I was wondering how the printer works? Is it with a two photon polymerization process? I’ve been reading, and this process uses lasers around 800 nm, so what is the wavelength of the laser that is incorporated in the printer

It uses a single beam.
The photo-activator in the resin is sensitive to near-UV light; the laser emits at 405 nm (violet).

The two photon polymerization doesn’t mean you need two beams. However, if they use a laser of 405 nm, how they control the polymerization at a specific point and prevent the polymerization of the entire tray?

Because they cure one layer at a time.
The layer thickness is limited by laser intensity and resin absorption rate.

It doesn’t need to cure at arbitrary points in a volume, it cures in a plane.

The earliest, oldest stereolithography systems used to use two beams (or two photons, as a more generalized concept). However, that’s needlessly complex, not to mention expensive, as you need a full vat of resin for every print and the ability to deflect the beam in an additional axis (while keeping the beam profile clean and collimated). Not to mention the fact the resin has to be totally transparent to the wavelength used.

As a consequence, this system has typically only been in use in very large and very expensive printers and ismostly getting phased out today.

But why the polymerization occur just at that plane? If you generate the radicals, these should start a polymerization through the entire tray. How do you control this?

By the way, thank you for your responses and time…

It’s not a chain-growth polymerization, or if it is, it’s highly localized. I’m very very far from an expert in that field (or even chemistry in general), but AFAIK, even with chain growth, you can modulate the propagation with additives, and limit it to a very small area.