The Research Of Beam Shifts In Two-dimensional Atomic Crystals

Graphene,just one layer or a few layers of carbon atoms,is a unique two dimensional(2D)atomic crystal.With the outstanding electronic and optical properties,it has many potential applications in future high-tech field,especially in photonics and optoelectronics devices.Graphene has become one of the most typical and representative new nanomaterials and attracted wide attention since it was reported in 2004.A hallmark of graphene is the exact zero overlapping between the valence and the conduction bands.The valence and conduction bands of graphene intersect at Fermi level,forming the so-called Dirac cone structure.Graphene is a semiconductor material with zero energy gal and has the smallest resistivity that has been found at present.Its minimal conductivity approaching the quantum limit provides a possibility of observing the anomalous quantum Hall effect.Meanwhile,the optical reflectivity,transmissivity,and absorption are determined by the fine-structure constants.The universally low absorption makes it almost transparent in a spectral range from near infrared to visible.When a spatially confined light beam reflects or refracts at the interface between two different materials,the photons with different polarization state will move to the opposite directions perpendicular to the refractive index gradient,which causes the incident beam splits into two beam with different polarization state.The beamshifts are known as the shifts of Goos-H?nchen and photonic spin Hall effect according to the directions parallel and perpendicular to the plane of incidence,respectively.As the different eigenstates between the Goos-H?nchen shift and photonic spin Hall effect,the research of beamshifts on the surface of graphene can explore the influence of polarization state and provide insights into the fundamental properties of spin-orbit interaction of light,especially in strong spin-orbit interaction.Meanwhile,the Goos-H?nchen shift and photonic spin Hall effect are extremely sensitive to the optical constants of graphene,especially near Brewster angle.It provides a simple and effective alternative for characterizing the physical and optical properties of graphene.In this paper,we first study the intrinsic physical mechanism of beamshifts,and then characterize the optical constants and physical thickness of graphene by beamshifts.Finally,we systematically studied the beamshifts of graphene in different models.The related work is as follows:1.Observation of tiny polarization rotation rate in total internal reflection via weak measurements.When a polarized light beam reflects at the interface of two different materials,the polarization state of light will experience a tiny rotation,which leads to the appearance of geometric phase and induces the photonic spin Hall effect.In partial reflection,the polarization rotation only appears in momentum space.The polarization rotation in momentum space induces a spin-dependent splitting in position space.While in total internal reflection,the polarization rotation in momentum space induces a spin-dependent splitting in position space(spatial shift),meanwhile,the polarization rotation in position space leads to a spin-dependent splitting in momentum space(angular shift).As the polarization rotation rate is very small,we use the so-called weak measurement technology to observe it.In the condition of partial reflection,we just need to amplify the polarization rotation in momentum space by weak value amplification.Unlike in partial reflection,we need to amplify respectively the polarization rotation in momentum and position spaces to observe it.By studying tiny polarization rotation rate in total internal reflection,we can better understand the photonic spin Hall effect and the spin-orbit interaction of light.As this divergence effect is closely related to Brewster angle,we can use it to characterize the optical constants of graphene.2.Precise identification of graphene layers at the air-prism interface.We can see that the symmetrically double-peak structure appears when a H polarized light beam reflects at the interface of two different materials.The symmetric double-peak structure is due to the beam divergence when the incident angle of the central wave vector meets Brewster’s law.As this divergence effect is closely related to pseudo-Brewster angle,we can use it to characterize the optical constants of graphene.Moreover,we find that the pseudo-Brewster angle is approximately linearly increased as the graphene layers increased.Therefore,the pseudo Brewster angle,like the identity number of graphene,distinguishes it from different layers.Due to the influence of the cross-polarization effect,the tiny V polarized light will appear and interfere with the double-peak structure when a H polarized light beam reflects at the interface of two different materials.By eliminating the cross-polarization component via the Glan laser polarizer,we can see clearly that the double-peak structure appears at the pseudo-Brewster angle and rapidly disappears near the pseudo-Brewster angle.It is worth noting that the double-peak structure appears at different angles of incidence in different layers of graphene.our scheme offer a simple and effective method to identify the layers of graphene and is fundamentally significant for theresearch of graphene in the future.3.A comparative study of beam shifts on zero-thickness model and slab model of graphene.In general,we study the optical properties of graphene by modeling it as a homogeneous slab with an effective thickness,while this model fails to predict the absorption and the phase of the reflected light.Therefore,the zero-thickness model of graphene has been proposed by fixing both the surface susceptibility and the surface conductivity to simulate the most experiments on the linear optical properties.By studying the beamshifts in two different models of graphene,we explored the role of surface susceptibility and surface conductivity.We find that the surface susceptibility and surface conductivity together determine the spatial shift of the Goos-H?nchen shift.The direction of the spatial shift is related to the surface susceptibility while the absolute value is attributed to the surface conductivity.Unlike the spatial shift,the angular shift is only related to the surface susceptibility.On the contrary,the spatial shift of photonic spin Hall effect is only related to the surface susceptibility while the angular shift is related to both the surface susceptibility and surface conductivity.Moreover,We find that the essential distinction between the two models of graphene is that the slab model does not well reflect the role of surface susceptibility.However,it does not mean that the two models will be well aggrement without considering the surface susceptibility.