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.

中文翻译：

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来自时间演化高阶 Pancharatnam-Berry 相位的旋转多普勒频移：超表面方法

声波或电磁波的多普勒频移已在许多不同的环境中得到广泛研究，如今，它代表了医学、工程、天体物理学和光学领域的强大工具。这种效应通常在通用能量-动量守恒定律的框架中描述。特别是，最近使用光携带轨道角动量证明了旋转多普勒效应。当波经历其哈密顿量的循环绝热变换时，已知获得所谓的 Pancharatnam-Berry (PB) 相位。在这项工作中，提供了庞加莱球上高阶 PB 相位时间演化与光的旋转多普勒频移之间直接联系的实验证据。在电信波长下运行的超表面用于对光波施加总（自旋和轨道）角动量 (TAM)，而两个 TAM 转换器确保庞加莱球上的闭合循环。通过旋转转换器之一，可以观察到显着的多普勒频移，而输出 TAM 没有变化。所提出的基于超表面的方法提供了新的先进方法来设计光的频率内容。