Gibson, G., Toninelli, E., Horsley, S. A. R., Spalding, G., Hendry, E., Phillips, D. and Padgett, M. (2018) Reversal of Orbital Angular Momentum arising from an extreme Doppler shift. [Data Collection]

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The linear Doppler shift is familiar as the rise and fall in pitch of a siren as it passes by. Less well known is the rotational Doppler shift, proportional to the rotation rate between source and receiver, multiplied by the angular momentum carried by the beam. In extreme cases the Doppler shift can be larger than the rest frame frequency and for a red-shift, the observed frequency then becomes 'negative'. In the linear case, this effect is associated with the time reversal of the received signal, but it can only be observed with supersonic relative motion between the source and receiver. However, the rotational case is different, if the radius of rotation is smaller than the wavelength then the velocities required to observe negative frequencies are sub-sonic.

Using an acoustic source at ≈100Hz we create a rotational Doppler shift larger than the lab-frame frequency. We observe that once the red-shifted wave passes into the 'negative frequency' regime, the angular momentum associated with the sound is reversed in sign compared to that of the lab-frame. These low velocity laboratory realisations of extreme Doppler shifts have relevance to superoscillatory ï¬elds, and offer new opportunities to probe interactions with rotating bodies and aspects of pseudo relativistic frame translation.

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