# Combining light of the same linear polarisation

Is there a way to combine two (coherent) beams that have the same polarisation and wavelength in a lossless manner such that the resultant beam has the same polarisation as the starting beams?

I'm aware that it is possible to combine two orthogonally polarised beams using a reverse polarising beam splitter, but the resultant beam will have a different polarisation than both the incident beams which is undesirable.

I also know that x:1-x beam splitters exist, but they would remove a large amount of the light coming in which is also undesirable.

• These beams are at the same wavelength, or different? Feb 24, 2019 at 1:57
• A y-junction in an optical waveguide?
– Cryo
Feb 24, 2019 at 3:44
• @ThePhoton These beams are of the same wavelength, I'll edit the question to highlight that. Feb 24, 2019 at 10:50
• @Cryo That looks like it could work, although the literature online seems sparse. Is there a paper showing how it works on beams and perhaps what the resultant field is as a function of the input fields? Feb 24, 2019 at 11:46
• You should be able to use the 1x2 splitters in reverse. Will single-mode (thorlabs.com/navigation.cfm?guide_id=2421) or multi-mode (thorlabs.com/navigation.cfm?guide_id=2482) fibre versions do? Single-mode will give you better performance, but you will need a good beam quality to have effective coupling, also single-mode will be more wavelength specific.
– Cryo
Feb 24, 2019 at 21:00

## 1 Answer

Yes, it can be done if the two beams are mutually coherent.

1. Keep the polarization of one of the beams vertical, and rotate the polarization of one of the beams to horizontal.
2.Combine the two beams by using a polarizing beamsplitter in reverse. If the phases of the two beams are precisely the same, this results in a single beam with linear polarization at 45 degrees.
2. A polarization rotator can then be used to orient the polarization in any desired direction.

Note: any slight phase difference between the two beams will result in elliptical instead of linear polarization at the output. This can be corrected downstream, but it's easier just to adjust the phase until the output polarization is linear at the output.

• I've tried looking at polarisation rotators, but there doesn't seem to be any way to describe them via Jones matrices. Are they combinations of half and quarter waveplates? Feb 24, 2019 at 18:55
• Wikipedia has a pretty good article on polarization rotators [en.wikipedia.org/wiki/Polarization_rotator]. Feb 25, 2019 at 2:02