Photonics Insights, Volume. 1, Issue 1, R03(2022)

Classical and generalized geometric phase in electromagnetic metasurfaces

Yinghui Guo1,2,3, Mingbo Pu1,2,3、*, Fei Zhang1,2,3, Mingfeng Xu1,2,3, Xiong Li1,3, Xiaoliang Ma1,3, and Xiangang Luo1,3、*
Author Affiliations
  • 1State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, China
  • 2Research Center on Vector Optical Fields, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, China
  • 3School of Optoelectronics, University of Chinese Academy of Sciences, Beijing, China
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    The geometric phase concept has profound implications in many branches of physics, from condensed matter physics to quantum systems. Although geometric phase has a long research history, novel theories, devices, and applications are constantly emerging with developments going down to the subwavelength scale. Specifically, as one of the main approaches to implement gradient phase modulation along a thin interface, geometric phase metasurfaces composed of spatially rotated subwavelength artificial structures have been utilized to construct various thin and planar meta-devices. In this paper, we first give a simple overview of the development of geometric phase in optics. Then, we focus on recent advances in continuously shaped geometric phase metasurfaces, geometric–dynamic composite phase metasurfaces, and nonlinear and high-order linear Pancharatnam–Berry phase metasurfaces. Finally, conclusions and outlooks for future developments are presented.


    1 Introduction

    In optics and electromagnetics, the geometric phase originates from the spin–orbit interaction (SOI) of light and describes the relationship between phase change and polarization conversion when light is transmitted or reflected through an anisotropic medium[1]. The general form of the geometric phase was developed by Berry in 1984[2]. He found that when a quantum system in an eigenstate is slowly transported around a circuit C by varying parameters R in its Hamiltonian H(R), it will acquire a geometrical phase factor exp(iγC). Since the pioneering work of Berry, the geometric phase has been applied in various fields of physics and expanded the understanding of state evolutions in different parameter spaces. The most common formulations of the geometric phase are known as the Aharonov–Bohm (AB) phase for electrons and the Pancharatnam–Berry (PB) phase for photons. Figure 1(a) shows a representative case of the AB effect. When a charged particle passes around a long solenoid, the wave function experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle’s wave function being negligible inside the solenoid[3]. Subsequently, Chiao et al. considered the manifestations of this phase factor for a photon in a state of adiabatically invariant helicity, and an effective optical activity for a helical optical fiber was predicted[4]. In 1987, Aharonov and Anandan noted that the appearance of the geometric phase did not necessarily go through an adiabatic process, and the geometric phase factor can be defined for any cyclic evolution of a quantum system[5]. Another important manifestation of the geometric phase in solids is known as the Zak phase[6], which underlies the existence of protected edge states.


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    Yinghui Guo, Mingbo Pu, Fei Zhang, Mingfeng Xu, Xiong Li, Xiaoliang Ma, Xiangang Luo. Classical and generalized geometric phase in electromagnetic metasurfaces[J]. Photonics Insights, 2022, 1(1): R03

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    Paper Information

    Category: Reviews

    Received: Apr. 26, 2022

    Accepted: Jul. 4, 2022

    Published Online: Aug. 3, 2022

    The Author Email: Pu Mingbo (, Luo Xiangang (



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