+++
title = "Opaque sample"
weight = 60
+++

## Depth profile of an opaque sample

We consider an opaque material layer (300 nm thick, refractive index $\delta=10^{-5}$, $\beta=3\times10^{-6}$) sandwiched between two vacuum layers.

The standing wave pattern arises from superposition of incident and reflected beams. The field amplitude can reach 2, giving maximum intensity of 4.

### 2D intensity map: depth vs angle

The intensity distribution as a function of depth $z$ and incident angle $\alpha_i$.

The black region in the lower left shows where the material is opaque and radiation cannot penetrate (below the critical angle $\theta_c \approx 0.256°$ at large depths).

{{< figscg src="/img/auto/varia/Opaque2D.png" width="500" class="center">}}

{{< show-ex file="varia/Opaque2D.py" >}}

### 1D profile: intensity vs depth

A slice at fixed incident angle $\alpha_i = 0.0044°$ showing the standing wave oscillations through the material layers.

{{< figscg src="/img/auto/varia/OpaqueVsDepth.png" width="500" class="center">}}

{{< show-ex file="varia/OpaqueVsDepth.py" >}}

### 1D profile: intensity vs angle

A slice at fixed depth $z = 100$ nm (in the upper vacuum layer) showing how intensity varies with incident angle.

{{< figscg src="/img/auto/varia/OpaqueVsAlpha.png" width="500" class="center">}}

{{< show-ex file="varia/OpaqueVsAlpha.py" >}}
