Mechanical Perspective on the Rotational Doppler Shift of a Single Photon

Main Article Content

Roberto Lozano


A theoretical model that relates the rotational Doppler shift of a photon and the rotational velocity of the lenses traversed by the beam of light, is presented. The mathematical relation, which is resolved in the context of a four-dimensional Minkowski flat spacetime and Cartesian coordinates, relates the rotational Doppler effect of a circularly polarized electromagnetic wave, caused by the transfer of spin angular momentum from a rotating object (lenses), with the coordinate acceleration of the rotating object, in the counter-propagating direction in which the photons move, and its angular velocity. From the analysis of the solved equation, it can be considered the generated coordinate acceleration and the theoretical possibility that it was obtained from the mechanical energy of a rotating object traversed by a beam of light, which, in turn, would generate a coordinate acceleration difference in the parallel and counter-propagating direction in which the photons move.

Spin angular momentum, coordinate acceleration, photon, rotational doppler effect.

Article Details

How to Cite
Lozano, R. (2020). Mechanical Perspective on the Rotational Doppler Shift of a Single Photon. Physical Science International Journal, 24(10), 62-67.
Original Research Article


Planck M. Über eine Verbesserung der Wienschen Spektralgleichung. Verhandlungen dtsch physik Ges. 1900;2:202-204.

Planck M. Zur theorie des gesetzes der energieverteilung im normalspectrum. Verhandlungen Dtsch Physik Ges. 1900; 2:237-245.

Rätzel D, Wilkens M, Menzel R. Gravitational properties of light—the gravitational field of a laser pulse. New J Phys. 2016;18:023009.

Garetz BA. Angular Doppler effect. J Opt Soc Am. 1981;71:609-611.

Garetz BA, Arnold S. Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate. Opt Commun.1979;31:1-3.

Courtial J, Dholakia K, Robertson DA, Allen L, Padgett M J. Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum. Phys Rev Lett. 1998; 80:3217.

Nienhuis G. Doppler effect induced by rotating lenses. Opt Commun. 1996;132:8-14.

Bretenaker F, Le Floch A. Energy exchanges between a rotating retardation plate and a laser beam. Phys Rev Lett. 1990;65:2316.

Bekshaev AYa. Manifestation of mechanical properties of light waves in vortex beam optical systems. Opt Spektrosk. 2000;88:904-910.

Basistiy IV, Bekshaev AYa, Vasnetsov MV, Slyusar VV, Soskin MS. Observation of the rotational doppler effect for optical beams with helical wave front using spiral zone plate JEPT Lett. 2002;76:486-489.

Korech O, Steinitz U, Gordon RJ, Averbukh ISh, Prior Y. Observing molecular spinning via the rotational Doppler effect. Nature Photon. 2013; 7:711-714.

Zhang W, Gao J, Zhang D, He Y, Xu T, Fickler R, Chen L. Free-space remote sensing of rotation at the photon-counting level. Phys Rev Applied. 2018;10:044014.

Barreiro S, Tabosa JWR, Failache H, Lezama A. Spectroscopic observation of the rotational doppler effect. Phys Rev Lett. 2006;97:113601.

Maxwell JC. A dynamical theory of the electromagnetic field. Phil Trans R Soc Lond P. 1865;155:459-512.

Nairz A. A class of metric theories of gravitation on Minkowski spacetime. Found Phys. 1996;26:369-389.

Vasilou E. Chapter 8. Curvature. In: M. Hazewinkel, Geometry of principal sheaves. Mathematics and Its Applications, (Springer Netherlands, 2005); 2005.

Dennis R, Wilkens M, Menzel R. Gravitational properties of light—the gravitational field of a laser pulse. New J Phys. 2016;18:023009.

Li G, Zentgraf T, Zhang S. Rotational Doppler effect in nonlinear optics. Nature Phys. 2016;12:736-740.

Tao Y, Gang W. Rotational Doppler shift for electromagnetic waves carrying orbital angular momentum based on spectrum analysis. AIP Conf Proc. 2017; 1820:090024.

Georgi P, Schilickriede C, Li G, Zhang S, Zentgraf T. Rotational Doppler shift induced by spin-orbit coupling of light at spinning metasurfaces. Optica. 2017;4(8):1000-1005.

Okulov AY. Rotational Doppler shift of a phase-conjugated photon. J Opt Soc Am B. 2012;29:714-718.

Qiu S, Liu T, Li Z, Wang C, Ren Y, Shao Q, Xing C. Influence of lateral misalignment on the optical rotational Doppler effect. Appl Opt. 2019;58:2650-2655.