---
title: "Dipole radiation patterns"
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{LFIEF patterns}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r demo, message=FALSE, echo=FALSE}
knitr::read_demo("LFIEF_patterns", package="planar")
```
Applying optical reciprocity to the problem of dipolar emission near a planar interface, we can obtain the radiation pattern (intensity vs angle) by modelling the near-field at the dipole location for plane-wave illumination at a range of incident angles.

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

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

### Dipole in a vacuum

We first confirm that the dipolar emission in a vacuum follows the expected `sin^2` pattern. We define a dummy simulation (no actual interface),

```{r dummy, fig.show='hold', fig.width=5,fig.height=5}
```

### Dipole near a thin gold film (Kretschmann configuration)

In the Kretschmann configuration, molecules situated on the air side will radiate predominantly in a narrow cone of angles, associated with the excitation of surface plasmon-polaritons (SPPs) radiating into the glass substrate. By reciprocity, the field enhancement experienced by a dipole near the metal layer is also obtained for a narrow range of angles where conservation of in-plane momentum between the incident light and the SPPs is satisfied.

```{r kretschmann, fig.width=11}
```