Optical vortex beam, carrying orbital angular momentum (OAM), is characterized with helical wavefront and donut-like intensity cross-section¹⁻⁴. High-intensity vortex beam is desired in numerous fundamental investigations and applications of laser-matter interactions in terms of nonlinear optical effects⁵, terahertz vortex wave generation⁶, laser ablation and material processing⁷, and beyond. However, the emission power of a single OAM beam is limited at present. Recently, the superposition of multiple vortex beams has shown the unique ability to tailor and enhance the vortex field. In principle, vortex beams carrying different OAMs are mutually orthogonal, providing the spatial modal basis set to generate a beam with space-dependent intensity⁸⁻¹⁰. Especially, by engineering the spatial-variant interference effect (constructive or destructive interference) with multiple collinear vortex beams (MCVBs), light can be confined to a smaller area¹¹. As a result, the localized optical intensity is significantly enhanced.

The MCVBs can be traditionally generated by the combination of multiple optical systems involving vortex beam generation and collinear superposition. The optical setup is complex and has a bulky volume, which is impractical for compact and miniaturized applications. Another main method to generate the MCVBs is based on spatial light modulators (SLMs)¹¹⁻¹³, which reduce the system volume to a certain extent, but generally suffer from low resolution. Moreover, low laser-induced damage threshold (LIDT) is another critical issue for typical SLMs, which limits the applications mainly in the fields of low laser power. When irradiated with high-power laser, thermal or nonthermal loading can lead to irreversible damage to the SLMs and thereby deteriorating the optical performance, which is the challenge for typical SLMs to be applied in high-power laser systems.

Optical metasurfaces aided by the rapid advances in nanofabrication provide an alternative approach to address these shortcomings. With the development of propagation phase¹⁴, generalized geometric phase¹⁵, asymmetric spin orbit interaction¹⁶, and catenary optics¹⁷, metasurfaces allow the arbitrary modulation of the phase, amplitude, and polarization of the incident beam with micro- and nanoscale^18,19. These unprecedented abilities open up a way for the miniaturization and integration of optical elements and systems. Numerous optical elements and versatile functionalities have been realized including metalenses²⁰⁻²³, optical holograms²⁴⁻²⁶, optical detection²⁷⁻²⁹, structured beam generation³⁰⁻³³, optical encryption³⁴⁻³⁶, and beyond. Recently, metasurfaces have been employed to generate and overlap the multiple vortex beams³⁷⁻³⁹. For example, Ming et al. have demonstrated the creation and manipulation of optical singularity structures by leveraging the superposition of multiple Laguerre-Gaussian modes with a single geometric metasurface³⁹. Additionally, a LIDT of 1.1 J/cm² (at 532 nm, 5 ns) has been recently verified for titanium dioxide-based metasurface⁴⁰. Nevertheless, it is worth noting that low LIDT is still a critical issue for metasurfaces, which is related to the intrinsically low damage threshold of the constituent materials and the local field enhancement effect during light-matter interactions. In the past few years, emerging femtosecond laser-induced form birefringence, known as a generalized metasurface⁴¹⁻⁴³, has provided fascinating opportunities for manipulating light with high transmittance and high LIDT^44,45.

In this work, to overcome the aforementioned limitations of the MCVBs generation for enhancing the vortex field, a single geometric metasurface with high LIDT is proposed and experimentally demonstrated based on femtosecond laser-induced form birefringence embedded in silica glass. The metasurface is designed by adopting the concept of a sliced phase pattern in the azimuthal direction, generating the MCVBs with equally spaced topological charge (l) for orthogonal-mode superposition. Optical hot spots with enhanced intensity and steady spatial propagation can be realized and modulated. As a proof of the concept, a single optical hot spot with an intensity gain larger than 3.4 within a propagation distance of 1 m is experimentally demonstrated and compared with calculation values. Benefiting from the nanoscale features in the laser-induced form birefringence, transmittance greater than 99.4% in the near-infrared range and LIDT as high as 68.0 J/cm² (at 1064 nm, 6 ns) are experimentally verified. The demonstrated high-threshold metasurface has promising applications in a host of high-power laser fields.

Figure 1(a) illustrates the schematic diagram of the metasurface designed for the generation and superposition of MCVBs. Unlike conventional methods that encode both amplitude and phase onto a phase-only filter simultaneously at the cost of conversion efficiency, our approach focuses solely on phase modulation. This is known as the phase-only modulation strategy, which is achieved by employing the concept of a sliced phase pattern in the azimuthal direction⁴⁶. As a Gaussian beam with circular polarization traverses the metasurface, MCVBs featuring equally spaced OAM charge number are generated. Additionally, the vortex field can be enhanced owing to the superposition effect.

Similar to previous work aimed at generating a pure single OAM channel, the sliced phase pattern modulates the phase of the output beam in the azimuthal direction. However, there is a crucial difference in the evolution of the azimuthal angle (α)-dependent phase. While a continuous spiral phase (lα) is applied for generating a pure single OAM, the sliced phase pattern comprises variant truncated spiral phases within different angular apertures with rotational symmetry. Figure 1(b) illustrates the principle behind the generation of MCVBs. The sliced phase pattern can be divided into M sets of angular transmission apertures, considering the N-fold rotational symmetry of the topological charge [M=2, N=2 in Fig. 1(b)]. Each set of angular apertures exhibits a spiral phase with pre-defined topological charges (l₁, l₂, …, l_M). When illuminated by a Gaussian beam, the m^th set of angular apertures redistributes the laser energy to OAM components with equally spaced topological charges l_m+kN (k is an integer, k=0, ±1, ±2,…). The power proportion of these OAM components, known as the OAM spectrum, is derived from helical harmonic decomposition⁴⁷⁻⁴⁹, as depicted in Fig. 1(b). By combining the phase patterns of angular transmission apertures, MCVBs can be obtained.

Following the approach for generating MCVBs, the phase of the metasurface is tailored to achieve localized optical intensity enhancement over a specific distance. The configuration of angular transmission apertures, the fold of rotational symmetry, the assigned topological charge within each angular aperture set, and the initial phase delay collectively govern optical intensity modulation. To illustrate this concept, a sliced phase pattern featuring 3 sets of angular apertures and one-fold rotational symmetry is demonstrated. This configuration is depicted in Fig. 2(b), where the azimuthal phase distribution is represented as:

$\phi (\alpha )=\{\begin{array}{cc}0& \alpha \in [\mathrm{0,2}\pi /3)\\ 3\alpha +{\beta }_1& \alpha \in [2\pi /\mathrm{3,4}\pi /3)\\ -3\alpha +{\beta }_2& \alpha \in [4\pi /\mathrm{3,2}\pi )\end{array}\mathrm{,}$(1)

where β₁ and β₂ are the initial phase delays between adjacent apertures. The intensity distribution of output-modified light at a certain distance z is calculated using Kirchhoff diffraction theory, with a chosen wavelength of 808 nm. The parameters β₁ and β₂ in Eq. (1) can be delicately optimized to maximize the intensity gain which is defined as the ratio of the peak intensity obtained with the sliced phase pattern to that of the Gaussian beam. Figure 2(a) illustrates the evolution of intensity gain at z=1 m relative to the initial phase delays β₁ and β₂. An intensity gain of 4.1 is achieved for β₁=0 and β₂=0. Correspondingly, the phase profile of the desired metasurface and OAM spectrum of the modulated beam are displayed in Fig. 2(b) and Fig. 2(c), respectively. Analysis reveals that OAMs with topological charges ranging from −4 to 4 are the main orthogonal modes utilized in constructing this beam. A single off-centered hot spot is observed in the intensity profile due to the constructive interference of the modulated beam, as shown in Fig. 2(d). As a comparison, lower intensity gains for cases indicated by white dotted lines in Fig. 2(a) are attributed to the generation of two hot spots in the intensity profile, as depicted in Fig. S1 (Supplementary information). Additionally, the intensity distribution of the modulated beam along the propagation direction is calculated, as shown in Fig. 2(e). Similar intensity profiles at different distances can be identified, which exhibit gradually decreased intensity gain and increased off-centered distance due to the diffraction effect. A more detailed investigation of the evolution of the superposed vortex field with respect to the sliced phase pattern combining different topological charges and initial phase delays is indicated in Supplementary information (see Section 1).

Laser-induced form birefringence nanostructures are harnessed to accomplish geometric phase modulation within the metasurface. These nanostructures can work just as subwavelength uniaxial form-birefringent crystals. When circularly polarized light illuminates these structures, a cross-polarized beam with opposite handedness is generated with an additional geometric phase of −2σθ₁ due to the photonic spin-orbit interaction^15,16,50, where θ₁ represents the azimuthal angle of the birefringent nanostructure controlled by the laser polarization direction, and σ=±1 denotes right-handed and left-handed circularly polarized beams, respectively. The conversion efficiency can be expressed as sin²(γ/2) without considering the optical loss of subwavelength structures, where γ is the phase retardance between the fast and slow axes. Therefore, to fabricate a metasurface with high conversion efficiency, the parameters of femtosecond laser ablation must be optimized to achieve a phase retardance of π. Additionally, the azimuthal angle of laser-induced form birefringence nanostructures is adjusted in accordance with the designed phase profile.

The experimental setup for fabricating femtosecond laser-induced form birefringence within silica glass (Corning 7980) is outlined in Fig. S5 (Supplementary information). Rectangular-modified regions were built by scanning a focused femtosecond laser in parallel lines, with an interval of 1 μm. More details regarding this fabrication system are provided in Materials and methods. Laser-induced form birefringence primarily arises from the nonlinear energy deposition of ultrafast laser pulses, making it highly dependent on laser writing parameters such as pulse duration, pulse density, pulse energy, and more. Figure 3(a) illustrates the angle of the fast axis, intensity, and retardance of femtosecond laser-modified regions under varying pulse durations, with a constant pulse energy of 1.1 μJ, pulse density of 33 pulses/μm, and laser polarization direction of 0°. The image of the fast axis angle indicates the generation of anisotropic nanostructures when the pulse duration exceeds 350 fs. The fast axis direction of the laser-induced anisotropic nanostructures is parallel to the laser polarization direction. Moreover, a range of nanostructure types, from isotropic to birefringent modifications, is discerned by quantitative measurement of the birefringence and transmittance, as depicted in Fig. 3(b). For pulse durations no more than 350 fs, modified regions exhibit ultra-high transmittance, and form birefringence is scarcely discernible as retardance approaches zero. UV-VIS absorption spectra further indicate the presence of laser-induced defects within silica glass (refer to Fig. S6, Supplementary information), suggesting the generation of isotropic (referred to as type I) modification for shorter pulse durations⁵¹. As pulse duration surpasses 350 fs, birefringent modification becomes apparent, showcasing significant duration-dependent retardance and transmittance, revealing two distinct forms of birefringence. For pulse durations ranging between 350 fs and 450 fs, ultralow-loss birefringence (referred to as type X) is achieved, characterized by a considerable increase in retardance with minimal impact on transmittance, approaching 100%. Consequently, longer pulse durations prove advantageous for enhancing the processing efficiency of ultralow-loss type X metasurfaces. Beyond 450 fs, nanogratings (referred to as type II) emerge within the laser-modified region. The retardance of type II initially increases before stabilizing, while transmittance experiences a rapid decline with longer pulse durations. Type II exhibits higher retardance but lower transmittance compared to type X. In principle, both type X and type II modifications can be utilized to fabricate metasurfaces. However, there is a significant disparity in transmittance, particularly for metasurfaces comprising multiple layers.

Typically, the formation of birefringent nanostructures within transparent materials stems from the cumulative effect of multiple laser pulses. Consequently, pulse density plays a pivotal role in shaping the birefringent properties of laser-modified regions, as illustrated in Fig. 3(c) and Fig. 3(d). Across a pulse density range of 13 to 5000 pulses/μm, with a fixed pulse duration of 450 fs and pulse energy of 1.1 μJ, it becomes evident that the angle of the fast axis remains aligned parallel to the laser polarization direction irrespective of the applied pulse density. However, both retardance and transmittance exhibit significant dependencies on pulse density. As pulse density increases, transmittance undergoes four distinct phases: initially remaining constant (13–33 pulses/μm), followed by a decrease (33–100 pulses/μm), then an increase (100–500 pulses/μm), and finally another decrease (500–5000 pulses/μm). Conversely, retardance demonstrates a straightforward positive correlation with pulse density. Based on the evolution of transmittance and retardance concerning pulse density, three distinct types of birefringent modification emerge: (I) type X for pulse densities up to 33 pulses/μm, (II) a transitional phase for pulse densities ranging from 33 to 100 pulses/μm, and (III) type II for pulse densities exceeding 100 pulses/μm. To maximize retardance and enhance transmittance for each layer, it is advisable to set pulse density as high as possible within the processing window of type X. The fluctuation in transmittance within the transitional region may be attributed to the disruption of type X modification and the progressive formation of type II modification, necessitating further experimental clarification.

Furthermore, Fig. 3(e) and 3(f) depict the retardance and transmittance maps as functions of pulse energy and pulse density, respectively, with a fixed pulse duration of 450 fs. Notably, type X (highlighted by the dashed box) typically emerges with lower pulse density and energy. Within the processing window for type X, elevating both pulse density and energy yields a greater retardance. However, as the pulse density and/or energy increase further, type X transitions to type II, characterized by higher retardance but lower transmittance. Scanning electron microscopy (SEM) images illustrating the typical laser-induced anisotropic nanostructures for type X and type II are provided in Fig. S7 (Supplementary Information). Type X exhibits abundant elongated nanopores with long-axis sizes ranging from tens to 100 nanometers, while type II showcases nanogratings with enlarged dimensions. Furthermore, it is noteworthy that type II demonstrates higher UV-VIS absorption spectra compared to type X (Fig. S6, Supplementary Information), indicating the presence of a higher concentration of defects within type II. The smaller feature size in type X leads to less scattered light⁵², contributing to its higher transmittance.

Since the retardance of single-layer form birefringence for both type II and type X is significantly less than λ/2, the implementation of multi-layer structures becomes necessary to achieve high conversion efficiency of the metasurface. The spacing between adjacent layers emerges as a critical factor in metasurface preparation. When the interval distance is too small, there is a risk of overwriting the preformed birefringent layer during subsequent layer fabrication and generating random ablation points. This can alter the birefringent optical properties, thus degrading the metasurface performance. Conversely, an excessively large interval distance can deepen the metasurface, potentially impacting its optical performance due to optical coupling among nanostructures. Figure S8 (Supplementary information) illustrates the relationship between the retardance of three-layer structures and interval distance. The retardance gradually diminishes with larger interval distances due to smaller layer overlapping, stabilizing when the interval distance reaches or exceeds 40 μm. Hence, 40 μm is deemed an appropriate interval distance. Subsequently, during metasurface preparation, the interval distance is set at 40 μm to ensure optimal performance.

Following the demonstration of femtosecond laser-induced form birefringence within silica glass, metasurfaces operating at 808 nm were fabricated, depicted in Fig. 4(a) and Fig. 4(b). For type II metasurfaces, laser processing employed parameters of 450 fs, 200 pulses/μm, and 1.1 μJ, while type X metasurfaces were produced with parameters of 450 fs, 33 pulses/μm, and 1.1 μJ. According to the retardance of single-layer form birefringence, four and 20 layers were fabricated for type II and type X metasurfaces, respectively. In addition, there is no difference in the laser processing parameter for fabricating different layers at different depths. The detailed parameters involved in the fabrication of type II and type X metasurfaces are summarized in Table S1 (Supplementary information). To mitigate the influence of polarization direction on femtosecond laser-induced retardance (as illustrated in Fig. S9, Supplementary information), stemming from the inherent anisotropy of laser-material interactions^53,54, consistent scanning direction with the polarization was maintained throughout the fabrication process of metasurfaces. Additionally, for simplicity, the continuous phase of the designed metasurface was segmented into 16 regions (referred to as the multi-level phase), as depicted in Fig. 4(e). Theoretical calculations demonstrate that the optical field modulated by the multi-level phase exhibits nearly identical properties to that modulated by the continuous phase, as shown in Fig. 5(a) and Fig. 5(c).

The images depicting the fast axis angle distribution within the prepared metasurfaces [Fig. 4(c) and Fig. 4(d)] reveal the attainment of a multi-level geometric phase in the azimuthal direction. Moreover, the insert lines in Fig. 4(d) reveal that these fabricated multi-level structures are the discretization of continuous catenary structures³². In principle, more continuous structures would be helpful for the improvement of efficiency. Figure 4(e) provides a quantitative assessment of the measured geometric phases compared to their design counterparts, demonstrating strong consistency. Furthermore, discernible differences in transmission are evident between metasurfaces of type II and type X [Fig. 4(f)]. Generally, type X metasurfaces exhibit higher measured transmittance across the UV-VIS-NIR spectral regions (250–2000 nm) compared to type II, with the disparity particularly pronounced in the visible and near-infrared spectral range. For instance, at a wavelength of 808 nm, the transmittance reaches 87.9% and 99.6% for type II and type X metasurfaces, respectively.

The metasurfaces exhibit localized optical intensity enhancement across varying propagation distances (0.2 m–1 m), as depicted in Fig. 5. Illuminated by a circularly polarized Gaussian beam with a wavelength of 808 nm, the metasurfaces were analyzed without a co-polarization analyzer during the capture of transmitted intensity distribution via a laser beam profiler. This setup aimed to demonstrate the high conversion efficiency of the fabricated metasurfaces. Experimental intensity distributions modulated by metasurfaces of type II and type X closely mirror simulation results, as evidenced in Fig. 5(a). Notably, an identical distribution of normalized intensity along the dashed line [indicated in Fig. 5(a)] is discernible between the simulated and experimental intensity patterns [Fig. 5(b) and Fig. S10, Supplementary information]. These compelling results attest to the exceptional performance of the fabricated metasurfaces. The measured intensity gain is defined as the ratio of the captured peak intensity of the metasurface-modulated beam to that of the original Gaussian beam. Consistent with simulation outcomes, the measured intensity gain diminishes progressively with increasing propagation distance, as shown in Fig. 5(c). Metasurfaces of type II and type X achieve intensity gains of 3.0 and 3.4 at the propagation of 1 m, respectively. It is noteworthy that the measured intensity gain for metasurfaces falls short of the simulation results. In the current experimental setup, the metasurfaces lack antireflective films on the front and rear surfaces of silica glass, resulting in additional transmission loss due to the reflection of pristine silica glass, in addition to the transmission loss of form birefringence. This combined transmission loss contributes to the observed decline in measured intensity gain. For metasurfaces of type X, where the transmittance of birefringent modification approaches unity, the primary transmission loss arises from the reflection of pristine silica glass. Consequently, a higher measured intensity gain is attained with metasurfaces of type X. Furthermore, other factors contributing to the difference between measured and simulated results include the imperfections in the incident Gaussian beam and slight geometric phase deviations, which may impact the generation of multiple collinear vortex beams and attenuate the corresponding superposition effect.

To showcase the resistance of the prepared metasurfaces against intense laser exposure, we assessed their LIDTs using the standardized 1-on-1 method outlined in ISO 21254. The testing apparatus utilized a laser with a wavelength of 1064 nm and a pulse duration of 6 ns. The LIDT, denoting the threshold at which damage occurs with 0% probability, is 18.7 J/cm² for the metasurface of type II [Fig. 6(a)]. Notably, the metasurface of type X exhibits a substantially higher LIDT of 68.0 J/cm² [Fig. 6(b)]. This significant variance in LIDT values can be attributed to laser-induced defects within the modification region. In comparison to type X, the femtosecond laser-induced modification process for type II is more aggressive due to the cumulative effect of more laser pulses. Consequently, it generates a greater density of defects during the formation of birefringent nanograttings (Fig. S6, Supplementary information). These defects serve as energy absorbers, facilitating the deposition of pulse energy during intense laser exposure and ultimately reducing the LIDT. Therefore, metasurfaces with excellent performance of beam modulation and high LIDT have been verified based on the characterization results shown in Fig. 5 and Fig. 6.

In summary, a single geometric metasurface based on a sliced phase pattern in the azimuthal direction is proposed and experimentally demonstrated to generate MCVBs with equally spaced OAM topological charge (l) for enhancing the vortex field. The phase-only modulation strategy enables high conversion efficiency for MCVBs generation. Moreover, the geometric metasurface has been fabricated by utilizing femtosecond laser-induced birefringent nanostructure embedded in silica glass, which shows outstanding properties of high transmittance, high damage threshold, and high conversion efficiency. This method is maskless, accessible, and flexible. As a proof of the concept, a single optical hot spot with the intensity gain larger than 3.4 within a propagation distance of 1 m is experimentally demonstrated and compared with calculation values. In addition, transmittance greater than 99.4% in the near-infrared ranges and LIDT as high as 68.0 J/cm² (at 1064 nm, 6 ns) are experimentally verified. Such LIDT is much higher than that of conventional metasurfaces, e.g. titanium dioxide-based metasurfaces. The demonstrated high-threshold metasurface shows promising prospects in a host of high-power laser systems. To improve the fabrication efficiency of such metasurfaces, spatial beam shaping (e.g. multifocus beam) will be applied to increase the retardance of form birefringence induced by a single scanning process.

Laser-induced form birefringence in silica glass (Corning 7980) was realized by progressive scanning of the femtosecond laser. The femtosecond laser was focused 200 μm below the surface of silica glass by an objective (10×, NA = 0.26). The fabrication process was carried out by a homemade femtosecond laser machining system which can control the laser parameters and 3-axial translation stage (Fig. S5, Supplementary information). The femtosecond laser was generated by a Yb-doped potassium gadolinium tungstate (Yb:KGW)-based mode-locked regenerative amplified femtosecond laser system (PH2-20, Light Conversion Ltd.). The central wavelength is 1030 nm, while the pulse duration (220 fs–10 ps) and repetition rate (1 kHz–1 MHz) are variable. The pulse energy was tuned by an optical attenuator consisting of a half-wave plate (HWP1) and a polarizing beamsplitting cube. The polarization direction was controlled by another half-wave plate (HWP2). The repetition rate was set at 205 kHz while the pulse duration ranged from 220 fs to 700 fs. Since the repetition rate was constant, the pulse density was tuned by changing the velocity of the translation stage. The interval of each scanning line was set at 1 μm. The interval-distance of layers was set at 40 μm for the fabrication of metasurfaces.

To analyze the morphologies of laser-induced birefringent nanostructures, the sample was polished and then etched in 1 mol/L KOH solution for 24 hours. The exposed nanostructures were imaged with scanning electron microscopy (Helios 5 CX, Thermo Scientific).

The retardance and angle of the fast axis of laser-modified regions were quantitatively measured through a commercial birefringence imaging microscope (Exicor® MicroImagerTM, Hinds Instruments). The transmittance was obtained by a microscope (BX53M, Olympus) equipped with a spectrograph (Nova-ex, Ideaoptics). The transmission spectrum and absorption spectrum of the prepared metasurfaces were measured by a UV-VIS-NIR spectrometer (Lambda 1050, PerkinElmer). For verifying the light field modulation capability of the fabricated metasurfaces, the metasurfaces were illuminated by a circularly polarized Gaussian beam with a wavelength of 808 nm at normal incidence. The modified light fields after the metasurface were directly captured by a laser beam profiler (Beamage-4M, Gentec-eo) located at different propagation distances. As a comparison, the intensity distributions of the Gaussian beam at corresponding propagation distances were captured as well.

The LIDTs of the prepared metasurfaces were measured by a standard 1-on-1 method according to ISO 21254. The wavelength and pulse duration of the test system laser are 1064 nm and 6 ns, respectively. The damage probability under different laser fluencies was calculated. The relationship between the damage probability and the laser fluence was linearly fitted to get the damage threshold of 0% probability. The damage threshold of 0% probability was the LIDT (1-on-1) of the metasurface.