1. Introduction

The infrared band between 8-13 µm is of great significance in detectors [1], aerospace [2], and astronomy [3]. Diamond [4] and sulfide materials [5]. D-ZnS is a composite sulfide materials combines the advantages of both diamond and zinc sulfide, which commonly used in infrared lenses and windows [6]. However, the high refractive index of D-ZnS results in strong Fresnel reflection (2.2-2.3 at 10 µm), which affects its performance in infrared stealth and imaging [7]. Surface antireflection techniques such as subwavelength structures [8] (SWSs) and antireflection coatings [9] (ARCs) can effectively reduce Fresnel reflection. ARCs have been widely used in many fields, but they have some critical limitations, such as easily damaged by thermal shock and sand erosion [10]. In contrast, SWSs processed directly on the surface can improve the reflection by providing a gradual equivalent refractive index and reducing Fresnel reflection to a greater extent by modifying the surface morphology. However, it is very difficult to process SWSs with small width groove, especially for composite materials and on curved surface, due to the uneven properties of the materials, neither nanoimprint nor chemical etching is suitable [11–13].As a prevalent fabrication method, femtosecond laser ablation enables efficient creation of subwavelength microstructures on various materials due to nonlinear absorption effects [14–16].

Curved-surface optical devices, such as windows and lenses, are crucial in various applications, offering improved aerodynamic performance and enabling integration into aircraft components [11,17,18]. By moving the position of the focal point, the femtosecond laser can fabricate structures at any spatial location, which is able to fabricate SWSs on curve surface. For femtosecond laser fabrication, the precision of the fabricated structure is usually related to the degree of focusing [19]. In order to produce SWSs with a small period, an objective with high magnification is needed to tightly focus the Gaussian laser and improve the spatial resolution [20]. However, due to the rapid weakening of the intensity of light after leaving the focal plane, it is difficult to produce subwavelength structures with deep grooves or craters on curved surfaces, which poses a challenge to the stability of the SWSs. To process curved surface structures, a light field with small focus diameter and constant intensity along the optical axis is necessary to solve the issue of limited depth and stability of SWSs resulting from the rapid weakening of light intensity outside the focal position.

Bessel beams, with long focal lengths and small focus diameters, are often used to handle structures with an aspect ratio of height to depth [21]. As a light with a needle-like distribution [22], Bessel beams are capable of cutting gold film at extremely fine widths and machining microholes in metal surfaces with a high depth to diameter ratio [23,24]. However, achieving widespread application of this method is impeded by the inherent challenges in attaining axial uniformity for experimentally obtained Bessel beams. Bessel beams can be reshaped to enhance their performance in various applications. Numerous reshaping methods have been proposed in the literature, including designing a mask to reduce the energy density of the side lobes [25], utilizing polarization design to produce multiple main lobes [26], and employing positive and negative cone lenses to control the working distance of the beam [27]. Spatial light modulator(SLM) can address this by providing a more uniform axial energy distribution and an extended non-diffracting zone [28]. However, the high cost and fragility of SLMs, stemming from the absorption characteristics of each layer of materials in their liquid crystal device structure, limit their use in high-power laser applications. Consequently, there is a growing need for simpler and more robust reshaping methods capable of generating uniform beams with extended non-diffracting regions. The most basic reshaping method that has been widely used in research is using a telescopic system to increase the cone angle and energy density of the Bessel beam [29]. This system proportionally transfers the intensity and phase distribution of the incident light field from the front of the system to the rear Bessel beams. A redesign of the system allows for the alteration of the energy and phase transfer process, subsequently impacting the spatial distribution of the Bessel beam.

Fabricating high-aspect-ratio, uniform, and optimized subwavelength structures (SWSs) on curved surfaces is crucial for numerous optics and photonics applications [30,31]. In this paper, we present a convenient approach using a Bessel-like beam to create SWSs with infrared band antireflection properties on large-area curved D-ZnS surfaces, as illustrated in Fig. 1. As shown in Fig. 1(b), we redesign the telescopic system to equalize the axial intensity distribution of the Bessel beam. The effectiveness of the Bessel-like beam in achieving uniform and optimized SWSs are demonstrated by optimizing the surface quality and transmission characteristics. The impact of the beam's cross-sectional intensity distribution on the morphology and composition changes during fabrication, and thoroughly discussed their influence on antireflection properties. Our designed Bessel-like beam maintains a stable, optimized surface over an extended z-position range during processing. Our work offers a valuable contribution to the field of optical fabrication, enabling the creation of large-area SWSs on plano-convex lenses and opening new research avenues in this area.

 

Fig. 1. Schematic diagram of experimental setup. (a) Schematic diagram of light path and machining method. (b) Diagram of Bessel beam reshaping methods and principles. (c) SWSs curve surface antireflection diagram.

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2. Materials and methods

2.1 Fabrication of SWSs

In our experiments, as illustrated in Fig. 1(a), we employed a 50 W fiber femtosecond laser system (Yacto Technology (YactoFiber)) to generate a femtosecond laser with a center wavelength of 1030 nm. The pulse duration and repetition rate are adjustable, and in this study, we choose a 350 fs pulse width to minimize thermal effects, and the repetition rate is set to 10 kHz to match the displacement stage's movement speed. The laser diameter is expanded using a beam expander and subsequently controlled to 7 mm by an aperture to mitigate certain light source imperfections. It is placed near the axicon to reduce diffraction effects. After controlling the intensity using a neutral density (ND) filter, the laser is shaped into a Bessel beam by an axicon (Edmund Inc.; base angle α=2°, refractive index n_ax= 1.45). The beam is then scaled down using a telescopic system consisting of a plano-convex lens (f = 150 mm) and a microscope objective (Olympus, 20x).

The microbeam's main lobe is smaller after compressed, with a diameter of 2.48 µm in air and a length of 0.722 mm. By adjusting the distances between the components in the telescopic system, the light intensity distribution in the direction of beam propagation can be reshaped and made suitable for larger-scale surfaces. During processing, the surface's uniform periodic structure is fabricated by directly moving the curved sample horizontally using a computer-controlled three-axis electric translation stage (Aerotech ANT 130). The scanning strategy is depicted in Figure S1. The D-ZnS is prepared via the hot pressing method and provided by the Tianjin Jinhang Institute of Technical Physics. The basic principles of optical reshaping and laser scanning paths are presented in the first chapter of the support information for readers’ reference.

2.2 Measurements and simulation

The fabricated SWSs’ microstructures and chemical components are characterized using scanning electron microscopy and energy dispersive x-ray spectrometry (SEM and EDS, S-4800 + EDS, Hitachi). The profile of the fabricated SWS is acquired using atomic force microscopy (AFM, EDGE, Bruker). The infrared transmission spectroscopy of the plate is measured employing a micro Fourier transform infrared spectrometer (µFTIR, Spectrum One, Perkin Elmer Instruments Co. Ltd.), with the incident light's polarization direction parallel to the processed groove structures, which is also maintained in our FTIR tests. A Fourier transform infrared spectrometer (FTIR, Excalibur 3100, Varian) and custom-built ramps are utilized to measure the transmission spectra at varying incident angles.

In the simulation, the electric field intensity (E) distributions for the fabricated surface are computed using Lumerical FDTD Solutions software to elucidate the impact of SWSs on the antireflection effect. The Blustine method is employed to calculate light intensity distributions under varying parameters of the telescopic system [32]. A plane wave light source is set to be incident vertically upon the sample surface. The FDTD mesh accuracy is set to 6, and the grid size is adjusted to 5 nm to accommodate the intricate anti-reflective structure morphology. The boundary conditions in the light propagation direction (Y) are configured as perfectly matched layers (PML) with infinite free space above and below, while the X direction, perpendicular to the light propagation, is set to periodic boundary conditions. The light source polarization direction is set parallel to the groove direction.

3. Results and discussion

3.1 Reshaping Bessel beam designed for curve surface fabrication

Telescopic systems, which are typically used for energy compression, can be modified to superimpose an additional lens phase without fragile SLMs and complex phase calculations. By increasing the distance between two lenses in the system, the outgoing light's central region exhibits a lower exit angle, while the periphery displays a higher exit angle. For Bessel beams, this modification is equivalent to assigning a higher cone apex angle to the rear segment of the Bessel beam, resulting in a stronger interference amplification effect. Thus, adjusting the distance between the two lenses effectively expands the diffractive region and homogenizes the main lobe intensity. A more detailed explanation can be found in Section 1.3 and Fig. S2-S4 of Supplement 1.

Figure 2 displays the simulated Bessel­like beam light intensity distribution reshaped by the telescopic system with varying lens distances. The reshaped light field distributions shown in Fig. 1(b) are modeled by Blustine method [32]. The reshaping of our system introduces three primary modifications to the beam: uniform axial intensity, reduced maximum intensity, and expanded main lobe's diameter. In traditional telescopes, the main lobe's light intensity swiftly peaks as it propagates, then drops to 42% of its apex at 300 µm, and falls to 10.5% at 600 µm; the simulated full width at half maximum (FWHM) is revealed to be 1.4 µm and main lobe's length at half maximum is 286 µm (Fig. 2(b)). As the separation between two lenses in the telescopic system increases, the beam length extends and the maximum light intensity diminishes (Fig. 2(b)-(e)). When the lens separation reaches 169 mm (Fig. 2(d)), the main lobe's peak energy density comprises 72% of the standard state. At a distance of 300 µm after the peak energy density point, the energy density dwindles to 38%, and it remains at 21% after 600 µm. The FWHM is calculated as 1.6 µm. By extending the lens separation by 20 mm (Fig. 2(f)), the main lobe's length at half maximum exceeds 714 µm, with its maximum energy density dropping to 48% of the standard distance, it remains a half after 600 µm, and the FWHM swelling to 2 µm. In contrast, another commonly considered approach involves reducing the apex angle of the conical lens by half. It results in a doubling of the main lobe's FWHM, while only extending the length of the main lobe by approximately twice. Additionally, this change is accompanied by a greater decay in energy density along the axial direction.

 

Fig. 2. Theoretical simulation of the effect of the reshaped telescopic system on Bessel­like beam intensity distribution. (a) Standard telescopic system, the distance between the two lenses is 159 mm. By increasing the distance between the two lenses in the telescopic system by 5 mm (b), 10 mm (c),15 mm (d) and 20 mm (e), the center of the outgoing light has a lower exit Angle and the periphery has a higher exit Angle, and the effective growth of the non-diffraction region and the homogenization effect of the main lobe light intensity are obtained

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3.2 Antireflection structure fabricated with Bessel-like beam

3.2.1 Surface topography change of Bessel beam fabricated SWSs

The antireflection effect of SWSs structure is related to the incident wavelength and structure size. In previous studies enhancing the depth-to-diameter ratio of SWSs can improve the structure's transmittance. When the aspect ratio exceeds 1.5, the optical transmittance can reach over 98%. The shortest working wavelength of SWSs is approximated using a simplified equation $:{\mathrm{\lambda }_{diff}} = \textrm{n} \cdot \textrm{p}$ where n is the refractive index and p is the SWSs period [10]. For D-ZnS materials (refractive index 2.2-2.3) and an 8µm infrared wavelength, the maximum period is about 3.47µm. Thus, a 3µm period is chosen in this study. The Bessel-like beam we designed retains Bessel beam characteristics in the cross-sectional direction, distinguished by a compact main lobe diameter and elevated main lobe density. It is expected to exhibit outstanding performance in the fabrication of SWSs. We investigated the effects of Bessel-like beams on surface morphology and composition using an unmodified telescopic system. Fig. S5 shows that a single-shot Bessel-like beam cannot create holes directly on the surface of D-ZnS. In this case, it is more efficient to fabricate microgrooves on the surface using a pulsed laser. Compared to a method that creates holes by tapping point-by-point with multiple pulses, this approach avoids frequent movement and stopping of the translation stage, resulting in increased efficiency and improved productivity.

Laser processing speed plays a crucial role in the fabrication of groove-shaped microstructures, as it impacts deposition density, energy uniformity, and overall efficiency, resulting in varying morphologies. Fig. S6 displays the fabrication outcomes obtained by utilizing varying energy levels. Under an optimal monopulse energy of 3 µJ, three distinct SWSs morphologies correspond to high speed (5 mm/s), medium speed (1 mm/s), and low speed (0.2 mm/s) processing:

At high speed (5 mm/s), the primary characteristic of the fabricated single groove is the presence of melting traces (Fig. 3(a)). When fabricating microgrooves at a 3 µm interval, an array of surface recasting traces is obtained, which is denoted as Texture A (Fig. 3(d), (g)). The high defect density in composite materials causes a free electron density far exceeding the critical density under main lobe lasers with high-energy density, leading to an increased proportion of thermal effects in material removal processes, which resulting in melting and recasting.

 

Fig. 3. Structural morphology characterization of surfaces fabricated at different velocities. (a, b, c) SEM images of microgrooves created at velocities of 5 mm/s, 1 mm/s, and 0.2 mm/s, respectively. (d, e, f) SWSs fabricated at velocities of 5 mm/s, 1 mm/s, and 0.2 mm/s, respectively. (g, h, i) Corresponding AFM profiles for (d, e, f). 3D profiles tested by AFM is demonstrated in Fig. S7.

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For medium speed (1 mm/s), the formation of deep groove can be attributed to the depth enhancement of plasma channel during ablation. As the laser increases the free electron density on the surface, the initial pulse-formed pit surface becomes metallic, reflecting and focusing the laser in the air. This process intensifies air ionization, forming a plasma channel and enhancing vertical plasma density and shock waves, which in turn gradually increase microgroove depth [33]. The microgroove width of 1.8 µm is significantly smaller than the SWSs’ period, benefiting from the narrow and intense main lobe of Bessel-like beam. When processing SWSs under these conditions, the obtained structure, named Texture B (Fig. 2(e), (h)), exhibits regular microstructures with widths under 2 µm, sharp edges, stable depths, and laser-induced periodic surface structures (LIPSS) confined to the edges. SEM images of Texture B at an oblique angle of 45° are shown in Fig. S8.

At a low speed of 0.2 mm/s, during single groove fabrication, the LIPSS width exceeds the selected 3 µm structural period, attributed to the side lobe's incubation effect at low speed. This causes variations in surface morphology during subsequent SWSs processing, as shown in Texture C (Fig. 3(f), (i)), characterized by a ripple-covered surface and irregular structures observed in AFM measurements. Due to the low energy density of the side lobe under a single pulse, the excited free electron density does not reach the critical level. However, some excited free electrons form self-trapping excitons or Frank pairs, which in turn contribute to the development of color center defects. These defects generate numerous free electrons under subsequent laser actions, causing an incubation effect. The surface free electrons produce surface plasmons, interfering with the laser to form the final ripple [34]. The increased ripple width triggers a chain of effects, including partial processing on the fabricated ripple structure's surface, higher free electron density, stronger thermal effects, and increased surface non-uniformity.

3.2.2 Surface composition change of Bessel beam fabricated SWSs

Diamond and zinc sulfide exhibit different ablation thresholds and characteristics under femtosecond laser action, which cause compositional changes in their composite materials when exposed to the laser. Table 1 reveals two notable compositional changes: a decrease in carbon content and an increase in oxygen content. All three textures, corresponding to different speeds, exhibit a decrease in carbon content. The diamond has a small grain size and high defect density, leading to a loared threshold and increased probability of ablation [35]. Thus, the diamond removal and ZnS retention on a specific shallow surface thickness, resulting in reduced carbon content.

Table 1. Chemical components (at%) of three typical surface structures.

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For Texture C, the incubation effect not only causes extensive LIPSS but also transforms diamond into graphite. Transformed graphite forms a graphite shell that protects the diamond from excessive ablation in subsequent pulses, resulting in a higher carbon content than Texture B [36]. The increased oxygen content in Textures B and C is partly attributed to the formation of covalently bound carbonyl (-C = O) groups during the graphitization process of diamond under low-energy conditions in the air [37]. The oxidation of ZnS is also a source of oxygen element, and the change in the zinc-to-sulfur ratio supports this analysis.

3.2.3 Reflection reduction capacity of Bessel-like beam fabricated SWSs

Both the morphology and compositional changes of SWSs influence the transmittance of surface. It is well-known that SWSs with smaller periods and deeper structures provide better transparency enhancement performance [10]. In this study, structure and composition are correspondingly bound, which means specific structures are related to particular compositional changes. To distinguish the roles of structure and composition in transparency enhancement and reflection reduction, FDTD method is employed to simulate the effects of structural uniformity and composition changes on transmittance.

Figure 4(a) illustrates the impact of SWSs with a 3 µm period on the electric field strength (Ex) at an incident wavelength of 10 µm. In the simulation, the microgroove depth is set to 1.5 µm, and the width is 2 µm, resembling the size of the processed structure. As the optical properties of D-ZnS are similar to those of ZnS, the refractive index parameter of ZnS is used for the simulation. For texture C, part of the surface features an additional 0.5 µm bump to simulate its rough surface state. To simulate surface composition change, a 0.2 µm deep surface layer is designated as the newly added component. Compared to regular periodic structures, irregular surface structures modulate the incident wavefront with non-uniform phase, altering the propagation direction of the electromagnetic field. As a result, uneven electromagnetic field distribution occurs, leading to optical information distortion and scattering. However, this does not negatively impact the total transmitted infrared light intensity.

 

Fig. 4. Transmission of three typical surface structures. (a) FDTD simulation of optical field modulation by regular SWSs (Texture B), irregular SWSs (Texture C), regular SWSs with ZnO surface (+ZnO), and regular SWSs with graphite surface (+C). (b) Transmission of three typical surface structures tested by µFTIR

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Surface composition changes represent another common factor affecting transmittance in laser processing. ZnO is an excellent optical absorbent in the ultraviolet band but exhibits minimal absorption in the infrared band. Consequently, a 0.2 µm thick ZnO layer does not significantly impact transmittance. However, when the structure surface contains a graphite layer, infrared light transmittance is substantially reduced. This reduction in transmittance, attributed to the graphite layer, can explain the lower transmittance of texture C compared to texture B in Fig. 4(b). The incident light field is significantly absorbed by the discrete graphite layer distributed from the surface to the sub-surface, resulting in a notable decrease in the intensity of the transmitted light field inside the material. Texture B, with its regular structure and low surface thermal effect under medium velocity, is optimal for D-ZnS antireflection.

In subsequent research, we aim to achieve texture B processing across a broader z-position range. Although there are some differences between the optical characteristics of crystalline ZnS and hot-pressed ZnS-Diamond, the simulated transmittance curves are still informative.

The transmittance of SWSs of texture B is measured at different incident angles. Figure 5(a) is a schematic diagram of the test method. The detected infrared light intensity distribution is set as 100% when the pine hole is placed in the system and without a sample. Compared to the plane surface (Fig. 5(b)), it has an obvious antireflection effect on the infrared light incident (Fig. 5(c)) and outgoing (Fig. 5(d)). For the incident surface, it has more than 75% transmittance in the 9-11 µm band at the incidence Angle of 0-40°, which shows its stable antireflection ability and applicability to large curvature infrared optical Windows. When the structure is processed on the outgoing surface of infrared light, the loss of light on the incident surface is large, so its transmittance is slightly lower than that of the incident surface. The antireflection effect is more obvious at the incidence Angle of 0-20°, and the antireflection effect gradually decreases with the increase of the incidence Angle. The results show that SWSs fabricated on the D-ZnS surface can achieve reflection reduction at wide incidence angles.

 

Fig. 5. Sample transmittance at different incidence angles. (a) Schematic diagram of the test method. (b) Bare D-ZnS transmittance at different incidence angles. (c) Transmissivity at different incidence angles when the incident surface is processed with SWSs. (d) Transmissivity at different incidence angles when the outgoing surface is processed with SWSs.

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3.3 Curved surface fabricated by the Bessel-like beam

As depicted in Fig. 2, increasing the lens separation in the telescopic system enhances the uniformity of the Bessel-like beam. However, the larger lens separation results in an increase in the main lobe diameter. Fig. S11 illustrates the outcomes when the lens separation in the telescopic system is extended to 179 mm. Due to the enlargement of the main lobe diameter and the reduction in energy density, the surface is covered with LIPPSs instead of forming the SWSs required for anti-reflection. Figure 6(b)-(e) show the morphologies of the structures fabricated at various Z-positions using the Bessel-like beam obtained with a lens separation of 169 mm. The SWSs for all samples are regular and well­ordered. Although the width of the LIPSS coverage displays some variations, the microgroove width remains relatively consistent across different Z-positions. The Z-position's zero point is set at the position where the beam just produce surface traces, with the axial direction of beam propagation being positive. The trench depth remains stable overall under different Z-positions. SWSs’ depth exceeds 600 nm when the Z-position ranges from 200 µm to 800 µm (Fig. 6(f)-(g)). In the µFTIR test, the transmittance of the 10 µm band within this interval exceeds 80% (Fig. 6(k)).

 

Fig. 6. Surface morphology and transmittance of structures fabricated at different Z-positions. (a) Schematic diagram of Z-position definition. (b)-(e)SEM of SWSs fabricated at Z-position 100 µm(b), 300 µm(c), 500 µm(d), and 700 µm(e). (f)-(i) AFM profiles corresponding to (b)-(e). (j) Structures’ depth variation of Bessel beam and Bessel-like beam under different Z-positions. (k) The transmittance of structures fabricated at different Z-positions.

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When the Z-position is 100 µm (Fig. 6(b)), the SWSs’ depth is less than 300 nm, and the surface exhibited a uniform ripple structure. This is probably due to inadequate refraction of the Gaussian beam's central part, caused by wear on the axial cone tip during use, resulting in low energy density at the beam front and insufficient ablation. When the Z-position ranged from 300 µm to 600 µm, the SWSs’ depth reaches a maximum and remained stable above 1000 nm, with little variation in morphology. The transmittance within this interval also exceeds 85%. As the Z-position continues to increase, the microgroove width expands, the depth decreases, and the surface coverage area of the ripple structure grows. However, the structure remaines regular. This can be attributed to the decreasing energy ratio of the main and side lobes near the spot's end, weakening the main lobe's energy density while increasing the side lobe's energy.

These results demonstrate that we can achieve high transmittance rates by obtaining optimized morphologies within a broader Z-position range. This confirms the correspondence between structural and compositional changes and the extent of transmittance optimization.

In order to verify the machining ability and effect of this method on curved surfaces, antireflection microstructure is fabricated on a convex lens without changing the height difference between the displacement platform and the lens. The diameter of the lens is 17.8 mm, the radius of the sphere is 43.2 mm, and the Z-position span of the surface is about 0.727 mm. For comparison, half of the lens is fabricated SWSs, while the other half is not (Fig. 7(a)). Figure 7(b) shows the lens morphology after processing taken by the camera, and half of the processed surface has a uniform antireflection structure. The structure uniformity of the sample can be observed in Fig. S11. A ring of unprocessed areas near the outer edge of the convex lens is due to the diffraction effects of the laser light passing through the aperture. In the thermography, the temperature of the half lens with antireflective structure is higher than that of the control lens (Fig. 7(c)). The thermal imager measures the temperature of the object by receiving the intensity of infrared rays, which proves the effectiveness of our fabricated antireflective structure.

 

Fig. 7. The demo lens and its infrared imaging ability. (a) Schematic of fabricated area. (b) The lens with half area fabricated antireflective SWSs. (c) Infrared image of a hot mass by the fabricated lens. (d) Test schematic diagram of infrared transmittance of samples.

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4. Conclusion

In conclusion, our innovative approach utilizes the non-diffraction characteristics of Bessel­like beams and a high main-lobe/side-lobe energy density ratio to effectively fabricate antireflection microstructures on curved surfaces. By redesigning the telescopic system, we improve the axial intensity uniformity of the Bessel beam, enhancing its capabilities in processing antireflective structures on curved surfaces. This method is easy to operate, and exploits the Bessel beam's advantages of small main lobe diameter and ultra-high aspect ratio.

In our study, we control the laser scanning speed during processing to obtain a regular antireflection surface structure with a high depth-diameter ratio and a low composition-affected zone on the D-ZnS surface. The transmittance test results for the 8-13 µm band demonstrate that the structure effectively improves transmittance at large incident angles, increasing it from approximately 75% to 85%. By adjusting the telescopic system, we achieve SWSs with a depth of more than 1 µm in a Z-position interval of over 300 µm, and SWSs with a depth of more than 0.6 µm in a Z-position interval of over 600 µm both for incident light with a diameter of 7 mm. Finally, we successfully fabricate a large-area antireflection structure on a plano-convex lens using this method without moving the Z-axis, proving its suitability for machining large-area surface structures with high efficiency and high aspect ratio.