The spatial (Δ_GH) and the angular (Θ_GH) Goos-Hänchen (GH) shifts for an Airy beam impinging upon a weakly absorbing medium coated with the monolayer graphene are theoretically investigated. The influence of the GH shift on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is discussed. A significant magnification of Δ_GH, which reaches its maximum of about three orders of wavelengths, is predicted. Our findings may provide a feasible tool to obtain a huge Δ_GH in experiments.

A pair of vortices, one of the multiple vortices, exhibits more adjustable parameters and attractive characteristics compared with a single vortex. By introducing a vortex pair on the Gaussian beam, we not only realize both longitudinal and transverse asymmetrical spin splittings, but also achieve the symmetrical ones via the purely optical strategy. Namely, the symmetries of the spin splittings can be controlled flexibly by the tunable vortices, offering another degree of freedom for the photonic spin Hall effect. Based on the geometric phase theory, physical insights into the symmetry-controllable spin Hall shifts involving the initial phase from the incident vortex beam are provided. These findings reveal the influence of vortices on the symmetry of the photonic spin Hall effect and provide further potential methods for developing spin-based nanophotonic applications.

The Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts for the reflection of the beam impinging upon a plane interface separating two temporally dispersive attenuative materials (TDAMs) are studied theoretically and numerically. It is revealed that at the critical angle θ _c , the GH shift arrives at a positive maximal value, while the IF shift reaches zero. Meanwhile, at the Brewster angle θ _B , a peak GH shift, which can be a negative or positive value, appears only at the TM(p)-polarization state. Apart from θ _c and θ _B , θ _m , a special and interesting incident angle related to n 1 ″ and n 2 ″ of the TDAMs is found, at which a negative and the following positive peak GH shifts and a knee point of the IF shift occurs. This is the first discovery to the best of our knowledge. To experimentally investigate these beam shifts in TDAMs in the near future, an experimental set-up developed by several previous ones is reported. Lastly, we present a scheme for measuring the complex refractive index of the weakly lossy TDAM by detecting the GH shift. These results will be applied to the complex refractive index sensor of the TDAM.

We theoretically study the Goos-Hänchen (GH) shifts of Gaussian beams reflected in parity-time (PT) symmetric multilayered structure coating graphene structures. And there are the exceptional points (EPs) in this structure, whose position can be adjusted by the real part of the dielectric constant and the incident angle. Moreover, we find that the value and direction of the GH shifts change significantly under different EPs, so we could control the GH shifts by the position of the EPs. When the dielectric constant is fixed, the GH shifts can also be adjusted by the Fermi energy of graphene and the period number of the PT-symmetric structure. With the increase of the period number of the PT system, the system will produce the Bragg resonance, which refers to the phenomenon of total reflection caused by the interaction between the wave and the periodic structure with a specific frequency. And at the Bragg resonance, the special GH shifts independent of the incident direction can be obtained with large reflectivity. In addition, the incident direction of the beam can also affect the GH shifts in this asymmetric structure. Our results may find great applications in highly sensitive sensors, optoelectronic switches, and all-optical devices.