Wave-Vector-Varying Pancharatnam-Berry Phase Photonic Spin Hall Effect Wenguo Zhu , 1,* Huadan Zheng, 1 Yongchun Zhong, 2 Jianhui Yu, 2,† and Zhe Chen 2 1 Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Jinan University, Guangzhou 510632, China 2 Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China (Received 17 August 2020; revised 29 November 2020; accepted 19 January 2021; published 22 February 2021) The geometric Pancharatnam-Berry (PB) phase not only is of physical interest but also has wide applications ranging from condensed-matter physics to photonics. Space-varying PB phases based on inhomogeneously anisotropic media have previously been used effectively for spin photon manipulation. Here we demonstrate a novel wave-vector-varying PB phase that arises naturally in the transmission and reflection processes in homogeneous media for paraxial beams with small incident angles. The eigenpolarization states of the transmission and reflection processes are determined by the local wave vectors of the incident beam. The small incident angle breaks the rotational symmetry and induces a PB phase that varies linearly with the transverse wave vector, resulting in the photonic spin Hall effect (PSHE). This new PSHE can address the contradiction between spin separation and energy efficiency in the conventional PSHE associated with the Rytov-Vladimirskii-Berry phase, allowing spin photons to be separated completely with a spin separation up to 2.2 times beam waist and a highest energy efficiency of 86%. The spin separation dynamics is visualized by wave coupling equations in a uniaxial crystal, where the centroid positions of the spin photons can be doubled due to the conservation of the angular momentum. Our findings can greatly deepen the understanding in the geometric phase and spin-orbit coupling, paving the way for practical applications of the PSHE. DOI: 10.1103/PhysRevLett.126.083901 The geometric phase, which arises when a classical or quantum system undergoes a cyclic and adiabatic evolution in its parameter space [1], is of primary importance in modern physics [2,3]. Obviously different from its dynamic counterpart, the geometry phase depends on the shape of the path that is taken. In optics, there are mainly two types of geometric phase: Rytov-Vladimirskii-Berry (RVB) [3] and Pancharatnam-Berry (PB) phases [4]. The former is associated with the evolution of the propagation direction of light, whereas the latter with the polarization evolution on the Poincar´ e sphere [1,5]. Spatially varying PB phases based on anisotropic media have been widely investigated, speeding up the development of integrated spin-photonic devices [6–11]. Inhomogeneous liquid crystals and meta- surfaces are frequently employed to design functional PB optical elements with energy efficiencies as high as nearly 100% [9,12–14]. Spin photons can be manipulated flexibly in the momentum space by arranging the optical axes of the anisotropic unit cells. The manipulated spin photons could, thus, be observed at a distance after the PB elements. The RVB phase occurs in nonparaxial light beams as well as paraxial beams in their reflection and transmission processes [15–18]. Because of the RVB phase, a linearly polarized light beam will undergo a transverse spin separa- tion when reflected by or transmitted through a homo- geneous interface, leading to the so-called photonic spin Hall effect (PSHE) [19]. This RVB phase is momentum dependent, and, thus, the spin separation occurs in the real space. The RVB phase is generally small and allows the spin separation of only a few tenths of wavelength, which is very difficult for observation [20]. Nevertheless, a hori- zontally polarized beam reflected near the Brewster angle can undergo a large spin separation [21]. However, the Fresnel reflection coefficient for p wave is near zero around the Brewster angle, and, hence, only a small part of the incident power will be reflected. To obtain a spin separation of 20λ (λ being the wavelength), the reflectivity is about −50 dB for an air-prism interface. Moreover, the larger the spin separation, the lower the reflectivity. This is because the reflectivity (energy efficiency) appears in the denom- inator in the expression for the spin separation [20,22]. Taking full advantage of this fact, large spin separations have been obtained with the assistance of lossy modes [23], surface plasmon resonances [24], and Dirac points [25] in the reflection scheme as well as of metamaterials [26] in the transmission scheme. However, all of these large separa- tions are accompanied with a low energy efficiency [27]. Although the small spin separation can be amplified by weak measurement techniques, they suffer from the same problem of low energy efficiency [17,28]. Besides, the spin separation is accompanied with distortion in the beam intensity profile. It was demonstrated that there are upper limits for the spin separation [27,29,30], which must be smaller than the intensity spot size. For a Gaussian, the PHYSICAL REVIEW LETTERS 126, 083901 (2021) 0031-9007=21=126(8)=083901(6) 083901-1 © 2021 American Physical Society