[Jarek Duda (OP)]

Optical photon is produced e.g. during deexcitation of atom, carrying energy, momentum and angular momentum difference.
So how is this energy distributed in space - what is the shape and size of single photon?

Looking for literature, I have found started by Geoffrey Hunter, here is one of articles: "Einstein’s Photon Concept Quantified by the Bohr Model of the Photon" https://arxiv.org/pdf/quant-ph/0506231.pdf

Most importantly, he claims that such single optical photon has shape similar to elongated ellipsoid of length being wavelength λ, and diameter λ/π (?), providing reasonably looking arguments:

1) Its length of λ is confirmed by:

– the generation of laser pulses that are just a few periods long;
– for the radiation from an atom to be monochromatic (as observed), the emission must take place within one period [10];
– the sub-picosecond response time of the photoelectric effect [11];

2) The diameter of λ/π is confirmed by:

– he attenuation of direct (undiffracted) transmission of circularly polarized light through slits narrower than λ/π: our own measurements of the effective diameter of microwaves [8,p.166] confirmed this within the experimental error of 0.5%;
– the resolving power of a microscope (with monochromatic light) being  “a little less than a third of the wavelength”; λ/π is 5% less than λ/3, [12];

Is it the proper answer?
Are there other reasonable answers, experimental arguments?

Updates: Paper by different author: https://arxiv.org/pdf/1604.03869

the length of a photon is half of the wave length, and the radius is proportional to square root of the wavelength

2021 "The size and shape of single photon" http://dx.doi.org/10.4236/oalib.1107179
Related: https://physics.stackexchange.com/questions/612110/is-it-possible-to-confine-a-photon-in-less-than-its-wavelength

Here is some paper trying to model emission of photon from hydrogen: https://link.springer.com/chapter/10.1007/0-306-48052-2_20

[evan_au]

The uncertainty principle dictates that if you know the position of a photon accurately, you don't know the energy (which is proportional to frequency) accurately.
- And once you measure a photon, it's position and/or energy is changed.
- So I think the question is ill-defined.

One observation, from a time when I was working with Radio-Frequency Interference: If you have a long slot (eg 1m long around an improperly sealed metal doorway), radio waves can escape from this long slot, even though the width of the gap is under a millimeter..
- So I suggest that, if they have the right polarization, photons can fit through a long, narrow gap with a width much smaller than a wavelength.
 

[Jarek Duda (OP)]

There should be some concrete evolution of EM field for single photon, having rho~|E|^2+|B|^2 energy density.

While it is a difficult question, we should at least try to know the basics like approximate size - and the two mentioned articles try to do it, most importantly discuss experimental arguments.
If not having anything better, we can start with discussing them - so what do you think e.g. about the experimental arguments quoted in the first post here? Are there any other?

For example, I remember there was argument that in Mach-Zehnder if we introduce ~1 period delay in one arm, we lose interference for single photons ... can anybody point some reference for that?

So I suggest that, if they have the right polarization, photons can fit through a long, narrow gap with a width much smaller than a wavelength.

Indeed this would interesting to check - maybe there are this kind of papers?

[Bored chemist]

It's fairly well known that you can pass photons through holes that are "too small", i.e. smaller than the wavelength.

But,as you decrease the size of the hole, there's no "sudden" cut off where they no longer go through, so there's no well defined "size".

[Jarek Duda (OP)]

Sure, the energy density of EM field of a photon might resemble ellipsoid as containing most of it hv energy, but there might be also some tail for the remaining part of energy.
Also, such hole is rather made of matter - leading to complex interactions with its orbitals, which might be difficult to properly interprete.

But generally I would indeed expect a gradual reduce of intensity for hole size at scale of wavelength - the first paper suggests wavelength/pi, e.g. based on microscope resolution:

the resolving power of a microscope (with monochromatic light) being  “a little less than a third of the wavelength”; λ/π is 5% less than λ/3, [12];

[Bored chemist]

. based on microscope resolution:

But microscope resolution is rather better than that
https://en.wikipedia.org/wiki/Super-resolution_microscopy
if you put some work into it.

[acsinuk]

The electro-magnetic photon is a tiny volume of spinning magnetic flux-current which tumbles forward when attracted by a voltage at right angles to the spin. It takes a Dirac 2 cycles to completely return to zero thus balancing the light unit.
Would show an image of 2 slit experiment but cannot attach for some reason.

[Bored chemist]

The electro-magnetic photon is a tiny volume of spinning magnetic flux-current which tumbles forward when attracted by a voltage at right angles to the spin. It takes a Dirac 2 cycles to completely return to zero thus balancing the light unit.

Technobabble.

[jeffreyH]

The electro-magnetic photon is a tiny volume of spinning magnetic flux-current which tumbles forward when attracted by a voltage at right angles to the spin. It takes a Dirac 2 cycles to completely return to zero thus balancing the light unit.
Would show an image of 2 slit experiment but cannot attach for some reason.

Whatever it is you are smoking, I would quit immediately.

[Jarek Duda (OP)]

"The size and shape of single photon" http://dx.doi.org/10.4236/oalib.1107179 has nice looking models of photon:



The big question is how true they are???
Sadly, while many claim that physics is nearly solved, we know nearly nothing about such basic questions like EM field configuration and dynamics of photon (wavepacket) ...

[alancalverd]

Important not to confuse a mathematical model (photon) with the phenomenon it models.Is it a particle? Is it a wave? No, it's a convenient mathematical representation of the cause of a phenomenon, so the idea that it might have the shape and size of a cannonball or a gnat's genitals is mere human vanity.

[Jarek Duda (OP)]

We know photon is EM wave - also from quantum perspective, it means e.g. ensemble of EM field configurations, wavepacket - we should know at least some its basic properties like size e.g. as uncertainty of position operator for such wavepacket.

[Origin]

we should know at least some its basic properties like size

It doesn't make sense to talk about the size of a photon, that would be something that would maybe make sense classically but not in the quantum world.

we know nearly nothing about such basic questions

Speak for yourself.

[Jarek Duda (OP)]

Size of photon makes sense also in QM: e.g. as width of wavepacket ( https://en.wikipedia.org/wiki/Wave_packet ), as uncertainty of quantum position operator, through adding terms in WKB approximation ( https://en.wikipedia.org/wiki/WKB_approximation ) etc.

So please elaborate what do you know about this basic question? (beside excuses)

[alancalverd]

This is a neat illustration of a travelling wave packet, but its Fourier components cover a very broad spectrum. Problem is that the spectrum of a single photon is very narrow, so this isn't a good illustration of a photon.

[Jarek Duda (OP)]

Sure very narrow in momentum spectrum, but rather nonzero: not a plane wave ... hard to imagine e.g. that photons going from screen to our eyes are plane waves (?)
If not zero, so what more specific can we tell about it?  (is this question of this thread)

[alancalverd]

And yet they interfere exactly as if they are plane (or at least spherical) waves

[Jarek Duda (OP)]

There is both EM wave governed by Maxwell equations, and quantum amplitude governed e.g. by Schrodinger -  "pilot" wave for psi=sqrt(rho) exp(-iS/hbar) Madelung substitution( https://en.wikipedia.org/wiki/Pilot_wave_theory#Mathematical_formulation_for_a_single_particle ).
For let say Mach-Zehnder interference, there is no doubts that "pilot" wave of quantum amplitudes propagates through both trajectories.

However, the question is about corpuscular part of wave-particle duality, does it also propagate through both trajectories, or maybe only through one like in this diagram (from http://redshift.vif.com/JournalFiles/V16NO2PDF/V16N2CRO.pdf ):


In case of interference of electron, it is elementary charge - cannot split in two, in experiments it is always nearly point-like charge ... also, scenarios with electron going through lower or upper arm differ by electric field around such setting influencing surrounding atoms - they are very different.
For single photons, there are e.g. these experiments measuring averaged trajectories of interfering photons: https://science.sciencemag.org/content/332/6034/1170.full


There are also experiments being able to use both wave and particle part of duality simultaneously, e.g. https://en.wikipedia.org/wiki/Afshar_experiment

So while quantum amplitude of single photon: the wave part of wave-particle duality seems to form e.g. plane waves, the corpuscular part seems to travel through a concrete trajectory (e.g. from the screen to our eyes).

[Expectant_Philosopher]

What if we are looking at the photon all wrong? Could the photon in reality be a continuous surface with no time dimension that exists in our perception as a particle?  It would surely explain spooky action at a distance if there was a continuous medium that connected all points in space at the same moment. 

[evan_au]

hard to imagine e.g. that photons going from screen to our eyes are plane waves (?)

But that is exactly how astronomers use interferometry in radio and optical telescopes.
- They assume that the photon arrives as a plane wave at widely separated points in space, and then combine them so that in-phase detections add, and out-of-phase photons average out.
- This technique gives extreme angular resolution
- Notably allowing imaging the black hole at the center of a nearby galaxy.
See: https://en.wikipedia.org/wiki/Event_Horizon_Telescope#Messier_87*