---
title: "Sensing in the Kretschmann configuration"
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{kretschamnn sensing}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r demo, message=FALSE, echo=FALSE}
knitr::read_demo("kretschmann_sensing", package="planar")
```
The Kretschmann configuration is commonly used for _sensing applications_: the sharp resonance associated with the excitation of SPPs at the metal/dielectric interface is strongly sensitive about the refractive index of the dielectric medium. 
Furthermore, because SPPs are associated with a exponential decay of the electric field in the surrounding medium, the technique provides a surface-sensitive, sub-wavelength, probe.

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

#### Setting up

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

We define a function to model our system with the parameters of interest: a semi-infinite incident medium (glass), a 50nm gold film, a thin layer of varying thickness and refractive index, and a semi-infinite dielectric medium of varying refractive index.

```{r simulation}
```

### Variation of the bulk medium

```{r loop, fig.width=12}
```


### Local sensitivity

We now look at the effect of changing the refractive index of a thin layer, of varying thickness.


```{r variation}
```
For an optical thickness approaching $\lambda / 2$, a new reflectivity dip appears, that is associated with the excitation of a guided mode. It is sharper than the standard SPP mode, because the modal field is mostly located in the dielectric layer.