+++
title = "Fresnel transmission"
weight = 20
+++

## Fresnel transmission from a depth-probe simulation

The **Fresnel transmission** T is the fraction of incident energy flux
that enters the substrate. It satisfies 0 ≤ T ≤ 1.

T differs from the depth-probe field intensity |ψ|² returned by the
default simulation. Standing waves can raise |ψ|² above 1, so
|ψ|² ≠ T in general.

To obtain T from a depth-probe simulation:

1. Observe the transmitted partial wave (`ZDirection_Transmitted`)
   at a point in the substrate, away from the film–substrate interface.
2. Apply the wavevector correction
   T = (k_{z,\text{sub}} / k_{z,\text{vac}}) × |ψ|².

The script prints a single number,
```
0.1943568705571461
```

Cross-check: the same angle (0.64°) is just above the critical angle of
the film (0.627°), so the specular simulation gives R = 0.806,
and T = 1 − R = 0.194 agrees with the depth-probe result.

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