Abstract The spin Hall effect of light (SHEL) is the microscopic spin-dependent splitting of light at an optical interface. Whereas the spin Hall shift under linearly polarized light is well-formulated, studies on the SHEL under elliptically or circularly polarized light have primarily relied on numerical computation. In this work, an explicit analytic formula for the spin Hall shift is derived under arbitrarily polarized incidence. Furthermore, from this explicit expression, we demonstrate that the spin Hall shift can be enhanced at any incident angle by using polarization degree of freedom and is independent of the Fresnel coefficients of an interface under circularly polarized light. The analytic formula will help us understand the SHEL under general polarization intuitively and realize unprecedented modulation of the SHEL.

Generalized analytic formula for spin Hall effect of light: shift enhancement and interface independence

Abstract Discovery of low-dimensional materials has been of great interest in physics and material science. Optical permittivity is an optical fingerprint of material electronic structures, and thus it is an important parameter in the study of the properties of materials. Spectroscopic ellipsometry provides a fast, robust, and noninvasive method for obtaining the optical permittivity spectra of newly discovered materials. Atomically thin low-dimensional materials have an extremely short vertical optical path length inside them, making the spectroscopic ellipsometry of low-dimensional materials unique, compared to traditional ellipsometry. Here, we introduce the fundamentals of spectroscopic ellipsometry for two-dimensional (2D) materials and review recent progress. We also discuss technical challenges and future directions in spectroscopic ellipsometry for low-dimensional materials.

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Spectroscopic ellipsometry for low-dimensional materials and heterostructures

Phase change materials, such as vanadium dioxide (VO2) and Titanium dioxide (Ti2O3) have received extensive attention because of the dramatic changes in their intrinsic properties during phase transitions. However, due to the rapid transition rate and wide dynamics, monitoring of processes is challenging. Previous detection methods are lack of speed and simplicity and require multiple interventions, which largely introduce human factors influencing the results and make it difficult to guarantee the accuracy and visualization. In this paper, the photonic spin Hall effect is used for real-time detection and highly sensitive analysis of the phase transition process of VO2 films. By incorporating with quantum weak measurement, the photonic spin-Hall shift acts as the pointer, and the phase transition process of VO2 is characterized effectively. The high measurement resolution with 63 S/(m μm) is achieved due to weak-value amplification. In our scheme, it does not involve any mechanical adjustment of optical components, thus enabling real-time, visual, non-contact detection of dynamic phase transition processes.

Highly sensitive real-time detection of phase change process based on photonic spin Hall effect

A light beam reflected and refracted at a sharp interface can acquire a momentum-dependent Pancharatnam–Berry (PB) phase, which produces a topological phase transition from one kind of spin–orbit interaction (e.g., spin-controlled vortex generation) to another (e.g., photonic spin-Hall effect). However, this process is extremely inefficient and difficult to observe directly in experiments, which also hinders its applications. Here, we propose to enhance significantly the topological phase transitions by c-cut uniaxial crystals. We first give a full-wave theory to describe the spin–orbit interactions of a beam passing through a c-cut uniaxial crystal and experimentally observe the topological phase transition process of the transmitted beam when the angle between the beam propagation direction and the optical axis direction changes. It is found that the efficiency of the spin–orbit interactions caused by the momentum-dependent PB phase can be increased as high as 50%, which is much larger than that at isotropic sharp interfaces. Our findings provide an alternative approach for manipulating the spin and orbital angular momenta of light and exhibit potential applications in the future spin–orbit photonic components.

Enhancing the efficiency of the topological phase transitions in spin–orbit photonics

Polarization plays a key role in fundamental science, and manipulating the evolutionary trends of longitudinal polarization states can provide new implements for light–matter interaction. However, existing 3D optical devices can only manipulate the polarization conversion in a single transverse plane. Recently, methods to control polarization by cascading bulky optical systems are miniaturized using metasurfaces. Nevertheless, it is quite challenging to generate focused beams with vectorial properties for metasurfaces carrying inhomogeneous polarization profiles. Here, a single‐layer all‐silicon metasurface operating in the terahertz (THz) band is demonstrated to address all those aforementioned challenges in one go, and pencil‐like beams with inhomogeneous polarization profiles can be imparted along the propagation direction. The introduction of a latitudinal polarization control factor representing the initial phase difference enables near‐even manipulation of the evolutionary trend of the longitudinal polarization state according to the extended focal depth. By manipulating the topological charges within two orthogonal circularly polarized channels to accomplish coherent superposition, a focused vortex beam with vectorial properties can be generated in desired planes. Two functional demonstrations based on this approach are established experimentally, offering promising opportunities for structured light on meta‐optics.

Manipulation of Longitudinally Inhomogeneous Polarization States Empowered by All‐Silicon Metasurfaces

The topology-induced phase transition (TPT) in spin-orbit optics refers to a process of topological transition from one kind of spin-orbit interaction (e.g., spin-controlled vortex generation) to another (e.g., photonic spin-Hall effect). However, it is not clear in the TPT how a light beam evolves from a vortex state with a topological charge of \ifmmode\pm\else\textpm\fi{}2 to nonvortex states with spin-Hall shifts. Here, we examine the orbital angular momentum content (vortex harmonics) of a typical TPT process, i.e., the spin-orbit interactions of a light beam transmitted through an optically thin slab, based on vortex mode decomposition. It is found that the two kinds of spin-orbit interactions and the intermediate states can be described in a unified framework by considering the superposition and competition of three vortex modes with topological charges of 2, 1, and 0 (or \ensuremath{-}2, \ensuremath{-}1, and 0). These findings provide an alternative perspective for understanding the two spin-orbit interactions of light in a unified form and can be extended to the TPT-like processes in other physical systems.

Zan Zhang

Papers

Vortex mode decomposition of the topology-induced phase transitions in spin-orbit optics

Beam shifts in two-dimensional atomic crystals