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A parallel beam of light comes out of a plano-convex lens and start to converge into focus, the question is, at that focal point, could the beam be parallelized again so it maintains the focal point diameter no matter the distance?

Hope I had explained myself right.

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You’ll never be able to maintain the focal point diameter, no matter the distance, due to diffraction. Diffraction makes perfectly collimated beams impossible, and diffraction gets worse the smaller the beam diameter.

But as for the optics, a concave lens can convert a converging beam into a collimated one. Of course, it wouldn’t work exactly at the focus of the convex lens (because the lenses need to be made confocal).

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You're asking if a beam's size can be reduced using lenses, so that a wide collimated beam becomes a narrow collimated beam. The answer to that is "yes". A beam expander consists of two lenses of different focal lengths, positioned so that the focal point of the first (larger, longer focus) lens is coincident with the focal point of the second lens. A collimated beam goes into the larger lens, comes to a focus, then is re-collimated by the second lens. The beam size is reduced by the ratio of the focal length of the second lens to the focal length of the first lens.

However, the reduced-diameter beam will not stay collimated forever. It will spread at a rate that depends on the wavelength and the beam diameter. See beam width and beam diameter in Wikipedia. For that matter, any collimated beam will spread unless it is somehow confined. The easiest way to confine a very small-diameter beam is to inject it into an optical fiber. In the fiber, the beam will stay a few microns wide until it exits the far end of the fiber.

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  • $\begingroup$ "depends on the wavelength and the beam diameter" You could add that narrower beams spread more rapidly. $\endgroup$ – Keith McClary Mar 3 at 5:39
  • $\begingroup$ True, could have added that, but figured that the two Wikipedia articles make it clear. $\endgroup$ – S. McGrew Mar 3 at 14:21
  • $\begingroup$ @S.McGrew so to resume, if I have an 80 Watts CO2 laser beam (which is collimated), I then use a plano-convex lens to reduce the beam diameter to a few microns, using another lens, I can mantain that beam diameter lets say for 100mm or so, right?. Maybe what i'm asking is too much, beacuse the beam energy is too high at that point. $\endgroup$ – lynspyre Mar 3 at 15:21
  • $\begingroup$ No, that won't work. If you examine the equations given in [en.wikipedia.org/wiki/Rayleigh_length], you will see that a beam a few tens of microns in diameter with a CO2 laser's wavelength of ~10 microns will spread very rapidly. $\endgroup$ – S. McGrew Mar 3 at 15:35
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Your best option is to confine the beam after focus in some structure that will guide it as waveguide.

Self guiding of near the focal spot size is possible in gases and matter however you need the reach ionization intensities.

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