How know The Laser Focused Spot Diameter

Theoretical calculation of the diameter d of the focused spot？

How much can the smallest focused spot of a certain wavelength of laser reach?  How to make the focus spot thinner?

Why do focusing systems use beam expander? ...

After the laser beam is focused by the lens, the minimum position of the spot is called the laser focus, as shown in the figure below.

The focal spot diameter d can be roughly calculated by the following formula:

d=2fλ/D

f is the focal length of the focusing mirror; λ is the wavelength of the incident beam; D is the diameter of the incident beam.

It can be seen from the formula that the spot diameter d of the focal point is proportional to the focal length f of the focusing mirror and the laser wavelength λ, and is inversely proportional to the diameter D of the incident beam.

If the light guide and focusing system can be designed as f/D≈1, the focal spot diameter can reach  d=2λ

This shows that after the fundamental mode Gaussian beam is focused by an ideal optical system, the minimum diameter of the focal spot can reach twice the wavelength (this is theoretical, but it cannot be achieved in practice.)

A few conclusions:

First: the light of a certain wavelength has a limit focusing spot size, and the limit value cannot be exceeded under any circumstances. The longer the wavelength, the larger the limit value; the smaller the wavelength, the smaller the limit value. This is why the focusing spot of the CO2 laser system is larger than that of the UV 355nm laser system. Many customers require the focusing spot to be small and how much precision to achieve. For example, some customers require that the precision of CO2 laser marking machine can reach 20um, but in fact d=2λ=2*10.6um=21.2um, so this precision It is simply impossible to achieve, and this requirement is not in line with the theory. So when you need fine marking, forget about cheap CO2 laser systems and try UV 355nm.

Second: reducing the focal length f is conducive to reducing the spot diameter d. This is also the reason why I advise customers to use a field lens with a smaller focal length when we require high marking accuracy. Of course, if the focal length is small, the format will inevitably decrease, because there is such a relationship between the format and the focal length: format = 0.7f. Therefore, it is a contradiction to make the focusing spot smaller and the format larger. Everyone hopes that the smaller the focusing spot, the better. On the premise that the focusing spot is small, the larger the scanning format, the better, but this kind of thing has both the fish and the bear's paw. It's impossible, it's just a balance between the two. In the cutting and welding system, there is no problem of format, but there are two other contradictions: first, the smaller f is, the distance between the focusing mirror and the workpiece is also reduced, and the waste gas and slag during processing will splash and adhere to the surface of the focusing mirror. Or the surface of the protective mirror will reduce the processing effect and the life of the focusing mirror or protective mirror. If 10 protective mirrors are damaged in a day, it will cost several hundred yuan, so it will not be worth it. Second, the smaller the f, the smaller the depth of focus, because the formula for calculating the depth of focus is:

The smaller the focal depth, the less penetration of the welding machine, and the cutting machine cannot cut thick plates.

Third: the use of beam expander can effectively reduce the focus spot. After the beam expander, D will become larger, and according to d=2fλ/D, the focus point d will become smaller.