# Will light, from two different (but identical) lasers injected into one end of a long fiber, come out form the other end with the same polarization?

Two beams of light from two lasers of the same type, with the same wavelength but different polarization, are coupled with 2X1 coupler into a 100m long single mode regular fiber. Each laser can be turned on or off at will to inject a single beam from either laser or a merged beam from two lasers, as needed.

We know that light in a fiber undergoes polarization due to imperfections, bends, and stresses.

Since both beams go through the same polarizing effects within the fiber will polarization of the merged beam on the other end of the fiber be the same as of each beam if measured separately?

            2X1 Coupler
Laser 1 ---------||          100m Fiber             ___
||--------------------------------|___| Polarimeter
Laser 2 ---------||


• as you have arbitrary initial polarizations, then you will have arbitrary end polarizations. Lets imagine your your fiber was instead a lambda/4 plate, one laser polarized along fast axis, the other polarized along 45° with respect to fast or slow axis. Then the output of laser 1 will still be linear while of laser 2 will be circular. Same as the example above. Depolarization from fiber propagation will be polarization dependent to some extent Commented Oct 14, 2023 at 16:28

Usually, you can't predict polarization.

Light propagates as an electromagnetic wave, with the electric field vector being perpendicular to the propagation vector. When two beams meet together, the electric fields must be added vectorially.

In nature, light is not polarized. That means if you graph the electric field vector in the normal plane over time then you would see a vector which moves randomly with constant amplitude (norm). If you polarized the light, then the vector will not make a random movement but will describe a figure which could be a circle, a line or an ellipse.

Unless you are explicitly told that there's a polarizator which outputs light with certain characteristics (linear, circular, elliptical, etc.), don't assume it's polarized. Even if there was a polarizator for each beam before the output you won't be able to predict how the two beams (electric field vectors) will "meet" so you won't be able to add them. Only if you put a polarizator at the output you can ask yourself if the light is polarized, but you would get two beams polarized of different frequencies.

So, without further information, you enter the fiber with natural (unpolarized) light and leave it with unpolarized light, too. Might you confused the fact that you still can recognize both beams because they are of different frequencies which doesn't mean that they have to be polarized in a specific way.

• The question commentary states that the two beams have different polarization so they are polarized. Also the question commentary states that they are of the same wavelength, so where did you come up with the idea to the contrary? Also, in nature there is plenty of polarized light, or partially polarized, for example light reflected from water, light passing through certain crystals or some organic substances. Commented Oct 14, 2023 at 10:55
• Classical light is always well polarized. Now it might be the case that you are measuring a light beam that is comprised of many different states of polarization (SOP) and then you conclude that the light is unpolarized.
– JQK
Commented Nov 22, 2023 at 23:30

SOme assumptiosn:

1. Each laser emits CW, ie. not pulsed thereby not considering nonlinear effects
2. Each laser is narrowband
3. The 2x1 coupler is a pure power splitter

AS a practical matter, the 2x1 splitter will induce different polarizations from stress induced birefringence, thus when launched into the single-mode 100 m the laser beams, in general, will not emerge with the same polarization.

• Polarization maintaining laser couplers are aplenty, so this type of coupler will not alter the polarization, and if such coupler is used then the question applies only to the polarization induced by the fiber. Commented Nov 25, 2023 at 4:26
• Nonlinear effects do not require pulsed light. Continuous light can also induce nonlinear effects in some materials, such as for example supercontinuum, which in turn would produce a multi-wavelength and multimodal light propagation in a fiber. Commented Jan 22 at 23:27
• @Jimski while CW light can induce nonlinear effects, I can always find a CW intensity level by which it'll not be possible to measure a nonlinear effect.
– JQK
Commented Jan 23 at 0:32

If we assume that the coupler is polarization maintaining and thus can be disregarded, then if we imagine that the polarization induced by the fiber is equivalent, for example, to the polarization of a lambda/4 plate then any arbitrary polarization of the light injected into the fiber will be altered in a way equivalent to passing the light through a lambda/4 plate. Consequently if the two lasers injecting the light into the fiber (one at a time) will have different polarization then the light beams of each laser exiting the fiber, will also have different polarization. And when both beams are turned on simultaneously then the combined beam exiting the fiber will have a polarization which will be different than that of each beam measured alone. (This answer is a derivative of comment made by José Andrade.)