**10.5 Time width or pulse width**

Pulse width is the duration of each laser pulse (ms). During the pulse on time, the workpiece senses the pulse power, and in the distance between the two laser pulses (pulse off), the parent material is cooling. The pulse width controls the heat input to the workpiece, the welding width, and the heat cycle. Increasing the pulse width expands the welding and HAZ dimensions due to the increased heat transfer time (**Figure 16**) [3–7, 13, 17, 19, 20].

In other words, the pulse width is a fine-tuning parameter, which is used to adjust the penetration and width of the weld and, if necessary, to stabilize the weld. By increasing the pulse width and prolonging the thermal transfer time, the weld dimensions (penetration, width, and HAZ). To increase the weld width, reduce the thermal cycle, and minimize depth variation, the pulse width must be increased.

It should be mentioned that the optimization of maximum power (peak power) and pulse width during LBW highly affect the joint quality. So that a very high maximum power causes spraying and improper joining. On the other hand, very small pulse width can cause spraying or lack of penetration.

**Figure 16.** *Schematic of the pulse width and power peak effects on the weld shape.*

**Figure 17.** *Visual relationship between the frequency, pulse width, and energy level.*

#### **10.6 Pulse energy**

From the point of view of the irradiated material, each laser pulse acts as a package of energy called pulse energy (pulse energy, (E, J)) and its relationship with the power peak (Pp, (J/ms), and pulse width (T, (ms)) (pulse width or pulse duration) (Eq. (4)) is in **Figure 17** [3–7, 13, 17, 19, 20].

$$E = P\_p \times T \tag{4}$$

#### **10.7 Frequency**

Frequency (f) indicates the number of pulses of the flash lamp and therefore the number of laser pulses per second (Eq. (5)). Frequency is expressed in Hertz (Hz) or pulse per second (PPS) as given in Eq. (1). On the other hand, the frequency inverse (1/f) is equal to the interval between two consecutive pulses. By knowing the amplitude of the laser pulse (T), we can estimate the time between two pulses, i.e. the laser extinction time. It also controls the heat input to the workpiece and the heat cycle [3–7, 13, 17, 19, 20].

$$f = \frac{1}{\text{Pulse period}}\tag{5}$$

#### **10.8 Average power**

The importance of this parameter is for welds using more than one pulse. In fact, the average power (Pave) of a laser source is obtained by multiplying the energy of each pulse by its frequency (Eq. (6)) [3–7, 13, 17, 19, 20].

$$P\_{ave} = E \times F \tag{6}$$

Medium power is applied when more than one pulse is required for welding. As the average power increases, the heat input rate increases; hence, with increasing the heat input, the penetration depth and weld width increase. In general, at constant power, the smaller the beam diameter, the more concentrated the heat and the smaller the weld pool. The diameter of a laser beam output can be increased by increasing the power. For instance, lasers with 1, 5, 10, and 25 kW powers have

diameters of 10, 25, 40, and 70 mm, respectively. The average power density of these diameters is between 6 and 13 W/cm<sup>2</sup> .

#### **10.9 Power intensity or density**

The density or power intensity (I) at any given moment is equal to the amount of direct power equal to the cross-sectional area of the beam (D) at the parent material surface (Eq. (7)). The diameter of the laser spot in the focus depends on the type of laser and its beam quality and the beam focusing system. Power density is a function of the beam focusing tool and the maximum laser output power [3–7, 13, 17, 19, 20].

$$I = \frac{Power}{\pi \frac{D^2}{4}}\tag{7}$$

In short, the amount of beam intensity determines the state of the welding process and the formation or non-formation of the keyhole. On the power peak, the penetration rate of the weld, the pulse width usually controls the heat input to the workpiece, and the power density controls the penetration rate of the weld.

#### **10.10 Optical specifications of the laser beam focusing system in the center**

The choice of laser beam focusing system depends on the type of process, the type of laser, and the workpiece material. In fact, the cross-sectional area of the laser beam at the focus, which is one of the two main factors in determining the laser intensity at the focus, depends on the choice of the focal length of the laser beam focusing system. The relationship between the laser spot diameter at focus (DF) and the focal depth or Rayleigh length (RL) with the focal length of the beam focusing system is given in Eqs. (8) and (9).

$$D\_F = M^2 \left(\frac{4}{\pi}\right) \lambda \left(\frac{f}{D\_L}\right) \tag{8}$$

$$R\_L = D\_F \left(\frac{f}{D\_L}\right) \tag{9}$$

where f is the focal length of the beam focusing system, λ is the laser wavelength and M2 is the quality factor of the laser beam. Rayleigh length is the distance at which the laser intensity reaches 70.7% of the maximum intensity at the focus and is considered as the focal depth or effective focal length. The larger the focal length of the focus system, the smaller the diameter of the laser spot in the focus (**Figure 18**) [3, 4, 6].

The intensity distribution due to the optical nature of lasers depends on the properties of the resonator, active medium, and pumping system. Although the intensity distribution at the cross-section of the beam is not uniform, it can be predicted according to the properties of the resonator, active medium, and pumping system and is considered as an intrinsic feature of each source. The best mode for intensity distribution is Hermite-Gaussian mode or TEM00, having the highest intensity in the center of the beam with an M2 factor of 1. High-power industrial lasers usually have a combination of TEM00 mode and higher modes in the beam. Therefore, the higher the share of higher modes, the larger the M2 factor, the greater the divergence, and the

**Figure 18.** *Schematic of the laser beam focusing system.*

lower the optical quality of the laser beam. To reduce the divergence and correct the beam of lasers with low optical beam quality, such as solid-state Nd:YAG sources, a special optical tool called a beam expander is used.
