Analytical Calculation of Dispersion Diagram of 1D Graphene-Based Periodic Structures

Document Type : Original Article

Abstract

In this paper, a novel analytical method is proposed to calculate the dispersion diagram of 1D graphene-based
periodic  structures.  The  structure  under  investigation  is  an  array  of  graphene  ribbons  with  different  chemical
potentials. In this method, the total transfer matrix of a unit cell of the structure is calculated using the reflection
and transmission coefficients of a plasmonic wave being incident onto a discontinuity in surface conductivity of
graphene. Then, the modes of the structure are obtained by calculating the eigenvalues of this matrix applying
the Floquet theorem. Furthermore, because the modes of the multilayer structure are poles of the reflection and
transmission  coefficients,  it  is  possible  to  identify  them  by  monitoring  the  phase  variation  of  reflection  and
transmission coefficients.  Therefore,  to  show  the  validity  and  accuracy  of  the  proposed  method,  the  dispersion
diagram  of  the  structure  is  calculated  using  the  reflection  pole  method  and  the  results  are  compared  with  the
approximate analytical method. This comparison shows that the proposed method has good accuracy while it is
simple and fast.

Keywords


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