# Collimated light directly into a multi-mode fiber

This is my question - Will a collimated, incoherent light, consists of a limited angle, that "hits" a multi-mode fiber facet exit the fiber as collimated? (just to be clear, no lens is involved. I assume the light is emerging as collimated at various angles).

• What do you mean by "exit the fiber as collimated"? Sep 21 '15 at 8:38
• @CuriousOne meaning that if I place a camera focused to infinity and looking at the fiber's exit facet, I will see an image.
– Dror
Sep 21 '15 at 9:10
• I see. My gut feeling is that it might depend on the length of the fiber and whether the fiber is bent. I would not expect to see a homogeneously lit field or some form of Gaussian illumination, if that is what you are after. I saw a setup like that in a machine vision lab once. The optical quality of the illumination was horrible. The solution was to have a fast rotating diffusing paper disk after the lamp which changed the entry angles of the light into the fiber randomly. The result was an amazingly homogeneous time averaged output. Sep 21 '15 at 9:24
• Thanks. I'm more interested in the imaging properties. Is there a reason light in specific input angle not to exit in the same angle? My guess theoretically it will. But I'm not sure - maybe the fiber constrains the input angles to discrete values, and that might damage the infinite-conjugate image?
– Dror
Sep 21 '15 at 9:35
• If you want to do actual imaging, then the solution is a fiber bundle. Sep 21 '15 at 9:36

In general, the answer is no, but with careful engineering you can achieve reasonable collimation at the output.

Depending on the exact fiber, the field is confined to a region of diameter $d$, where $d$ is typically less than $100\mu$. So even if the field arrives at the output with no phasefront curvature, the divergence angle is of the order of $\lambda/d$, i.e. of the order of 10 milliradians. You can only reduce this angle by broadening the width of the field.

Now we strike a big problem. The field is transported through the fiber by a system of modes, which all have different propagation speeds along the fiber. So a collimated input will in general be output with a hopelessly scrambled phasefront, particularly if the fiber is of the "bendy" kind typically used for communications. You'll simply see a mess in the farfield.

However, if you engineer the fiber refractive index profile e.g. varying like $n(r) \approx n_0\,\operatorname{sech}(g\,r)$ where $r$ is the distance from the optical axis, and can keep the fiber straight and strain free, then a collimated field will be periodically reassembled with distance along the lens; the period length is $2\pi/g$. So you need to engineer the length and profile correctly, and take steps to make sure that the rod is not strained. You now have a GRIN lens, rather than a fiber!

• Hi, striking the big problem - Isn't phase irrelevant here? - I'm considering a non-coherent light..
– Dror
Sep 21 '15 at 9:44
• @Dror: Imaging with non-coherent light is still based on the phase of the wavefront. The only thing you can do is to "undo" the distortion by the fiber, which is usually done with a phase conjugating mirror. The problem I see there is that the fiber changes the wavefront by more than $2\pi$, while the practical mirrors can't do that. I don't know if that has a significant influence on static images. Probably not. Sep 21 '15 at 9:55
• @Dror Normal transmission of light is when each photon interferes only with itself. So you must consider the coherent sum of propagated modes. This is why wavefront aberration is always important in imaging systems, even when lit by incoherent light. Light your microscope with incoherent light: it won't cure the effects of aberration by a crap lens in the slightest. Look at the shadow of a razor's edge backlit by an incandescent globe: you'll still see diffraction fringes. Sep 21 '15 at 10:03
• @CuriousOne ,WetSavannaAnimal Thanks for clarifying those. Are GRIN fibers of 200um diameters X ~100mm length feasible for manufacturing?
– Dror
Sep 21 '15 at 10:09
• @Dror If the overall diameter can be about 0.5 to 1mm, then that may be doable. I would contact GRINTech in Germany grintech.de. You're talking about a relay lens and they make 0.5mm diameter ones of 50mm length as a standard product. See what you can do with that. Sep 21 '15 at 10:50