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Laser Beam Expansion

  1. Aug 14, 2009 #1
    For my experiment I need to take a 0.8 mm HeNe beam to 20 mm beam. Since we just want illumination, it appears there is not need for beam expander or a setup of special lens (there are a few configurations online).

    It was suggest to use a Plano-convex cylindrical lens. I talked to application engineers from Edumnds and Newport, they said that the thin-lens approximations are sufficient if finding the correct focal length.

    However, I am still struggling. It's a beam of light. I have been saying that the object high is the radius of the beam, but what do I put for the object distance. I want to say it is infinity, but it appears it could be a little arbitrary.

    I am pretty stuck on this.
  2. jcsd
  3. Aug 14, 2009 #2


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    This might sound incredibly stupid, but why do you need a laser for this? If all that you want is illumination, why not just use a tight-beam flashlight (with an HeNe frequency filter if the colour is important)? I assume that you have a good reason, but I always shoot for the path of least resistance.
  4. Aug 15, 2009 #3

    Andy Resnick

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    Expanding a raw laser beam (if you really need to do this; Danger's comment is spot on) can most easily be done with two lenses- a low power (10x is usually ok, 40x is the maximum) microscope objective (cheap ones are fine), and a second collimating (plano-convex) lens. Shoot the laser in the back of the objective, and it will fan out at approximately the numerical aperture of the objective (less, since you are not filling the entrance pupil). Then it's simple geometry to calculate the focal length (and diameter) of the plano-convex lens. The focal length is the distance from the focus of the objective to the lens (and that is also how far apart you will space the lenses), and the diameter of the lens is a little larger than the collimated beam diameter.
  5. Aug 26, 2009 #4
    I am not sure why I cannot use a lamp w/ a 633 nm filter. I am using a separate HeNe to to illuminate a point of interest for a CCD camera, I would think it would interfere w/ the camera, since the lamp emits in various directions, but I guess it could be collimated. My advisor told me to use ABCD matrices, which I am not entirely sure. Classes starting and doing a different project for my MS, I do not have the time to teach myself the subjects of advanced optics.

    My thinking is.... that I can find the Gaussian beam parameters before and after it goes through this optical system, which consists of the space b/t the laser aperture and first lens surface + the refraction from each lens surface. From there I am hoping I can find the distance from the laser head to the first lens surface.

    Am I on the right track or am misunderstanding Gaussian beams?
    Last edited: Aug 26, 2009
  6. Aug 26, 2009 #5
    The laser beam has both a physical width and a divergence. The product of these two quantities is usually a constant. the output beam width is about 0.8 mm. If you use a planar-convex lens with a 10 cm focal length to focus the beam to a waist, then I estimate that that at (20/0.8) x 10 cm beyond the focal point [10 (1+20/0.8) cm beyond the lens] the beam will be about 20 mm width..
  7. Aug 26, 2009 #6
    I do not fully follow your estimation. It appears to me that your diverging the beam from the focal point of the lens and this divergence rate is associated w/ the lens?
  8. Aug 26, 2009 #7
    Not quite. I am using a 10-cm focal length plano-convex lens (focusing lens) to make a real focus 10 cm beyond the lens. The beam then diverges from the focal point with the same convergence angle between the lens and the focal point. So, at about 10 cm x 20/0.8 = 250 cm beyond the focus, the beam width should be about 20 mm.
    Last edited: Aug 26, 2009
  9. Aug 26, 2009 #8

    Andy Resnick

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    This sounds more complicated than it needs to be. Am I correct that all you want to do is somehow generate a 20mm diameter spot of illumination given a 0.8mm diameter laser beam?
  10. Aug 28, 2009 #9
    Well, yes and no. If you want to find the system parameters in the absolutely correct way, then yes, you are on the right track. This is a very complex way to do the optics, though which seems highly unnecessary for what you are trying to do (get a large laser spot). The simple approach would be to simply assume the laser beam is collimated and use ray optics to define the expansion at some distance.

    If you really want to understand Gaussian beams then you'd have to best have a single mode laser (or at least some idea of the modes present) and then you'd have to use the laser cavity parameters to define the output beam. Having done that one can then calculate the beam diameter for all space and entering various thin lenses in the beam you can calculate new beam diameter progression with distance. A Collins chart is a quick graphical way to examine this. But I doubt this is the sort of detail you are looking for.

    Just get a bag of lenses of various focal lengths and play with them for crying out loud! By the way, it doesn't much matter with you laser but with a high powered laser you want to use a negative rather than positive lens so the beam does not go through a focus. If you have enough power, the laser beam can actually ionize the gas in the air.
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