# How can I build a micrometer diameter laser beam from a common laser diode?

In order to build a lighting system for a microscope (with a digital camera) I want to make a very small diameter laser beam (parallel, rather than convergent). If possible around 1 um diameter.

How could I build such a laser using a common diode laser?

• Daft idea. You are going to magnify reflected laser light into the back of your retina? For fun? – Donald Gibson Jan 31 '18 at 2:30
• I don't get why this is downvoted. It's a legitimate question, although care is required when working with lasers. The question doesn't state that the beam will be directed into the microscope lense and eyes of the observer. – Bart Jan 31 '18 at 11:45
• Can you explain why you don't want to illuminate more of the object? This is a strange thing to do with a microscope. – Carl Witthoft Jan 31 '18 at 15:43
• The microscope is fitted with a digital camera, no eye in the way – Manu de Hanoi Feb 1 '18 at 6:37
• @CarlWitthoft not so strange, have a look at confocal laser scanning microscopes – Manu de Hanoi Feb 1 '18 at 6:41

Why this is hard

One micron is on the border of what is theoretically possible. You cannot create a parallel ray at this scale. One micron is almost as small as the wavelength of the light you are trying to focus, so the usual rules of optics don't apply.

Lasers normally produce what is known as a Gaussian beam, and they have a distinctive shape. You can focus them down to a small dot, but only if you are willing to let the beam get a lot wider before and after the spot. Looking side on at the beam, you'll get something like this:

(image from wikipedia)

The point where the beam is at it's narrowest is known as the "waist". At that point the beam has a diameter of $W_0$. At a distance of $Z_R$ from the waist, in either direction, the beam has grown to twice the area, or $\sqrt2$ times the diameter.

The equation which links $W_0$ and $Z_R$ is: $$Z_R = \frac{\pi W_0^2}{\lambda}$$ Where $\lambda$ is the wavelength of the laser you are using. If we assume a 1000nm cheapish laser diode, and a 1um waist, then $Z_R$ is 3.1um. If you go to an expensive blue laser, you can get $Z_R$ up to 7.7um.

How to do it

You will need to bring the laser beam into a convergent lens, and place the sample at the focus. The convergent lens must be very high quality, and it must be held and oriented with micron accuracy. Realistically, you probably won't be able to obtain a good enough single lens, so you will need an assembly of lenses. A microscope objective would probably work, but you won't be able to get a second one close enough to the sample.

I expect the best option would be to buy a microscope with this feature built in. That also has the added advantage that it will have all the safeguards necessary to make sure the beam never makes it to the eyepieces.

• thanks for your answer, I want a parallel beam, therefore there is no focal point and no waist, are you sure the above applies ? – Manu de Hanoi Feb 1 '18 at 6:54
• @ManudeHanoi the last paragraph is most apt... – Solar Mike Feb 1 '18 at 7:33
• @ManudeHanoi The above is pretty much a fundamental law of physics of light. There are some loopholes, for example if you can immerse your sample and lens in toxic high-refractive-index oil, you might be able to double the length of the waist. Otherwise you're stuck with the equation above. You'll need to accept a bigger waist, shorter Zr, or use a shorter wavelength laser. – Jack B Feb 1 '18 at 11:26

If you have one convex and one concave lens, you can effectively make the laser beam smaller and more concentrated while still having a parallel ray. I believe it's called a galilean lens. It would take some effort to place them accurately that you have a width of only 1um though. If it's concentrated enough (which it certainly is if converged to 1um) it can easily burn your skin and much more easily your eyes. Your eyes don't repair themselves when damaged more than the slightest bit. Take care when working with lasers.

• hmmmm.... OP didn't specify a parallel beam. Then again, he didn't not specify one. – Carl Witthoft Jan 31 '18 at 15:44
• @CarlWitthoft i do prefer a parallel beam – Manu de Hanoi Feb 1 '18 at 17:05

If you want a small illumination area on the object plane, start by focussing your source onto a 1-micron pinhole, then relay that pinhole (a single biconvex lens will suffice) to the object plane. Be aware that:
1) rather little light will make it through the pinhole
2) due to diffraction effects, you will get a center spot and surrounding rings of illumination. As Jack B pointed out in his answer (for a parallel beam), you can't do better than this.