultrasonic waves in hollow elastic pipes into arbitrary non-axisymmetric flexural waves that have a constant angular profile along the pipe axis. To achieve this we create an elastic analogue to optical spiral phase platesthe elastic spiral phase pipe. Three possible configurations of the elastic spiral phase pipe are presented which allow the efficient generation of nonaxisymmetric flexural waves from an axisymmetric, longitudinal forcing. The theory leverages the dispersive nature of the guided elastic waves that are supported in pipes through a defined relative refractive index. As such we include a spectral collocation method used to aid the design of the elastic spiral phase pipe that is corroborated with numerical simulations and then experimentally verified.

Elastic Orbital Angular Momentum

“…To demonstrate the transfer of elastic OAM in a coupled solid-fluid system, efficient excitation of pure flexural modes in elastic pipes is required. Here we outline the theory behind the elastic spiral phase pipe [32] by first considering its optical analogues.…”

“…For the demonstration of elastic OAM transfer, we utilise the experimentally verified eSPP of [32], with the same properties as the pipe considered in Fig. 2 in the main text.…”

“…As such there is zero average elastic OAM. Fortuitously, the recent advent of the elastic spiral phase pipe (eSPP), analogous to optical spiral phase plates [32,33], enables arbitrary F (m, n) modes to be efficiently excited, via mode conversion, which boast a constant angular profile along the pipe axis. We demonstrate in Fig.…”