Graduate Photon number needless conservation, consolidation possible?

[kiwaho]

We know lepton conservation law, that means multiple neutrinos can not be consolidate to big single neutrino.
But photon is boson not lepton, no need of conservation, does that mean it is possible to combine or fuse a bunch of photons into ONE big photon, or say, more energetic photon, i.e following reaction could be true?
γ₁ + γ₂ + γ₃ + … γ_n = γ_big
If possible, ideal optic lens can be used to focus photons to produce higher energy light, i.e. forced blue-shift. lot of amazing applications, e.g. make violet from visible light, doubling light frequency, etc.
And how many barns of cross section for above reaction?
Of course, energy and linear/angular momenta conservation should be obeyed, in this case, the reactant photons Jπ all are 1-, then resultant photon can be any integer spin and parity, such as 1+, 10-, ...

 

[jfizzix]

You'll be happy to know that such processes do exist:

For example, in nonlinear optics, second harmonic generation at the quantum level involves pairs of photons at one frequency getting converted into single photons at twice the frequency. There's also sum frequency generation, and higher harmonic generation as well. These processes have both quantum mechanical and classical treatments in optics, but in the quantum mechanical process, photons can be exchanged for pairs or groups of other photons so long as total energy and momentum is conserved. Momentum conservation is tricky since wavelength depends on the index of refraction, but in the right materials, it can and has been done.

For example, green laser pointers (532nm) operate using second harmonic generation where pairs of photons at 1064nm get converted to photons at 532nm with a high degree of efficiency.

 

[kiwaho]

waiting for more comments

 

[jfizzix]

As far as conservation of spin goes, photons that are linearly polarized are in an even superposition of +1 and -1 for the z-component of their spin angular momentum. Photons can in fact only have those values for spin angular momentum, so the higher frequency photons generated from combining pairs or groups of lower frequency photons will also have a z-component of spin in an even superposition of -1 and 1. This doesn't violate any conservation laws, since there are many ways for these z-components to add up to a net value of +1 or -1.

Calculating the scattering cross sections of these sorts of interactions seems to be very uncommon in nonlinear optics, perhaps because the wavelengths in nonlinear optics are so much longer than those in high energy physics (nearIR to near UV), and that fully classical treatments of many nonlinear optical processes (including multiple harmonic generation) already exist.

 

[kiwaho]

As far as conservation of spin goes, photons that are linearly polarized are in an even superposition of +1 and -1 for the z-component of their spin angular momentum. Photons can in fact only have those values for spin angular momentum, so the higher frequency photons generated from combining pairs or groups of lower frequency photons will also have a z-component of spin in an even superposition of -1 and 1. This doesn't violate any conservation laws, since there are many ways for these z-components to add up to a net value of +1 or -1.

Calculating the scattering cross sections of these sorts of interactions seems to be very uncommon in nonlinear optics, perhaps because the wavelengths in nonlinear optics are so much longer than those in high energy physics (nearIR to near UV), and that fully classical treatments of many nonlinear optical processes (including multiple harmonic generation) already exist.

spin and parity of ground state of photon is 1-, but photon can seem to be excited to other states, where spin and parity can be changed to any value.
Most nuclear de-excitation in gamma photon emission can have 2 spin change, special nucleus can have as high as 8 spin. e.g. the gamma of Ta-180m is 8-(from 9- excited state to 1+ ground state.)
so 1- photon seems only to appear in atom level, but most 2- in nuclear level.

 

[kiwaho]

there is a paper on high spin photon study by Ottawa university researchers:
Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges