Study On Mode Scattering In Non-Hermitian Optical System Under Temporal And Spatial Modulations

Non-Hermitian optical system is an optical system with open boundary or material with gain or loss,and its Hamiltonian can be represented by a non-Hermitian operator.The degeneracy point of Hamiltonian in Hermitian system is called Dirac points,where the eigenvalues degenerate but the eigenvectors do not.In non-Hermitian system,the degeneracy points of eigenvalues are called exceptional points(EPs),and the eigenvectors are also degenerate.As in reality,there are loss in many materials,such as metal,dielectric medium with impurities,or loss caused by open boundary,such as photonic crystal slab,two-port scattering structure,it is very important to study EPs in non-Hermitian optical system for the development of optical devices.Many unique optical effects can be realized in EPs,such as chiral mode conversion in waveguide.When light is incident from different directions,the scattering properties including transmission and reflection,are different.Due to the existence of EPs,the eigenvalues of non-Hermitian systems are multivalued functions,and there are branches in the corresponding Riemann surfaces.If an EP is encircled along the Riemann surface in the parameter space,the modes will be scattered,and the mode in the initial state will change to another mode in the final state.The change is not affected by the loop path which shares strong robustness.Using this property,we can design and fabricate on-chip waveguide structure to control the mode.It has great significance in the application of non-reciprocal optical devices such as optical isolators.Besides,spatial or temporal modulation on gain and loss in non-Hermitian systems can produce many novel physical effects,such as parity-time symmetry(PT symmetry)systems,which are built from spatial modulation of gain and loss.The wavevector and frequency of the photon can be changed by spatial and temporal modulation of the refractive index.In previous studies,people pay more attention to the modulation of the real part of refractive index,such as various spatial periodic or quasi-periodic structures.In recent years,it has been found that the imaginary modulation also has positive significance for manipulating photons.In optical waveguide,when the real part of refractive index is modulated as an even function,and the imaginary part is modulated as an odd function,the system satisfies PT symmetry,EPs appear at the threshold of PT symmetry breaking.In EPs,light propagation is usually asymmetric.In addition,the intensity of the output mode or the reflectance and transmittance of the incident light can be controlled by changing the modulation phase.The specific research contents of this work are as follows:Firstly,we construct a non-Hermitian system using the composite structure of graphene and metal grating.The formation mechanism of EPs is revealed and its application in the field of high sensitivity sensor is explored.In the middle infrared band,the scattering system composed of metal and graphene is a non-Hermitian system.EPs are formed when the eigenvalues and eigenvectors of the scattering matrix degenerate.Whether the eigenvalues and eigenvectors degenerate depends on whether the reflectance of incident light at one port of the structure is zero.With the help of Fano resonance,two points with zero reflectance,namely two EPs,can be generated in the reflectance spectrum by adjusting the chemical potential of graphene.In the vicinity of EPs,as the incident wavelength or chemical potential of graphene is slightly changed,light reflectance and transmittance will change dramatically,which benifits to the development of highly sensitive sensors.In addition,in the position of EPs,unidirectional invisibility can also be realized.Light incident from one port will not be reflected,while light incident from the other port will be reflected.We have also explored the topological properties of multiple EPs in the system.The results provide a theoretical basis for the development of novel photoelectric switches,modulators,absorbers and optical sensors.Secondly,asymmetric mode conversion based on encircling moving EPs is proposed and realized.We use silicon on insulator structure to realize the dynamic encircling of moving EPs.The sub-wavelength grating structure is adopted in the waveguides,which is convenient to control the effective refractive index of modes in the waveguides.The mode is lossless in the uniform SWGs waveguide.In order to realize non-Hermitian waveguide system,a scattering boundary is designed in one waveguide to cause radiation loss.In the parameter space composed of the width of another waveguide and the distance between two waveguides,the position of EPs depends on the radiation loss.By choosing appropriate loss distribution and path of the loop parameters,the dynamic encircling of fixed EPs and moving EPs can be realized.Compared with encircling fixed EPs,encircling moving EPs has more obvious advantages: shorter waveguide length or lower mode loss.Electron beam lithography and plasma etching were used to prepare the experimental samples.The transmittance of the incident odd mode and even mode through the samples at different wavelengths was measured.The experimental results are in good agreement with FDTD simulation.Modes conversion is asymmetric,and the conversion efficiency is as high as 90%.Thirdly,the scattering properties of modes in temporally or spatially modulated waveguide are studied.As the real and imaginary parts of the refractive index of waveguide are modulated temporally or spatially,modes scattering,including modes conversion and transmission,is asymmetric when they are incident from different directions.As the spatial modulation wavevector or temporal modulation frequency matches the wavevector or frequency difference of the two modes in the waveguide,mutual coupling will occur between the modes.If only the real part of the refractive index is modulated,the total energy of the modes is conserved.The imaginary part modulation will cause the gain or attenuation of energy.When the real part and the imaginary part of the refractive index are both modulated,the intensity of the transmitted mode changes with modulation phase difference between them.By using temporally complex modulation,non-reciprocal mode conversion can be realized in single modulation region,while real modulation requires more independent modulation regions.Finally,the laser-coherent perfect absorption singularity,unidirectional and bidirectional reflectionless EPs are realized by using spatially complex modulation waveguides.When the modulation wavevector is twice the incident wavevector,waveguide modes with the same wavevector and opposite direction are generated.In single modulation waveguide,the eigenvalues and eigenvectors of the scattering matrix are degenerated by changing the modulation phase difference between the real and imaginary modulation.EPs with unidirectional reflectionless property are realized.In addition,we introduce imaginary modulation to two segmental waveguides.By changing the modulation phase and length,there are laser-coherent perfect absorption singularity and bidirectional reflectionless EPs in the scattering matrix.In the laser-coherent perfect absorption singularity,the reflectance and transmittance of the incident light at both ends of the waveguide are infinite.In EPs,the reflectance and transmittance are zero and unitary,respectively.