Year: 2023
Author: François Fillion-Gourdeau, Emmanuel Lorin, Steve Maclean
Communications in Computational Physics, Vol. 34 (2023), Iss. 1 : pp. 235–260
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0011
Communications in Computational Physics, Vol. 34 (2023), Iss. 1 : pp. 235–260
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Graphene isothermal coordinates Beltrami equation gravitational lens waveguide finite volume method genetic algorithm Dirac equation.