The Enhancement And Modulation Of Photonic Spin Hall Effect In Graphene-based Structures

When a linear polarization beam propagates through inhomogeneous media,circularly polarized light（left-and right-handed circular polarizations）of opposite spin directions is separated in the lateral direction perpendicular to the incident surface.This interesting phenomenon is called the photonic spin Hall effect（PSHE）.It can be regarded as a direct optical analogy of the spin Hall effect in an electronic system where the refractive index gradient plays the role of electric potential and the spin electrons are replaced by spin photons.The PSHE has been demonstrated to originate from an effective spin-orbit interaction,governed by the conservation law of total angular momentum.Due to the intimate relationship between the spin-dependent splitting and refractive index gradient,the PSHE is considered as a potential tool for the precision measurement,and it plays a significant role in determining the small changes of structural parameters for material.In recent years,the PSHE has been applied in the design of optical sensors,which may offer the new opportunity for improving the sensitivity of optical sensors.However,photonic SHE is generally a very tiny phenomenon due to the weak spin-orbit coupling,and the corresponding spin-dependent splitting is in the nanometer scale,which greatly hinders its application.Hence,controlling and enhancing the PSHE remains an open challenge,which is highly beneficial to facilitate its application in modern photonics.Until now,several methods have been put forward to enhance the photonic SHE,based on the Brewster angle,surface plasmon resonance,optical tunneling effect and so on.Recently,two-dimensional atomic crystals hold great promise in the rapid development of PSHE,due to their extraordinary electronic and photonic properties.Graphene,a one-atom-thick of carbon atoms arranged in a hexagonal honeycomb lattice,has attracted enormous interest.Previous reports have demonstrated that the PSHE can be effectively enhanced and tuned by varying the Fermi energy of graphene.Based on the above knowledge,we make a certain exploration on the enhancement and manipulation of the PSHE for reflected and transmitted light,and extend it to the practical application of refractive index sensors.Some creative work and the corresponding results are summarized as following:（1）By taking advantage of tunable optical properties of graphene via the external optical pumping,a novel and flexible method（i.e.optical pumping）to manipulate the PSHE of graphene-based structure is proposed.For the four-layered structure of prism-graphene-air-substrate,the spin shift for H polarized incident beam can reach its upper limitation（i.e.half of the beam waist）under the optimal pumping power of 0.4 W.Such a giant spin shift is associated with the zero value of the real part of graphene conductivity and its large ratio of||/||.It should be noted that the ability of controlling the PSHE is not limited to the above structure with an air gap.The air gap can be replaced by other dielectric layers,while the optimal pumping power and incident angle should be accordingly changed.Then,on the basis of this research,a refractive index sensor based on the PSHE via optical pumping is proposed and applied to the detection of cancer cells.The results show that our proposed refractive index sensor based on the PSHE can not only discriminate the normal cells and cancer cells（i.e.gastric,liver and epidermal cells）,but also distinguish the cancer cells of different concentrations.The sensitivity of PSHE-based sensor is very excellent,which is about four orders of magnitude greater than that based on the resonance optical tunneling effect.Finally,the sensitivity of sensors can be flexibly modulated by the external optimal pumping.There are two critical values of pumping power,and the excellent sensing performance can be obtained near these two critical pumping powers.Thus,the sensing performance is very sensitive to the power of optical pumping,and the pumping power should be optimized in order to achieve the superior sensitivity.We believe that the refractive index sensor based on the PSHE has broad application prospects in biomedical,drug screening and early cancer diagnoses.（2）We propose the one-dimensional graphene-silica aerogel photonic crystal,and the PSHE for transmitted light in the terahertz region is investigated.It is found that the PSHE can be significantly enhanced by introducing the graphene layer into adjacent silica aerogel layers.From the perspective of Fresnel coefficients,the phase of transmission coefficients plays a significant role in determining the tunable PSHE of transmitted light.The giant spin shift is concentrated in two different regions（the low frequency and high frequency regions）.The significant feature of low frequency region is the strong spin shift over broad angle and frequency ranges,which is affected by the period number and Fermi energy of graphene.For the high frequency region,the considerable spin shift can be observed by adopting a large value of period number.Therefore,through a suitable design of the period number and Fermi energy of graphene layer,the PSHE behavior of transmitted light in this graphene-based photonic crystal could be effectively tuned in both low and high frequency regions.（3）The enhanced PSHE of reflected light in a four-layered structure of prism-graphene-air-substrate over broadband regions is explored.We discuss the dependency of the spin shift with respect to the indicant angle,the thickness of air gap,and also the Fermi energy of graphene.By optimizing the thickness of air gap and the Fermi energy of graphene,the considerable spin shift in broadband regions covering the terahertz,infrared and visible regions can be realized around Brewster angle.The only difference is that the Brewster angle of infrared and visible regions is almost near 33.5°,while that in the terahertz region increases dramatically with the decrease of incident frequency.However,for the different frequency ranges of incident light,the relation between the spin shift and Fermi energy of graphene is different,which is attributed to the varying sensitivity of graphene conductivity to the Fermi energy of graphene in different frequencies of incident beam.These findings may lead to some potential application for developing photonic devices in broadband regions.（4）The coherent perfect absorption（CPA）-laser mode and the PSHE of transmitted light are investigated by introducing the graphene into parity-time（PT）symmetric system with balanced loss and gain.We find that the CPA-laser mode is also present with the insertion of graphene.The value of spin shift undergoes the transition from positive to negative one at the point of CPA-laser mode,which corresponds to the sudden change of the phase of Fresnel transmission coefficient.The giant spin shift can be achieved around this transition point.Then we study the effect of Fermi energy of graphene on the PSHE behavior.Results point out that by increasing the Fermi energy of graphene,the CPA-laser point moves to the thinner dielectric layer（i.e.loss and gain layers）.In other words,the thickness of device will be reduced when the Fermi energy of graphene adopts a large value.Therefore,these finds may provide a new method for the miniaturization of spin-based photonic devices in the future.