# Numerical Analysis of the Helmholtz Green's Function for Scalar Wave Propagation Through a Nano-hole on a Plasmonic Layer

## TL;DR

This paper presents a detailed numerical analysis of the Helmholtz Green's function to understand scalar wave propagation through a nano-hole on a plasmonic layer, including a review of the analytic formulation based on the nano-hole radius.

## Contribution

It provides a comprehensive numerical study of the Helmholtz Green's function and compares it with the analytic formulation for nano-holes on plasmonic layers.

## Key findings

- Numerical results illustrating Green's function behavior in various transmission regions.
- Comparison between numerical and analytic formulations.
- Insights into wave propagation characteristics through nano-holes.

## Abstract

A detailed numerical study of the Helmholtz Green's function for the description of scalar wave propagation through a nano-hole on a plasmonic layer is presented here. In conjunction with this, we briefly review the analytic formulation taking the nano-hole radius as the smallest length parameter of the system. Figures exhibiting the numerical results for this Green's function in various ranges of the transmission region are presented.