> For the complete documentation index, see [llms.txt](https://anufrievroman.gitbook.io/freepaths/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://anufrievroman.gitbook.io/freepaths/basic-tutorials/parabolic-lens.md).

# Parabolic lens

Collimation and focusing using parabolic lenses

In the `examples/parabolic_lens_collimation.py` example, we create a collimated phonon flux by reflecting phonons from a parabolic surface. The figure below illustrates the concept:

<figure><img src="https://664157142-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F7rdk0xqy0YirGWqTjhkv%2Fuploads%2FKOiee8VzWyzgA7B2lM3X%2Fimage.png?alt=media&amp;token=5a1cc12e-45ee-4e81-a030-76efed7efcba" alt="" width="563"><figcaption><p>Concept of collimation and focusing using parabolic surface.</p></figcaption></figure>

We place the parabolic boundary at the bottom and move the hot spot that emits the phonon to *y* = 300 nm, as shown in the input file:

```
# Hot and cold sides:
COLD_SIDE_POSITION_TOP = True

# Phonon source:
PARTICLE_SOURCES = [Source(y=300e-9, size_x=100e-9,  size_y=100e-9, size_z=THICKNESS, angle_distribution="uniform")]

# Parabolic mirror:
HOLES = [ParabolaBottom(tip=0, focus=300e-9)]
```

Note that `angle_distribution="uniform"` because we need to emit phonons in all directions evenly. This model produces the following structure, which collimates phonons after reflection from the parabolic boundary:

<div><figure><img src="https://664157142-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F7rdk0xqy0YirGWqTjhkv%2Fuploads%2FLxcRzZqpmqitPYn1p4F2%2Fimage.png?alt=media&amp;token=5bcd454b-5881-4e14-9b43-ecd6a50e7abf" alt=""><figcaption><p>Phonon trajectories show collimation of phonons reflected from the parabolic boundary.</p></figcaption></figure> <figure><img src="https://664157142-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F7rdk0xqy0YirGWqTjhkv%2Fuploads%2FsyuIewUGVhrNgW5Ig85z%2Fimage.png?alt=media&amp;token=6b7f5c03-58eb-43d3-80a3-d3d9bd5da071" alt=""><figcaption><p>Angular distribution shows that many phonons have an angle of zero degrees at the top of the structure (blue), while the initial distribution was uniform (red).</p></figcaption></figure></div>

The parabolic lens can also be inverted and placed at the top as follows

```
# Phonon source:
PARTICLE_SOURCES = [Source(x=0, y=0, z=0, size_x=WIDTH,  size_y=0, size_z=THICKNESS, angle_distribution="directional")]

# Parabolic boundary:
HOLES = [ParabolaTop(tip=1000e-9, focus=100e-9)]
```

Here, the source is placed at the bottom, while the parabola is at the top.

### Reference

* Singh et al. [Applied Physics Letters, (2023)](https://aip.scitation.org/doi/10.1063/5.0137221)