Rotational Doppler shift of the light transmitted behind a rotating object with rotational symmetries: rotational Doppler shift of the transmitted light

Abstract

We investigate both theoretically and experimentally the decomposition of a fundamental Gaussian beam transmitted behind an absorbing propeller-like object. We use a Laguerre Gaussian basis which modes carry orbital angular momentum. The main contributing components correspond to modes having the same rotational symmetry as the object, thus enabling pattern recognition. When the object is rotated, the frequency of the modes of the basis experiences a rotational Doppler shift characterizing the movement, that can be easily detected. Potential applications in target recognition and rotation identification are then considered, including rotational Doppler shifts using microwaves.

Rotational Doppler Effect: A Review

“…Rotational doppler shifts have been reported on the transmitted light [62,63] on the LG modes that are multiple of the symmetry of the object, with excellent agreement with the above predictions. A rotational Doppler effect has also been reported from a fundamental beam diffracted by a rough surface that have been embossed with a given rotational symmetry.…”

Rotational Doppler effect on reflection upon an ideal rotating propeller

“…There would be no extra, nor cascade Doppler effect. In the absence of such a mirror, the system corresponds to a bistatic radar system with a rotational Doppler effect as explained in [17].…”

“…Therefore, in reflection, the rotational Doppler effect has been limited to the scattering by rough surfaces [8][9][10], or to the reflection on phase conjugated mirrors [11], metasurfaces and helicoidal reflectors [12,13] or prisms [14]. Very recently, it has been shown that a rotational Doppler shift can be isolated in the decomposition of the image of an object having a rotational symmetry in a bistatic configuration [15][16][17]. Then, the ques-tion arises whether the decomposition of the usual fundamental beam reflected on a rotating object could induce rotational Doppler shifts that could be measured, enabling unambiguously rotation identification.…”