Any diode or DPSS laser needs optics of some kind, as beam from the device itself has high divergence .. up to 40 degrees for diode lasers.

So even to get collimated (as close to parallel as possible) beam you need optics.

There is also limit to how small the spot can be. Surprisingly to get smaller dot, you need larger lens (output aperture), and/or shorter wavelength.

Check the image:

On the left there is a source, let's say laser diode.

Then there is lens. First lets follow bright red curve. That is how collimated beam looks like. The beam will look like this if the source is placed exactly at focal distance from the convex lens (yeah, assuming it is a point source, which diode laser basically is).

Such beam is parallel at the aperture (exit hole of teh apparatus), but due light diffraction it cannot be parallel forever .. it slowly changes into divergent beam, and at a distance the beam is basically a cone, with some apex angle, and with the apex on the centerline at the aperture (thin black line).

The angle is called divergence angle, and when expressed in milliRadians, or mRads, it can also be used like size at distance for small angles (which are common):

spot size = distance * divergence (in Rad).

This is due to the fact, that for very small angles (under 1 degree) angle expressed in radians equals (or is very close) to sinus and tangents of that angle.

So common 1 mRad (0.001 Rad) divergence will create spot 1m across at 1000m range.

Divergence only describes beam shape well at large distances .. where the beam is close to cone shape.

Divergence for collimated beam is governed by wavelength of the laser, and for aperture size - or in simple terms, lens diameter.

And it is divergence = wavelength / aperture size (all sizes must be in same units).

Sadly this is only ideal diffraction limited divergence .. most lens won't be able to achieve that, especially if they are strong so they can be placed close to the diode .. so then the real divergence can be somewhat bigger .. like 1.5 times, or even 2 times.

This also depends on how we measure 'spot diameter'. The energy usually falls from center of the spot with Gaussian curve .. different levels are used for defining the 'border' of the spot. So you can also see the formula multiplied by 2/PI (or PI/2 ? not sure ATM), but for our estimates it's fine as it is.

Interestingly the divergence of the collimated beam can also be used to estimate minimum spot size for close focus. That's the dark red / brown line.

Same laser, same lens. We moved the lens a bit so the beam is focused to some closer point, not parallel at aperture. It forms a waist at some distance (with collimated beam, it too has a waist .. at the aperture).

Here the beam transforms from cone to parallel .. and then to cone again. Divergence at the distance is worse, and spot at the distance will be large .. but at the waist it will be smaller then anywhere in collimated case.

It's called close focus when the beam is thinner at waist then at aperture .. or in other words, when the waist does not lie at aperture.

This is obviously how lasers are focused for data storage, and usually for burning (not always, if you cut deep, you want the beam roughly same diameter along the cutting depth).

You see how the waist of close focus beam touches the collimated beam divergence cone ? That's how it works. If you use formula for close focus, all additional distances cancels out and you came out with same formula as for ideal collimated beam divergence.

So if the divergence of collimated beam is 1mRad, it means that you won't be able to get smaller spot than 1m at 1000m using collimated beam .. but it also means you will be able to get spot about 0.1 mm at distance 100mm.

This formula is not enough for designing complex laser optics, as it only works with ideal limits .. but it is useful for basic idea about what's possible ..