Goos-H?nchen Shift And Optical Bistability In Composite Graphene-dielectrics Non-Hermitian Systems

Goos-H?nchen(GH)shift and optical bistability are two important topics in the field of optical research,which have positive significance for the design and preparation of optical devices such as optical switches,optical storage and highly sensitive sensors.GH shift is the lateral shift and angular deviation of the reflected beam relative to the position predicted by geometrical optics.Optical bistability is a nonlinear phenomenon in which the transmission characteristics of an optical system depend on the input light intensity.Of which an input intensity corresponds to two stable resonant outputs.How to design and find appropriate structures or materials to increase GH shift and reduce the threshold of optical bistability are the key problems to be considered at present.With reference to the lattice structure of solid,people put forward the concept of photonic crystal,which provides a new approach to solve the above problems.At the bandgap edge of the photonic crystal,there is large GH shift,and the optical field localization of the defect photonic crystal can effectively reduce the threshold of bistability.On the other hand,graphene,as a new two-dimensional material,has unique electrical,mechanical and optical properties.In terahertz band,graphene not only has fast speed optical response and tunable conductivity,but also has significant nonlinear effect,which provides a new opportunity for the study of GH shift and bistability as well.In the traditional photonic crystal design,people only consider the real part of refractive index,but ignore the influence of the imaginary part.Based on the design concept of non-Hermitian optics and considering the real and imaginary parts of refractive index simultaneously,many peculiar optical phenomena have been found,which provides a new way for regulating photon transmission.Therefore,we synthesize graphene and multilayer dielectrics to form non-Hermitian photon system,and study the unique characteristics of GH shift and bistability.Researches show that,in the vicinity of exceptional point(EP),the phase of the reflection coefficient is singular,resulting in giant GH shift.When the non-Hermitian system meets the parity-time(PT)symmetry,the localization and nonlinear effects of the optical field can be significantly enhanced by varying the gain-loss factor of system,which effectively reduces the threshold of the optical bistability.In addition,the optical properties of GH shift and bistability can be flexibly tuned by the chemical potential of graphene.The main work is included as follows:Firstly,the GH shift in graphene-dielectric composite non-Hermitian system is studied.The dielectrics contain with gain and loss.The graphene is placed at the center of the composite structure to enhance the coupling between graphene and light field.When the incident light impinges upon the system from two opposite directions,the reflectance is not the same.Two EPs can be obtained in the parameter space,which correspond to the zero points of the reflectivity when the incident light is in different directions.The reflection coefficient phase experiences ±? dislocation at the EPs.Meamwhile,the eigenvectors of scatting matrix degenerate at the EPs.The imaginary part curves of two eigenvalues demonstrate crossing around the EPs,while the real part curves appear anti-crossing.The GH shift of reflected beam can be positive or negative near the EPs.The GH shift reaches to the maximum as the parameters are infinitely close to the EPs,so EPs are the singular points of GH shift.In addition,the EPs and GH shift can be controlled by adjusting the chemical potential of graphene.Secondly,we investigate the GH shift in PT-symmetric and nearly PT-symmetric non-Hermitian systems.The refractive indices of dielectrics are modulated to satisfy PT-symmetry in spatial distribution.In the parameter space composed of the incident angle and gain-loss factor,the EPs split and coherent-perfect-absorption-laser point(CPA-LP)arises.At the EPs and CPA-LP,the energy of the light field is mainly distributed in the center of the structure.Near the EPs,the GH shift of the reflected beam is about dozens of incident wavelengths.The dielectric refractive index of the middle layer is modulated to make the structure approach to PT symmetry,and an isolated EP appears in the parameter space.Near the isolated EP and CPA-LP,the GH shift tends to be infinite,which demonstrates that the isolated EP and CPA-LP are the singularities of GH shift.Thirdly,graphene array and photonic crystal(PCs)microcavity are combined to form a composite structure to achieve tunable optical bistability with low-thresholds.Dielectrics arrange alternately to form PCs with a defect layer,and the graphene is embedded in the interface of different dielectrics and the center of the defect layer.The structure can be regarded as a Fabry-Perot cavity composed of two Bragg-gratings,in which Bragg gratings are the reflector of the resonant cavity and the defect layer is the cavity body.The optical field localization of the defect mode can enhance the nonlinear effect of graphene,so as to realize the optical bistability with low thresholds.In addition,the thresholds and thresholds interval of optical bistability can be tuned by the chemical potential of graphene and the Bragg periodic number.The device can be applied to low power dissipation all-optical switches and optical memories.Finally,to further reduce the threshold of optical bistability,graphene is introduced into dielectrics structure to construct PT symmetric non-Hermitian optical system.The real and imaginary parts of refractive index are modulated simultaneously to satisfy PT-symmetry.The optical field of the defect mode is localized at the center of the structure,while the nonlinear effect of graphene,which is at the maximum of the optical field,can be greatly enhanced,so as to realize the optical bistability with low thresholds.When the gain-loss factor of dielectric increases,the optical field becomes more localized.At the same time,EPs began to split,resulting in a further decrease in the bistable threshold and a further increase in the interval of the the upper and lower threshold.In addition,the phase transition between bistability and non-bistability can be realized by changing the incident wavelength and the chemical potential of graphene.