Enhancement Of Goos–H(?)nchen Shift In Graphene Structure

Goos–H(?)nchen(GH)shift is a transverse shift of the reflected light beam occurring from the position predicted by geometrical optics when a beam of light is totally reflected at the interface between two media.Because of their potential applications in the fields of biomedicine,chemical sensors,dectors and optical measurements,many theoretical and experimental researchers have focused on the investigations of the GH shifts in these years.Since its discovery in 2004,monolayer graphene,a single layer of carbon atoms,has attracted extensive attention in many fields,such as physics,electronics and chemistry due to its special properties.It has been confirmed that monolayer graphene has the linear dispersion relation and its carriers behaviors are governed by the massless Dirac equation.With the advent of graphene family,the investigations of GH shift have extended to these kinds of materials.In this work,we investigate the GH shifts of several hybrid structures with monolayer graphene by the combination of the rigorous coupled-wave analysis and stationary phase method.The main research works of this paper are listed as follows:First,we investigate the GH shift of monolayer graphene supported by multilayer photonic crystal grating(MPCG)structure by the combination of the rigorous coupled-wave analysis and stationary phase method.It is found that the GH shift can be dramatically enhanced by the MPCG structure,whose value can be up to two thousand times of incident wavelength at the specific frequency.We show that such the enhanced GH shift of monolayer graphene based MPCG structure may be ascribed to the excitation of the guide mode resonances of the multilayer photonic crystal grating structure.Moreover,the GH shift of the hybrid structure has a strong dependence on the geometrical parameters of the MPCG structure.The enhanced and controlled GH shift obtained in the designed nanostructures holds their great potential for tunable optoelectronic devices.Secondly,we discuss the feasibility of enhancing and adjusting the GH shift in a hybrid structure with single-layer graphene strip array and dielectric grating.It is observed that the positive or negative enhanced GH shift can be achieved at the specific incident wavelength,which is more than one hundred times of incident wavelength.The enhancement of the GH shift obtained here can be attributed to the excitation of guided mode resonance in dielectric grating and surface plasma resonance in single-layer graphene array.In addition,the chemical potential of the single-layer graphene and the geometric parameters of grating structure can be used to control the profiles of GH shifts,where the latter even can change the sign of the GH shifts from positive to negative.Our results help to promote the two-dimensional materials in the application of photoelectric device and development.Finally,we study the GH shift of monolayer graphene/SiO₂ photonic crystal structure.It can be observed that the GH shift can also be enhanced at a given operating frequency,whose magnitude is more than 300 times of the incident wavelength..This enhanced GH shift is due to the fact that the monolayer graphene/SiO₂ photonic crystal structure significantly promotes the interaction between light and many layers of monolayer graphene.In addition,the tunability of the optical conductivity of monolayer graphene creates the conditions for the tunable GH shift.We also found that the value of the GH shift can flexibly adjusted by controlling the optical conductivity of monolayer graphene and the thickness of the dielectric layer.Our results suggest the potential applications of this multilayered structure in biosensor optical switches and other optoelectronic detection fields.