Attenuation and shrinking beam simulation for beam quality measurement of high-power lasers

introduction
High-power lasers are the core components of key national development fields such as laser nuclear fusion, laser weapons, and laser M2 manufacturing [1-3]. The beam quality factor is the main parameter to characterize the transverse characteristics of high-power lasers, which takes into account both the laser beam width and the far-field divergence angle, covering both the near-field and far-field characteristics of the laser [4-5]. The analysis of beam quality is conducive to exploring the mode field change mechanism of high-power lasers, so as to better design and manufacture laser devices. Mastering the above parameters can also help to evaluate the dynamic changes in the near-field and far-field characteristics of the laser, and to control and utilize the laser mode field to improve the near-field or far-field characteristics of the laser. Therefore, beam quality measurement plays an important role in the development and application of high-power lasers.

Currently, beam quality measurements rely mostly on beam quality analyzers. With the development of high-power laser technology, there is an increasing demand for beam quality measurement of large-aperture high-power lasers [6]. For example, in order to suppress the thermal lensing effect of the optical system, the caliber of the optical system with high-power lasers also increases with the laser power [7]. The output of the collimated beam of the 30 kW fiber laser with fiber bundle reaches the order of 50 mm, and the current commercial beam quality measurement system cannot meet the beam quality measurement of high-power and large-aperture lasers. Spricion's BSQ SP920 is similar to Cinogy's Cinsquare in that it is only used for beam quality evaluation of low-power lasers. Due to the limitation of the size of the optical components of the system and the size of the detector target surface, the maximum beam diameter of the laser that can be measured by the above equipment is 10 mm. Primes' FM+ can measure the beam quality of high-power lasers, but only for focused spots, with a maximum beam aperture of 5 mm. The LQM+ can be used for high-power laser beam quality measurements with a maximum beam diameter of 15 mm. Therefore, it is necessary to develop attenuation and shrinking beam components for high-power beam quality measurement to meet the increasing measurement aperture and power requirements in the laser field.

In this paper, the attenuation and shrinking technology of high-power laser beam quality measurement is studied, the attenuation and shrinking beam component model is established, and the simulation analysis is carried out to study the influence of the wave aberration generated by the attenuation and shrinking beam component on the beam quality factor under high-power laser irradiation.

 1 Beam Quality Measurement Principle
M2 laser beam quality factor As a core index to measure the quality of laser beam, it can quantitatively reflect the quality of laser beam. It is currently the most ideal parameter for evaluating the beam quality of high-power fiber lasers [8]. The beam quality factor is defined as

where: denotes the laser wavelength; indicates the width of the laser beam waist; Indicates the half-divergence angle of the laser far-field.
The principle of the beam quality factor is to calculate the beam width of the laser based on the definition of the second-order moment of the light intensity, and then calculate the beam quality factor by using the hyperbolic fitting method [9-11]. In order to avoid the interference of useless information such as noise and diffraction effects in laser measurement experiments, it is also necessary to automatically correct the light intensity calculation area. The hyperbolic fitting method is currently the accepted method for measuring beam quality factors, and it is also large.A schematic diagram of the measurement principle of the calculation method [12] used by most commercial beam quality analyzers is shown in Figure 1.

As the laser propagates in free space, its trajectory is hyperbolic [4]. Therefore, after obtaining the light intensity distribution of the laser at different positions and calculating the beam width of the spot, the obtained beam width can be fitted with its position on a hyperbola, and the beam waist width and the far-field divergence angle of the laser beam can be obtained according to the fitting curve equation, so as to calculate the beam quality factor of the laser.

 2 Attenuation component design simulation
2.1 Simulation of the effect of thermally induced phase contrast of attenuating components on beam quality factor

In order to measure the quality of high-power laser beams, the laser is attenuated to the order of microwatts or less. Optical components undergo thermal deformation under intense laser irradiation, which in turn causes laser thermally induced aberration [13]. Using the COMSOL Multiphysics software, the thermal deformation of the laser was simulated based on the finite element method, and the thermoinduced aberration was added to the complex amplitude distribution of the laser, and the beam quality factor calculation model was brought into the calculation model to calculate the influence of the laser thermally induced aberration on the laser beam quality factor.
The simulation parameters are set as follows: the laser wavelength is 1 080 nm, the spot radius is 24.3 mm after beam expansion collimation, and the laser mode is the standard
The mode mode is distributed, the ambient temperature is 20 °C, and the optical components are CORNING7980 fused silica glass (CORNING7980, Zeyuan Optics). The optical element is fixed by the peripheral pressure ring method, and the parameters of the optical element are shown in Table 1.

To perform a thermal deformation analysis of an optical component using the COMSOL Multiphysics finite element method, the target optics are first meshed, as shown in Figure 2(a). Fig. 2(b) shows the simulation results of the instantaneous temperature distribution of the CORNING7980 fused silica glass irradiated at 3 kW laser power for 300 s. The temperature gradually increases from the periphery of the CORNING7980 fused silica glass to the center, reaching a maximum of 26.2 °C at the center of the circle and a maximum temperature of 6.2 °C. Figure 2(c) CORNING7980 simulation results of the thermal deformation distribution of fused silica glass at 3 kW laser power.

The maximum deformation of the optical element is at the center of the laser, and then slowly decreases to the position of no thermal deformation at the edge of the optical element, and the maximum thermal deformation of the center of the optical element is 16.3 nm at 300 s. Once the thermal deformation has been simulated using the finite element method in the COMSOL Multiphysics software, the laser thermally induced aberration can be calculated.

As shown in Figure 3, a factor measurement model for the multi-location spot method was established according to the ISO 11146 international standard [14]. Firstly, the complex amplitude of the laser to be measured is generated, and the wavefront distortion caused by the thermal lensing effect of the attenuation component is simulated by the COMSOL software, and the wavefront distortion is added to the complex amplitude. Then, according to the angular spectrum diffraction formula, the light intensity distribution of the laser at different positions in free space is obtained. Then, based on the definition of the second-order moment of light intensity, the beam width of the laser spot at different positions is calculated, and the hyperbolic fitting of the laser beam width at different positions is carried out, and finally the beam quality factor under the thermal lens effect of the attenuating component is calculated.

Figure 4 calculates the peak-to-valley (PV) values of thermally induced aberrations as a function of the laser beam quality factor. The intensity of the laser light used in the simulation

is a Gaussian-like distribution. As can be seen from Figure 4, when the peak-to-valley (PV) value of thermally induced aberration is 131 nm, the beam quality factor of the laser is changed by 1.00 becomes 1.10, and when the PV value of thermoinduced aberration is 82 nm, the beam quality factor of the laser changes from 1.00 to 1.05. Therefore, according to the above simulation, if the peak-to-valley (PV) value of the thermal aberration of the optical element is less than 82 nm, the influence on the laser beam quality factor is less than 5% in the measurement of the high-power fiber laser beam quality factor.

 2.2 Simulation of the influence of the polarization characteristics of attenuated components on the beam quality factor M2
When a high-power laser passes through the attenuation component at an angle, the polarization state of the light will change due to the different reflection and transmission coefficients of the S and P waves in the reflected and refracted light, so that an error will occur when measuring the laser beam quality factor. The influence of the polarization characteristics of the attenuation component on the laser beam quality factor M2 is studied by simulation, and the simulation program process is shown in Figure 5, including four steps: eigenmode calculation, reference light generation, virtual transmission and fitting calculation.

First, the simulation needs to determine the type and number of linear polarization mode (LP) polarization modes that can be transmitted in the fiber according to the given fiber parameters and wavelengths, and calculate the complex amplitude distribution of the eigenmodes that can be propagated. The parameters are set as follows: the core diameter of the fiber is 20 μm, the diameter of the cladding is 400 μm, the numerical aperture of the core is 0.06, the numerical aperture of the cladding is 0.46, and the normalized frequency is
3.49 with a laser wavelength of 1 080 nm. There are 6 types of LP molds, namely LP01, LP02, LP11e, LP11o, LP21e, and LP21o. By changing the coefficients of polarized light in the X and Y directions, the P and S rays can be controlled. From the linear superposition theory of eigenmode, the normalized complex amplitude of the reference fiber endface can be obtained. for
In order to simulate and calculate the laser beam quality factor, it is also necessary to obtain the complex amplitude distribution at the target surface of the camera, so the complex amplitude of the optical fiber end face needs to be virtually transmitted through the 4F system to obtain the complex amplitude distribution at the conjugate position with the optical fiber end face. The number of pixels in the image is required to be large enough to set a suitable pixel size, that is, the image resolution must be high enough. Table 2 shows the parameter settings of the image matrix before polarization phase-shift interference in this simulation.

After obtaining the far-field complex amplitude distribution to be measured, a virtual 4F system was constructed to obtain the near-field complex amplitude distribution of the conjugate position between the 4F system and the optical fiber end face. It should be pointed out that in terms of parameter setting, in order to prevent the difference between the near-field and far-field spot sizes from being too large, the number of pixels is too large, resulting in the occurrence of problems such as large memory occupation and slow operation of the simulation program, the focal length of the first lens is not suitable here If it is too large, a suitable system magnification can be obtained by changing the parameter value of the focal length of the second lens. Table 3 shows the virtual 4F system in the simulation system.

After the far-field complex amplitude distribution of the reference light is simulated, the light intensity can be calculated based on the complex amplitude distribution and the hyperbolic fitting square can be used. The laser beam quality factor M2 under different polarization states is calculated.

Fig. 6 is the simulation of the beam quality factor under different polarization states, Fig. 6(a) is the simulation of the S beam depolarization, it can be seen that the beam mass factors of the depolarized light in the X direction and the Y direction are 1.766 and 1.760, respectively, Fig. 6(b) is the simulation of the P beam depolarization, it can be seen that the beam quality factors of the depolarized light in the X and Y directions are 1.805 and 1.852, respectively, and Fig. 6(c) is the simulation of the normal polarized light, it can be seen that The beam quality factors of polarized light in the x-direction and y-direction are 1.818 and 1.932, respectively. Through the above data analysis, it can be seen that the beam quality factor of a single polarization direction is different from that of the original output light, and when the beam passes through the attenuation component, if the depolarization phenomenon occurs, the beam quality factor will be affected, so that the final beam quality factor M2 result is smaller.

 3    Design principles and simulations of bundle shrinking components
Telescope systems are a common means of achieving laser beam reduction collimation. The optical system of the beam reduction assembly is composed of a lens group, using a Galilean type system, a single-mode fiber laser with a central wavelength of 1 064 nm is used as a light source, the fiber laser is emitted parallel from the reference plane, and then collimated through the lens 2 after convergence through the lens 1, and the diameter of the exit spot is one-third of the diameter of the incident spot, of which the materials used in the lens 1 and 2. All are fused silica, as shown in Figure 7.

In the beam quality measurement system, the manufacturing and assembly errors of the telescope system will cause wavefront distortion, which will affect the measurement of beam quality factor. In order to accurately calculate the beam quality factor, a simulation model of the beam shrinking component was established, as shown in Figure 8. Firstly, the laser complex amplitude to be measured is generated, and the wavefront distortion caused by the manufacturing and assembly of the beam reduction component is simulated by Zemax software, and the wavefront distortion is added. Complex amplitude on . Then, according to the angular diffraction formula, the light intensity distribution of the laser at different positions in free space is obtained. Then, based on the definition of the second-order moment of light intensity, the laser spot beam widths at different positions are calculated, and the laser beam widths at different positions are fitted hyperbola, and the beam quality factor is finally calculated. Zemax software was used to simulate the wave aberration due to the change in the field of view of the bundle reduction assembly. The influence of the wave aberration caused by the change of the field of view on the laser beam quality factor is analyzed.

Figure 9 shows the wavefront diagram of the beam shrinking component and its coefficients in the field of view of 0°. Wavefront analysis by Zemax software shows that when the laser wavelength is 1 080 mm, the PV value is 0.003 9, which is lower than the design requirement and its main ray RMS is 0.001 1 [15].

Figure 10 shows the fitting curve of the laser beam quality factor with the addition of a beam shrinking component at a 0° field of view. By calculating the laser beam quality factor M2 model, the laser beam quality factor M2 of the beam shrinking component at 0° field of view can be simulated. The beam waist position in the X direction is 270 mm, the beam waist position in the Y direction is 277 mm, the waist radius in the X direction is 0.573 mm, and the waist radius in the Y direction is 0.572 mm, the beam quality factor M2 in the x-direction is 1.033 8, and the beam quality factor M2 in the y-direction is 1.034 0.

Continue to increase the angle of the field of view in the x-direction, and the Zenick coefficient under different fields of view is obtained in Zemax. With the angle of the field of view in the x-direction
With the increase, the coefficients of the tilt term, comet term, defocus term, image scatter term and spherical aberration term in the X direction all increase, while the inclination term and comet term coefficients in the y direction remain unchanged, and the coefficient of the inclination term in the X direction increases the most. The above data are added to the calculation model of the laser beam quality factor M2, and the laser beam quality factor M2 corresponding to the field of view is calculated.

Figure 11 shows the beam quality factor M2 under different field of view angles. It can be seen that with the increase of the field of view in the x-direction, the horizontal beam quality factor M2 and the vertical beam quality factor M2y deteriorate gradually. When the field of view increases from 0° to 7.2°, the beam quality factor M2 increases from 1.033 0 to 1.085 5. The simulated beam quality factor M2 of the 7.2° field of view is 5% larger than that of the 0° field of view. From this simulation, it can be seen that in order to ensure the accuracy of the subsequent experiments, the incident light should be guaranteed when installing the beam shrinking assembly
The angular field of view between the optical axis and the center of the beam shrinking component is less than 7° (the influence is less than 5%), otherwise the measurement of the beam quality factor M2 will be greatly affected.

4 Conclusion
In order to solve the problem that the current beam quality analyzer can only be used for the beam quality evaluation of small-aperture and low-power lasers, the simulation research of attenuation and beam reduction technology for beam quality measurement of high-power lasers is carried out in this paper. Based on the Zenic polynomial and the calculation model of the beam quality factor, the influence of the wavefront distortion of the beam shrinking component on the laser beam quality measurement was studied and analyzed, and the Zemax simulation was used to analyze the light when the angle of view between the incident light and the center optical axis of the beam reduction component was less than 7° during the experimental setup. The impact of beam quality factor measurements is 5% smaller. A theoretical calculation model of laser thermally induced aberration is established, and the PV value of thermally induced aberration is simulated
Less than 82 nm, the effect on beam quality is less than 5%. A simulation model of the influence of laser polarization characteristics on beam quality is established, and it is concluded that when the beam passes through the attenuation component, if depolarization occurs, the beam quality measurement result will be smaller.