# Cascaded Rotational Doppler Effect

## TL;DR

This paper introduces and experimentally verifies the cascaded rotational Doppler effect, demonstrating how frequency shifts can be doubled through mirror-imaged rotational processes, with potential applications in high-precision detection of rotating systems.

## Contribution

The paper presents the first experimental demonstration of cascading rotational Doppler effects, leveraging mirror symmetry and parity conservation to amplify frequency shifts.

## Key findings

- Frequency shift can be doubled via cascading rotational Doppler processes.
- Experimental verification using a rotating half-wave plate and mirror setup.
- Potential for high-precision detection of rotating objects from molecules to celestial bodies.

## Abstract

We propose and substantiate experimentally the cascaded rotational Doppler effect for interactions of spinning objects with light carrying angular momentum. Based on the law of parity conservation for electromagnetic interactions, we reveal that the frequency shift can be doubled through cascading two rotational Doppler processes which are mirror-imaged to each other. This effect is further experimentally verified with a rotating half-wave plate, and the mirror-imaging process is achieved by reflecting the frequency-shifted circularly polarized wave upon a mirror with a quarter-wave plate in front of it. The mirror symmetry and thus parity conservation guarantees that this doubled frequency shift can be further multiplied with more successive mirror-imaging conjugations, with photons carrying spin and/or orbital angular momentum, which could be widely applied for detection of rotating systems ranging from molecules to celestial bodies with high precision and sensitivity.