Calculating Laser Focal Power & Focused Beam Waist

Question

If I focus a 1 watt, 405nm laser with a 25mm fl lens what is the power at the waist. I see calculators online but none that make sense. Rather than just telling me can you put your equations you use to solve for these items. I would also like to know the minimal distance or bream waist i can focus my laser beam down to depending on my lens and how big the beam is before having it hit the lens. This chart shows different apertures and focal lengths to get the beam waiste. I see that power intensity (w/cm2) is 250/d(mm)2 x power. But i get a ridiculous number so please help.

Answer 1

The power stays the same (other than loss at the lens), but the intensity (power per unit area) will increase when you focus down.

In order to calculate your spot size (beam waist), you need to use the equations for a Gaussian beam (assuming you have a Gaussian beam, but it's a reasonably good approximation for most laser beams). There's a good intro with the relevant equations in this article: https://www.rp-photonics.com/gaussian_beams.html

Answer 2

The power is always 1 watt, but when the spot has an area of 1um x 1um the power density is 10 up to the 12 watts per meter squared. The numbers above are based on the fact that your laser beam has a divergence of say 0.1 deg, that is why the spot is not infinitely small. Also most lenses you buy are spherical (you can spend more to get aspheres) and a spherical lens does not focus perfectly (called spherical aberration and its easy to see with simple geometry.) The aperture is the size of the lens and diffraction from this aperture is what causes the spot size to increase (wiki Airy disk). So get a big lens with short focal distance but note these 2 factors work against each other.