Laser cutting machines as the name suggests, uses lasers to cut into specified materials. This is achieved by generating a laser beam due to stimulation of a laser medium or gain medium. The stimulation of the molecular or electronic transitions will drop to a lower energy lever from the high state that it was and that will activate the laser beam. The beam will then be reflected with the use of internal mirrors until it reaches the energy levels that allow it to focus in one directed beam of homochromous light. Direction is often achieved by strategically placed internal mirrors or fiber optics which guides the light to a lens where it can then be focused on the item to be cut.
Lasers typically cut from the edge with ease, but if you would want to start cutting from the middle of an item, you would need to use the laser to bore a hole at the required starting point first. There are diverse types of laser machines even though they all pretty much cover the same general requirement. The fact is that there are many ways to cut sever materials with a laser which includes melting, burning, vaporizing, engraving, etc.
This is normally referred to as melt and blow or fusion cutting. It is a process that utilizes high pressures of gas to blow away the melted material as the laser melts it. Instead of heating the material to the point of evaporation, it is simply melted to a point and the high pressure gas blows it away thus eliminating the need for the laser heat to be turned up any higher, especially if the material type may react unfavorably to high levels of heat. This is often used to cut metals.
As the name suggests, this cutting involves high levels of heat where the material is heated by the beam to a point where it penetrates and creates a hole. This is often used on certain types of plastic and wood.
This is also called flame cutting which works similarly to a torch with the exception of oxygen blown fire. Instead of fire, the laser beam does the burning and it is often used to cut thick, solid metals such as carbon steel.