# Splitting a light wave

It is possible to split a single light wave/photon into two using a half-silvered mirror. Is it then possible to split the two waves into four, eight, etc? I've not found an experiment that has done this – has it been done?

It is possible to split a single light wave/photon into two using a half-silvered mirror. Is it then possible to split the two waves into four, eight, etc? I've not found an experiment that has done this – has it been done?

Photons can indeed be "split", but not by something as simple as a half-silvered mirror. In a process called parametric down conversion (PDC), photons entering a crystal of a birefringent material such as BBO (beta barium borate) or KDP (potassium dihydrogen phosphate) can be split into two orthogonally polarized photons called the signal and idler. The frequencies of the signal and idler photons sum to the frequency of the original "pump" photon. Depending on the experimental conditions, the ratio between the signal and idler photons can be tuned as desired, so yes, it would be possible to split a photon precisely in two (this has been done).

One point here is that, since this all happens inside a dense medium, it is probably better to think of the original photon as being destroyed, and the two new photons (signal and idler) created by interaction of the pump with the atoms of the birefringent material, than as a single photon that gets split into two parts.

Ah, that's fascinating – orthogonally polarized photons – might those be related to electro/magnetism parts of the wave?

But what I was getting at was a quantum 'split', so you fire a light wave at a half-silvered mirror, and you then have a 50/50 chance of finding it in either of the two directions, and when you do find it, you find the whole of the wave.

I would like to know whether this can be done over and over, 'splitting' the beam without detecting it so that, for instance, there is a 50% chance of finding it in one direction and a 25% chance of finding it in two other directions.

Gold Member
Photons can indeed be "split", but not by something as simple as a half-silvered mirror. In a process called parametric down conversion (PDC), photons entering a crystal of a birefringent material such as BBO (beta barium borate) or KDP (potassium dihydrogen phosphate) can be split into two orthogonally polarized photons called the signal and idler. The frequencies of the signal and idler photons sum to the frequency of the original "pump" photon. Depending on the experimental conditions, the ratio between the signal and idler photons can be tuned as desired, so yes, it would be possible to split a photon precisely in two (this has been done).

One point here is that, since this all happens inside a dense medium, it is probably better to think of the original photon as being destroyed, and the two new photons (signal and idler) created by interaction of the pump with the atoms of the birefringent material, than as a single photon that gets split into two parts.

It would almost seem that, since total freq is conserved, total energy is conserved too.

This means that, while there's is no theoretical limit to how often they could be split, you'd reach a point where you're trying to split an extremely low energy photon into two ... uh ... extremlyier low energy photons.

Frame Dragger
It would almost seem that, since total freq is conserved, total energy is conserved too.

This means that, while there's is no theoretical limit to how often they could be split, you'd reach a point where you're trying to split an extremely low energy photon into two ... uh ... extremlyier low energy photons.

You'd run into the Planck scale, or near it... near it I suppose since we're "walking" by half distances.

EDIT: SpectraCat: I am working on a large PM for you, with a few questions re that FEL I was talking about for the writing. I'm working on getting the technical language down re the Phase Conjugation to compensate for Bloom and other effects so that you don't have to struggle with my imprecise lingo.

@DaveC: Wouldn't the Planck scale be that theoretical limit for the photon? If not, I'd like to know because I am WAY off (entirely likely)

But what I was getting at was a quantum 'split', so you fire a light wave at a half-silvered mirror, and you then have a 50/50 chance of finding it in either of the two directions, and when you do find it, you find the whole of the wave.

I would like to know whether this can be done over and over, 'splitting' the beam without detecting it so that, for instance, there is a 50% chance of finding it in one direction and a 25% chance of finding it in two other directions.

Yes, you can do so. In fact, this is one method to characterize light. You check the cross-correlation of the photon number in the exit ports of the beam splitter. If you have a single photon state present, these photon numbers will ba anticorrelated and the probability of a simultaneous detection in both arms will be 0. You can extend this setup from second order (1 beam splitter, two exit ports) up to arbitrary order by inserting more beam splitters and checking more exit ports.

Staff Emeritus
It is possible to split a single light wave/photon into two using a half-silvered mirror. Is it then possible to split the two waves into four, eight, etc? I've not found an experiment that has done this – has it been done?

I think what you're getting at here is what is going on at a beam splitter. The answer to this is, it depends on your experimental set up.

If you have detectors that detects which direction a photon goes after the beam splitter, than you'll get an either or. A photon will go either one way, or the other, not split into two halves. If you have an interferometer where you wait until both of the photon's possible path recombine, then you'll get a result consistent with the photon "interfering with itself" (i.e. single photon interference). This is the typical interference pattern that we know.

These two papers have more detailed description of such a thing:

http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
http://departments.colgate.edu/physics/research/Photon/root/ajpbs02.pdf

Zz.