Abstract

We introduce theoretical methods for describing the optical response of two-dimensional (2D) materials patterned at the nanoscale into both arrays of ribbons along a planar surface and spherical particles. Fourier-Floquet decompositions of the electromagnetic fields are used in order to obtain the reflectance, transmittance and absorbance of the nanoribbon array. The spherical particles consist of a vacuum or dielectric core, coated by single 2D material layers. A Mie theory, with boundary conditions modified to accommodate a 2D material at the interface, is applied to theoretically examine these spherical particles. As examples of 2D materials, we consider the excitonic response of hexagonal boron nitride in the ultraviolet, and of the transition-metal dichalcogenide WS₂ in the visible. The most important steps and equations for implementing the various methods are provided as a means to an easy introduction to the theory of patterned 2D materials. This renders the article a toolset for investigating the patterning of any 2D material with the intention to tune their optical response and/or introduce hybridization schemes with their excitons. The methods are not restricted to exciton polaritons in 2D semiconductors, but can be applied, by simple replacement of the optical conductivity, to 2D materials exhibiting any polaritonic response.

Abstract

We introduce theoretical methods for describing the optical response of two-dimensional (2D) materials patterned at the nanoscale into both arrays of ribbons along a planar surface and spherical particles. Fourier-Floquet decompositions of the electromagnetic fields are used in order to obtain the reflectance, transmittance and absorbance of the nanoribbon array. The spherical particles consist of a vacuum or dielectric core, coated by single 2D material layers. A Mie theory, with boundary conditions modified to accommodate a 2D material at the interface, is applied to theoretically examine these spherical particles. As examples of 2D materials, we consider the excitonic response of hexagonal boron nitride in the ultraviolet, and of the transition-metal dichalcogenide WS₂ in the visible. The most important steps and equations for implementing the various methods are provided as a means to an easy introduction to the theory of patterned 2D materials. This renders the article a toolset for investigating the patterning of any 2D material with the intention to tune their optical response and/or introduce hybridization schemes with their excitons. The methods are not restricted to exciton polaritons in 2D semiconductors, but can be applied, by simple replacement of the optical conductivity, to 2D materials exhibiting any polaritonic response.

Abstract

We introduce theoretical methods for describing the optical response of two-dimensional (2D) materials patterned at the nanoscale into both arrays of ribbons along a planar surface and spherical particles. Fourier-Floquet decompositions of the electromagnetic fields are used in order to obtain the reflectance, transmittance and absorbance of the nanoribbon array. The spherical particles consist of a vacuum or dielectric core, coated by single 2D material layers. A Mie theory, with boundary conditions modified to accommodate a 2D material at the interface, is applied to theoretically examine these spherical particles. As examples of 2D materials, we consider the excitonic response of hexagonal boron nitride in the ultraviolet, and of the transition-metal dichalcogenide WS₂ in the visible. The most important steps and equations for implementing the various methods are provided as a means to an easy introduction to the theory of patterned 2D materials. This renders the article a toolset for investigating the patterning of any 2D material with the intention to tune their optical response and/or introduce hybridization schemes with their excitons. The methods are not restricted to exciton polaritons in 2D semiconductors, but can be applied, by simple replacement of the optical conductivity, to 2D materials exhibiting any polaritonic response.

Abstract

We introduce theoretical methods for describing the optical response of two-dimensional (2D) materials patterned at the nanoscale into both arrays of ribbons along a planar surface and spherical particles. Fourier-Floquet decompositions of the electromagnetic fields are used in order to obtain the reflectance, transmittance and absorbance of the nanoribbon array. The spherical particles consist of a vacuum or dielectric core, coated by single 2D material layers. A Mie theory, with boundary conditions modified to accommodate a 2D material at the interface, is applied to theoretically examine these spherical particles. As examples of 2D materials, we consider the excitonic response of hexagonal boron nitride in the ultraviolet, and of the transition-metal dichalcogenide WS₂ in the visible. The most important steps and equations for implementing the various methods are provided as a means to an easy introduction to the theory of patterned 2D materials. This renders the article a toolset for investigating the patterning of any 2D material with the intention to tune their optical response and/or introduce hybridization schemes with their excitons. The methods are not restricted to exciton polaritons in 2D semiconductors, but can be applied, by simple replacement of the optical conductivity, to 2D materials exhibiting any polaritonic response.