# Optics

The science and engineering of light!
When dealing more specifically with individual photons, we usually call it photonics.

## Parallel light

Often just called collimated light due to the collimator being the main procedure to obtain it.
However, you move very far away from the source, e.g. the Sun, you also get essentially parallel light.

## Lens

The most important type of lens is the biconvex spherical lens.

## Biconvex spherical lens

Focal length
Each side is a sphere section. They don't have to have the same radius, they are still simple to understand with different radiuses.
The two things you have to have in mind that this does are:
• converges parallel light to a point at center at distance known as the focal length.
This is for example why you can use lenses to burn things with Sun rays, which are basically parallel.
Conversely, if the input is a point light source at the focal length, it gets converted into parallel light.
• image formation: it converges all rays coming from a given source point to a single point image. This amplifies the signal, and forms an image at a plane.
The source image can be far away, and the virtual image can be close to the lens. This is exactly what we need for a camera.
For each distance on one side, it only works for another distance on the other side. So when we set the distance between the lens and the detector, this sets the distance of the source object, i.e. the focus. The equation is:
where and are the two distances.

## Focal length (f)

If you pass parallel light.
For a biconvex spherical lens, it is given by:
where:
• n: f nidnex

## Carl Zeiss SMT

Subsidiary of Carl Zeiss AG and also part owned by ASML, sole optics vendor of ASML as of 2020.

## Point light source

Can be approximated with a diaphragm.

## Photonics

The science and engineering of photons!
A bit more photon-specific than optics.

## Photon polarization

The knowledge that light is polarized precedes the knowledge of the existence of the photon, see polarization of light for the classical point of view.
The polarization state and how it can be decomposed into different modes can be well visualized with the Poincaré sphere.
One key idea about photon polarization is that it carries angular momentum. Therefore, when an electron changes orbitals in the Schrödinger equation solution for the hydrogen atom, the angular momentum (as well as energy) change is carried out by the polarization of the photon!

## Polarization of light

This section discusses the pre-photon understanding of the polarization of light. For the photon one see: photon polarization.
People were a bit confused when experiments started to show that light might be polarized. How could a wave that propages through a 3D homgenous material like luminiferous aether have polarization?? Light would presumably be understood to be analogous to a sound wave in 3D medium, which cannot have polarization. This was before Maxwell's equations, in the early 19th century, so there was no way to know.

## Polarizer

A device that modifies photon polarization.

## History of polarization

Particularly cool is to see how Fresnel fully understood that light is somehow polarized, even though he did not know that it was made out of electromagnetism, clear indication of which only came with the Faraday effect in 1845.
spie.org/publications/fg05_p03_maluss_law:
At the beginning of the nineteenth century the only known way to generate polarized light was with a calcite crystal. In 1808, using a calcite crystal, Malus discovered that natural incident light became polarized when it was reflected by a glass surface, and that the light reflected close to an angle of incidence of 57° could be extinguished when viewed through the crystal. He then proposed that natural light consisted of the s- and p-polarizations, which were perpendicular to each other.

## Malus' Law

Matches the quantum superposition probability proportional to the square law. Poor Étienne-Louis Malus, who died so much before this was found.

## Poincaré sphere

A more photon-specific version of the Bloch sphere.
In it, each of the six sides has a clear and simple to understand photon polarization state, either of:
• left/right
• diagonal up/diagonal down
• rotation clockwise/counterclockwise
The sphere clearly suggests for example that a rotational or diagonal polarizations are the combination of left/right with the correct phase. This is clearly explained at: Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)".

## Acousto-optic modulator

An optical multiplexer!

## Optical table

For example, that is how most modern microscopes are prototyped, see for example Video "Two Photon Microscopy by Nemonic NeuroNex (2019)".
This is kind of why they are also sometimes called "optical breadboarbds", since breadboards are what we use for early prototyping in electronics. Wikipedia however says "optical breadboard" is a simpler and cheaper type of optical table with less/no stabilization.