High power beam properties and parameters

The efficient material processing with high power beams requires suitable spot diameter and high beam quality at the same time to achieve maximum potential. Laser beam quality can be characterised by properties shown in Figure 15 which represents an axially symmetric Gaussian beam, when transverse electric field and irradiance distribution are following the Gaussian functions, propagation along the z axis.

Figure 15. Cross-section of an axially symmetrical Gaussian laser beam propagation along the z axis. (Anon, n.d.c)

The high power laser beam quality is described by the beam parameter product (known as BPP, dimension is mm×mrad) which is convertible to other beam quality values (see equation 11.0) such as K value and M² value also called the beam propagation factor. The BPP parameter usually is used to describe the beam quality of the solid-state lasers (Nd:YAG, fiber, diode, and disk laser), when K (or K-factor) and M² are used to indicate CO₂ laser beam quality. K-factor is commonly used in Europe, while M² (dimensionless) frequently used in the USA. (Steen & Mazumder, 2010)

The BPP is the product of a laser beam the half of full divergence angle θ (dimension is mrad, the far-field) and the radius of the beam at its narrowest point, so-called the beam waist diameter w0. The BPP can be estimated according to the next equation (Steen &

Mazumder, 2010; Olsen, 2000):

0θ w

BPP= (11.0)

BPP K values), however real beams realistically cannot reach 1 and therefore M²>1.

In fact, the beam parameter product indicates how well the beam can be focused to a small spot, in other words this properties can be called as the focusability of a laser beam (focusability = 1/BPP). Lower value of BPP indicates that laser beam has better quality (the BPP for an ideal beam is λ/π, also called as diffraction-limited Gaussian beam). In other words, lower BPP values give possibility to focus a very small spot as possible. (Quintino et al., 2007), (Abt et al., 2008), (Weberpals et al., 2007)

The function w(z) which is the radius of the beam at a longitudinal distance z, can be calculated according to the following equation (Siegman, 1986):

( )

The radius of curvature R(z) (or the wavefront radius of curvature in spreading laser beam) can be calculated by the next equation (Siegman, 1986):

( )

Another very important laser beam parameter is the Rayleigh length zR (or Rayleigh distance, Rayleigh range) of the focused beam which is the distance between the focal point (z = 0 focal plane position or when R(z) is totally flat) and the plane where the radius of focal point is increased by 2 (since 2⋅w₀), therefore the cross-section area of the focal point is doubled, along the direction of propagation (Siegman, 1986):

λ

According to the equation 15.0 a decreasing BPP parameter provides increased Rayleigh length.

The depth of focus b (depth of field or confocal parameter) is the distance between two planes located from the beam waist (z = 0) in either directions at the Rayleigh length along the direction of propagation as shown in Figure 16, therefore the depth of focus is equal to the doubled Rayleigh length. Consequently, the depth of focus point is such a distance where the highest and almost equal laser beam power density is concentrated throughout whole cross-sectional area. Depth of focus depends on focal point radius and laser wavelength (Siegman, 1986; Ion, 2005):

λ π

2 2 w

z

b= _R = (16.0)

Focal point diameter and position. Focal point diameter influence the power density (or laser intensity) which is equal to total laser power divided by spot area, and therefore can be a critical beam parameter. For traditional welding applications the focal point diameter usually lies in the range of 0.2-0.6 mm to achieve suitable power density and penetration for welding applications (Kannatey-Asibu Jr., 2009). Too large a spot diameter, for example 1-2 mm, requires very high power and therefore it is not efficient processing, however too small focal point diameter can create sagging and even cutting conditions of the material due to very high power intensity (Salminen & Fellman, 2007).

The main characteristics of the focusing process for fiber lasers are demonstrated in Figure 16.

Figure 16. The representation of the optical system of a high-power fiber laser which include collimation and focusing optics. The focal length is ffoc and the collimation length is fcol. NA is the numerical aperture of the delivery fiber and zR is the Rayleigh length. (Abt et al., 2008)

According to the Figure 16, the focal point diameter (denoted as d0) depends on the half of full divergence angle (denoted as θ0), the beam quality factor, and laser beam wavelength (Abt et al., 2008):

Where dcol is collimated (or unfocused, raw) beam diameter which is between collimation and focusing lenses. From the equation 17.0 it can be concluded that focal point diameter also depends on beam quality and focal length.

Apparently, the equation 17.0 shows that with fixed focal length and focal point diameter, with shorter wavelength lasers with better beam quality (fiber and disk lasers), it is possible to reduce unfocused beam diameter which leads to reduction in diameter of collimation lens and optics in general, as a result, it provides increased mobility of the welding system.

In addition, from equation 17.0 it can be seen that focal length (which is fixed during manufacturing since it depends only on the welding head) controls two major parameters such as laser beam diameter and depth of focus, where longer focal length leads to larger spot diameter and depth of focus, and vice versa as shown in Figure 17. Manufacturing importance is that higher focal length provides technological flexibility and more importantly does not allow to damage processing optics by liquid melt from molten pool and ejected plasma plume from the welding area (Kannatey-Asibu Jr., 2009).

Figure 17. The focal length and corresponding depth of focus. (Kannatey-Asibu Jr., 2009)

In case of laser systems which utilise beam transportation by fiber system, the focal point diameter can be also calculated through the optical magnification (OM) and fiber core diameter (df) (Abt et al., 2008):

col foc f

f f

d f OM d

d₀ = = (18.0)

According to equation 18.0 it can be stated that focal point diameter can be more finely focused with smaller focal core diameter.

Practically, to measure precisely focal point diameter is impossible. Usually there are several definition of the focal point diameter such as full width at half-maximum (FWHM, see Figure 18) which contains energy inside of the beam where the laser power is 50% of laser power maximum, width at 1/e² intensity (contains 86.4% laser energy, where drop is 13.5% as shown in Figure 18) which is used for TEM00, diameter containing 86% of total beam energy (D86), and second order moment (4σ) according to ISO 11146. (Migliore, 1996)

Figure 18. Schematic representation of the Gaussian irradiance distribution profile (longitudinal mode) on the left (Anon, n.d.c). The beam spot profile and intensity distribution

of (a,b) LP₀₁ mode and (c,d) LP₀₂ mode on the right (Iadicicco et al., 2013).

Focal point position can play a vital role in laser welding since it effect on weld geometry and quality in general. For the clarification an example with different focal position is explained from typical experiments conducted by Vänskä et al. (2013).

Figure 19. Schematic representation of the focal spot position from +2 to -2 (from left to right). Austenitic stainless steel EN 1.4404, welding speed 2 m/min. (Vänskä et al., 2013) As can be seen from Figure 19 for welding operation focal position below surface is recommended to acquire the highest penetration as possible. Moreover, focal spot position has an effect on weld shape. Yamazaki & Kitagawa (2012), Shin & Nakata (2010) and Liu et al. (2008) reported similar results by using 10 kW fiber laser welding system. As a result, in autogenous laser welding it is advisable to have a focal position on the top surface (0 mm) or slightly below the top surface if focal spot diameter provides suitable power density (Steen &

Mazumder, 2010).