Focal length and mounting distance
In general, there are two types of focusing CO2 laser lenses: Plano convex lenses which have one convex surface (convex = dome-like curvature) and one flat surface, and meniscus lenses which have one convex surface and one concave surface (concave = hollow curvature). In most CO2 laser cutting machines, meniscus lenses are used because they produce a smaller focus diameter (see next section). In some CO2 laser machines, CO2 laser lenses type plano-convex are used because their production costs are a little bit lower. For a laser user who thinks about replacing a plano-convex lens by a meniscus lens, it is important to check if the focus position can be adjusted correctly. Even if a plano-convex lens and a meniscus lens have same diameter, thickness and focal length, the focus position of the meniscus lens can be several mm higher if compared to the plano-convex lens. Reason is that the focal length of a lens is defined as the distance between the focus and the so-called principal plane. The principal plane is defined according to a scientific rule and is located somewhere inside the lens. For checking the position of the focus in a CO2 laser cutting head, it is much more useful to know the "Mounting distance" of the lens. It is defined as the distance between the edge of the lower surface and the focal plane and therefore connected directly to the position of the focus within the cutting head. If the mounting distance of replacement optics is different from the mounting distance of the original ZnSe lens for CO2 laser, it might happen that the focus position is shifted such that it cannot be corrected within the adjustment range of the cutting head. On the other side, it is possible to extend the adjustment range by using lenses with different mounting distances. All CO2 laser lenses are made of Zink Selinide (ZnSe lenses)
Spherical aberration means that the focus position of the outer portion of the laser beam is closer to the lens than the focus position of the inner portion (see picture). As a consequence, the focus diameter is not zero, but has some extension which can be calculated by the following formulas:
df = 0.0286 (din)3 / (FL)2 (plano-convex lenses)
df = 0.0187 (din)3 / (FL)2 (meniscus lenses)
df = focus diameter, din = diameter of incoming beam,
FL = focal length
din = 20 mm,
FL = 3.75":
>>> df = 0.025 mm (plano-convex lens)
>>> df = 0.017 mm (meniscus lens) The example shows that meniscus lenses produce smaller focus diameters than plano-convex lenses. The difference is significant especially at large beam diameters and short focal lengths. In order to minimize this effect, meniscus lenses are used in most CO2 laser cutting systems. In most practical applications, however, there is a second and much more important effect which influences the focus diameter. It is called diffraction and described in the next section.
A laser beam is an electromagnetic wave and therefore has properties similar to water waves or sound waves. One consequence of this wave-like nature is that a laser beam cannot be focussed to a sharp point. Instead the focus has a spot size which can be calculated as follows:
df = (4/Π) M2 λ FL / din
df = focus diameter, M2 = beam quality, λ= laser wavelength,
FL = focal length of focussing lens, din = diameter of incoming beam
Examples: ( λ = 10.6 µm, M1 = 2)
din = 20 mm, FL = 7.5" >> df = 0.13 mm
din = 20 mm, FL = 3.75" >> df = 0.065 mm
First of all, the example shows that focus diameters are much larger than the values calculated in the section above. This means that in most cutting applications, spherical aberration can be neglected. Diffraction is therefore the most important effect concerning focus diameters. In general, the formula shows that by decreasing the focal length, the focus diameter is decreased as well, with the consequence that the intensity of the laser beam is increased. As high laser intensity is useful in most cutting applications, focal length should be as short as possible. However, a short focal length has the disadvantage that the beam diameter increases rapidly above and below the focus. Therefore, maximal thickness of materials which can be cut efficiently is very limited, and the optimal focal length increases with increasing thickness of material.
Absorption and thermal lensing
During laser operation with several kilowatts, the focusing lens is heated because it absorbs a small portion of the laser power. Absorption takes place mainly in the AR coatings and at dirt on the lens. At a new clean lens with standard AR coating, absorption is typically 0.2% of the incoming laser power. A CO2 laser lens such as Ophir's BLACK Magic is a low absorption lens (lower than 0.15%). During use in a CO2 laser cutting machine, absorption increases gradually due to increasing amounts of dirt on the lower surface. When the lens needs to be replaced, absorption usually is in the range 0.3 to 0.4%. Heating of the lens causes additional surface curvature due to thermal expansion and increases the refractive index of the lens material (ZnSe lens). As a consequence of these effects, the lens focal length becomes shorter, and the focus position cannot be predicted exactly because it depends on many parameters like laser power, intervals laser on/off, cleanliness of lens, and others. Therefore, use of low absorption CO2 laser lenses with can make the focal length more stable and therefore improve reliability of the cutting process. If there are dirt particles on the lens, the lens material is not heated uniformly, but mainly at the areas close to these dirt particles. As a consequence, focusing properties become worse; focus diameter increases, and cutting quality decreases. So if a certain "critical" amount of dirt has accumulated on the lens, it needs to be replaced. However, it might still work fine at reduced laser power.