De-coherent parallel laser processing of ultradense nanopores for high-density, large-area 3D optical phase encoding

Domain: physics
Published: 2026-01-20
Editorial outcome: major_revision

Abstract
Single-beam femtosecond laser pulse scan can surpass the diffraction limit of conventional focusing systems, enabling deep sub-wavelength single-spot modifications via nonlinear absorption at the focus. However, extending this capability to multi-beam parallel processing has been fundamentally limited by the diffraction limit (~λ/2). Herein, we experimentally and theoretically clarify that this limitation stems from spatial coherence and temporal sequence interference, inducing laser-matter interaction crosstalk, non-uniform modifications, and sparse duty-cycle structures. To address this, we propose a de-coherent parallel direct laser writing (Dc-PDLW) strategy, utilizing a patterned single pulse together with a de-coherent holographic algorithm (SSP-BM) to ensure multi-foci polarization orthogonality and eliminate spatial coherence. This method achieves single-shot fabrication of ultra-dense nanopore arrays, with 300 nm (~λ/4) resolution in crystals. We further demonstrate centimeter-scale 3D Pancharatnam–Berry phase plates and voluminous cipher sequences, realizing high-density 3D phase and polarization coding.

Introduction
In the field of nanophotonics, the duty cycle emerges as a pivotal metric for quantifying the percentage of the active part in a periodic system. The engineering of duty-cycle in nanostructured elements at the sub-wavelength scale has been demonstrated to enhance the precision of spatial optical phase encoding and structural unit density, thereby enabling unparalleled control of electromagnetic fields1–3. This, in turn, facilitates the integration of high-resolution wavefront shaping4–6, efficient optical phased arrays7, dynamic holographic reconstruction8–10, and multifunctional optical elements11–13. The combination of high-duty-cycle architectures with femtosecond laser direct writing (FLDW) technology demonstrates unique fabrication advantages, including the absence of a mask and the ultra-short pulse characteristics14, which enable non-thermal fusible spatial optical phase encoding with true 3D nanoscale precision in transparent media15–18. This development paves the way for breakthroughs in technologies, such as meta-surface fabrication, LIDAR manufacturing, computational holography, integrated photonic circuits, and optical information encryption, among others.

In the pursuit of efficient spatial optical phase encoding, single-beam processing with femtosecond lasers has been demonstrated to yield sub-wavelength single-spot sizes that overcome the diffraction limit thanks to nonlinear absorption effects19–21. However, in conventional serial laser processing15,22, the structure spacing in unit-by-unit fabrication modes is constrained by light-field redistribution effects arising from spatial coherence. This constraint impedes the fabrication of high-duty-cycle architectures23,24. In consideration of the aforementioned point, the parallel processing using multifocal beams is proposed as a strategy of bypassing the light-field redistribution effects caused by the seed structure to eliminate the spatial coherence. The multi-beam parallel processing can be achieved through various beam-splitting and wavefront-shaping techniques, such as the diffractive optical elements25, the micro-lens arrays26,27, and computational holography based on the Weighted Gerchberg-Saxton (WGS/GSW) iterative algorithm28, and the non-iterative optimal rotation angle algorithm29, the superimposed phase design14. Among these methods, the WGS/GSW iterative algorithm has great flexibility and the best parallel beam uniformity, making it a widely-used method for generating complex multi-beam patterns. However, it is important to note that GSW algorithms do not uniquely determine the phase during the iteration process, which can lead to wavefront disorder that may degrade processing performance30–34, especially under high numerical aperture (NA) focusing conditions. In particular, in the context of this study, where adjacent focal spots are brought into close proximity and their optical fields begin to overlap, this wavefront disorder can induce complex spatial coherence effects, making it difficult to surpass the coherent diffraction limit that constrains the minimum achievable spacing between adjacent spots (≈1.47λ/NA)35. Furthermore, by controlling the polarization orthogonality between adjacent beams, the spatial coherence effects of the optical fields can be effectively eliminated, thereby reducing the minimum achievable spacing between adjacent focal spots by half (≈0.73λ/NA)36, approaching the coherent diffraction limit. However, in multi-focus parallel femtosecond laser processing, the spacing between adjacent focal spots has consistently been constrained by the coherent diffraction limit. In contrast, single-foci parallel femtosecond laser processing, which enables the fabrication of nanostructures with sub-100-nanometer features37–42.

Here, we propose a de-coherent parallel direct laser writing (Dc-PDLW) strategy, leveraging a patterned single pulse and a de-coherent holographic algorithm that combines a stripe segmentation phase hologram with a binary mask (SSP-BM) to eliminate the interaction crosstalk generated by spatial coherence and temporal sequence interference effects, which allows for the machining of large-scale 3D free-designed optical phase encoding in hard and brittle materials. A schematic diagram of multi-foci phase hologram generation and polarization orthogonality is shown in Fig. 1a. The non-iterative strip segmentation phase hologram circumvents the uneven intensity distribution problem under tight focusing, while the binary mask eliminates coherence between adjacent focal spots, together enabling single-shot fabrication of ultra-dense nanopore arrays. A comparison of the minimum dual-pore spacing achieved by different algorithms is presented in Fig. 1b. With the SSP-BM algorithm, we achieve machining of nanostructures at high-duty-cycle, as well as dense linear array structures. Subsequently, it is demonstrated that the strength of the birefringence effect increases as the dual-pore spacing decreases, which also signifies that there is an augmentation in the capabilities of optical phase encoding, as shown in Fig. 1c. Moreover, the higher modulation efficiency Pancharatnam–Berry phase plate structure is processed using this approach, and a demonstration of polarization-related 3D large area information encryption is also conducted. Dc-PDLW strategy demonstrates strong potential for large-scale 3D high-duty-cycle optical phase encoding, with promising applications in diffractive optical elements, integrated photonic devices, and information encryption.

Results
The principle of the de-coherent parallel direct laser writing process

In conventional serial laser processing, the employment of the FLDW method may be affected by the temporal sequence interference effect, resulting in the redistribution of the light field. As shown in Fig. 1d1, d2, the latter incident beam is markedly influenced by the original structure (located to the right of the latter incident beam), resulting in a shift of its peak energy and a distortion of the Gaussian distribution (Fig. 1d2), which in turn leads to a deviation from the ideal distribution of the structure produced by the latter pulse (see Supplementary Text S1 for more details).

In contrast, parallel laser processing employing holographic beam shaping generates multiple focal spots simultaneously, effectively avoiding cumulative field perturbations and material-induced non-uniformity inherent to serial exposure43,44. Particularly under tightly focused conditions (i.e., high-numerical-aperture systems), non-iterative optical phase holograms produce a uniquely determined phase distribution, ensuring uniform and stable multifocal generation without parasitic diffraction artifacts45,46. A direct comparison of the focal field distributions (under the Debye approximation, Fig. 1e) and corresponding processed structures (Fig. 1f1, f2) confirms that the iterative method induces energy redistribution and additional diffraction orders near the focus, leading to structural distortions and evident side flaps (Fig. 1f1).

Given the aforementioned considerations, we suggest a non-iterative SSP-BM algorithm, which applies stripe segmentation and binary masking to the phase hologram. The corresponding optical path is illustrated in Fig. 1e. The non-iterative phase hologram formulae for an arbitrary spatial position distribution based on the Debye diffractive electric field distribution formulae are as follows47–49 (see Supplementary Text S2 for a detailed derivation):

φM(x0, y0) = 2/λ * π * (R * NA * (Δx + Δy)) (1)

where φM is the phase loaded into SLM. Δx and Δy are the displacements of the center of focus. R is the radius of the phase plane. NA is the numerical aperture of the objective lens. nt is the material refractive index.

To achieve a high-duty-cycle, the concept of hologram partitioning is introduced. Among its forms, strip partitioning enables parallel processing of multiple focal spots while maintaining high uniformity45,50,51. Furthermore, in order to achieve a further minimization of proximity crosstalk, it is necessary to consider the effect of the phase term. A common method of reducing the effect of phase term interference is the adjustment of the polarization state36,52–59. In actual processing, the binary phase hologram is a widely utilized method for the control of polarization states at varying positions across multiple focal spots46,60. In accordance with this, we propose the combination of a binary mask with a strip segmentation phase hologram as a means of ensuring the elimination of the crosstalk generated by spatial coherence and temporal sequence interference effects (Detailed derivations are provided in the Supplementary Text S3-S4). This approach can effectively reduce the intensity fluctuations and crosstalk between spots at the nanoscale, thereby breaking the diffraction limit.

Theoretical analysis has thus far validated that SSP-BM can eliminate the effect of crosstalk, thus enabling a high-duty-cycle nanostructure via the Dc-PDLW approach incorporated with the threshold effect of multiphoton absorption, which are intuitively displayed in Fig. 1f3. A comprehensive overview is provided in Fig. 1f4, which presents the central light intensity profile. It can be observed that the GSW algorithm yields a structure with an evident side flap. In contrast, the non-iterative algorithm, although it resolves the side flap issue due to the wavefront disorder, still exhibits a similar pronounced crosstalk as the GSW algorithm. This has been effectively addressed in the SSP-BM algorithm, as evidenced by the absence of interference between the adjacent focal spots (see Supplementary Text S5 for a comparison between the non-iterative ORA algorithm and the SSP-BM algorithm).

To demonstrate the superiority of the SSP-BM algorithm, a customised structure fabricated with SSP-BM overserved by SEM images is shown in Fig. 1g. The flowchart of the hologram generation is illustrated in Fig. 1h (M denotes the number of focal spots; N denotes the number of partitions):

Step 1: Define the custom multi-focus array to be loaded, and determine M according to the number of focal spots. Then, according to the required positions, attach the corresponding XY coordinates to the focal spots in M different positions, and calculate the non-iterative phase hologram.

Step 2: Determine N partitions based on actual processing needs. Subsequently, the entire phase hologram (Main area) is divided into N partitions (Subarea). Then, the M focal spots generated in the first step are filled into the subarea.

Step 3: Generate a binary phase mask, and superpose the phase overlapped by partitions with the binary phase mask to obtain the final machining phase hologram.

Uniform parallel processing achieved via de-coherent parallel direct laser writing technology, enabling fabrication of high-duty-cycle nanopore structures

Although the feasibility of the SSP-BM algorithm has been demonstrated through theoretical calculation and simulation, the complex light-matter interactions involved in Dc-PDLW make the process considerably more challenging. The effectiveness and efficiency of the method are further evaluated in the fabrication of nanophotonic structures under various parameters. In our experiment, M=2 was chosen as the standard experimental configuration (see Supplementary Text S6-S7 for 3D demonstrations with large M).

Herein, N is a core parameter determining the fabrication performance. Figure 2a illustrates the influence of N on the uniformity of bifocal spots denoted as Q, which quantitatively describes the intensity consistency between the two beams of a dual-focus beam. Q is defined as Q = 1 - (Imax - Imin)/(Imax + Imin), where I represents the light intensity. It can be seen that the uniformity of bifocal spots exhibits an increase with N. Upon reaching N=95, the uniformity tends to reach a saturation, resulting in a uniformity value of 99.4%. (Quantitative Comparison of Bifocal Uniformity Generated by the SSP-BM Algorithm and Other Algorithms in Supplementary Table S1).

The distance between adjacent pores in the structure is a significant indicator of the efficacy of the methods employed to achieve a high-duty-cycle. The definition of spacing is given in Fig. 2b. The algorithm preset spacing and location required during processing are achieved by changing the X and Y parameters in the non-iterative phase hologram, as outlined in Eq. (1).

The deposition of laser energy into the interior of the material may result in the formation of micro-cracks, micro/nanovoids, and localised amorphisation, contingent upon the processing conditions employed. It is also essential to consider space co-operation effects in order to prevent the formation of heat-affected zones, cracks, voids, or residual stress61. Therefore, the setting of the laser parameters is particularly important in actual processing. When discussing the influence of laser energy on dual-pore spacing in actual processing, we set the algorithm preset spacing to a relatively large value to ensure a large energy interval. As the laser energy increases, the laser-induced modification region becomes larger (Fig. 2c). When the pulse energy is 550 nJ, the gap width is 879 nm, with a total width of 1412 nm. With an increase in laser energy to 850 nJ, the gap width decreases, reaching a minimum of 551 nm and a total width of 1727 nm. Accompanied by the increasing laser energy, nanopores are created at the centre of the light intensity, and a ring-shaped amorphous region is created around it due to the effect of the shock wave, which leads to an increase in the size of the nanopore structure62,63. Concurrently, the diameter of the individual nanopores within the bi-focus nanostructure increases, while the nanopore gap width is diminished as a consequence of internal squeezing. In order to achieve processing with a high-duty-cycle, it is of great interest to ascertain the minimum dual-pore spacing that a given algorithm can actually achieve during Dc-PDLW (see Supplementary Text S8 for the nanopore structure under the condition of large dual-pore spacing conditions). As the algorithm’s preset spacing decreases, we compared the processing results of the SSP-BM and the GSW algorithm. At 300 nm preset spacing, the bifocal nanopore structure processed by SSP-BM was just distinguishable (Fig. 2d1), whereas the nanopore by the GSW was not (Fig. 2d2). The slight ellipticity of the nanopore in Fig. 2d1 mainly stemmed from the vector polarization effect of linearly polarized light in a tightly focused optical system64. When the preset spacing was reduced to 200 nm—approaching the diameter of a single nanopore—both algorithms failed to resolve the two nanopores (Fig. 2d3, d4). Notably, at a further reduced preset spacing of 100 nm, the structure processed by SSP-BM remained elliptical, in contrast to the circular single nanopores obtained via the GSW (Fig. 2d5, d6).

To demonstrate the processing superiority of the SSP-BM algorithm, we performed several experiments and compared the dual-pore spacing, which appears to be distinguishable with the iterative algorithm and the unit-by-unit serial writing method under identical laser parameters (224 fs, 450 nJ). As shown in Fig. 2e, the bi-focus nanopore structure exhibits substantial concordance with the prediction of the SSP-BM algorithm, with an average value of 321 nm and a minimum observation pitch of 292 nm. In contrast, the iterative algorithm exhibits an average dual-pore spacing of 545 nm due to the disorder of the wavefront and the inability to effectively address multi-beam crosstalk, as previously discussed. The deviated effect of light field redistribution is pronounced when linearly polarized light is employed for unit-by-unit conventional serial laser processing, resulting in a larger average dual-pore spacing of 601 nm. The results illustrate the superiority of the Dc-PDLW method for realizing high-duty-cycle processing.

Meanwhile, the samples were subjected to EDS (Energy dispersive X-ray spectroscopy) analysis, as illustrated in Fig. 2f. This reveals that during the processing of the bifocal structure, the formation of nanostructures resulted in the original structure being compressed inwards, causing the main constituent elements Al and O in sapphire to be compressed from the outside to the center near the midpoint of the connection. Consequently, the element distribution exhibits a distinct peak at the center of the connection (superior to the outermost unmodified zone), whereas the distribution of pore elements following laser-induced modification corrosion manifests as a valley. Furthermore, the compression zone correlates with the defined gap zone65,66.

To further demonstrate the processing flexibility and superiority of Dc-PDLW, we processed dual-pore structures (Fig. 3a1–a3) and circular dual-pore arrays (Fig. 3c1, c2) based on different spacing settings (Fig. 3b). This was done to verify its efficiency in manipulating optical phase and birefringence. Additionally, it aimed to confirm that the component can serve as a unit of a birefringent device, similar to a nanofin unit. The refractive index variation of nanostructures with different dual-pore spacing was obtained by quadriwave lateral shearing interferometry67 using a wavefront phase sensor (as shown in Fig. 3a2). The results show that the maximum refractive index change of the structure after laser irradiation reached -0.25 × 10-3 (Fig. 3a3). As illustrated in Fig. 3b, the red profile line denotes the refractive index change of the large-spacing bifocal structure, and it can be observed that the refractive index curve contains a distinct double peak. As the dual-pore spacing decreases, the refractive index change becomes co-influenced by the bifocal nanostructures, as illustrated by the blue profile line, appearing as a superposition of bimodal phase delays that manifests in the form of a single peak. Fig. 3c1-c2 illustrates a circular dual-pore array structure that demonstrates the large-scale, 3D phase and birefringence encoding capabilities of the Dc-PDLW method. Therefore, decreasing dual-pore spacing enhances the duty cycle and refractive index modulation, establishing a basis for birefringent structure fabrication. The compact system architecture of Dc-PDLW benefits from the employment of SLM, making it fully scalable in mass production. During the large-scale processing of a micro-nano birefringent device, it takes less than 3 min to achieve a complete phase encoding process (2x2 mm). The high processing rate of micro- and nano-optical products demonstrates the great potential and full feasibility of Dc-PDLW technology in practical applications.

Applications of de-coherent parallel direct laser writing technology

From an application perspective, the proposed Dc-PDLW approach introduces a fundamentally new class of anisotropic dual-pore nanostructures that are significantly different from existing laser-induced anisotropic structures, such as self-assembled nanogratings68,69, type-X birefringent structures70, and isotropic nanovoids71. Unlike these prior methods, which rely on multi-pulse accumulation or near-field enhancement and consequently suffer from limited controllability and scalability, our SSP-BM-based strategy achieves subwavelength features with a single pulse, enabling predictable birefringence tuning, high uniformity, and precise polarisation encoding. Beyond its technical innovation, this method provides complete freedom in polarization optics design, allowing simultaneous control over both birefringence magnitude (Fig. 1c) and optical-axis orientation (Fig. 4b), and underscoring the strong potential of this approach for high-density, polarization-resolved optical storage and advanced photonic device fabrication.

The Dc-PDLW method can be efficiently extended from a point into line-like structures, enabling the inscription of 3D photonic devices. At the same time, this technology is employed to generate dense, highly integrated diffraction gratings (Fig. 4a), where hologram control allows precise regulation of the grating period (d). A decrease in the grating period leads to an increase in the diffraction angle. For periods of d=1 μm and d=2.5 μm, the diffraction angles are measured to be 0.14 and 0.05, respectively. The resulting curve agrees well with the grating diffraction formula. Further results on the influence of laser energy on gratings can be found in Supplementary Text S9.

Another important application lies in geometric phase and polarization encoding, which can be achieved through space-variant retardance engineered in Dc-PDLW–inscribed anisotropic nanostructures (see Supplementary Text S10 for more details). Benefiting from the de-coherent parallel processing nature of Dc-PDLW, the inter-feature spacing can be significantly reduced, enabling stronger and more precise refractive-index modulation for accurate phase and polarization control. Here, by employing the Dc-PLDW method to modulate the dual-pore spacing and relative orientation of the bifocal nanostructure, equivalent to the engineering of birefringence and the rotation of the optical axis, a polarization-selective grating (Pancharatnam–Berry phase plate structure) is processed70,72,73. Figure 4b shows structures fabricated with a sub-diffraction spacing using the SSP-BM algorithm (~500 nm, the right inset of Fig. 4b), thereby demonstrating that our Dc-PDLW method can reliably achieve super-resolution machining of large-area 3D diffractive optical elements. Bifocal nanostructures tilted at different azimuthal angles at different locations were sequentially written until a 180-degree cycle is completed, as illustrated in the upper left inset of Fig. 4c. Besides, it can be observed that under orthogonal linearly polarized light, different parts of the PB phase plate structure exhibit different brightness. Modifying the angle of the orthogonally polarized light results in a change in the intensity of the light-dark cycle of the structure due to polarization sensitivity, as shown in the right inset of Fig. 4c.

Given that the different spacing and relative orientation of bifocal nanostructures present varying degrees of light intensity under polarized light illumination, this property can be exploited for the encryption of polarization-related information74–76. As shown in Fig. 4d, two messages that include a QR code and an image of a qiushie eagle are inscribed overlapped but with different azimuthal angles. It is evident that when observed through natural light illumination, the QR code information is partially obscured by the eagle pattern, rendering it unreadable. Under a correct observation condition with orthogonal polarized light at 45° and 135°, the encrypted information can be displayed clearly. Figure 4e provides another example of the encryption of messages within a QR code, whereby only the requisite azimuth angle is inscribed within the designated square area. The remaining portion of the square is fixed with dual-pore structures, oriented at an angle that is orthogonal to the inscribed angle. As can be observed, when the image is viewed under natural light, the entire pattern appears completely unreadable. In contrast, when the image is viewed under orthogonally polarized light at 45° and 135°, the QR code information appears readable. The results demonstrate the feasibility of utilizing the Dc-PDLW method for the encryption of polarization-related information (see more demonstrations in Supplementary Text S11–S13).

In conclusion, we have proposed a de-coherent parallel direct laser writing (Dc-PDLW) strategy for the inscription of a nanopore array with an ultra-dense distribution, which is achieved by superimposing a non-iterative strip segmentation phase hologram combined with a binary phase mask, in conjunction with wet etching, to create a nanopore structure with a high-duty processing cycle. The principle of achieving super-resolution and crosstalk cancellation using this method has been elucidated and investigated. The non-iterative process eliminates the wavefront disorder of the iterative algorithm, and partitions combined with a binary phase mask eliminate crosstalk generated by spatial coherence and temporal sequence interference effects, thereby ensuring that the feature size of the spacing is in the subwavelength region. The efficiency of the Dc-PDLW is demonstrated by the production of a 3D large-area PB phase plate structure, which exhibits excellent diffraction efficiency and polarization sensitivity. Dc-PDLW exhibits remarkable 3D large-area optical phase encoding capabilities, which portend significant potential for applications in the domain of information encryption. It is particularly well-suited for inscribing meticulously designed phase encodings with nanoscale feature sizes and high efficiencies in a diverse array of materials. Concurrently, the minimum dual-pore spacing is anticipated to be diminished further, potentially through the deployment of larger NA objectives or the utilization of shorter processing wavelengths. The proposed method will facilitate further development of encrypted messages, computational holography, optical storage, and integrated photonics.

Methods
Sample preparation

In our experiments, commercially available Z-cut bulk sapphire wafers with dimensions of 10 × 10 × 0.2 mm (thickness) and full-side polishing were employed. For the fabrication of dual-pore structures, the laser energy was adjusted to a level slightly above the modification energy threshold of sapphire, inducing modification at a depth of 50 μm beneath the sapphire surface. Subsequent to modification, the upper surface of the sapphire was polished until the modified structure was completely exposed.

Ultrafast Laser Processing System

The experimental setup of the femtosecond laser processing system is illustrated in Figure S1. A femtosecond laser system (Pharos, Light Conversion Ltd.) with a pulse duration of 224 fs, a repetition rate of 10 kHz, and a central wavelength of 1030 nm was employed. The polarization of the laser beam was controlled by rotating a half-wave plate (HWP1). Subsequently, the phase hologram was loaded into the liquid crystal SLM (spatial light modulator, Hamamatsu LCOS X13138 series, reflection-type) in order to generate multiple focal spots with a nano-scale distance. A 4f system was constructed by employing two lenses with focal lengths of 400 mm (L1) and 600 mm (L2), respectively. HWP2 coordinates the binary phase mask to achieve an orthogonal polarization state. Subsequently, the beam is focused 50 µm below the sapphire sample surface using an oil immersion objective with a numerical aperture (NA) of 1.25. A CCD camera was employed to assess the uniformity of the multifocal light spot. The sapphire samples were mounted on a 3D translation stage (SmarAct), which provides a positioning resolution of 1 nm.

Structural Characterization

After fabrication, the sapphire samples were preliminarily examined under an optical microscope (Olympus BX53M). The fine structures were further characterized through a SEM (scanning electron microscope, Zeiss), after polishing and etching (40% HF, 80°C, 60 min). Energy-dispersive X-ray spectroscopy (EDS) analysis was performed simultaneously with the SEM measurements on the same region of the sample, enabling in-situ elemental composition characterization while acquiring structural information. The optical phase difference of dual-pore arrays were mearsured by quadriwave lateral shearing interferometry using a wavefront phase sensor (Phasics Sid4).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper proposed a new method that enabled multi-beam parallel processing with a spacing between adjacent two beams (point spacing) of less than 1/3 of the laser wavelength. The authors presented both theoretical and experimental approaches to validate the capabilities of the proposed method with demonstrations of several related applications. The technique is useful for fabricating 3D photonic devices with high throughput through parallel processing. Therefore, the reviewer considers that this manuscript can be accepted for publication in Nature Communications, but some major revisions based on the following comments are required before being accepted.\nMajor Comments:\nPaper title:\nThe title of the paper sounds like it does not do justice to the content of this paper. The reviewer feels that “multi-beam parallel processing” is much more important than “single-pulse laser pattering”.\nLine 119:\nWhat does “the latter incident beam” mean? Are two beams incident with some delay time? If yes, how long is the delay time? In this process, two beams must be simultaneously incident.\nFig. 2 d1:\nBoth nanopores appear to be transversely elongated elliptical in shape. Why not circle?\nFig. 2 f (lower):\nEDS measurement must have been done after the chemical etching. If so, the low-density regions should be removed by the etching (in fact, nanopores are created in the SEM image). Why is the relative content at the nanopores still lower than that at the surrounding areas (< 100 nm and > 1200 nm)?\nLines 273 – 276\nIn my understanding, the unit-by-unit writing means the single beam processing, right? If so, why is the deviation effect of the redistribution of the optical field caused by spatial coherence more pronounced in the single-beam processing?\nApplications\nThe authors demonstrated thee applications of diffraction gratings, a polarization-selective grating (Pancharatnam–Berry phase plate structure), and encrypted QR Codes. However, all elements look like being fabricated with pointing spacings much larger than 1/3 of the laser wavelength. To show the superiority of this technique over the other techniques, all elements should be fabricated with a pointing spacing smaller than 1/3 of the laser wavelength.\nMinor comments:\nEnglish should be edited, for e. g.,\nLine 67: the GS iterative algorithm has has great flexibility -> the GS iterative algorithm has hgreat flexibility\nLine 81: Schematic diagram of spatial and polarization decoherence as shown in Fig. 1a1-a3. -> Schematic diagram of spatial and polarization decoherence is shown in Fig. 1a1-a3.\nAbbreviations such as SLM, SEM, and EDS should be spelled out when they first appear in the manuscript.\nLine 100:\nfs laser -> femtosecond laser\nFig. 1 a4:\n“2025” in the table should be replaced by “this work”.\nLine 152:\n“,” is necessary after the equation.\nLine 153:\nRemove a blank (an indent) before “where”.\nLine 221:\nUniformity should be defined. It should be a ratio of intensity of two beams.\nWhat is “d”?\nLine 236:\n“.” Is missing after “appearances”.\nLine 249:\nThe point spacing -> The total spacing (?)", "reviewer_2": "This study presents a novel approach to overcoming the diffraction limit in parallel laser processing using femtosecond laser pulses. This research introduces the de-coherent parallel direct laser writing (Dc-PDLW) strategy, which utilizes a combination of a patterned single pulse and a de-coherent holographic algorithm to surpass the traditional diffraction limit in multi-beam laser processing. By effectively managing spatial coherence and temporal sequence interference, the study achieves a resolution of 300 nm (~λ/4), setting a record for parallel laser processing.\nThere has been a recent push in the field to explore the limits of laser processing using this general approach, but I have not seen this specific methodology i.e.non-iterative strip segmentation phase holograms which avoid uneven energy distribution, and binary masks to customize polarization states and eliminate coherence between focal points. The work is potentially a breakthrough contribution from the authors. The significance of this work is underlined by its application to produce large area three-dimensional structures such as Pancharatnam–Berry phase plates and voluminous cipher sequences, demonstrating advanced high-density phase and polarization coding capabilities in 3D.\nI believe this is a significant breakthrough expands the potential of femtosecond laser processing for complex, high-resolution micro- and nano-fabrication tasks.\nIt is excellent work and worthy of rapid publication. However, I may suggest (optionally) that the authors consider including comments on the implementation of the Dc-PDLW approach. This clearly involves a sophisticated and precise setup, requiring advanced optical components and meticulous alignment. Whilst this may be possible with unlimited research time, does this limit the approach's potential application and scalability? Is it indeed possible to scale the technique for large-scale production. A few comments (in the conclusions perhaps) would be useful here.\nThe work is very well written, nicely presented and extensively referenced. There a just a few grammatical and typo errors which need addressing.", "reviewer_3": "Reviewer Comments – Recommendation: Reject\nThe submitted manuscript presents a study on the fabrication of ultradense nanopore arrays using a de-coherent parallel direct laser writing (Dc-PDLW) strategy based on a non-iterative strip segmentation phase hologram combined with a binary phase mask (SSP-BM). The authors claim that this method improves uniformity and reduces crosstalk in multi-focus femtosecond laser processing, enabling high-resolution structures and polarization-sensitive encoding.\nThe manuscript demonstrates certain technical merit, such as the integration of polarization control and holographic beam shaping. Therefore, the paper has some scientific value as it experimentally confirms that the SSP-BM approach can fabricate subwavelength structures with a specific polarization control strategy.\nHowever, I must conclude that the novelty and significance of the work are insufficient for publication in Nature Communications, due to the following critical concerns:\n1. Lack of originality in concept:\nThe proposed method is conceptually similar to previous works [1,2], which have already demonstrated polarization control in parallel femtosecond laser processing using spatial light modulators. The approach adopted in this manuscript does not significantly depart from those existing methods, and the incremental improvement offered is relatively modest.\n2. Overstated limitations of iterative algorithms:\nThe authors criticize iterative hologram design methods, such as the Gerchberg–Saxton (GS) algorithm, for introducing wavefront disorder. However, they overlook important developments in improved iterative methods, such as the Weighted GS (WGS) algorithm, which effectively suppresses multi-beam inhomogeneity. These improved techniques can generate high-uniformity multifocal arrays and should not be dismissed without quantitative comparison.\n3. Low diffraction efficiency likely due to polarization geometry:\nThe proposed system uses a 45° linearly polarized beam incident on a liquid crystal on silicon (LCOS) SLM with a binary phase mask. Given this optical configuration, the diffraction efficiency is likely very low. In practical laser processing applications, especially those requiring high throughput and energy efficiency, low-efficiency holograms are generally unacceptable.\n4. Resolution claims are not surprising given known nonlinear effects:\nThe reported spatial resolution of 300 nm (approximately λ/4) is attributed to the suppression of crosstalk via polarization control. However, such resolution is not unprecedented in femtosecond laser processing due to nonlinear absorption and threshold effects. Therefore, the result is not as remarkable as the authors suggest.\nIn conclusion, although the authors have provided some experimental validation of the SSP-BM method, the conceptual novelty, technical innovation, and impact are insufficient to meet the high standard of Nature Communications. The paper would be more appropriate for a specialized journal focused on laser fabrication or applied optics.\nReferences:\n[1] S. Hasegawa and Y. Hayasaki, \"Polarization distribution control of parallel femtosecond pulses with spatial light modulators,\" Opt. Express 21, 12987–12995 (2013).\n[2] S. Hasegawa and Y. Hayasaki, \"Holographic Vector Wave Femtosecond Laser Processing,\" Int. J. Optomechatronics 8, 73–88 (2014)."}, "author_response": "Response to reviewers\nReviewer #1:\nThis paper proposed a new method that enabled multi-beam parallel processing with a spacing\nbetween adjacent two beams (point spacing) of less than 1/3 of the laser wavelength. The\nauthors presented both theoretical and experimental approaches to validate the capabilities of\nthe proposed method with demonstrations of several related applications. The technique is\nuseful for fabricating 3D photonic devices with high throughput through parallel processing.\nTherefore, the reviewer considers that this manuscript can be accepted for publication in\nNature Communications, but some major revisions based on the following comments are\nrequired before being accepted.\nResponse: We sincerely thank the reviewer for recognizing the novelty, technical rigor,\nand potential impact of our work. We are very encouraged by the reviewer’s positive assessment\nthat the proposed method enables multi-beam parallel processing with inter-spots spacing\nbelow one-third of the laser wavelength, thereby breaking the conventional coherent diffraction\nlimit—and that it holds promise for high-throughput 3D photonic device fabrication.\nFollowing the reviewer’s valuable suggestions, we have carefully revised the manuscript\nto further strengthen its clarity and completeness. Specifically, we:\n1. Expanded the theoretical analysis section to more clearly explain the physical basis of\ncoherence suppression and the determination of the ultimate spacing limit.\n2. Enhanced the experimental validation by including new quantitative comparisons\nbetween the proposed SSP-BM method and conventional iterative algorithms (Table\nS1).\n3. Refined the application demonstrations to better highlight the relevance of ultradense\nnanopore arrays for polarization-resolved optical storage and 3D photonic device\nfabrication.\nWe believe these revisions have significantly improved the manuscript and addressed the\nreviewer’s expectations for publication in Nature Communications.\nMajor Comments:\nPaper title:\nThe title of the paper sounds like it does not do justice to the content of this paper. The reviewer\nfeels that “multi-beam parallel processing” is much more important than “single-pulse laser\npattering”.\nResponse: We thank the reviewer for this insightful remark. In the original title, we\nemphasized “single-pulse laser patterning” to highlight that our process achieves high\nefficiency with a single laser pulse. However, this nuance can be overlooked at first glance—\nespecially in the title—whereas the phrase “multi-beam parallel processing” more clearly\nconveys the outstanding throughput and efficiency of our approach. Therefore, we have\nchanged the manuscript title to “De-coherent Parallel Laser Processing of Ultradense\nNanopores for High-Density, Large-Area 3D Optical Phase Encoding” to highlight the\ncentral advantages.\nQuestion 1: Line 119\nWhat does “the latter incident beam” mean? Are two beams incident with some delay time? If\nyes, how long is the delay time? In this process, two beams must be simultaneously incident.\nResponse: Thank you for this meaningful question. We will answer your concerns in turn.\nWhat does “the latter incident beam” mean?\nIn the position mentioned in the article, “the latter incident beam” is the beam settings of\nthe conventional serial laser processing method. In the aforementioned processing, the notion\nof sequential incident light is typically employed.\nAre two beams incident with some delay time? If yes, how long is the delay time?\nYes, there is a delay time between two pulses in conventional serial laser machining\nmethods. The delay time depends on the material to be processed, and the effect of heat\naccumulation [Nature Photonics 2, 219-225 (2008).]. Typically, the delay time is 1 ms to 1 μs,\nwhich corresponds to a laser repetition frequency of 1 kHz to 1 MHz.\nIn this process, two beams must be simultaneously incident.\nYes, in our parallel laser processing method, two beams must be simultaneously incident.\nThis is indeed the case: in our parallel-processing scheme, the two (or more) beams are\ngenerated by phase hologram loaded onto a single spatial light modulator (SLM). After leaving\nthe SLM, they traverse the same optical path, so they strike the sample simultaneously, with no\nmeasurable temporal delay between them.\nTo avoid misunderstandings, we have made changes in the text and in the figure notes: add\n“the conventional serial laser processing method” to the body of the text you mentioned, and\nblue-label it. (Lines 56, 106, 138, 212, and 263)\nQuestion 2: Fig. 2 d1:\nBoth nanopores appear to be transversely elongated elliptical in shape. Why not circle?\nResponse: We sincerely thank the reviewer for this insightful question. The slight\nellipticity observed in Fig. 2d1 arises from a combination of optical and spatial interference\neffects inherent to multi-beam parallel femtosecond laser processing. Specifically:\n1. Crosstalk effects in linearly arranged multi-focus arrays:\nThe elongation arises primarily from the coherent crosstalk between neighboring foci\ngenerated by the spatial light modulator (SLM). When the focal points are arranged along a straight\nline, the corresponding phase hologram exhibits periodicity analogous to a circular moiré pattern\ndue to the regular grid alignment. After Fourier transformation by the objective lens, this periodic\nstructure leads to localized energy convergence along the connecting line between adjacent foci,\nproducing elliptical rather than circular energy distributions at the focus [Opto-Electronic Advances\n7, 240082 (2024); Optics Letters 30,2086-2088 (2005).]. This effect becomes more pronounced as\nthe inter-spot spacing decreases or the number of foci increases.\n2. Distribution geometry effects:\nWe have verified that when using a non-collinear (e.g., triangular, Fig. R1(a1-a2, b1-b2))\nspatial distribution of foci, this crosstalk effect is effectively suppressed, resulting in nearly circular\nnanopores. This phenomenon can be attributed to the fact that the aggregated crosstalk of the three\npoints is partially canceled out due to the triangular distribution. This observation is consistent with\nour supplementary data (Fig. S12c3), where nonuniform and triangular distributions yield improved\nroundness and uniformity.\nFigure R1. (a1-a2) Optical micrographs of close-up 3-pore structures with (b1-b2) corresponding\nSEMs. Scale bars: 500 nm. Both optical and electron microscopy confirm that the fabricated\nnanopores exhibit excellent circular symmetry. (c–d) Comparison between simulated and\nexperimentally observed focal spot profiles at different numerical apertures (NA). It is revealed that\nunder high-NA focusing conditions (NA > 0.8), a slight asymmetry (maximum ellipticity ≈ 1.12) may\noccur due to the vectorial nature of tightly focused linearly polarized light.\n3.Effect of Debye diffraction：\nThe generation of SSP-BM holograms is based on Debye diffraction theory, which inherently\naccounts for high-NA focusing conditions and partially corrects the associated aberrations.\nNevertheless, due to the substantial numerical aperture (NA) of the processing objective, a minor\nresidual asymmetry in the focal field distribution can persist. As a result, slight ellipsoidal features\n(with a maximum ellipticity of approximately 1.12) are occasionally observed when linearly\npolarized light is employed [Acta Physica Sinica 61, 234202-234202 (2012)].\nImportantly, this weak ellipticity does not negatively impact the birefringence magnitude\nor polarization sensitivity of the fabricated structures. The birefringence strength in our\napproach is primarily governed by the focal spacing and processing period, rather than by the\nminor asymmetry of individual focal spots. As experimentally confirmed in Fig. 4, the overall\npolarization-resolved response of the fabricated birefringent devices remains highly stable and\nuniform, demonstrating that the observed ellipticity is negligible for both structural\nfunctionality and optical performance.\nQuestion 3: Fig. 2 f (lower):\nEDS measurement must have been done after the chemical etching. If so, the low-density\nregions should be removed by the etching (in fact, nanopores are created in the SEM image).\nWhy is the relative content at the nanopores still lower than that at the surrounding areas (<\n100 nm and > 1200 nm)?\nResponse: We thank the reviewer for this insightful question. Indeed, the EDS analysis\nwas performed after chemical etching. The observed difference in elemental distribution arises\nfrom two combined effects: structural extrusion at the pore boundaries and signal attenuation\ncaused by the nanopore cavity, as explained below.\n1. Structural extrusion in the edge region (< 100 nm and > 1200 nm).\nDuring nanopore formation, the femtosecond-laser-induced shock wave expands radially\noutward from the focal center, leading to local structural extrusion in the surrounding material\n[Physical Review Letters 96, 166101 (2006)]. The central region experiences the strongest\ncompression and material transformation, while the adjacent regions are partially squeezed outward\nby the shock wave [Advanced Materials 18, 1361-1364 (2006).]. After wet etching, the highly\nmodified amorphous region at the center is selectively removed to form the nanopore cavity. The\nedge regions, however, undergo densification or even transient high-pressure phase formation\nduring the shock-induced extrusion process, making them more resistant to etching. As a result,\nthese edge regions exhibit relatively higher elemental signal intensity in the post-etching EDS maps,\nconsistent with our measurements. The schematic diagram of shock wave diffusion during\nprocessing is shown in Fig. R2.\nFigure R2. Schematic diagram of the direction of shock wave diffusion and compression during\nformation of the nanopore. The yellow arrow indicates the direction of shock wave propagation.\n2. EDS signal attenuation caused by the nanopore cavity.\nEnergy-dispersive X-ray spectroscopy (EDS) detects element-specific X-rays generated by\nhigh-energy electron excitation. However, nanoscale cavity structures can obstruct or scatter the\nemitted X-rays, thereby weakening the detected signal from the nanopore region. This geometric\nattenuation effect causes the apparent elemental content at the nanopore center to appear lower than\nthat of the surrounding dense material, even though the actual composition difference may be\nnegligible.\nQuestion 4: Lines 273 – 276\nIn my understanding, the unit-by-unit writing means the single beam processing, right? If so, why\nis the deviation effect of the redistribution of the optical field caused by spatial coherence more\npronounced in the single-beam processing?\nResponse: Thank you for these insightful questions. Yes, the unit-by-unit writing means the\nsingle-beam processing or serial laser processing method.\nThe spatial-coherence–induced deviation arises from the interference between the incident\nlaser field and the field scattered by pre-existing nanopores. Specifically, the first laser pulse forms\na nanopore within the material. After a delay longer than the cavity-formation time (>1 ms, allowing\nfull cooling and solidification), a subsequent pulse is delivered nearby, with a center-to-center\nspacing of <0.61 λ/NA. This second pulse encounters the scattering field from the existing nanopore,\nand the interference between the two fields redistributes the local optical intensity, shifting the\nlocation of the peak intensity (Fig. 1 d1-d2). Numerical simulations confirm that this effect becomes\nstronger and the positional deviation more pronounced as the inter-pore spacing decreases or the\nnanopore diameter increases (also see in [Advanced Functional Materials 34, 11 (2024) 2306870.]).\nIn single-beam serial processing, each pulse arrives sequentially and is therefore inevitably\naffected by the residual structural modifications produced by the preceding pulse (Fig. S2).\nConsequently, the spatial-coherence-induced optical-field redistribution and associated positional\ndeviation are more pronounced in serial (unit-by-unit) processing [Light: Science & Applications 9,\n41 (2020)].\nIn contrast, the parallel laser processing method involves the simultaneous incidence of multiple\nbeams, rather than sequential delivery. At this timescale, the formation of a strongly scattering\nnanopore has not yet occurred (the structural formation happens on microsecond–millisecond\ntimescales). The transient plasma generated during the femtosecond exposure induces only a weak,\nsymmetric refractive index modulation (Δn < 0.03) [Nat Photonics 18, 799-808 (2024)], far smaller\nthan the Δn ≈ 0.76 contrast of a nanopore, and thus does not introduce inter-beam field redistribution.\nTherefore, the deviation caused by field redistribution is negligible in parallel processing.\nWe thank the reviewer for pointing this out. This is a misunderstanding caused by our error in\nexpression. The intended meaning was “the deviation effect caused by the redistribution of the\noptical field,” rather than “the deviation effect of the redistribution of the optical field caused by\nspatial coherence.” We have revised the corresponding sentence in the revised manuscript to clarify\nthis point.\n(Lines 261-264) “The deviated effect due to the light field redistribution effect is pronounced when\nlinearly polarized light is employed for unit-by-unit conventional serial laser processing, resulting in a\nlarger average dual-pore spacing of 601 nm.”\nFigure S2. Schematic diagram of the deviation effect of the redistribution of the optical field in the\nsingle-beam serial laser processing. (a) Scheme of electrodynamic dynamic. The nanopore structure\nproduced by the first pulse is much smaller than the processing wavelength scale in both size and\nprocessing distance, which distorts the energy distribution. (b) Top view of the deviation effect of light\nfield redistribution.\nQuestion 5: Applications\nThe authors demonstrated thee applications of diffraction gratings, a polarization-selective grating\n(Pancharatnam–Berry phase plate structure), and encrypted QR Codes. However, all elements\nlook like being fabricated with pointing spacings much larger than 1/3 of the laser wavelength.\nTo show the superiority of this technique over the other techniques, all elements should be fabricated\nwith a pointing spacing smaller than 1/3 of the laser wavelength.\nResponse: Thank you for point out this. To avoid confusion and to highlight the sub-\nwavelength fabrication capability, we have revised the manuscript as follows:\nFig. 2d (main text) and the newly added high-magnification SEM image (Fig. 4b in the revised\nmanuscript) clearly present structures fabricated with sub-diffraction spacing using the Dc-PDLW\nmethod. These results experimentally confirm that our method can reliably achieve super-resolution\npatterning with point spacings smaller than 1/3 λ.\nFurthermore, the newly added SEM images verify the uniformity and reproducibility of each\nnanopore, demonstrating that all functional elements, including diffraction gratings, polarization-\nselective gratings, and QR-code–based devices, which all can indeed be fabricated under the same\nsubwavelength condition. These clarifications and additional data collectively underscore the high\nthroughput and resolution advantages of the proposed technique.\nWe believe these clarifications and additional data make it clear that functional elements can\nindeed be produced at dual-pore spacings below 1/3 λ, underscoring the throughput and resolution\nadvantages of our technique.\nFig. 4b. SEM image of fabricated PB phase plate, showing enlarged structural units (right) with\norientation angles of 0°, 45°, 90°, 135°. Scale bars: 500 nm.\nMinor comments:\nEnglish should be edited, for e. g.,\nResponse: We greatly appreciate the time you’ve taken to suggest these valuable formatting\nand detail corrections. We have incorporated all changes into the revised manuscript and clearly\nmarked each update. Thank you for your patience and insightful guidance.\nLine 67: the GS iterative algorithm has great flexibility -> the GS iterative algorithm has great\nflexibility\nResponse: In the revised version, the errors have been corrected (Line 66).\nLine 81: Schematic diagram of spatial and polarization decoherence as shown in Fig. 1a1-a3.\n->Schematic diagram of spatial and polarization decoherence is shown in Fig. 1a1-a3.\nResponse: In the revised version, the errors have been corrected (Line 89).\nAbbreviations such as SLM, SEM, and EDS should be spelled out when they first appear in the\nmanuscript.\nResponse: In the revised version, the errors have been corrected (Line 398, 408, and 214).\nLine 100: fs laser-> “femtosecond laser\nFig. 1 a4: “2025” in the table should be replaced by “this work”.\nLine 152: “,” is necessary after the equation.\nLine 153: Remove a blank (an indent) before “where”.\nResponse: Thank you very much for the reminder, in the revised version has been completed\nand labeled accordingly (Line 394, 153, 154, and Fig. 1 b)\nLine 221: Uniformity should be defined. It should be a ratio of intensity of two beams. What is “d”?\nResponse: The definition of uniformity has been supplemented (Line 216-219).\n“d” means the algorithm preset point spacing. It is mentioned here to illustrate that the point\nspacing of the bifocal points is freely controllable by the hologram design, in order to emphasize\nthe technical flexibility. Since it was not central to the core message, it has been removed to avoid\nmisinterpretation.\nLine 236: “.” Is missing after “appearances”.\nResponse: Thank you very much for the reminder, in the revised version has been completed\nand labeled accordingly (Line 232).\nLine 249: The point spacing -> The total spacing (?)\nResponse: This does not require modification. The point spacing is specifically interpreted to\nmean the algorithm preset spacing. The algorithm presets the point spacing meaning the point\nspacing that the bifocal points generated by SSP-BM should theoretically have, which is jointly\ndetermined by the pre-set Δx and Δy. To avoid misinterpretation, the original description of \"point\nspacing\" has been replaced with \"algorithm preset spacing\" and marked with a blue label. (Line\n224-253).\nReviewer#2:\nThis study presents a novel approach to overcoming the diffraction limit in parallel\nlaser processing using femtosecond laser pulses. This research introduces the de-\ncoherent parallel direct laser writing (Dc-PDLW) strategy, which utilizes a\ncombination of a patterned single pulse and a de-coherent holographic algorithm to\nsurpass the traditional diffraction limit in multi-beam laser processing. By effectively\nmanaging spatial coherence and temporal sequence interference, the study achieves a\nresolution of 300 nm (~λ/4), setting a record for parallel laser processing.\nResponse: We sincerely thank the reviewer for the positive and encouraging assessment of our\nwork. We are pleased that the novelty of the proposed de-coherent parallel direct laser writing (Dc-\nPDLW) strategy and its ability to surpass the diffraction limit in multi-beam processing have been\nclearly recognized. We particularly appreciate the reviewer’s acknowledgment of our demonstration\nof 300 nm (~λ/4) resolution as setting a new benchmark in parallel laser processing. This feedback\nfurther motivates us to refine the manuscript to ensure that the conceptual advances, methodological\ndetails, and potential applications of Dc-PDLW are communicated with maximum clarity and\nimpact.\nThere has been a recent push in the field to explore the limits of laser processing using this\ngeneral approach, but I have not seen this specific methodology i.e.non-iterative strip segmentation\nphase holograms which avoid uneven energy distribution, and binary masks to customize\npolarization states and eliminate coherence between focal points. The work is potentially a\nbreakthrough contribution from the authors. The significance of this work is underlined by its\napplication to produce large area three-dimensional structures such as Pancharatnam–Berry phase\nplates and voluminous cipher sequences, demonstrating advanced high-density phase and\npolarization coding capabilities in 3D.\nResponse: We are deeply grateful to the reviewer for highlighting the novelty and potential\nbreakthrough nature of our methodology. Indeed, the development of the non-iterative strip\nsegmentation phase hologram (SSP) was motivated precisely to overcome the uneven energy\ndistribution issues often encountered in iterative holograms, while the binary mask (BM) provides\nrigorous polarization customization to eliminate coherence between focal points. We are especially\npleased that the reviewer recognizes the significance of extending this strategy to large-area three-\ndimensional structures such as Pancharatnam–Berry phase plates and voluminous cipher sequences,\nwhich exemplify the high-density phase and polarization coding capabilities enabled by Dc-PDLW.\nWe appreciate this encouraging feedback, which reinforces the broader impact of our work in\nadvancing ultrafast laser nanofabrication.\nI believe this is a significant breakthrough expands the potential of femtosecond laser processing\nfor complex, high-resolution micro- and nano-fabrication tasks.\nResponse: We sincerely thank the reviewer for recognizing the significance of our work. We\nagree that the proposed Dc-PDLW strategy expands the potential of femtosecond laser processing\nfor complex, high-resolution micro- and nano-fabrication tasks, and we appreciate this encouraging\nassessment of our contribution.\nIt is excellent work and worthy of rapid publication. However, I may suggest (optionally) that\nthe authors consider including comments on the implementation of the Dc-PDLW approach. This\nclearly involves a sophisticated and precise setup, requiring advanced optical components and\nmeticulous alignment. Whilst this may be possible with unlimited research time, does this limit the\napproach's potential application and scalability? Is it indeed possible to scale the technique for\nlarge-scale production. A few comments (in the conclusions perhaps) would be useful here.\nResponse: We sincerely thank the reviewer for the positive evaluation and constructive\nsuggestion. We agree that it is important to address the implementation and scalability of the Dc-\nPDLW approach. In the revised manuscript, we have added comments in the Methodology section\ndiscussing the practical implementation and scalability of the Dc-PDLW approach, covering optical\nsetup complexity, component requirements, and potential routes to scale. The added content is as\nfollows:\n“The compact system architecture of Dc-PDLW benefits from the employment of SLM, making\nit fully scalable in mass production. During the large-scale processing of a micro-nano birefringent\ndevice, it takes less than 3 minutes to achieve a complete phase encoding process (2 mm x 2mm).\nThe high processing rate of micro- and nano-optical products demonstrates the great potential and\nfull feasibility of Dc-PDLW technology in practical applications” (Lines 299-304)\nThe work is very well written, nicely presented and extensively referenced. There a just a few\ngrammatical and typo errors which need addressing.\nResponse: We sincerely thank the reviewer again for the positive assessment of our work and\nfor highlighting its presentation quality. We have carefully re-checked the manuscript and corrected\nthe grammatical and typographical errors to further improve clarity and readability.\nReviewer #3 (Remarks to the Author)\nReviewer Comments – Recommendation: Reject\nThe submitted manuscript presents a study on the fabrication of ultradense\nnanopore arrays using a de-coherent parallel direct laser writing (Dc-PDLW) strategy\nbased on a non-iterative strip segmentation phase hologram combined with a binary\nphase mask (SSP-BM). The authors claim that this method improves uniformity and\nreduces crosstalk in multi-focus femtosecond laser processing, enabling high-\nresolution structures and polarization-sensitive encoding.\nThe manuscript demonstrates certain technical merit, such as the integration of\npolarization control and holographic beam shaping. Therefore, the paper has some\nscientific value as it experimentally confirms that the SSP-BM approach can fabricate\nsubwavelength structures with a specific polarization control strategy.\nHowever, I must conclude that the novelty and significance of the work are\ninsufficient for publication in Nature Communications, due to the following critical\nconcerns:\nResponse: We would like to present our sincere gratitude to the reviewer for the time and\nconstructive feedback. We are encouraged that the reviewer acknowledged the technical merit and\nscientific value of our work, particularly the integration of polarization control with holographic\nbeam shaping and the successful fabrication of subwavelength structures using a polarization\ncontrol strategy. We greatly appreciate these valuable comments, which have helped us further\nimprove the clarity and quality of our manuscript. In particular, we fully understand the reviewer’s\nconcern regarding the perceived lack of novelty and significance for Nature Communications.\nHowever, we believe that the decision stems from a misunderstanding of the conceptual innovation\nand scientific significance of our work. and we appreciate the opportunity to clarify the unique\nconceptual contributions, technical advances, and application-oriented breakthroughs presented in\nthis study. We wish to clarify several key points below.\n1. Conceptual innovation:\nOur work goes beyond established polarization-controlled or holographic beam-shaping\ntechniques. It introduces a fundamentally new physical mechanism that overcomes the coherent\ndiffraction limit in parallel femtosecond laser writing - a limitation that has not been systematically\naddressed by prior iterative methods (e.g., GS or WGS). The proposed de-coherent parallel direct\nlaser writing (Dc-PDLW) framework identifies the intrinsic spacing limit between adjacent foci\nand demonstrates how coherence suppression allows this limit to be surpassed, enabling the\nrealization of ultradense subwavelength nanostructures.\nTo clarify our motivation, Fig. R1 presents a fabricated “Siemens Test Star” consisting of\nperiodic dual-pore arrays with gradually decreasing spacing from the outer to the inner regions,\nproduced using double beams with identical polarization (generated by GSW algorithm) and\northogonal polarization (generated by SSP-BM algorithm) states. This figure provides a direct\nvisual comparison of the processing resolution achievable with and without polarization control\nin dual-beam parallel fabrication. The results reveal the intrinsic limitation of coherent multi-\nbeam irradiation imposed by the coherent diffraction limit: in the coherent FLDW case, the\ncentral region (indicated by a red circle in Fig. R1(a)) exhibits complex, high-frequency\ninterference-like patterns, with the maximum resolvable spatial frequency reaching v₀; in\ncontrast, the non-coherent FLDW configuration yields a much clearer central region (marked\nby a red circle in Fig. R1(b)), where the maximum resolvable spatial frequency is reduced to\nv₀/2. These observations clearly demonstrate how varying degrees of coherence fundamentally\ninfluence the achievable processing resolution in parallel femtosecond laser fabrication.\n Figure R1. Fabricated “Siemens Test Star” composed of periodic dual-pore arrays with\ngradually decreasing dual-pore spacing from the outer to the inner regions, produced using\ndouble beams with (a) identical polarization and (b) orthogonal polarization states.\n2. Technical advancement beyond iterative methods:\nWhile iterative algorithms such as GS or WGS achieve uniform multifocal arrays, they suffer\nfrom phase indeterminacy and wavefront disorder, particularly under high-NA focusing. In contrast,\nour non-iterative strip-segmentation phase plus binary mask (SSP-BM) approach deterministically\ndefines the phase and eliminates speckle noise and ghost foci (see Fig. S12). Furthermore, the SSP-\nBM method uniquely supports local polarization segmentation, an essential feature for\nexperimentally probing and suppressing inter-focal crosstalk—something no iterative approach can\nachieve.\n3. Broader scientific and application relevance:\nOur study establishes a new regime of high-throughput, sub-diffraction nanostructuring that\ncomplements nonlinear threshold effects in single-spot processing. This compatibility bridges the\ngap between precision and scalability, enabling ultrahigh-density, polarization-encoded 3D\nnanostructures for optical data storage, integrated photonics, and 3D metasurfaces.\nIn light of these clarifications and newly added quantitative comparisons (Table S1),\nwe\nrespectfully submit that the novelty and impact of our study were underestimated. The work offers\nboth fundamental insight into the coherence limit of laser fabrication and a technically practical\nroute to surpass it — contributions that align strongly with Nature Communications’s scope of\npublishing conceptually significant advances.\nReviewer Comment 1/4\nConcerns 1: Lack of originality in concept:\nThe proposed method is conceptually similar to previous works[1,2], which have already\ndemonstrated polarization control in parallel femtosecond laser processing using spatial light\nmodulators. The approach adopted in this manuscript does not significantly depart from those\nexisting methods, and the incremental improvement offered is relatively modest.\nReferences:\n[1] S. Hasegawa and Y. Hayasaki, \"Polarization distribution control of parallel\nfemtosecond pulses with spatial light modulators,\" Opt. Express 21, 12987–12995 (2013).\n[2] S. Hasegawa and Y. Hayasaki, \"Holographic Vector Wave Femtosecond Laser\nProcessing,\" Int. J. Optomechatronics 8, 73–88 (2014).\nResponse: We sincerely thank the reviewer for this valuable comment. We fully\nacknowledge that the use of spatial light modulators to manipulate the polarization state of\nindividual beams in multi-beam parallel femtosecond laser processing has been well established\nin prior studies, including the seminal works [1,2] referenced by the reviewer, which achieved\nefficient fabrication of polarization-dependent structures such as self-organized nanogratings\n(Laser Photonics Rev 2024, 18, 2300891. https://doi.org/10.1002/lpor.202300891). However,\ndespite these advances, the fundamental spacing limitation and crosstalk mechanisms inherent\nin such parallel configurations have not been systematically addressed—a challenge that our\npresent study directly overcomes.\nHowever, despite these important advances, the fundamental spacing limitation and\ncrosstalk mechanisms inherent in such parallel configurations have not been systematically\ninvestigated—a challenge that our present study directly addresses. From a methodological\nperspective, our de-coherent parallel direct laser writing (Dc-PDLW) approach can also be\nbroadly classified within this general framework of polarization-controlled parallel laser\nprocessing. Nevertheless, the present work goes far beyond a mere technical refinement. The\ncentral focus of this study is to elucidate and overcome a fundamental yet previously\nunexplored question: what determines the ultimate spacing limit between adjacent spots or lines\nin parallel laser writing, and how this limit can be exploited to realize ultradense\nnanostructures.\nSpecifically, we respectfully emphasize that the present study achieves substantial progress\nover previous works of polarization control in parallel femtosecond laser processing using\nSLMs ([1,2] for example, herein), introducing a fundamentally new type of subwavelength\nstructures of dual-pore anisotropic nanostructures for dense 3D phase and polarization encoding\nwithin crystalline materials. Our study addresses a fundamentally different scientific problem\nand achieves substantial technical and application-oriented advancements, as detailed below:\na) Distinct scientific focus and motivation:\nPrevious works (e.g. [1,2]) primarily focused on the parallel fabrication of birefringent\nnanostructures with controllable orientation, that is, realizing various polarization-dependent\nfeatures by local polarization modulation. In contrast, this work focuses on a problem that has\nnever been addressed before: the fundamental limit of spacing between adjacent foci in parallel\nlaser processing and its determining factors.\nIn principle of wave optics, it is well known that in optical imaging systems, the diffraction-\nlimited resolution is λ/2 under coherent illumination and can be improved to λ/4 under\nincoherent illumination [Photon. Res. 11, 442-455 (2023)]. However, in laser processing\nsystems—which are typically highly coherent, this principle is not directly transferable, making\nit especially challenging to reach such resolution levels. Our work overcomes this barrier by\neffectively suppressing spatial coherence in the laser writing process, enabling unprecedented\nfeature densities in 3D.\nFurthermore, in order to clarify our motivation, Fig. R1 presents a fabricated “Siemens Test\nStar” consisting of periodic dual-pore arrays with gradually decreasing spacing from the outer\nto the inner regions, produced using double beams with identical polarization (generated by\nGSW algorithm) and orthogonal polarization (generated by SSP-BM algorithm) states. This\nfigure provides a direct visual comparison of the processing resolution achievable with and\nwithout polarization control in dual-beam parallel fabrication. The results reveal the intrinsic\nlimitation of coherent multi-beam irradiation imposed by the coherent diffraction limit: in the\ncoherent FLDW case, the central region (indicated by a red circle in Fig. R1(a)) exhibits\ncomplex, high-frequency interference-like patterns, with the maximum resolvable spatial\nfrequency reaching v₀; in contrast, the non-coherent FLDW configuration yields a much clearer\ncentral region (marked by a red circle in Fig. R1(b)), where the maximum resolvable spatial\nfrequency is reduced to v₀/2. These observations clearly demonstrate how varying degrees of\ncoherence fundamentally influence the achievable processing resolution in parallel\nfemtosecond laser fabrication.\nFigure R1. Fabricated “Siemens Test Star” composed of periodic dual-pore arrays with gradually\ndecreasing dual-pore spacing from the outer to the inner regions, produced using double beams with\n(a) identical polarization and (b) orthogonal polarization states.\nb) Substantial technical advancements:\nTechnically, our method represents a marked improvement in both resolution and energy\nutilization efficiency. The SSP-BM algorithm eliminates speckle artifacts and significantly improves\nintensity uniformity under tight focusing condition (see Fig. 2a). Its stripe-segmentation and binary-\nmask design enables independent phase and polarization control for each subregion, providing\nsuperior control of the multi-focal field distribution compared with previous SLM-based\npolarization modulation schemes.\nOn one side, in prior studies [1,2], the polarization control can avoid mutual interference\namong side lobes, yielding the smallest spacing between adjacent spots of ≈0.73λ/NA. Here,\nour work further introduces the de-coherent parallel direct laser writing framework, which\nemploys polarization orthogonality and decoherence holography to suppress spatial coherence\nand interaction crosstalk between adjacent foci, thus achieving spot-to-spot spacing as small as\n~0.25λ in transparent materials—well beyond the previously reported limit of 1.44 × dₐᵢᵣᵧ\n(≈0.73λ/NA).\n(Lines 70-78) “In particular, in the context of this study, where adjacent focal spots are brought into\nextremely close proximity and their optical fields begin to overlap, this wavefront disorder can induce\ncomplex spatial coherence effects, making it difficult to surpass the coherent diffraction limit that\nconstrains the minimum achievable spacing between adjacent spots (≈1.47λ/NA) [35]. Furthermore, by\ncontrolling the polarization orthogonality between adjacent beams, the spatial coherence effects of the\noptical fields can be effectively eliminated, thereby reducing the minimum achievable spacing between\nadjacent focal spots by half (≈0.73λ/NA) [36], approaching the coherent diffraction limit.”\nOn the other side, in terms of energy efficiency, as discussed in our response to Comment\n3, the system achieves an energy utilization efficiency of no less than 25%, or up to 44% when\nthe zero-order beam is used as one of the foci, which is substantially higher than typical systems\nof 3.7% (ref. [1]). Combined with the high damage threshold of the SLM (>700 W/cm²) and\nthe full laser energy (up to 6 W available), the system allows simultaneous fabrication of 10×10\nsubwavelength units per pulse (see Fig. S6), yielding two orders of magnitude higher\nthroughput than single-beam scanning approaches.\nFurthermore, the synergy between Dc-PDLW (de-coherent parallel direct laser writing)\nand the nonlinear threshold effect enables both subwavelength feature sizes and subwavelength\ninter-spot spacing (see Fig. R2 and Fig. 4b), achieving truly ultradense nanoscale structuring\nthat has not been realized in previous polarization-controlled studies.\n(Lines 78-82) “However, in multi-focus parallel femtosecond laser processing, the spacing between\nadjacent focal points has consistently been constrained by the coherent diffraction limit. In contrast,\nsingle-focus femtosecond laser processing can readily surpass this limitation owing to the strong\nnonlinear threshold effect of femtosecond pulses, which enables the fabrication of nanostructures with\nsub-100-nanometer features [37-41].”\nFigure R2. (a1-a2) Optical micrographs of close-up 3-pore structures with (b1-b2)\ncorresponding SEMs. Scale bars: 500 nm.\nc) Broader application perspective:\nIn previous studies (including [1,2]), laser-induced polarization-dependent structures (such\nas nanogratings) have been primarily utilized for fabricating diffractive optical elements and\noptical data storage, where multi-beam parallel processing was introduced mainly to enhance\nprocessing or read/write efficiency. Such approaches have been extensively reported across\nvarious material systems [Laser Photonics Rev 2024, 18, 2300891.\nhttps://doi.org/10.1002/lpor.202300891]. Here, we would like to clarify the key distinctions\nbetween these previous works and the present study, by emphasizing the application-driven\nnovelty of our work:\n(1) Advantages for encrypted optical storage:\nCompared with existing anisotropic nanostructures, such as laser-induced self-assembled\nnanogratings, type-X birefringent structures, and burst-mode few-pulse isotropic nanovoids—\nour dual-pore approach offers substantial improvements in fabrication efficiency, polarization\ncontrol precision, and reproducibility:\n Self-assembled nanogratings require multiple pulses, produce feature sizes of several\nmicrons, and exhibit lower duty cycles. Their formation relies on near-field\nenhancement and multiphysics coupling, which are often material-dependent and\nunpredictable, whereas our approach uses a single pulse to achieve subwavelength (<1\nμm) features with linear, predictable birefringence tuning.\n Type-X birefringent structures also require multiple pulses and typically yield feature\nsizes from several to tens of microns, far larger than the dense nanopores achieved\nhere.\n Burst-mode isotropic nanovoids depend on complex intracavity or extracavity pulse\nshaping and still rely on near-field effects, limiting their controllability and scalability.\nIn contrast, our SSP-BM strategy circumvents near-field instabilities, ensuring both\nuniform modifications and accurate polarization encoding.\n(2) Advantages for non-encrypted storage and beyond:\nIn applications such as Braille-like records (Supplementary Fig. S12), our approach\ndemonstrates further advantages:\n The overall pattern size can be significantly reduced.\n The uniformity of each nanopore ensures a very low error rate in information retrieval,\nhighlighting the reliability of our encoding strategy.\nTogether, these aspects underline that our contribution is not simply an incremental\ntechnical refinement. Instead, it opens a new pathway for scalable, high-density, polarization-\nresolved optical storage and phase encoding, with strong implications for both practical\ndevices and fundamental photonics research.\n(3) Full freedom in polarization optics design:\nBy introducing dual-pore anisotropic nanostructures as the elementary units, our method\nallows simultaneous and precise control over both birefringence magnitude and optical-axis\norientation. This capability provides the complete set of degrees of freedom required for the\ndesign and fabrication of polarization diffraction optical elements, which has not been\nachievable with previous laser-written structures.\n(Lines 306-317) “From an application perspective, the proposed Dc-PDLW approach\nintroduces a fundamentally new class of anisotropic dual-pore nanostructures that are significantly\ndifferent from existing laser-induced anisotropic structures, such as self-assembled nanogratings68,\n69, type-X birefringent structures70, and isotropic nanovoids71. Unlike these prior methods, which\nrely on multi-pulse accumulation or near-field enhancement and consequently suffer from limited\ncontrollability and scalability, our SSP-BM-based strategy achieves subwavelength features with a\nsingle pulse, enabling predictable birefringence tuning, high uniformity, and precise polarization\nencoding. Beyond its technical innovation, this method provides complete freedom in polarization\noptics design, allowing simultaneous control over both birefringence magnitude (Fig. 1c) and\noptical-axis orientation (Fig. 4b), and underscoring the strong potential of this approach for high-\ndensity, polarization-resolved optical storage and advanced photonic device fabrication.”\nIn summary, while our work builds upon the foundational principle of SLM-based\npolarization control, it advances the field substantially by (i) identifying and overcoming the\nfundamental spacing limitation in parallel laser writing, (ii) introducing a decoherence-based\nholographic strategy with high energy efficiency and flexibility, and (iii) demonstrating new\nclasses of ultradense, functionally encoded 3D nanostructures.\nReviewer Comment 2 / 4\nConcern 2: Overstated limitations of iterative algorithms:\nThe authors criticize iterative hologram design methods, such as the Gerchberg–Saxton (GS)\nalgorithm, for introducing wavefront disorder. However, they overlook important\ndevelopments in improved iterative methods, such as the Weighted GS (WGS) algorithm, which\neffectively suppresses multi-beam inhomogeneity. These improved techniques can generate\nhigh-uniformity multifocal arrays and should not be dismissed without quantitative comparison.\nResponse: We sincerely thank the reviewer for this insightful comment. We fully agree\nthat iterative hologram design methods such as the Gerchberg–Saxton (GS) and Weighted GS\n(WGS) algorithms have made important contributions to achieving high-uniformity multifocal\narrays. The WGS algorithm, in particular, effectively suppresses beam inhomogeneity and has\nbeen successfully applied in various holographic beam-shaping scenarios.\nHowever, it is important to note that the GS/WGS algorithms are primarily designed for phase\nshaping, and cannot independently control the polarization states of individual foci. Therefore, they\nare unsuitable for investigating the core scientific problem addressed in our study: the fundamental\nlimit of spacing between adjacent foci in parallel laser processing and its determining factors. As\nemphasized in our response to Comment 1, the present work goes far beyond a mere algorithmic\nimprovement. It addresses a conceptual problem that has not been previously explored. Hence,\nwhile we have retained the necessary comparisons to highlight methodological distinctions, we have\ndeliberately streamlined discussions of algorithmic performance to maintain the manuscript’s focus\non the fundamental physical and processing insights. In the revised manuscript, we have\nintentionally avoided excessive discussion on the relative merits of different algorithms, as such\ndebate deviates from the central focus of our study. Instead, we have streamlined and downplayed\nthis part, while adding Table S1 to provide a clear quantitative comparison.\n(Lines 65-82) “Among these methods, the WGS/GSW iterative algorithm has great flexibility and\nthe best parallel beam uniformity, making it a widely-used method for generating complex multi-beams\npatterns. However, it is important to note that GSW algorithms do not uniquely determine the phase\nduring the iteration process, which can lead to wavefront disorder that may degrade processing\nperformance[30-34], especially under high numerical aperture (NA) focusing conditions. In particular,\nin the context of this study, where adjacent focal spots are brought into extremely close proximity and\ntheir optical fields begin to overlap, this wavefront disorder can induce complex spatial coherence effects,\nmaking it difficult to surpass the coherent diffraction limit that constrains the minimum achievable\nspacing between adjacent spots (≈1.47λ/NA) [35]. Furthermore, by controlling the polarization\northogonality between adjacent beams, the spatial coherence effects of the optical fields can be\neffectively eliminated, thereby reducing the minimum achievable spacing between adjacent focal spots\nby half (≈0.73λ/NA) [36], approaching the coherent diffraction limit. However, in multi-focus parallel\nfemtosecond laser processing, the spacing between adjacent focal points has consistently been\nconstrained by the coherent diffraction limit. In contrast, single-focus femtosecond laser processing can\nreadily surpass this limitation owing to the strong nonlinear threshold effect of femtosecond pulses, which\nenables the fabrication of nanostructures with sub-100-nanometer features [37-41].”\nFurthermore, in order to clarify the motivation of this research, Fig. R1 presents a\nfabricated “Siemens Test Star” consisting of periodic dual-pore arrays with gradually\ndecreasing spacing from the outer to the inner regions, produced using double beams with\nidentical polarization (generated by GSW algorithm) and orthogonal polarization (generated by\nSSP-BM algorithm) states. This figure provides a direct visual comparison of the processing\nresolution achievable with and without polarization control in dual-beam parallel fabrication.\nThe results reveal the intrinsic limitation of coherent multi-beam irradiation imposed by the\ncoherent diffraction limit: in the coherent FLDW case, the central region (indicated by a red\ncircle in Fig. R1(a)) exhibits complex, high-frequency interference-like patterns, with the\nmaximum resolvable spatial frequency reaching v₀; in contrast, the non-coherent FLDW\nconfiguration yields a much clearer central region (marked by a red circle in Fig. R1(b)), where\nthe maximum resolvable spatial frequency is reduced to v₀/2. These observations clearly\ndemonstrate how varying degrees of coherence fundamentally influence the achievable\nprocessing resolution in parallel femtosecond laser fabrication.\nFigure R1. Fabricated “Siemens Test Star” composed of periodic dual-pore arrays with gradually\ndecreasing dual-pore spacing from the outer to the inner regions, produced using double beams with\n(a) identical polarization and (b) orthogonal polarization states.\nAdditionally, from the standpoint of tightly focused femtosecond laser processing, iterative\nalgorithms still face intrinsic limitations. As shown in Fig. S12c1-c2, even WGS-based\nholograms exhibit residual speckle noise and ghost images under high-NA focusing conditions,\nleading to reduced stability and reproducibility during material processing. Moreover, because\niterative algorithms cannot uniquely determine the phase during convergence, they are prone to\nwavefront disorder and local-optimum trapping. These issues become particularly pronounced\nwhen adjacent foci are closely spaced and their focal fields begin to overlap, which severely\nlimits the achievable density of parallel processing (Fig. R1).\nFig. S12 c1-c2. Simulation comparison of machining letters generated using the SSP-BM algorithm\nand the GSW algorithm. (Note: Although the WGS method can generate high uniformity of peak\nintensity through optimization, but speckle artifacts are difficult to avoid in tight focusing conditions.\nIn contrast, the suggested SSP-BM approach can address the problem of speckle artifacts, enabling better\nfabrication quality)\nIn contrast, our proposed SSP-BM algorithm—based on a non-iterative design—uniquely\ndetermines the phase distribution in a single computational step, effectively avoiding both the\nspeckle noise problem and the local convergence issue. Moreover, by introducing a strip-\nsegmentation and binary-mask strategy, SSP-BM enables localized polarization control for each\nbeam, a capability fundamentally beyond the reach of iterative algorithms. A quantitative discussion\ncomparing the algorithms has been added to the Table. S1, that SSP-BM shows its superiority in\nterms of uniformity, in addition to the flexible control of multiple focuses and the efficiency of\nhologram generation, offering greater advantages in actual processing.\nTable. S1. Quantitative comparison between the SSP-BM algorithm and the iterative algorithm GS, as\nwell as the optimized iterative algorithm GSW/WGS, and the non-iterative algorithm ORA (Holograms\nfor comparing homogeneity for generating close point pairs).\nReviewer Comment 3 / 4\nConcern 3: Low diffraction efficiency likely due to polarization geometry\nThe proposed system uses a 45° linearly polarized beam incident on a liquid crystal on\nsilicon (LCOS) SLM with a binary phase mask. Given this optical configuration, the diffraction\nefficiency is likely very low. In practical laser processing applications, especially those\nrequiring high throughput and energy efficiency, low-efficiency holograms are generally\nunacceptable.\nResponse: We appreciate the reviewer’s concern regarding diffraction efficiency in the\nproposed optical configuration. In our system, when a 45° linearly polarized beam is incident on the\nliquid crystal on silicon (LCOS) spatial light modulator (SLM), approximately 50% of the incident\nlight is modulated by the SLM (as detailed in Supplementary Text S4), while the remaining 50%—\ncorresponding to the orthogonal polarization component—remains as the zero-order beam with a\npolarization state of either 0° or 90°. When the zero-order beam is filtered out and only the\nmodulated portion is used for processing, the effective diffraction efficiency is 50% × 97% (the\ntransmittance of the SLM), resulting in an overall efficiency of approximately 48.5%. Alternatively,\nwhen the zero-order beam is intentionally utilized as one of the processing foci, the overall\ndiffraction efficiency can reach 97%. Besides, the experimental measurement of the ratio of the\nenergy after the objective lens to the energy incident on the SLM shows that the overall efficiency\nof the system is 25% and 44% respectively. Therefore, the proposed method achieves an energy\nutilization efficiency no lower than 25%, which is well within the acceptable range for parallel\nfemtosecond laser processing systems.\nMoreover, the typical pulse energy required to fabricate the dual-pore nanostructures\ndemonstrated in this work is on the order of hundreds of nanojoules per pulse—significantly lower\nthan both the peak pulse energy of commercial femtosecond laser systems (typically on the order of\nhundreds of microjoules) and the damage threshold of the SLM (greater than 700 W/cm²). This\nenables single-shot fabrication of many dual-pore units simultaneously (for example, a 10 × 10\narray as shown in Fig. S6), resulting in a two-order-of-magnitude enhancement in processing\nthroughput compared with single-beam scanning approaches.\nFig. S6. (a) Phase hologram and (b) optical microscopy image of a 10×10 dense array\nfabricated using Dc-PDLW.\nTherefore, we believe that the polarization geometry adopted in this work does not necessarily\nlead to low diffraction efficiency. Instead, the overall optical configuration achieves an optimal\nbalance between energy utilization, processing throughput, and system simplicity.\nReviewer Comment 4 / 4\nConcern 4: Resolution claims are not surprising given known nonlinear effects\nThe reported spatial resolution of 300 nm (approximately λ/4) is attributed to the\nsuppression of crosstalk via polarization control. However, such resolution is not\nunprecedented in femtosecond laser processing due to nonlinear absorption and\nthreshold effects. Therefore, the result is not as remarkable as the authors suggest.\nResponse: We appreciate the reviewer’s thoughtful comment. We fully agree that\nnonlinear threshold effects are well known to enable sub-diffraction feature sizes in isolated\nsingle-spot femtosecond laser processing. However, our work addresses a fundamentally\ndifferent limitation—namely, the minimum achievable spacing between adjacent foci in\nparallel multi-beam processing. In conventional multi-focus configurations, the spacing\nbetween adjacent spots has long been constrained by the coherent diffraction limit. In contrast,\nthe nonlinear threshold effect in single-focus fabrication determines the minimum feature size\nof an isolated modification. These two mechanisms play complementary roles: the nonlinear\nthreshold effect defines how small an individual feature can be, whereas our de-coherent\nparallel writing strategy determines how closely adjacent features can be positioned within a\ndense array.\nBy introducing orthogonal polarization states and suppressing both spatial coherence and\ntemporal sequence interference, our SSP-BM approach effectively eliminates crosstalk\nbetween neighboring beams, allowing the spot-to-spot spacing to shrink below the conventional\nλ/2 barrier—approaching the coherence-free limit of λ/4. This capability bridges the gap\nbetween sub-diffraction single-spot resolution and large-area, high-throughput multi-spot\nfabrication. While sub-λ/4 features have been achieved in isolated single-spot configurations,\nextending such resolution uniformly across parallel arrays has not been previously\ndemonstrated. Therefore, our work does not merely replicate nonlinear shrinkage effects, but\nrather establishes a new framework that brings sub-diffraction precision into scalable, de-\ncoherent, large-area femtosecond laser fabrication.\nFurthermore, the synergy between Dc-PDLW (de-coherent parallel direct laser writing)\nand the nonlinear threshold effect enables both subwavelength feature sizes and subwavelength\ninter-spot spacing (see Fig. R2 and Fig. 4b), achieving truly ultradense nanoscale structuring\nthat has not been realized in previous polarization-controlled studies.\n(Lines 78-82) “However, in multi-focus parallel femtosecond laser processing, the spacing between\nadjacent focal points has consistently been constrained by the coherent diffraction limit. In contrast,\nsingle-focus femtosecond laser processing can readily surpass this limitation owing to the strong\nnonlinear threshold effect of femtosecond pulses, which enables the fabrication of nanostructures with\nsub-100-nanometer features [37-41].”\nFigure R2. (a1-a2) Optical micrographs of close-up 3-pore structures with (b1-b2)\ncorresponding SEMs. Scale bars: 500 nm.\nTherefore, the proposed Dc-PDLW strategy is compatible with and complementary to the\nnonlinear threshold effect of ultrafast laser–matter interaction, rather than contradictory to it.\nReviewer Comment\nIn conclusion, although the authors have provided some experimental validation\nof the SSP-BM method, the conceptual novelty, technical innovation, and impact are\ninsufficient to meet the high standard of Nature Communications. The paper would be\nmore appropriate for a specialized journal focused on laser fabrication or applied\noptics.\nResponse: Thank you again for your careful review. We believe our detailed responses to all\nfour concerns and the accompanying revisions strengthen the manuscript’s novelty and impact. We\nrespectfully ask that you reconsider our submission for Nature Communications."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Thank you for revisions. The author has appropriately addressed my comments and questions in the “Response to Reviewers.” However, many of these have not been incorporated into the main text of the manuscript. The discussions and descriptions arising from my comments and questions should be included in the main text of the manuscript. If the authors do this, this paper can be accepted for publication in Nature Communications. Further review of revised version is unnecessary.", "reviewer_2": "This was already a strong contribution, but the authors have made substantial improvements in the form form of an expanded (and more convincing) theoretical section, new experimental data and improving the relevance through an improved application demonstration section. The change in the paper title gives an improved significance to this work. They have done an excellent job and I believe the paper now meets/exceed the requirements for publication.", "reviewer_3": "The authors have provided satisfactory responses to my comments, and the manuscript has been properly revised accordingly. I find the revisions adequate and support the publication of this paper."}, "author_response": ""}]

Decision letter