## 1 Introduction  
Nowadays, Laser Beam Cutting (LBC) is the most widely used process in industry for cutting different sheet materials. Laser machining is capable to cut a very large range of materials that covers almost all categories (metals, composites and ceramics). This peculiarity is due to the thermal nature of the laser process that depends on the material thermal behavior rather than on its mechanical properties. Thermal energy is provided by the laser beam and converted into heat. The laser beam can be focused on the material surface to a very small spot and, being electromagnetic radiation, it does not involve mechanical cutting force, tool wear and vibration. Thus, LBC is suitable for cutting hard or brittle materials as well. The laser beam interacts with the electrons of the material, and part of the energy is absorbed, producing a highly localized rise in temperature up to melting, vaporization or chemical state change. These different physical phenomena that govern the laser-material interaction mainly depend on chemical and physical properties of the material such as absorptivity, thermal conductivity, as well as the laser characteristics including wavelength and power density [1,2]. Melting cutting is by far the most common method for metal cutting, whereas vaporization cutting is typically used for materials with low vaporization energy and high irradiation lasers. Chemical state change cutting is used for some organic materials instead, when the increase in temperature leads to the rupture of the chemical bonds between the molecules. In melting cutting, the molten material is removed from the groove by a pressurized gas assistant jet. Depending on the material to be cut, the auxiliary gas can be inert or active. The first one protects the surface from oxidation, whereas the second one (usually oxygen) generates an intense exothermal reaction that increases the temperature of the cutting area, thus allowing thicker cuts and higher speeds. Compared to plasma cutting, laser machining offers several benefits such as automation capability and reduced production costs, and it provides higher-quality kerfs [3], even though it allows cutting thinner sections. The main limiting factor of the LCB is the high temperature reached in the process, and the consequent thermal damage induced into the material machined, such as the formation of Heat Affected Zone (HAZ), recast layer, drag line and slag attachment. CO\({}_{2}\) gas laser and solid-state laser are the most established types of lasers for industrial cutting of metals. CO\({}_{2}\) gas lasers (\(\lambda\) = 10.6 \(\upmu\)m) are widely adopted because of their high output power and good beam quality. However, high power efficiency, ease of beam guidance, high beam quality and ten times shorter wavelength are some of the advantages of solid-state disk and fiber lasers [4]. Indeed, very different wavelengths lead to diverse absorption behaviors. Steel has acceptable absorption for CO\({}_{2}\) laser generated wavelength. Conversely, solid-state lasers (also known as 1 \(\upmu\)m radiation) have found a niche application in industrial-scale laser cutting of highly reflective materials such as copper, aluminum and gold [5]. However, CO\({}_{2}\) laser cutting of aluminum alloys, although not common, may be of industrial interest. The use of a higher-power source, such as CO\({}_{2}\) laser source, combined with highly pressurized assistant gas may overcome these limitations. Solid-state disk and fiber lasers provide better performance in melting cutting of thin stainless steel sheets (up to 2 mm) with nitrogen as assisting gas, due to the higher beam quality. Under these conditions, solid-state lasers achieve considerably higher cutting speed and surface quality than CO\({}_{2}\) lasers. Nevertheless, the spread between the maximum cutting speeds is reduced when increasing sheet thickness. Conversely, in oxygen-assisted laser cutting, solid-state lasers and CO\({}_{2}\) lasers exhibit comparable performances in term of cutting speed and cut edge quality.