Digital Engineering in Diffractive Optics for Precision Laser Processing

Abstract

This article focuses on the application of digital engineering in diffractive optics for precision laser material processing. It examines methods for the development of diffractive optical elements (DOEs) and adaptive management approaches that enhance the accuracy and efficiency of laser processing. Key achievements are highlighted in numerical modeling, machine learning applications, and geometry optimization of optical systems, along with the integration of dynamic DOEs with laser systems for adaptive beam control. The discussion includes the development of complex diffractive structures with improved characteristics and new optimization approaches. Special attention is given to the application of DOEs in micro- and nanostructuring, additive manufacturing technologies, and their integration into high-performance laser systems. Additionally, challenges related to the thermal stability of materials and the complexity of adaptive DOE control are explored, as well as the role of artificial intelligence in enhancing laser processing efficiency.

1. Introduction

Digital engineering and laser material processing have advanced significantly through the integration of cutting-edge technologies and techniques. Modern lasers combine high performance, reliability, and versatility, enhancing processing quality and increasing efficiency across various materials [1,2]. The use of machine learning methods and numerical modeling enables the prediction of processing results and optimization of laser beam parameters [3]. To enhance processing accuracy, controlling the spatial energy distribution of the laser is of particular importance [4]. Diffractive optical elements (DOEs) allow for the adaptive control of beam parameters [5,6] and are applied in thermal processing, surface structuring, welding, and nanostructure synthesis [7]. Their use expands the functional capabilities of laser systems, improving processing quality and ensuring optimal energy distribution in technological processes [8].

The application of digital technologies is essential for the design and manufacturing of DOEs. Modern data processing algorithms enable the adjustment of process parameters, while physics-informed neural networks (PINNs) and reinforcement learning (RL) methods improve inverse design and optimize the geometry of optical systems [9]. The application of digital design and optimization methods for DOEs ensures their adaptation to specific tasks, allowing for flexible control of laser beam characteristics. Numerical models and machine learning algorithms enhance the predictability of laser material processing, while real-time monitoring systems facilitate dynamic adjustments of parameters [10].

The complexity of development necessitates improvements in numerical modeling methods and optimization algorithms. The integration of digital twins, machine learning, and automated micro- and nanoprocessing systems enables improved precision in DOE manufacturing, minimizes deviations from calculated parameters, and reduces time and resource costs [11]. Despite considerable progress, there remains a need for further advancements in the digital design and control of DOEs for laser material processing. Key challenges include improving the precision of spatial energy distribution control, particularly in complex processing conditions [12,13,14], creating more effective modeling algorithms [15,16,17], integrating adaptive DOEs with monitoring and feedback systems [18,19,20], and using artificial intelligence (AI) methods to reduce development time and enhance accuracy [21,22].

The main purpose of this article is to analyze modern methods of digital design and adaptive control of DOEs, as well as to provide recommendations for their integration into laser material processing. This article discusses computational methods for designing and optimizing DOEs, the application of digital technologies in laser material processing, methods of adaptive control of dynamic DOEs, and the integration of adaptive optical elements into technological processes. This approach makes it possible to identify key directions for the development of digital engineering in diffractive optics and laser material processing, laying the foundation for the creation of the next generation of highly efficient photonic devices and systems.

2. Computational Methods for the Design and Optimization of DOEs

DOE design methods continue to evolve, leveraging advanced algorithms and computational approaches to enhance efficiency and performance. These methods also address important challenges, including the suppression of scattering noise and the enhancement of diffraction efficiency [23,24,25]. Since DOE design methods based on the Fresnel and Fraunhofer diffraction integrals are limited to small diffraction angles, the Rayleigh–Sommerfeld diffraction integral is used to expand design capabilities [26,27]. This method overcomes these limitations, enabling the accurate modeling of diffraction at large angles and allowing for the development of optical elements suitable for a wider range of conditions. To achieve these capabilities and enhance design accuracy, numerical optimization methods are actively employed, which have become standard practice in DOE design [28]. These methods are widely used in creating advanced optical systems, including multilayer and hybrid optical elements, as well as in developing complex structures for beam shaping and control [29,30].

The numerical design process of DOEs, presented in Figure 1, involves five main steps: phase optimization, phase conversion modulo 2π, quantization, beam propagation modeling, and verification [27]. During the phase optimization step, a phase map is generated, typically using polynomials in ray-tracing software. In the original source, the term “binary surface phase” (shown at the top of Figure 1) refers to a model adopted in the software used (e.g., Zemax^®). However, from a physical perspective, the term “continuous phase map” is more accurate. The converted phase map is used to form a kinoform profile and quantized to create single- or multi-level structures, allowing for efficiencies of up to 99% [31]. Modeling and verification help assess optical element parameters such as focal length, spot size, and depth of focus. Finite-difference time-domain (FDTD) simulations are employed for complex focusing conditions [32].

Such hybrid approaches combining geometric optics and diffraction theory allow for an efficient design of complex structures. The method presented in [33] for computing the eikonal function generates the required intensity distributions, including those with discontinuous boundaries. By using this solution as a starting point for Fourier transform algorithms, it is possible to create quasi-regular or piecewise-smooth microreliefs, simplifying the DOE design process with improved properties and a high-quality structure. Figure 2 illustrates the results of the experimental implementation of this approach, including photographs of the fabricated DOE and images of the microrelief obtained using an optical microscope and interferometer during measurements, confirming the high precision and quality of the created structures.

The modified Gerchberg–Saxton algorithm, referred to as transport of amplitude into phase (TAP-GSA) in [34], improves phase profile control and reduces scattering noise by applying phase retrieval for multiplexing, which is particularly important for the shaping of laser beams in DOEs. Research in [35] demonstrates that combined numerical diffraction analysis methods, such as the rigorous coupled-wave analysis (RCWA) method, combined with optimization algorithms, such as ensemble learning, expand the capabilities for designing complex DOE structures. In [36], a differentiable method for designing DOEs using multi-level B-splines for phase distribution assignment is proposed. This gradient descent optimization method enables the obtaining of continuous phase distributions, contributing to the creation of more regular microreliefs and improving their fabrication.

The application of optimization algorithms, such as particle swarm optimization (PSO) and simulated annealing (SA), in combination with the finite-difference time-domain (FDTD) method, is particularly relevant for precision laser processing tasks. These methods enhance the accuracy of controlling diffraction characteristics, such as intensity distribution and scattering angles, which is particularly important for designing optical systems [37]. Hybrid algorithms combining PSO and SA show improved uniformity of holographic projections and greater effectiveness of DOE design compared to traditional algorithms, such as Gerchberg–Saxton [38].

One of the significant achievements is the introduction of a dynamic iterative correction algorithm for DOE design, which enables dynamic adjustment of the target information during iterative calculations. This improves the design quality by reducing light intensity non-uniformity and the root-mean-square error in beam shaping tasks [39]. Another important development is a hybrid method for designing diffractive optics using hardware–software integration. This approach combines digital differentiable models with computational visualization, enabling end-to-end optimization of DOE profiles. These methods offer great potential for applications requiring compact optical systems, such as optics with extended depth of field [40].

Modern digital methods for DOE design contribute to advancements in microfabrication technologies, ensuring precise adjustment and replication, which is critically important for miniaturizing and integrating optical systems into various applications. In [41], research indicates that numerical modeling allows for the precise control of structure parameters, and the minimal discrepancies between the calculated and experimental data confirm the effectiveness of these approaches. In the field of inverse design, which involves calculating the parameters of a DOE structure based on the given output signal characteristics, methods using step-transition phase algorithms (STPAs) for optimizing wide-angle DOEs have been introduced. This method enhances the uniformity of the created light structures while maintaining high diffraction efficiency, which is useful for tasks requiring precise light control [42].

Integrating programmable diffraction with digital neural networks opens new possibilities for optimizing diffractive optical processors. This combination of digital neural networks and optics allows for effective interaction with electromagnetic waves, expanding the capabilities of optical visualization and sensor systems [43]. Such methods pave the way for creating highly efficient optical systems capable of adapting to changing conditions, which is especially important for modern applications requiring high speed and accuracy of information processing. In the context of laser material processing, these technologies enable the shaping of complex laser beams, providing precise control over energy distribution and improving processing quality.

Computational visualization plays an important role in DOE design for precision laser processing by modeling complex optical interactions and reducing the need for long experiments and empirical parameter adjustments. The application of AI enhances the efficiency and accuracy of phase profile shaping, as well as improves the control of manufacturing parameters through machine learning. Deep learning improves DOE development in tasks such as beam shaping, zero-order suppression, and adaptive laser beam control. The use of AI also accelerates the simulation of diffraction optics behavior, reducing design cycles and simplifying prototyping, making these methods indispensable for precision laser processing technologies [44,45].

Optical elements capable of efficiently controlling the physical parameters of light play a crucial role in modern optics and nanophotonics. Spatial light modulators (SLMs), especially liquid crystal spatial light modulators (LC-SLMs), allow real-time modulation of the amplitude, phase, and polarization of light, making them crucial for beam shaping and control. Figure 3 illustrates how LC-SLMs can modulate the light field to generate various types of beams. Depending on the input data provided by the computer, LC-SLMs can produce both single and composite images. Loading appropriate holograms into LC-SLMs allows the generation of beam types such as Bessel beams, finite-energy beams, Hermite–Gaussian beams, Laguerre–Gaussian beams, and optical vortex beams, as demonstrated in Figure 3c,d [46].

One of the promising approaches to enhancing the functionality of SLMs is the use of the geometric phase, which arises from photon spin–orbit interaction in anisotropic materials, such as liquid crystals. Unlike dynamic phases, the geometric phase depends only on geometry, making elements resistant to manufacturing errors. The liquid-crystal-mediated geometric phase opens up new possibilities for the design of DOEs with a wide range of functions, including beam control and structuring [47]. In [48], a method for shaping linear laser beams with diffraction-limited widths based on Gaussian beams using flat liquid crystal optical elements is presented. This approach provides high diffraction efficiency, as the scattering of power into the zero diffraction order is minimized during beam shaping, thereby improving the accuracy and efficiency of energy transfer into the desired shape. The proposed design method can be used for various complex beam shapes, expanding their applicability in optical systems.

One potential direction for advancement is the development of complex SLMs that can simultaneously control the amplitude and phase of light waves. In [49], a flat-panel complex SLM is presented, consisting of two layers of liquid crystal panels with in-plane switching, allowing for two degrees of freedom for voltage control. This architecture enables the modulation of light at the individual pixel level, which differs fundamentally from traditional macropixel modulation methods and enables complex light modulation over the entire free surface. Theoretical simulations and experimental data confirm the possibility of three-dimensional holographic image reconstruction without conjugated noise. This approach opens up new prospects for wide application in advanced wave optical technologies.

An important area of research is the development of light field modulation algorithms for SLMs, which are essential for controlling light in various technologies. In [50], advances in light field control algorithms for digital micromirror devices (DMDs) and liquid crystal SLMs were analyzed. The existing algorithms, their influence on optimization methods, and their application in various technologies are examined. Special attention is given to the innovations achieved using different coding schemes and SLMs for manipulating light fields. The prospects and challenges faced by SLM control technologies are discussed, and potential paths for further development are proposed.

These achievements reflect the overall trend of combining traditional optical design methods with advanced computational technologies, contributing to the development of more efficient and versatile diffractive optical elements. New approaches, such as the use of AI and optimization algorithms, expand the capabilities of DOE design. AI automates the optimization process, reducing the time required to find solutions and improving the accuracy of calculations, thus eliminating the need for prolonged iterations. Optimization algorithms, such as PSO and SA, provide flexibility and adaptability to complex design conditions. These methods also take into account multiple factors simultaneously, including geometry, diffraction characteristics, and error resilience, contributing to the creation of more complex and efficient optical systems.

The use of LC-SLMs with advanced computational methods significantly enhances the functionality of optical elements, allowing precise control of light distribution in real time. This opens up new opportunities for laser processing, adaptive optics, and the creation of complex light structures. The development of optimization algorithms and machine learning promotes the design of more precise and efficient light control systems, which is crucial for precision laser processing and high-tech applications.

3. Digital Engineering in Laser Material Processing Using DOEs

Digital engineering is a crucial tool in the design and improvement of DOEs and in enhancing the efficiency of laser technologies. The use of DOEs allows for the flexible control of the laser beam energy distribution, which contributes to achieving high precision and processing speed. These elements shape laser beams with specified characteristics, thereby significantly improving material processing quality and efficiency. DOEs, when tuned to adjust laser beam parameters, can transform standard Gaussian profiles into shapes such as donut or top-hat, providing a uniform energy distribution across the surface. This enhances the stability and accuracy of laser processing. The ability to split a single beam into multiple sub-beams enables the parallel processing of multiple objects, increasing productivity and reducing the overall processing time. Furthermore, DOEs offer adjustable beam parameters without the need for physical intervention or the recalibration of equipment. For example, they can control the beam direction by changing the phase of light waves on their surface. This is especially important for high-precision processes, such as micromachining or cutting complex contours. Thus, tunable DOEs significantly increase the flexibility and productivity of laser processing [27].

The surface microrelief of DOEs ensures precise control over the shape and intensity distribution of the laser beam, creating beams with predetermined energy profiles. This improves processing quality and increases the accuracy of processes such as cutting, drilling, and ablation. The high resistance of DOEs to laser damage makes them effective for high-power laser systems, which are widely utilized in various industries [51]. In [52], a method is presented for shaping a laser beam with a central spot and a ring, allowing for the regulation of the energy ratio between these components. This approach optimizes the laser welding process, reducing defects such as spattering and porosity, which are particularly critical in high-speed welding. One progressive approach is the use of DOEs to shape laser beams with a uniform intensity distribution (top-hat) and increased depth of focus. In [53], the integration of such elements into laser-based microprocessing systems is described, minimizing energy variations on the processed surface and providing more precise control over processing parameters. While SLMs, a specific type of diffractive optical element, are effective in beam shaping, other diffractive elements can offer even greater control over the beam shape even at high powers, which is crucial for laser micromachining applications.

DOEs significantly enhance the efficiency of laser processing by splitting the laser beam into multiple sub-beams. This not only increases the processing speed but also contributes to a more uniform microstructure formation. In laser nanostructuring, this approach is especially relevant for creating functional surfaces such as superhydrophobic coatings. Due to the high processing accuracy provided by DOEs, regular micro- and nanoreliefs can be formed, imbuing materials with new properties, including water-repellent and anti-icing capabilities. In [54], the potential of this method for the aerospace, medical, and automotive industries is emphasized. In [55], a method of interference laser processing with an expanded beam, implemented with a picosecond solid-state laser based on an ytterbium diode, is described. This method enables the formation of microstructures with high productivity—more than 200 cm²/min—on various metals such as stainless steel, Invar, and tungsten. The application of DOEs to split the original beam into two with subsequent focusing allowed high-precision surface structuring with controllable hydrophobic properties. Figure 4 illustrates the experimental setup for interference laser patterning with a marked shift between the interference and focal planes. It also presents the evolution of surface structures on stainless steel under varying pulse energies after 1000 consecutive laser pulses. The first image corresponds to a pulse energy below 1 mJ (0.81 J/cm²), demonstrating periodic patterns with a ~1 µm groove depth and nanoscale protrusions resulting from surface melting. The second image, at approximately 1 mJ, shows broken grooves and a reduction in nanoscale protrusions. The third image, at 3 mJ, displays the formation of ~4 µm wide micropillars, driven by thermal gradients and melt flow between valleys and peaks [55].

DOEs are widely used in high-performance laser processing technologies. They allow powerful ultrashort laser pulses to be converted into several parallel beams, significantly increasing processing speed and productivity. This is particularly relevant for surface microstructuring tasks in industries such as printing, consumer goods manufacturing, and tool production. For example, the use of DOEs in laser embossing technology has enabled high-speed processing and functional microstructure formation over large areas [56]. The development of multi-beam optical systems, which enhance the productivity of laser processing, especially in micro- and nanostructuring, is a promising direction. The use of DOEs divides the original laser beam into an array of partial beams with a controlled intensity distribution [57]. Unlike microlens arrays, DOEs ensure precise positioning and power stability for each beam, which is especially important for parallel material processing.

The use of DOEs enables the splitting of the initial laser beam into multiple beams, significantly increasing productivity through parallel processing. When used with a galvanometric scanner, DOEs form a regular matrix of irradiation points, improving surface processing uniformity and energy distribution accuracy. This enhances the quality of processes such as drilling, cutting, and texturing by providing more uniform laser exposure. The use of optical systems with minimal distortion improves laser spot positioning accuracy, expanding the possibilities for the precise processing of large surface areas [58].

The application of DOEs to split a picosecond laser beam into an array of micro-spots has enabled the simultaneous formation of multiple micro-channels on cemented tungsten carbide [59]. Achieving a uniform intensity distribution ensured high processing productivity and precise micro-channel geometry formation with depths of up to 55 μm and low surface roughness (<1.2 μm). The use of high-speed scanning and beam splitting into an array of 1 × 15 spots reduced thermal accumulation and ensured stable material ablation, which is critical for high-precision applications in microengineering and microelectromechanical systems. The combination of DOEs with a synchronized galvanometric scanner enabled the scaling of ultrashort pulse processing while minimizing thermal impact [60]. This resulted in an increase in material removal speed and enabled high-speed drilling, achieving rates of tens of thousands of holes per second, which significantly enhanced the capabilities of processing hard materials in production environments [61,62]. Various metallic materials, including copper, brass, AISI 304 steel, nickel, silver, and gold, were processed, demonstrating the versatility of this approach for materials with different physicochemical properties.

Laser structuring of graphite anodes for lithium-ion batteries significantly improves their electrochemical performance by optimizing electrode structure, which enhances lithium diffusion efficiency. In [63], it was demonstrated that using DOEs to split the laser beam during picosecond processing at two wavelengths, 532 nm and 355 nm, reduces the processing time by nearly an order of magnitude, compared to single-pulse methods, while maintaining the geometry of the structures and the mechanical integrity of the electrodes. It was also noted that to achieve industrial processing speeds, laser systems with ultrashort pulses and kilowatt-level power are necessary, making this technology economically viable for large-scale lithium-ion battery production.

In [64], a two-step strategy for splitting a laser beam using DOEs is described. In the first stage, refractive polarization elements are used to divide the original beam into several sub-beams, which are then directed to separate processing modules. In the second stage, each sub-beam is further split by the DOEs before focusing on the surface. This scheme was successfully tested on a prototype of a kilowatt femtosecond laser for the micro-drilling of titanium plates used in the aerospace industry. Special attention was given to the resistance of the system to thermal loads and the prevention of damage when operating with high-power beams. In [65], a multi-beam nanostructuring approach using a laser system with ultrashort pulses and a DOE, the system being capable of generating more than two-and-a-half thousand spots in a matrix area of about one square millimeter, is presented. This method allowed the effective formation of periodic laser-induced periodic surface structures (LIPSSs) and the application of infrared radiometry to measure thermal processes in real time. The achieved productivity of LIPSS nanostructuring was about two square centimeters per minute, demonstrating the method’s potential for creating functional surfaces with improved mechanical, biological, and optical properties.

The use of DOEs has also found its place in high-speed laser surface structuring technologies. In [66], the application of direct laser interference patterning (DLIP) in a roll process is demonstrated. By employing diffractive elements and cylindrical telescopes, an elongated top-hat profile was shaped, which increased the processing speed to 0.2 m²/min when texturing metal foils with picosecond laser pulses. This approach has opened new prospects for industrial DLIP applications, including the manufacturing of batteries with enhanced specific capacity.

One of the problems with DLIP technology remains the uneven intensity distribution caused by the Gaussian beam profile, which is typical for most commercial lasers. In [67], a diffractive beam shaper in a four-beam interference scheme is proposed for creating a square top-hat profile in the interference region. A comparison between the traditional and improved configurations showed that using a top-hat profile allows for the formation of deeper, more uniform structures while maintaining similar productivity. Additionally, the process efficiency was increased by ensuring the uniformity and high accuracy of microstructures. In [68], a laser surface texturing (LST) method using a single DOE is proposed, replacing complex multi-beam DLIP systems. This approach offers broader possibilities for spatial shaping and amplitude modulation, simplifying the optical system configuration and increasing the flexibility of processing. Thus, the use of digital technologies in the design and optimization of DOEs plays a key role in the development of modern laser processing methods.

Advancements in digital optical technologies continue to expand the possibilities for laser processing, enabling higher precision and adaptive control over laser beams. One approach involves integrating femtosecond laser ablation (fs-LA) with diffractive optics to improve processing efficiency and quality. Fs-LA minimizes thermal effects, making it applicable for the micro- and nanostructuring of a wide range of materials, including polymers, semiconductors, and metals [69]. The use of GHz-range pulse bursts influences ablation efficiency and quality by affecting heat accumulation and material removal dynamics [70]. Additionally, studies on single-pulse fs-LA have shown the presence of nanoscale thermal effects that influence material structuring and surface morphology [71]. The integration of fs-LA with digital DOEs could enable adaptive beam shaping, improving precision and reproducibility in microstructuring applications.

Using fs-LA in liquid environments, such as isopropanol, enhances surface structuring by facilitating the self-organization of LIPSSs with ultra-fine periodicity on various materials [72]. Such structures modify optical properties and could be utilized in applications requiring enhanced light–matter interactions, such as biosensing. Further advancements in nanoscale laser processing could be achieved by incorporating digital diffractive optics, offering improved control over pattern formation and structuring accuracy.

DOEs enhance femtosecond laser processing by enabling precise beam shaping and efficient multiplexing of laser beams. By splitting a single beam into multiple sub-beams, DOEs increase processing speed, improve uniformity, and enhance fabrication precision [73,74,75]. Their combination with digital engineering techniques further optimizes beam shaping, supporting applications in plasmonic nanostructuring, laser patterning, and high-throughput material processing.

In addition, vortex laser beams, generated using DOEs, including SLMs, enable the structuring of photosensitive materials with high spatial precision. Digital engineering methods optimize the shaping of vortex beams, facilitating controlled mass transport and microrelief formation on azopolymer films [76,77,78]. Furthermore, structured light fields influence light–matter interactions at both the micro- and nanoscale, shaping optical field distribution and localized energy deposition for modern optical applications [79,80].

In [81], the application of laser beam shaping technology in the additive manufacturing of metallic materials is explored. It is shown that using DOEs enhances process stability, reduces thermal gradients, and minimizes defects such as porosity and coarse grain size. When welding aluminum alloys with modulated beams shaped by DOEs, a more stable molten pool was achieved, and weld quality was improved compared to that of traditional Gaussian beams. In [82], the influence of modulated intensity profiles of disk laser beams shaped with DOEs on the welding process of an aluminum–magnesium alloy was investigated. The modulated beam produced a more uniform temperature distribution in the molten zone, reducing the likelihood of pores and cracks. The improved weld morphology ensured a tensile strength of more than 80% of the base material strength.

In [83], the use of DOEs to improve the shape of the laser beam in heat conduction mode welding is presented. Unlike traditional round beams, the specially shaped energy distribution allows achieving the required geometry of the weld seam, which is particularly important when performing complex joints. Welding was performed using a 5 kW continuous-wave fiber laser [84]. To minimize heat input, welding tests were conducted under conditions of a short beam–material interaction time. Electroless nickel-plated stainless-steel sheets with a thickness of 0.3 mm and copper–nickel-plated steel sheets with a thickness of 0.4 mm were used. Overlap welding with seam formation was studied using ring- and C-shaped laser spots. These spots were shaped by passing a collimated multimode laser beam through DOEs for each spot type and then through a focusing lens. Figure 5 shows the intensity distributions for the ring- and C-shaped spots. Numerical optimization methods were used for analysis, which allowed for the investigation of integral energy characteristics, temperature gradients, and the geometry of isotherms in the molten zone. It was found that the most precise structuring is achieved by adapting the shape of the laser beam, which highlights the key role of DOEs in precise laser processing tasks [85]. It was noted that the complexity of predicting the laser beam intensity profile to achieve the desired weld geometry remains the main technical barrier, as the trial-and-error method commonly used is costly and labor-intensive.

Ref. [86] is dedicated to the development of DOEs made from monocrystalline diamond, designed to shape a square-shaped laser spot when using the laser beam in the green spectral range for welding copper. A methodology for designing and manufacturing binary phase structures with the possibility of creating multi-level elements to enhance energy efficiency is presented. The experimental results showed high uniformity in the shaped top-hat profile of the beam, which contributed to more precise control over the weld pool. The influence of the laser beam shape on copper welding with green wavelength laser radiation was discussed in [87]. The application of DOEs to shape adapted intensity profiles of the laser beam significantly improved the welding process. For welding copper, which is traditionally difficult to process due to its low absorption capacity, elliptical beam shapes were employed, which significantly reduced spatter formation and improved process stability at high laser powers. The findings of the study indicated that creating a specific beam geometry using reflecting DOEs contributed to expanding the welding area with limited heat exchange and improving the weld quality.

In [88], a method for improving the laser welding process of stainless-steel components using DOEs, which divides the laser beam into multiple small spots instead of one, is presented. This solution helped prevent the formation of molten material ejections caused by the rapid evaporation of zinc during laser heating. The results showed that using multiple spots significantly increased the welding stability, especially in the presence of zinc. In [89], the effect of the intensity profiles of disk laser beams shaped by DOEs on the welding process of aluminum–copper alloys in heat conduction mode at powers greater than 3 kW was investigated. Parameters such as the shape of the molten zone, process stability, dynamics, and surface roughness were considered. The shaped beams contributed to improved welding stability, expanded the heat conduction mode area, and reduced surface roughness to values close to those of polishing, while increasing the cross-sectional area of the weld seam. The results showed that a high peak intensity does not necessarily lead to instability in the molten zone, and the intensity distribution plays a crucial role in the process.

DOEs for redistributing the power density of the laser beam contribute to controlling thermal effects, providing the creation of a desired temperature field in the processing zone. Digital engineering methods significantly improve the quality, efficiency, and reliability of laser material processing by adapting the laser beam shape to specific tasks. The development of such tailored shapes involves two main stages. The first stage involves computational modeling of the required laser beam intensity distribution. This is achieved by solving the inverse heat conduction problem, in which the necessary intensity distribution is calculated to achieve the desired temperature profile within the material. This modeling considers various time scenarios and application types, including surface treatment and precise material positioning. In the second stage, optical systems are designed according to the calculated data to reproduce the required beam shapes and complex intensity distributions. The use of digital modeling at each of these stages enables high accuracy and also allows laser processes to be adapted to various tasks without the need for physical reconfiguration of the equipment. A method based on solving the inverse heat conduction problem was proposed within this approach, which makes it possible to align the maximum temperatures in the center and at the periphery of the thermal influence zone [90]. This results in an increase in the width of the target isotherms and the expansion of the processing area per unit of time. Experimental verification of this approach was carried out for uniform laser hardening of chromium–nickel–molybdenum steel. The result of the adaptation of the power density distribution in the laser spot for steel heat treatment according to the proposed algorithm is presented in Figure 6.

DOEs provide precise shaping of a predetermined intensity distribution in the focal plane, which opens new possibilities for fine control of the properties and operational characteristics of processed parts. In [91], a method for laser material processing to improve the operational characteristics of gas turbine engine components is described. This method uses a high-power laser in combination with an optical system that includes a DOE, which focuses the laser beam into a line with maximum power density at the center. This facilitates the shaping of the required spatial intensity profile and effective irradiation of the material, improving the coating properties, reducing porosity, and enhancing the bond strength with the base material, while preventing cracks and delamination.

In [92], experimental studies on laser beam shaping by a reflecting DOE were conducted. A collimating system was used to increase the aperture of the initial beam. The results showed that during laser treatment of dual-phase steel samples, regions of full hardening, partial hardening, and annealing could be formed. The formation of such structures is determined by temperature field distribution and differences in cooling rates in the thermally treated zone. To precisely shape the laser beam and control the supplied energy, DOEs are used, which allow for the required adjustment of the thermal effect on the material.

Thus, the integration of digital engineering with DOEs has significant potential in advancing laser material processing. DOEs enable flexible beam shaping, ensuring uniform energy distribution and enhanced stability. By splitting the laser beam into multiple sub-beams, processing speed is increased. Additionally, highly precise periodic structures can be formed through interference, which is particularly useful for microstructuring and surface texturing. In high-power applications, DOEs improve weld quality, stabilize molten pools, and provide precise thermal control. Digital modeling further optimizes temperature profiles, enabling faster and higher-quality processing without the need for equipment reconfiguration. These advancements highlight the potential of DOEs to improve the accuracy, flexibility, and productivity of laser manufacturing across various industries.

4. Digital Design and Adaptive Control of Dynamic DOEs

Digital design methods have become an essential tool for the development and control of dynamically adjustable DOEs capable of real-time beam parameter correction. One promising direction is the use of liquid crystal elastomers as substrates for micro- and nanostructured elements. These elastomers offer sufficient flexibility to dynamically tune diffraction gratings for the creation of adaptive optical devices, filters, and holographic displays [93]. However, their use is limited to low-power lasers due to the insufficient thermal and mechanical stability of liquid crystal structures.

For photo-oriented liquid crystal structures, algorithms have been developed to control the polarization and phase distribution of light, enabling their adaptation to various optical tasks [94]. Local changes in the orientation of liquid crystal molecules are used to create diffraction gratings, multistable elements, and high-efficiency lenses. The use of dual-frequency liquid crystals and chiral nematics expands the possibilities for beam control and enhances adaptability. There is also active development of stretch-responsive diffractive elements, which opens new possibilities for adaptive optical systems [95]. Direct laser writing in liquid crystal gels enables the creation of mechanically tunable diffraction gratings with variable periods and intensity distributions under stretching or compression, providing flexible control over beam characteristics.

In the field of 3D printing of DOEs, digital technologies are an integral part of the process, ensuring accurate scaling of structures from micrometers to nanometers [96]. The application of deviation compensation algorithms allows the creation of micro-optical components with high precision [97]. Moreover, the method of thermocapillary-programmable shape changes in liquid films expands the possibilities for producing high-precision diffractive elements used in 3D microscopy and other high-precision applications [98]. This approach provides temperature and shape control of the applied material, enabling the creation of elements with specified phase characteristics.

Digital design methods are actively utilized for the development of metasurface DOEs based on nanostructures, providing precise control over the parameters of light beams [99]. Active metasurfaces can dynamically change their optical properties, allowing for the effective manipulation of light parameters in both time and space. This enables various optical effects, such as wavelength shifting, temporal reversibility of light waves, and controlled refraction. These properties contribute to the development of compact and energy-efficient optical components used in high-precision laser systems and other photonic devices [100].

Electroactive metalenses have been developed that are capable of dynamically changing their optical properties under the influence of an electric voltage [101]. These devices can switch between different optical states by controlling the metal–dielectric transitions in their nanostructures. This flexibility enables on-demand changes in the routing, focusing, and overall functionality of optical components, opening new possibilities for the development and integration of ultra-compact photonic systems. Further advancements in this field are reflected in [102], which describes organic metasurfaces capable of dynamic optical property changes at visible frequencies through the use of conductive polymers. These metasurfaces allow the flexible control of optical functions without the need for complex connection schemes, significantly simplifying their design. This demonstrates the high potential of conductive polymers for creating next-generation reconfigurable optical devices.

The active metasurfaces described in [103] provide dynamic control of light polarization with sub-picosecond resolution, making them valuable in laser processing and optical scanning. However, the use of such systems is limited by material degradation under prolonged laser exposure, control complexity, and high cost. Integrating metasurface DOEs with microelectromechanical systems (MEMSs) enables the creation of compact and rapidly adjustable optical devices, such as varifocal lenses for real-time focal length adjustment [104]. Figure 7 shows a schematic of the tunable focus doublet, consisting of a stationary metasurface on a glass substrate and a movable metasurface on a silicon nitride membrane. The membrane can be electrostatically actuated to adjust the distance between the two metasurfaces. As shown in the schematic, a small change in lens separation (~1 μm) leads to a significant shift in the focal length (~36 μm) during electrostatic actuation. This significantly expands the application of such devices in optical scanning and microscopy, although their thermal sensitivity remains a limiting factor. At the same time, methods for improving the thermal stability of metasurface-based optical systems are actively being developed, including changes in the shape and size of nanostructures. These improvements will enhance the reliability and stability of such systems under high loads, laying the foundation for their successful use in high-power lasers and other modern optical devices [105].

Thus, digital design and adaptive control methods for DOEs demonstrate high efficiency in the development of next-generation photonic devices. The use of materials with variable optical properties opens up possibilities for creating customizable real-time beam control systems. Challenges with the thermal sensitivity of the materials used and control complexity are being gradually mitigated by emerging solutions. This expands the application of adaptive DOEs in laser systems and highlights the potential of digital design for creating reliable and flexible photonic devices.

5. Integration of Adaptive Optical Elements in Laser Material Processing

SLMs, as dynamic DOEs, are important for digital beam shaping. Their ability to modify phase or amplitude in real time provides flexibility, allowing efficient adaptation of light fields for microstructuring tasks. LC-SLMs, in particular, are in high demand, as they provide precise adjustment of phase and amplitude characteristics of beams for various laser microprocessing applications [106]. DMDs are used for light control and find applications in laser material processing [107,108]. Despite offering less flexibility than phase-based SLMs, DMDs offer high switching speeds, making them suitable for microfabrication.

In [109], methods for enhancing laser processing resolution are described, including the use of adaptive optical elements to control the laser beam. One such method involves using an SLM to modulate the laser beam at the pixel level. This enables the formation of laser structures, including those formed by multi-point irradiation, which significantly reduces processing time. Phase modulation of the laser beam with the SLM is achieved by employing crystals with a defined anisotropy, allowing polarization changes and the creation of complex laser structures, including computer-generated holograms (CGHs). These technologies contribute to high-precision laser microprocessing with improved resolution and reduced thermal exposure.

The integration of programmable adaptive DOEs based on an SLM allows the shape and configuration of irradiation zones to be modified in real time, enhancing the accuracy of laser processing. Flexible control of the amplitude and phase of light waves makes it possible to create various structured patterns on the processed surface. This adaptability improves processing results for complex reliefs, micro-drilling, and micro-texturing. Rapid switching of structured patterns achieves high precision in surface formation, ensuring more stable processing quality [58].

Two-photon polymerization (TPP) using femtosecond lasers enables the creation of micro- and nanostructures with high precision. Using an SLM to control light fields allows the processing of complex shapes in a single exposure [110]. The development of 3D-switchable DOEs, capable of dynamically changing their functions, is a progressive direction. TPP capabilities allow recording multiple diffraction elements in a single layer of liquid crystal material, which can be activated or deactivated by changing the voltage. Recording at various depths of the LC layer provides flexibility in switching functions and creating various images or patterns [111]. This method is particularly relevant for programming functions with minimal pixelation and the highest precision of reproduction.

Algorithms that control the phase and amplitude of the laser beam enhance processing accuracy. In [112], SLMs with enhanced capabilities for aberration correction and energy distribution optimization were proposed. This digital approach eliminates artifacts in beam shaping, such as astigmatism and unshifted central spots caused by zero diffraction order. In the experiments, a linearly polarized He-Ne laser beam was used. It was focused into two types of intensity distributions: a square top-hat profile and a homogeneous donut-shaped beam. These beam shapes are commonly applied in laser processing to enhance precision and efficiency by tailoring energy input to specific applications. To improve beam shaping accuracy, phase masks were optimized using a diffractive neural network (DNN) approach. The training process plays a crucial role in this optimization, allowing the system to iteratively refine the phase masks based on numerical simulations. By leveraging neural network-based training, the method achieves phase and amplitude modulation, allowing high-precision beam shaping without the need for additional experimental corrections [112]. Figure 8 illustrates the optimized phase masks for different target distances, compensating for aberrations such as astigmatism, pixel crosstalk, and unmodulated reflections. The phase values can exceed 2π because phase mask optimization accounts for crosstalk and aberrations, so the usual restriction of phase values to the [0, 2π) range does not always apply. As noted in [113], typical LCoS-SLMs can have a phase modulation range greater than 2π, allowing for more precise distortion compensation.

The use of CGHs, accelerated by graphics processing units (GPUs), ensures flexible beam shape modification in real time [114]. This method is widely used for micro- and nanostructuring tasks. Liquid crystal SLMs with CGHs demonstrate resistance to picosecond pulses [115], and effective cooling maintains phase stability, highlighting their potential for high-precision material processing. A hybrid drilling method for hard transparent materials, discussed in [116], combines the capabilities of femtosecond lasers for microhole creation with selective wet etching, ensuring their precise shape. This approach allows the creation of microscopic holes of various shapes without conicity and the formation of multilayer structures with high accuracy. The use of SLMs with CGHs significantly reduces processing time and expands production capabilities in semiconductors and catalysts.

The pulse burst generation method for dynamic laser material processing, described in [117], is based on using SLMs with orthogonal linear polarizations. High-energy laser pulses were converted into pulse bursts with a high frequency. By using two SLMs with orthogonal polarizations, each channel was modulated independently, increasing process flexibility. The use of hybrid CGHs for multi-point microstructuring of surfaces contributed to increased processing accuracy and reduced material ablation speed. This digital design method opens significant prospects for parallel material processing using adaptive optics.

In [118], a method for digital control of phase distribution using a nematic liquid crystal layer in laser powder bed fusion for improving the mechanical properties of bulk metallic glasses is presented. This ensured uniform temperature distribution, reduced the risk of crystallization, and improved the amorphousness of the final material structure. In [119], the use of SLMs based on a liquid crystal matrix deposited on a reflective silicon substrate (LCOS-SLMs) for femtosecond laser processing is described. Phase control of the laser beam allowed for aberration correction, focal field design, and beam splitting into sub-beams for parallel processing, increasing productivity and reducing the time for 3D printing of complex metal parts.

Adaptive optical technologies are widely used in laser material processing due to their ability to flexibly adjust the spatial energy distribution of the beam and correct aberrations when processing the internal structures of workpieces [120]. The use of nematic SLMs allows continuous phase control in the range of [0, 2π] radians and the creation of phase discontinuities between adjacent pixels for more efficient beam shaping and parallel use. This opens new possibilities for precise 3D structuring of materials. Further development of SLM technologies aimed at increasing operational speed and resistance to high powers expands their scientific and industrial application prospects.

In [121], an approach for applying machine learning to program the phase modulation function of a thermo-optically addressed, liquid-crystal-based spatial light modulator (TOA-SLM) is described. This system offers significant potential by providing adaptive optical control over the spatial phase of ultrashort laser pulses, which is crucial for high-precision laser material processing. A neural network trained with minimal experimental data can effectively generate low-order spatial phase distortions, enabling precise phase modulation. The network solves the inverse problem by identifying the required control beam profiles based on a prescribed phase profile, allowing real-time optimization of beam parameters. As shown in Figure 9, the architecture of the neural network consists of a contracting–expanding stack of convolutional layers connected at two spatial scales to ensure accurate phase modulation prediction. This method facilitates the integration of adaptive optics, improving focusing and beam shaping.

The digital design of phase characteristics for SLM ensures effective aberration compensation and the elimination of laser beam focus distortions. This allows for high precision and quality in laser material processing, which has been applied in the “stealth dicing” process of semiconductor wafers [122,123]. In particular, it became possible not only to correct the total number of flyback regions but also their precise distribution on the SLM surface, increasing the intensity of focusing inside the wafer. This improved the efficiency and accuracy of processing, enhanced wafer separation quality, and increased process productivity.

Advanced digital design algorithms have significantly improved the efficiency of laser “stealth dicing” (LSD) in cutting transparent materials such as quartz glass [124]. The use of SLMs with CGHs enabled the shaping of multiple coaxial focal points along the depth of the material, ensuring higher processing accuracy. The application of an enhanced three-dimensional Gerchberg–Saxton (3D-GS) algorithm with feedback ensured uniform energy distribution among the beams. This solution enabled flexible adjustment of the inter-focus distance and reduced cut roughness, thereby improving the precision of laser material processing.

Digital control of laser pulse phase profiles using SLMs has improved the accuracy of forming ring-shaped random structures in multimode gradient-index (GRIN) fiber [125]. The optimization of parameters such as pulse energy, SLM refresh rate, and the positioning of structures contributed to an increase in the level of Rayleigh backscattering and the expansion of the reflection spectrum. This creates new prospects for the development of high-precision fiber lasers and optical systems.

SLMs are used to control the phase profile of femtosecond laser pulses, which improves the process of graphitization of diamond electrodes [126]. Regulation of the energy distribution and wavefront of the pulses provides control over the diameter and specific resistance of the created graphite structures, contributing to increased accuracy and efficiency of radiation-resistant detectors. In [127], methods for forming multiple non-overlapping spot arrays with minimized mutual influence of the points are described. Step-by-step modification of these arrays with each laser pulse reduces speckle noise, ensuring uniform material removal and high surface quality.

In [128], a technology for surface irradiation of metal using a laser and optically addressable liquid crystal spatial light modulator (OASLM) is described, which accelerates the additive manufacturing process and improves the resolution compared to point scanning methods. A system with a nanosecond laser and an OASLM with a damage threshold of 500 mJ/cm² is presented, providing a resolution of about 100 μm. The use of OASLM allows the modification of the beam for 3D printing of metal objects. The development of OASLMs with a higher damage threshold for additive manufacturing is also planned.

Digital design provides a comprehensive approach to creating optical systems, including the development of beam shaping algorithms and real-time energy distribution control using SLMs. This provides extensive opportunities for scientific research and industrial applications, contributing to increased flexibility, accuracy, and speed of laser material processing. To achieve further progress, it is necessary to enhance the thermal resistance of SLMs and reduce computational delays, which remain an important task for future research.

The integration of static DOEs with dynamically controlled SLMs provides the opportunity for more flexible control of beam characteristics in real time, which is especially important for applications in medicine, aerospace, and industrial sectors [129]. The combination of efficient beam splitting and shaping with the dynamic control of their parameters has increased the efficiency of multi-beam processing. This solution is expected to be used in biomedicine to improve the biocompatibility of implants and to enhance the surface properties of tools. Phase-only SLMs can also be applied to model and evaluate the characteristics of designed multilayer DOEs that create complex phase profiles using multiple discrete levels. Ref. [130] demonstrates the creation of various diffraction profiles using an SLM and their modal evaluation, including performance analysis. Even with a limited number of levels, high accuracy in profile shaping was achieved, which opens up new prospects for DOE design.

Moving DOEs, which are zone plates with microrelief surfaces capable of reflecting or transmitting a beam and performing translations, rotations, or oscillatory motions, provide opportunities for real-time control of beam shape and intensity. These elements allow for flexible adaptation of beam parameters to current material processing tasks, ensuring high precision and prompt changes without the need for complete system reconfiguration. In [131], it was demonstrated that the use of freeform diffractive optics with dynamic adjustment made it possible to create a uniform surface layer with improved mechanical properties during laser thermal hardening of steels. Additionally, the proposed laser annealing method has been successfully applied to process aluminum–magnesium and low-alloy titanium alloys, expanding their forming capabilities and improving the accuracy of manufacturing aerospace components. It was also found that the energy redistribution of the beam during pulsed laser welding increases the strength of welded joints in nickel superalloys. The use of moving DOEs in these processes has improved the operational characteristics of gas turbine engine components, opening new prospects for their use in complex industrial tasks requiring a high level of laser impact control.

Energy redistribution with an increase in intensity at the periphery of the laser spot due to the transfer of part of the energy from the center is an important application of moving DOEs [132]. Dependencies of energy redistribution and changes in the focal length at different positions of the DOE were identified. Experimental studies using a high-power continuous-wave laser confirmed the high accuracy of intensity control, which demonstrates the reliability of this method. In [133], the effectiveness of moving DOEs for changing beam shapes and dynamically controlling their intensity in real time was demonstrated. This allowed for increased accuracy in laser processing and greater flexibility in controlling thermal processes and confirmed the ability to adapt the beam to various processing tasks.

Rotating DOEs, used in a cascade optical system for multi-beam processing, are discussed in [134]. A functional prototype of such a system was presented, and a simulation assessment of spot positioning accuracy was conducted, confirming the possibility of flexible control over the spatial parameters of beams and opening additional prospects for improving the processing accuracy and adaptability of laser processes.

Thus, the digital design and dynamic control of DOEs play an important role in advancing laser technologies. The use of SLMs allows flexible adjustment of beam parameters, contributing to improved accuracy, speed, and quality of processing. The integration of adaptive optical systems with machine learning algorithms expands the application possibilities of lasers in medicine, aerospace, and industry. However, to fully unlock the potential of such systems, challenges such as insufficient thermal resistance and high computational delays must be overcome. Solving these challenges will require in-depth scientific research and the development of innovative technologies capable of taking laser systems to a new level of efficiency.

Flexible control of beam power distribution remains an important factor in improving the efficiency of laser processes. Moving DOEs with microrelief reflecting or transmitting surfaces are used to shape the beams of high-power lasers, allowing flexible adjustment of the beams and improving processing quality without the need for complete system reconfiguration. To optimize thermal processes, algorithms for solving inverse heat conduction problems are used, which ensures a specified distribution of temperature fields in the processing zones and, as a result, increases productivity and processing quality. Beam energy redistribution technologies also enable efficient control of thermal processes in real time, providing precise control over processing parameters. The integrated use of dynamically controlled optical elements and high-precision design methods forms the foundation for a new generation of laser technologies capable of meeting the growing demands of scientific research and industrial production.

6. Discussion

Digital engineering in optics integrates advanced methods of digital design, modeling, and adaptive control of laser beams, opening up new possibilities for precision laser processing. Digital optics encompasses areas such as digital design, laser technologies, and the use of metamaterials for light manipulation. Unlike analog optics, digital technologies enable light control with nanometer precision [135]. Digital lasers provide real-time mode adjustment, which is particularly useful for processes requiring high accuracy [136]. Such methods can be integrated with diffractive optics to enhance the precision and efficiency of micro- and nanostructuring.

An important direction of digital engineering in diffractive optics is the development and optimization of DOEs, enabling precise laser beam shaping for various applications, including micro- and nanostructuring, holography, and adaptive optical systems. Modern optimization algorithms and machine learning open new opportunities for improving DOE performance by accounting for nonlinear effects, temperature variations, and other factors affecting the stability and efficiency of laser processing.

Vectorial digital optics can improve image quality in complex conditions, such as light distortions when passing through heterogeneous media. Additionally, these technologies can be adapted to improve the efficiency of laser material processing [137]. The integration of digital technologies into laser systems opens new opportunities to improve the accuracy, flexibility, and productivity of laser processing [138,139].

Vector field manipulation has been applied in laser processing to improve laser–material interactions. In [140], a high-threshold metasurface was demonstrated that generates and superposes multiple collinear vortex beams, achieving high conversion efficiency for high-power applications. In [141], patterned vector optical fields (PVOFs) were utilized in femtosecond laser processing to create complex microstructures on silicon. This method can also be extended to 3D microstructure fabrication via two-photon polymerization. In [142] femtosecond vector vortex laser ablation in tungsten was explored, enabling the formation of laser-induced periodic surface structures (LIPSSs) and chiral textures for advanced microstructuring.

Geometric phases induced by liquid crystals have attracted attention in planar optics due to their ability to efficiently shape light beams. Liquid crystals, with their unique optical properties, allow the creation of complex microstructures for various optical applications. Photopatterning technologies and liquid crystal materials utilizing geometric phase enable the fabrication of both transmissive and reflective elements capable of beam steering and focusing. In [143], demonstrated the successful application of liquid crystal technologies for creating highly efficient lenses with large apertures and reduced focal lengths.

These advancements demonstrate the potential of digital methods in light control and laser material processing. Further research focuses on improving adaptive optical systems, developing new algorithms for DOE optimization, and integrating artificial intelligence methods to enhance the accuracy and stability of laser processes.

The digital design and adaptive control of DOEs have significantly advanced the development of high-precision and flexible photonic devices used in laser material processing technologies. The introduction of DOEs and modeling methods allows the effective control of laser systems, adapting processing parameters to real-time changes and thus improving productivity and quality. The integration of computer science, AI, and advanced optical technologies greatly increases the accuracy and efficiency of laser operations [144]. Digital models and digital twins help optimize laser processing methods, minimizing defects. AI and machine learning enhance the reliability, accuracy, and flexibility of laser systems in processing various materials [145,146]. However, despite the achieved successes, challenges remain that require further efforts to overcome.

One of the key challenges is the thermal sensitivity of materials used in DOEs. Liquid crystal structures, despite their advantages in dynamically changing optical properties, have limited thermal stability, which restricts their use in high-power laser systems. New materials and methods to enhance thermal resistance are being developed to address this challenge. It is important that improvements in thermal resistance ensure the stability and reliability of materials under prolonged exposure to laser beams. The use of metasurfaces capable of dynamically changing their optical characteristics opens new possibilities, but it is associated with limitations related to degradation during long-term use. This requires the development of protection and stabilization methods for such elements to increase their longevity and reliability.

Another challenge is the difficulty of controlling adaptive DOEs. The implementation of such technologies in industry requires the development of high-precision components and efficient methods for their integration into systems. Programming and controlling these systems require significant computational power and highly skilled specialists, which limits their use in real-world conditions. Especially in situations where quick decision-making and high precision are required, such systems become complex to apply and need further optimization to ensure reliability and efficiency.

Digital control of light fields using SLMs and moving DOEs faces several limitations. Despite the high flexibility of these devices, they cannot always provide ideal accuracy under extreme loads. To improve efficiency, new algorithms for aberration compensation and phase distribution optimization need to be developed. High switching speed and accuracy make these devices valuable for a wide range of applications. However, for successful integration into industry, specific tasks related to each particular laser material processing operation need to be addressed.

A promising area is integrating machine learning and AI with the digital design of DOEs, which will improve the accuracy and speed of light field control and enable adaptive algorithms to optimize laser process parameters in real time. However, the implementation of such technologies faces a number of challenges, such as the complexity of training neural networks and the need for large data volumes and substantial computational power. Implementing these methods requires developing new approaches and ensuring successful integration with existing laser processing and micro- and nanomaterial technologies.

Despite these challenges, the potential of the digital design and adaptive control of DOEs is immense. The implementation of such technologies in various industries, including aerospace, medicine, and high-precision laser systems, will significantly improve the quality and accuracy of material processing, creating new opportunities for the development of innovative photonic devices. Key areas for future research should include improving the thermal stability of materials, developing more accessible and user-friendly control systems, and integrating new computational analysis methods and AI.

7. Conclusions

Advancements in the digital design of DOEs and their integration with numerical modeling and AI methods have unlocked new opportunities for enhancing the efficiency of laser material processing. The algorithms used in the design, which combine various light control techniques, optimize laser beam characteristics, improving processing precision and reducing scattering.

Adaptive control methods for DOEs, including programmable SLMs, enable real-time control over laser beam parameters, which is particularly critical in complex technological processes. The integration of AI not only shortens the design time but also improves the modeling accuracy, facilitating the development of more advanced, functional optical systems.

The integration of DOEs with digital engineering has great potential for advancing laser material processing. DOEs allow flexible beam shaping, such as donut and top-hat profiles, ensuring uniform energy distribution and improving stability. By splitting a single laser beam into multiple sub-beams, the processing speed is increased and the thermal gradients are reduced, making the method effective for microstructuring and surface texturing.

In high-power applications, DOEs provide precise control over thermal effects, stabilizing melt pools and improving weld quality in materials such as steel, aluminum, and copper. Digital modeling further optimizes temperature profiles by generating predefined intensity distributions, enabling faster and higher-quality processing without requiring reconfiguration of equipment. These innovations emphasize the crucial role of DOEs in advancing laser-based manufacturing.

The development of dynamic DOEs holds significant potential for next-generation photonic devices. The use of materials with dynamically adjustable optical properties, such as liquid crystal elastomers and photo-oriented liquid crystal structures, enables real-time beam control. This paves the way for adaptive optical devices like tunable gratings, lenses, and holographic displays.

Metasurface DOEs offer precise control over light in both time and space. Active metasurfaces and electrically tunable metalenses expand functionality by enabling fast, compact, and reconfigurable optical systems. Despite challenges related to thermal sensitivity and material degradation, continuous improvements in thermal stability and structural resilience promise broader adoption in laser systems.

The integration of adaptive optical elements into laser technologies opens up vast opportunities for enhancing the precision, flexibility, and speed of material processing. The use of LC-SLMs allows real-time control of the amplitude and phase of laser beams, facilitating the creation of complex structures and improving the quality of processing surfaces. Modern algorithms for designing beam phase profiles provide high accuracy in aberration correction and ensure uniform energy distribution. The use of CGHs, accelerated by GPUs, allows for flexible beam parameter adjustments and high performance in micro- and nanostructuring. Future developments in laser technologies are expected to focus on increasing the thermal resistance of SLMs and reducing computational delays, which will unlock the full potential of adaptive optical systems across a wide range of applications.

Movable DOEs, which redistribute beam energy and adjust focal distance, enhance the quality and precision of material processing. These elements are particularly valuable for adapting laser processes to different materials and geometries. Beyond microprocessing, they are also valuable for thermal treatments, laser welding, and additive manufacturing, enabling real-time control over energy distribution and focal positioning. This improves process customization and surface finish, minimizes thermal distortion, and increases efficiency in complex geometries.

The digital design and adaptive control of DOEs enhance the flexibility and precision of laser material processing, improving productivity and quality. However, challenges such as material thermosensitivity and the complexity of integrating adaptive DOEs into industrial processes remain. Overcoming these challenges requires advancements in thermal-resistant materials and control algorithms. The integration of AI and machine learning offers new opportunities to dynamically adjust laser parameters, improving efficiency and accuracy.

As laser technologies evolve, the integration of adaptive optical systems will continue to be essential for fostering innovation and expanding the possibilities of both scientific research and industrial advancements.