High-power nanosecond ultraviolet (UV) lasers have been widely applied in laser lift-off, laser annealing, laser transfer, and other fields, but their output is usually partially coherent light with nonuniform intensity distribution. To meet the high requirements of beam uniformity for precision machining, a homogenizer with microlens arrays is proposed. The microlens array homogenization technology based on the principle of beam splitting and superposition has attracted extensive attention due to its advantages of high energy utilization, insensitivity to wavelength, and good availability of unstable multimode beams. However, the current research on the homogenization technology of microlens arrays mostly adopts the ray tracing method of geometric optics, ignoring the diffraction effects that seriously affect the performance of homogenized beams, such as multi-beam interference and the finite aperture effect. Therefore, we design the microlens array homogenizer following the partially coherent diffraction principle and perform the quantization analysis of the influence of homogenizer parameters on the performance of output laser beams.

Partially coherent light can be described by the cross-spectral density function (CSD), but direct application of CSD to the simulation involves quadruple integral calculation, which takes a long time. Therefore, the pseudo-mode representation of CSD is used to simplify the numerical process and reduce computational time. By combining the pseudo-mode representation of partially coherent light and coherent light diffraction theory, we build a numerical simulation model of a microlens array homogenizer for high-power UV lasers and quantitatively analyze the parameters of the homogenizer. Specifically, an excimer laser source with different spatial coherence along the horizontal (short axis) and vertical (long axis) directions is represented as an incoherent superposition of mutually uncorrelated pseudo-modes, i.e., the coherent plane-wave modes obtained from the Gaussian Schell-model (GSM). Then, the diffraction field of each mode passing through the microlens array homogenizer is calculated according to the angular spectrum diffraction theory and superimposed to achieve a uniform output laser beam. Moreover, the influence of parameters such as laser coherence, defocus, array spacing, and misalignment on the uniformity and edge steepness of output laser beams is discussed comprehensively. Through the simulation optimization, a high-quality microlens array homogenizer is provided, which can output a sharp square laser beam with uniformity of less than 1.5%. At the same time, the reliability of the theoretical design and the accuracy of parameter impact analysis are verified by experiments.

Firstly, the intensity distributions of excimer laser-homogenized beams on different axes (Fig. 1) are compared, and it is found that for short-axis beams with high spatial coherence, the multi-beam interference effect is stronger, which can produce obvious interference fringes and results in a decrease in beam uniformity. For long-axis beams with low spatial coherence, the beam uniformity is higher due to negligible interference effects, and the beam edges are not as sharp as short-axis beams. To meet the precision machining requirements of beam uniformity less than 1.5%, the method of increasing the defocus distance is used to reduce the effect of interference on the homogenized beam so that the short-axis uniformity is reduced from 5.3% to 0.17% (Table 1). The reason is that the size of discrete spots formed by interference becomes larger with the increase in defocus distance, and these spots overlap each other to smooth the periodic oscillation of the homogenized beam. In addition, simulations show that the sharpest-edged homogenized beam can only be obtained when the spacing between two microlens arrays is equal to the focal length of the second lens (Fig. 5). Furthermore, the condition of microlens array misalignment is discussed (Fig. 7). When the decenter or tilt is small, the oscillation effect of the homogenized beam is gradually enhanced as the decenter or tilt increases owing to the incomplete superposition of sub-beams from the microlens array. When the decenter or tilt increases to a large value, such as a decenter equal to 0.4 mm, the homogenized beam will split into multiple beams due to the energy leakage of the adjacent sub-apertures of the microlens array. If both decenter and tilt exist, the effect of misalignment will be intensified, which makes it easier for the beam to split. However, due to the periodic structure of the microlens array, as the misalignment continues to grow, the output homogenized beam returns from the split state to the single-beam state, and the superimposed sub-beams are staggered by exactly one array period. Finally, the phenomenon of the homogenized beam splitting in the case of microlens array misalignment is observed experimentally (Fig. 8). The change of the uniform beam with increasing defocus distance is consistent with the theoretical analysis results, which illustrates the reliability of the theoretical design method and the accuracy of the parameter analysis.

In this paper, the research on UV laser homogenization technology based on microlens arrays is carried out. Specifically, the pseudo-mode decomposition theory and the angular spectrum diffraction transmission algorithm are employed to build a numerical model for fast calculation of partially coherent light passing through the microlens array homogenizer, and an excimer laser is used as a simulated light source. Through the analysis of parameters such as defocus and array spacing, the optimal design parameters are determined, and the square beams with sharp edges and high uniformity are realized. Then, the influence of microlens array misalignment on the beam profile and uniformity is discussed in detail, which provides a reference for setting the assembly tolerance of the homogenization system. In addition, the reliability of the theoretical design and the accuracy of the parameter impact analysis are demonstrated through experiments.