Since the light wave bounces off the inner walls of the cable many times (total reflection), does it lose its coherence?
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Things that cause a laser beam to lose coherence are things like being absorbed and randomly re-emitted by some molecule, or being mixed with parts of the beam from farther away than the coherence length of the source.
If you had a poor enough fiber that its pulse dispersion was more than the laser source's coherence time, it would de-cohere the beam on that second principle. But such a fiber would be nearly useless for data transmission because of the pulse spreading. Possibly the low-cost plastic fibers used in illumination applications could do this if used with a source with short enough coherence time.
If you want to demonstrate it experimentally, shine the light output from a fiber onto a screen (or detector card if you're using IR) and see if there's a speckle pattern.
answered Aug 13, 2017 at 15:52
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$\begingroup$ Thanks for the answer! Is the laser beam divergent when it comes out of a fiber? I was wondering because 3D Printers use lenses to focus the beam out of a fiber (I think). $\endgroup$ Commented Aug 14, 2017 at 10:37
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$\begingroup$ @D.Niermann, yes, any light beam coming out of any aperture (even the best-collimated laser beam outputs) will diverge eventually due to diffraction. The output of a fiber will diverge immediately. The angle depends on the type of fiber. $\endgroup$ Commented Aug 14, 2017 at 14:48