Rotational Doppler Frequency Shift from Time-Evolving High-Order Pancharatnam–Berry Phase: A Metasurface Approach

The Doppler frequency shift of sound or electromagnetic waves has been widely investigated in many different contexts and, nowadays, represents a formidable tool in medicine, engineering, astrophysics, and optics. Such effect is commonly described in the framework of the universal energy-momentum conservation law. In particular, the rotational Doppler effect has been recently demonstrated using light carrying orbital angular momentum. When a wave undergoes a cyclic adiabatic transformation of its Hamiltonian, it is known to acquire the so-called Pancharatnam–Berry (PB) phase. In this work, an experimental evidence of the direct connection between the high-order PB phase time evolution on the Poincaré sphere and the rotational Doppler frequency shift of light is provided. A metasurface operating at telecom wavelengths is employed to impose a total (spin and orbital) angular momentum (TAM) on the light wave, while two TAM converters ensure a closed cycle on the Poincaré sphere. By rotating one of the converters, a significant Doppler frequency shift is observed without variation of the output TAM. The proposed metasurface-based approach offers new advanced ways to engineer the frequency content of light