Can Photons Really Split into Multiple Photons?

[professor]

photon "splitting"

I have heard a thing or two about photons splitting into more photons and dividing the original energy amongst themselves, but have never really heard it explained. I suppose it should work out just fine with photons having no mass, but just te be sure, is there some transformation equation that accounts for this (for instance if you put in one with 1 initial charge, and then it comes out as 2 each with half of the initial, or is it a bit more complex than that... seems a bit too simple in an area generally dealing with so many tensors and vectors i don't know what do do with myself.

 

[Claude Bile]

The energy of a single photon can be split via intermediatory processes using nonlinear optics. The process as a whole is called parametric down-conversion and devices that perform this process are called Optical Parametric Oscillators (OPOs). Parametric down-conversion is a three-photon interaction between the pump, the signal (which is the wavelength we want to generate) and the idler, so by conservation of energy;

w_pump = w_signal + w_idler (Where w denotes angular frequency).

Obviously there are many combinations of w_signal and w_idler, however there is an additional constraint, namely conservation of momentum.

k_pump = k_signal + k_idler (Where k denotes the wave-vector).

This is otherwise known as the phase-matching condition. The frequencies that satisfy these equations will be the ones that are generated in significant amounts.

The photon energy can be 'split' in this way because the response of the atom to an applied Em field becomes nonlinear at high intensities, meaning additional frequency components are generated. Parametric down-conversion is actually the reverse process of another well-known nonlinear process - Sum-frequency generation.

Entire textbook chapters are devoted to this topic, I have done my best to summarise the important points, googling some terms mentioned above may yield more information, alternatively you can post more questions and I will do my best to answer them.

Claude.

P.S. For some reason, latex was not working, hence the typed equations.

 

[pallidin]

Can this type of "split" occur with a free-space photon? No.
PDC is an interactive function of a photon with a bound electron.

 

[professor]

thanks both- pallidins footnote helped me put this to a more specific image

 

[lightgrav]

Can this type of "split" occur with a free-space photon? No.
PDC is an interactive function of a photon with a bound electron.

PDC requires a non-linear medium in order to control the outcome.
But a lone photon in free space could split into 3 real photons
yet conserve Energy, momentum, and angular momentum (spin).
Because photons are bosons, the reason that they do NOT do it
must come from their size - they travel as field waves, not particles.