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

Abstract

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.

Evolution of Pancharatnam-Berry phase on a hybrid-order Poincaré sphere based on vortex half-wave plates

“…In a report in 2011, the PB phase of evolution on a HOPS was experimentally measured for the first time in relation to the total angular momentum(TAM, Jl =+ ) of the beam [13] . In 2021, Yue et al verified that a high-order PB phase evolving over time can produce a rotational Doppler shift [14] . Furthermore, the hybrid-order Poincaré sphere (HyPOS) was proposed to represent cylindrical vector vortex beams, whose north and south poles representing scalar vortices with different topological charges and orthogonal polarization states [15][16][17][18] .…”

The Rotational Doppler Effect of Twisted Photons in Scattered Fields

“…[8,9] Its physical mechanism has been theoretically studied in terms of the dynamic evolution of the Pancharatnam-Berry phase or momentum and energy conservation. [10][11][12] Considerable attention has been paid to exploiting this scheme in astrophysics, [13] nonlinear optics, [14] Doppler cooling, [15] nonreciprocity, [16] vectorial Doppler metrology, [17] Quantum measurement, [18] and so on. [19,20] Particularly in rotator detection, numerous types of rotators (macro targets, [21] flow vorticities, [22] spinning particles, [23] and so on [24,25] ) have been successfully measured using vortex waves at different frequencies (acoustic waves, [26] radio waves, [27] light waves, [21] and even white light [28] ), even in remote sensing.…”

Ultrahigh Precision Angular Velocity Measurement using Frequency Shift of Partially Coherent Beams

“…This approach has been extensively studied under various conditions. [20,[25][26][27][28][29][30][31][32][33][34][35] Furthermore, utilizing the phase spectrum variation of OAM state broadening after a single OAM beam truncated by a spinning object is one of the low-speed measurement schemes. [36] Recently, a vector method was proposed to exploit a vectorial beam with spatially variant polarization.…”