Reversal of orbital angular momentum arising from an extreme Doppler shift

Gibson, G. M. , Toninelli, E., Horsley, S. A.R., Spalding, G. C., Hendry, E., Phillips, D. B. and Padgett, M. J. (2018) Reversal of orbital angular momentum arising from an extreme Doppler shift. Proceedings of the National Academy of Sciences of the United States of America, 115(15), pp. 3800-3803. (doi: 10.1073/pnas.1720776115) (PMID:29581257) (PMCID:PMC5899465)

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Abstract

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 be observed only 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 subsonic. Using an acoustic source at ≈100 Hz we create a rotational Doppler shift larger than the laboratory-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 with that of the laboratory frame. These low-velocity laboratory realizations of extreme Doppler shifts have relevance to superoscillatory fields and offer unique opportunities to probe interactions with rotating bodies and aspects of pseudorelativistic frame translation.

Item Type:Articles
Additional Information:This work was supported by the European Research Council (TWISTS, Grant 192382). D.B.P. acknowledges support from the Royal Academy of Engineering. E.T. acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) Center for Doctoral Training in Intelligent Sensing and Measurement (EP/L016753/1).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Gibson, Dr Graham and Phillips, Dr David and Toninelli, Mr Ermes and Padgett, Professor Miles
Authors: Gibson, G. M., Toninelli, E., Horsley, S. A.R., Spalding, G. C., Hendry, E., Phillips, D. B., and Padgett, M. J.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Proceedings of the National Academy of Sciences of the United States of America
Publisher:National Academy of Sciences
ISSN:0027-8424
ISSN (Online):1091-6490
Published Online:26 March 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Proceedings of the National Academy of Sciences of the United States of America 115(15):3800-3803
Publisher Policy:Reproduced under a Creative Commons License
Data DOI:10.5525/gla.researchdata.577

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
636381EPSRC Centre for Doctoral Training in Sensing and MeasurementAndrew HarveyEngineering and Physical Sciences Research Council (EPSRC)EP/L016753/1SCHOOL OF PHYSICS & ASTRONOMY