The elastic spiral phase pipe

Observation of Elastic Orbital Angular Momentum Transfer

“…where, in the frequency domain, the velocity, v is re- lated to the pressure p through v = −1 iωρ ∇p and * denotes complex conjugation. At the observable depth this is obscured due to the background field excited from the compressional mode that is unconverted by the eSPP, since it is not perfectly efficient [40]. As such at the measurement plane, marked by the dash-dotted line in Fig.…”

“…As such we require a device to ensure their efficient generation. The recent advent of the elastic spiral phase pipe (eSPP) [40] achieves this. This structure removes the necessity to rely on conventional means of complex arrangements of transducers or phased arrays (e.g by comb arrays or non-axisymmetric partial loading [41,42]).…”

“…It consists of a spiral region of the pipe that endows incoming axisymmetric waves with a helical phase profile, similar to OAM generation by optical and acoustic analogues [21,22,46]. The spiral pipe used here has already been characterised [40], comprising an aluminium pipe of density ρ = 2710 kgm −3 , Young's Modulus E = 70 GPa and Poisson's ratio ν = 0.33. The inner and outer diameters of the pipe are d 1 = 40 mm and d 2 = 60 mm respectively.…”

“…The spiral region of the pipe is specifically designed to convert L(0, 2) modes to F (3, 2) modes at 62 kHz, and is formed of by CNC milling a thickness of 6 mm from the pipe into three spiral steps of length h s = 63 mm. This step profile is determined via the method in [40], where an effective refractive index relates the two speeds of the incoming and converted waves through…”

“…To reduce the length of the step size the spiral is partitioned into three turns such that h s = h 0 /3. The wavespeeds of each mode are determined through the dispersion of the pipe, evaluated by spectral collocation [40,47].…”