This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in cur...This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime,a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile.The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm.Then,the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates.These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method.The graphene surface deformation is finally optimized,also using a genetic algorithm,to reproduce the desired index of refraction.Some analytical results and numerical experiments are performed to illustrate the methodology.展开更多
Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens(LCL),which has dual functions of diffusion cell and image formation.The diffusion images on the focal plane of ...Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens(LCL),which has dual functions of diffusion cell and image formation.The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations,the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution.Guided by the calculation conditions,the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper.The spatial and temporal concentration profile Ce(z,t)of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL;Then,the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C)=D0×(1+α1C+α2C2+α3C3+…).The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z,t).The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z,t)with Ce(z,t).Finally,the obtained polynomial D(C)is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL.Based on the ray propagation law in inhomogeneous media and the calculated n(z,t),the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C).The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.展开更多
文摘This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime,a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile.The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm.Then,the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates.These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method.The graphene surface deformation is finally optimized,also using a genetic algorithm,to reproduce the desired index of refraction.Some analytical results and numerical experiments are performed to illustrate the methodology.
基金the National Natural Science Foundation of China(Grant No.11804296)the Joint Key Project of Yunnan Province,China(Grant Nos.2018FY001-020 and 2018ZI002)the Fund from the Educational Department of Yunnan Province,China(Grant No.2016CYH05).
文摘Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens(LCL),which has dual functions of diffusion cell and image formation.The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations,the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution.Guided by the calculation conditions,the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper.The spatial and temporal concentration profile Ce(z,t)of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL;Then,the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C)=D0×(1+α1C+α2C2+α3C3+…).The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z,t).The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z,t)with Ce(z,t).Finally,the obtained polynomial D(C)is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL.Based on the ray propagation law in inhomogeneous media and the calculated n(z,t),the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C).The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.
