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If I understand things correctly, the optical fibers used for (long-range) data transmissions are generally single-mode fibers, transmitting light in the 1300-1500 nm spectrum.

Now, could such a fiber transmit visible light (~400-700 nm) a short distance, say a few meters? Or does the fiber have a property that prohibits transmission of shorter wavelengths?

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Answer: Definitely yes. The "window" 1300-1600nm is a concept that is really only practically meaningful for kilometres of fibre: even tiny attenuation co-efficients are significant for long distances. For several metres, it's an altogether different thing: the attenuation co-efficient could be three orders of magnitude higher than for kilometre length fibres before it becomes as noticeable as in the latter kinds of fibre. So yes a few metres of almost any optical fibre will bear light with little loss over a few metres.

What will be different, however, is that fibre that is one moded for 1300 - 1600nm will almost certainly not be one-moded for visible light. A fibre's mode parameter:

$$V = k \, \sqrt{n_{co}^2-n_{cl}^2}$$

where $k$ is the freespace wavenumber and $n_{co},\,n_{cl}$ the core and cladding refractive indices, sets whether the fibre will be one-moded; for a step index profile round core fibre, the fibre is one moded iff $V < \omega_{0,1}\approx 2.405$ where $\omega_{0,1}$ is the first zero of the Bessel function of the first kind of order nought, so $\omega_{0,1}$ is the smallest positive solution to $J_0(V) = 0$. Whenever $V > \omega_{0,1}$, the fibre supports more than one mode.

$V$ is also critically related to the fibre's guiding strength. The bigger $V$ is, the less loss light suffers in going around bends or from any roughness on the core-cladding interface. So fibre designers like to set $V$ as high as they can, which means that if they want a one-moded fibre, they are constrained to $V<2.4$. Typically $V$ is between 2 and 2.2 at the designed-for working wavelength. So if a fibre is designed to have $V=2$ at $\lambda = 1300{\rm nm}$, its $V$ value will be 4 at 650nm and it will support three modes.

So now suppose you couple your visible light into the fibre and look at the mode field shape by cleanly cleaving the other fibre end and holding it above a piece of paper. You will see the farfield diffracted version of the fibre's field and it will have nulls (dark lines) in it and the field pattern will "squirm" and shift as you bend the fibre and thus alter the relative delays of the three propagating modes, thus changing the beating or intereference between them. If you do the same for a truly one-moded fibre, the farfield pattern does not change as the fibre is bent.

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Great answer, thank you! –  user2078515 Jan 31 at 9:13
    
@user2078515 You're welcome! –  WetSavannaAnimal aka Rod Vance Jan 31 at 22:51

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