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# Photon

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Initially light was though of as a wave because it experienced interference as shown by experiments such as:
But then, some key experiments also start suggesting that light is made up of discrete packets:
and in the understanding of the 2020 Standard Model the photon is one of the elementary particles.
This duality is fully described mathematically by quantum electrodynamics, where the photon is modelled as a quantized excitation of the photon field.

## Light

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### Wave-particle duality

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The history of light if funny.
First people thought it was a particle, as per corpuscular theory of light, notably Newton supported the corpuscular theory of light.
But then evidence of the diffraction of light start to become unbearably strong, culminating in the Arago spot.
And finally it was undertood from Maxwell's equations that light is a form of electromagnetic radiation, as its speed was perfectly predicted by the theory.
But then evidence of particle nature started to surface once again with the photoelectric effect. Physicists must have been driven mad by all these changes.

#### Corpuscular theory of light

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The Quantum Story by Jim Baggott (2011) page 2 mentions how newton's support for the corpuscular theory of light led it to be held for a very long time, even when evidence of the wave theory of light was becoming overwhelming.

### Optical fiber

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### Radio

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#### History of radio

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##### Hertz electromagnetic wave experiments
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Heinrich Hertz's main initial experiment used a spark-gap transmitter. It is not something that transmits recorded sounds like voice: it only transmits noisy beeps. And as such was used for

#### Carrier wave

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Early transmitters such as the spark-gap transmitter could only send noises to send Morse code.
To send voice and music, amplitude modulation had to be developped. And a key ingredient of this is the carrier wave.
The problem is, the carrier wave needs to have somewhat high frequencies, in the hundreds of kHz TODO why. But as you might imagine, that is hard to achieve by mechanical means such as a hand cranck like Hippolyte Pixiis alternator!
Interestingly, some of the first carrier wave generators were actually mechanical, e.g. the Alexanderson alternator.
But clearly such mechanical machines were not very scalable, and soon more electronic devices were introduced, notably the vacuum tube.

### Speed of light

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#### Speed of light experiment

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Bibliography:

#### Emission theory (vision)

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It is so mind blowing that people believed in this theory. How can you think that, when you turn on a lamp and then you see? Obviously, the lamp must be emitting something!!!
Then comes along this epic 2002 paper: https://pubmed.ncbi.nlm.nih.gov/12094435/ "Fundamentally misunderstanding visual perception. Adults' belief in visual emissions". TODO review methods...

#### Faster-than-light (FTL)

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In special relativity, it is impossible to travel faster than light.
One argument of why, is that if you could travel faster than light, then you could send a message to a point in Spacetime that is spacelike-separated from the present. But then since the target is spacelike separated, there exists a inertial frame of reference in which that event happens before the present, which would be hard to make sense of.
Even worse, it would be possible to travel back in time:
##### Faster-than-light implies time travel
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### Electromagnetic spectrum

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#### Radio wave (1 m or more, 300 GHz or less)

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This is likely the easiest one to produce as the frequencies are lower, which is why it was discovered first. TODO original setup.
Also because it is transparent to brick and glass, (though not metal) it becomes good for telecommunication.
Some notable subranges:
##### Microwave (1 mm - 1 m, 300 MHz - 300 GHz)
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Micro means "small wavelength compared to radio waves", not micron-sized.
Microwave production and detection is incredibly important in many modern applications:
###### Microwave source
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Microwave only found applications into the 1940s and 1950s, much later than radio, because good enough sources were harder to develop.
One notable development was the cavity magnetron in 1940, which was the basis for the original radar systems of World War II.
###### Cavity magnetron (1940)
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Apparently, DC current comes in, and microwaves come out.
TODO: sample power efficienty of this conversion and output spectrum of this conversion on some cheap device we can buy today.
###### Microwave transmission
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###### Microwave transmission for trading
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Finance is a cancer of society. But I have to admit it, it's kind of cool.
https://arstechnica.com/information-technology/2016/11/private-microwave-networks-financial-hft/ The secret world of microwave networks (2016) Fantastic article.
###### Wi-Fi (2-6 GHz)
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This frequency range is likely chosen to allow faster data transfer than say, FM broadcasting, while still being relatively transparent to walls (though not as much).

#### Visible spectrum (420-680 nm, 400-700 THz)

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420 to 680 nm for sure, but larger ranges are observable in laboratory conditions.

## Photon spin

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Original 1931 experiment by Raman and Bhagavantam: http://dspace.rri.res.in/bitstream/2289/2123/1/1931%20IJP%20V6%20p353.pdf

## Radiation pressure

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### Nichols radiometer

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Experimental setup to observe radiation pressure in the laboratory.

### Solar sail

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Application of radiation pressure.

## Single photon production and detection experiments

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You can't get more direct than this in terms of proving that photons exist!
The particular case of the double-slit experiment will be discussed at: single particle double slit experiment.
Bibliography:

### Spontaneous parametric down-conversion (SPDC)

Phenomena that produces photons in pairs as it passes through a certain type of crystal.
You can then detect one of the photons, and when you do you know that the other one is there as well and ready to be used. two photon interference experiment comes to mind, which is the basis of photonic quantum computer, where you need two photons to be produced at the exact same time to produce quantum entanglement.

### Two photon interference experiment

The basic experiment for a photonic quantum computer.
Can be achieved in two ways it seems:
Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): https://www.youtube.com/watch?v=ld2r2IMt4vg No maths, but gives the result clear: the photons are always on the same side.

### Photomultiplier

#### Photomultiplier tube

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Can be used to detect single photons.
It uses the photoelectric effect multiple times to produce a chain reaction.

#### Silicon photomultiplier

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Here is a vendor showcasing their device. They claim in that video that a single photon is produced and detected:

## Squeezed state of light

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## Optics

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

### Collimator

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#### Collimated beam

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##### Parallel light
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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

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

#### Biconvex spherical lens

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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: $$f1​=S1​1​+S2​1​ (1)$$ where and are the two distances.
##### Focal length (f)
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If you pass parallel light.
For a biconvex spherical lens, it is given by: $$f1​=n(R1​1​+R2​1​) (2)$$ where:
• n: f nidnex

### Point light source

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Can be approximated with a diaphragm.

### Photonics

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

#### Photon polarization

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The knowledge that light is polarized preceedes 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
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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
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A device that modifies photon polarization.
###### History of polarization
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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.
https://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
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Matches the quantum superposition probability proportional to the square law. Poor Étienne-Louis Malus, who died so much before this was found.

#### Poincaré sphere

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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 14. "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)".

#### Photonics equipment

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##### Acousto-optic modulator
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An optical multiplexer!
##### Interferometer
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###### Fabry-Pérot interferometer
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##### Optical fibre
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##### Optical table
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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.