Direct Mechanical Detection and Measurement of Wave-Matter Orbital Angular Momentum Transfer by Nondissipative Vortex Mode Conversion

We quantitatively report on the rotational mechanical effect of wave orbital angular momentum on matter by nondissipative vortex mode conversion. Our experiments consist of ultrasonic waves reflected off freely spinning helical acoustic mirrors that are capillary trapped at a curved air-water interface. Considering helical mirrors with integer topological charges these results represent the demonstration of the experiment proposed by Allen et al. originally introduced in the optical domain [Phys. Rev. A 45, 8185 (1992)], whose quantitative implementation remains elusive to date whatever the nature of the wave. The study is further generalized to helical mirrors with fractional charges.

Figure 1

Acoustic radiation torque experiment. (a) Designed helical mirror, here with $\ell =2$, with $(\mathbf{r},\mathit{\varphi },\mathbf{z})$ the unit vectors of the cylindrical basis. (b) Sketch of the setup, where the camera is used to record the rotational dynamics of the helical mirror from its flat side. (c) In situ bottom view of a helical mirror, where the printed marker is on the back side of the mirror used to monitor its angular dynamics $\phi (t)$.

Figure 2

(a) Power $P$ intercepted by the helical mirror as a function of its distance $d$ from the transducer. (b) Corresponding power $P^{\prime }$ of the reflected field intercepted back by the transducer for $0\le \ell \le 5$. Also, $\ell =1^{*}$ refers to a helical mirror with unit topological charge and infinite extent. Both $P$ and $P^{\prime }$ are normalized to the total output power $P_0$ of the transducer. (c) Normalized intensity distribution of the incident wave in the meridional plane ($x$, $z$) as a function of $z$ for $d=100\mathrm{mm}$. (d) Same as in panel (c) for the reflected field with $\ell =2$.

Figure 3

(a) Typical trajectory, in the ($x$, $y$) plane, of the marker at the backside of the spinning helical mirror over $\sim 3$ full turns. (b) Experimental dynamics of the azimuthal angular coordinate of the marker $\phi$, which is evaluated from the trajectory shown in panel (a), taking $\phi =0$ at $t=0$. Data refer to an $\ell =5$ helical mirror. Thick gray curve: experimental data. Thin dark circle: best circular (a) and linear (b) fit.

Figure 4

Typical relaxation dynamics of the angular position of the helical mirror, where $t=t_0$ refers to the time at which the acoustic source is turned off. Thick gray curve: experimental data. Thin dark curve: fit giving access to the ratio $C/J$. Data refer to an $\ell =5$ helical mirror.

Figure 5

(a) Acoustic torque as a function of its topological charge. Markers: experimental data. Solid line: linear fit. Inset refers to radiation force balance measurement.(b) Calculated far-field normalized intensity and phase distribution of the wave reflected off the helical mirror for $\ell =2$ and 2.5. Panels refers to the range $-5\le (k_{x}R,k_{y}R)\le 5$.