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If instead you have incoherent light, rather than having nice electromagnetic modes to propagate, it is a little different. For example you wouldn’t get much light into the single mode optical fiber. But you could do something like put two apertures separated by a distance and have a roughly collimated light. The diffraction angle will depend slightly on the wavelength, but could still put a lens or set of lenses to expand or focus the light or to collimate the light. Same as before the chromatic aberration of the lenses and type of lenses can matter some, but big picture it would work.

I'm asking in general how to collimate it, but my idea was use a parabolic mirror, then focus all wavelengths into a very short optical fiber, then get the light back into vacuum. Would this work? Is there a better way?

HackerEarth

Each wavelength will have a little bit of chromatic dispersion due to the lens, unless you choose to use a special lens.

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Before collimating, the beam will have diverged a bit to a radius of 5cm, the range of the wavelengths is 1400-1600nm and I don't want to lose more than 30% of initial power.

Devpost

There are some details, each wavelength will travel at a slightly different speed through the fiber due to waveguide dispersion and material dispersion.

Good lasers have Gaussian beams. Gaussian beams are never perfectly collimated, but larger diameter beams have a small beam divergence. To get a larger diameter beam, use a beam expander.

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But in the big picture, if you start out with a nice beam, you can usually use a lens or a set of lenses to collimate the beam, and each wavelength can be treated as a slightly different problem.

For wavelength division multiplexing your 100 different wavelengths could each be produced by an individual laser. They could then be sent through a single mode optical fiber and then your could collect the light coming out of the optical fiber. That ligh does each wavelength will be fairly nice almost Gaussian spot that will diverge. You could put a collimating lens where the spot is 5 mm and get a collimated beam. It would act pretty much like a Gaussian beam.