Maximum reflectance and transmittance of films coated with gapped graphene in the context of Dirac model

TL;DR

This paper derives analytical formulas for the maximum and minimum reflectance of optical films coated with gapped graphene, considering multiple reflections, and demonstrates significant effects in the infrared spectrum with potential applications.

Contribution

It provides new analytical expressions for reflectance limits of graphene-coated films using the Dirac model, including film thicknesses and numerical analysis in infrared regions.

Findings

Graphene coating increases maximum reflectance by up to 65% in the far-infrared.

Maximum transmittance can exceed 90% with appropriate film thickness.

The formalism applies to films with frequency-dependent refractive index and accounts for multiple reflections.

Abstract

The analytic expressions for the maximum and minimum reflectance of optical films coated with gapped graphene are derived in the application region of the Dirac model with account of multiple reflections. The respective film thicknesses are also found. In so doing the film material is described by the frequency-dependent index of refraction and graphene by the polarization tensor defined along the real frequency axis. The developed formalism is illustrated by an example of the graphene-coated film made of amorphous silica. Numerical computations of the maximum and minimum reflectances and respective film thicknesses are performed at room temperature in two frequency regions belonging to the near-infrared and far-infrared domains. It is shown that in the far-infrared domain the graphene coating makes a profound effect on the values of maximum reflectance and respective film thickness leading to a relative increase of their values by up to 65% and 50%, respectively. The maximum transmittance of a graphene-coated film of appropriately chosen thickness is shown to exceed 90%. Possible applications of the obtained results are discussed.