---
title: "Total and radiative decay rate modifications for a dipole near a semi-infinite metal interface"
date: "`r format(Sys.time(), '%d %B, %Y')`"
author: "baptiste Auguié"
output:
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 2
    fig_width: 7
    fig_height: 4
    fig_caption: true
vignette: >
  %\VignetteIndexEntry{decayrates}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---


```{r demo, message=FALSE, echo=FALSE}
knitr::read_demo("decay_rates", package="planar")
```
A dipole is placed near a semi-infinite air/metal interface with orientation either parallel or perpendicular to the interface.

```{r load, echo=FALSE,results='hide', message=FALSE}
```

#### Setting up

```{r setup, results='hide'}
```

Reproducing Fig. 6.1, p. 304 from Principles of Surface-Enhanced Raman Spectroscopy. 

```{r simulation, message=TRUE, fig.width=10}
```

The total decay rates peak at the wavelength of excitation of planar SPPs ($\varepsilon=-1$) at the interface, they represent a non-radiative loss channel. The radiative decay rate in the upper medium has a trough at the wavelength where $\varepsilon=0$ ($D=0$ in the metal, by continuity $En=0$ above the interface), therefore by virtue of reciprocity the perpendicular dipole will not emit.