# Combining the energy from two optical fibers transmitting visible light

Can this be done?

It wouldn't violate energy conservation...

I've tried looking at 1xN beamsplitters used in reverse. But it won't work, since using them in reverse also splits the incoming power and portion of it (commonly, 50%) gets lost inside the splitting device.

Assume laser light with the same wavelength in the fibers.

To complete the discussion, could you also comment what will happen if the light in both fibers is solar, collected from free space.

Theoretically yes, though the answer to your question may depend on the properties of the two sources.

If, for example, the two sources have different wavelengths, then you need a glass surface with an optical coating that reflects the one wavelength and transmits the other. By the principle of reversibility, if you had one source with the two wavelengths mixed, you would be able to use the same coated surface to split the two wavelengths out, and if you reverse the direction, the paths taken should not change.

From your question though I get the sense that you are talking about two sources with the same wavelength. In that case they need to be coherent and in phase with each other, and you can use a regular 50-50 beamsplitter.

This also follows from the principle of reversibility, though it is not as obvious. If you have one source then you can certainly use a 50-50 beamsplitter to split it into two beams and couple those into optical fibers. So, you must be able to do the same thing in reverse. However as you correctly noted, if you simply aim both beams into the beamsplitter, you'll get two beams out.

The trick is to think of the reversed system slightly differently. In the reversed system, you have two input beams, one of intensity $I$ just like you expected, and a second input beam of zero intensity. These combine in the beamsplitter into two output beams of intensity $I/2$ which are in phase with each other.

Therefore, in the forward case, the two input beams must also be in phase with each other! If they are, then they will destructively interfere to produce a zero-intensity output beam at one port, and constructively interfere to produce the desired output beam of intensity $I$ at the other port.

This is assuming an ideal lossless beam splitter with all beams perfectly aligned, etc. In reality, you will not get perfect transmission (nor would you in the reverse case) but you will get much better than 50%.

• Thank you for your detailed answer! I was reading similar analysis on a fiber optic manufacturer's web page, yet it very much lacked the detail and reasoning you have provided for the case of two laser beams with the same wavelength. It will take me some time to wrap my head around this. :) – user7641 Oct 13 '16 at 22:05
• I edited the question to note what is the wavelength of the sources. Could you comment what would happen also if the two incoming beams (in the two fibers) come from free-space collected solar light. Can one combine the power of such beams. – user7641 Oct 13 '16 at 22:07

There is a theorem in optics (I don't recall the exact details of it) stating that it is impossible to combine two beams of light with zero loss if the two beams are otherwise identical. In other words, if they have the same polarization, same wavelength, etc. then the best one can do would be to use a beam splitter, which inevitably implies a loss of optical power. If some parameter is different, say the wavelength, then one can in principle use for example a diffraction grating to combine them with theoretically no loss in optical power.

• flippiefanus, thank you for your informative answer – user7641 Oct 13 '16 at 21:59

It depends on the property of the two sources as ptomato explained. You can have a look to beam combining article in optic encyclopedia to have a general vision (https://www.rp-photonics.com/beam_combining.html?s=ak) . But a few precisions:

• If the two sources have different wavelenghts you can use spectral combining using a dichroic mirror or a grating.
• If the two sources have different polarisation states, you can use a polarisation beam splitter. Either a fibered one or a cube.
• If the two sources are coherent you can use coherent beam combining which need the use of a locking phase control loop, to make the two sources interfer in a constructive way.
• If the two sources are not coherent but have very close wavelenghts, you can use a less performant technic wich is a tiled configuration with a corner cube as you can see in the schema and the photo below: