Ultrafast laser processing based on femtosecond laser sources minimizes heat-affected zones through nonthermal processes, which is important for high-precision processing [1–3]. Enhancing spatial resolutions in ultrafast laser processing is becoming increasingly crucial in many fields, such as semiconductor fabrication, the automotive industry, and medicine [4,5]. The precision and spatial resolution of laser processing primarily depends on the focal spot size of the laser beam. However, the diffraction nature of light generally limits the achievable spot size, depending on the numerical aperture (NA) of the lens and the wavelength ($\lambda$) of the focused laser beam.

Under tight focusing using a high-NA lens, a radially polarized beam notably generates a small focal spot compared with conventional linearly or circularly polarized beams [6,7]. This focusing property stems from the generation of a longitudinal electric field at the focus [8] and has been successfully exploited to improve the spatial resolution in laser scanning fluorescence microscopy [9,10]. Hence, a radially polarized beam may be a promising candidate for further enhancing the processing accuracy and resolution in ultrafast laser processing, particularly under high-NA conditions. However, the boundary conditions of electric fields at workpiece interfaces should be considered in the use of a radially polarized beam. The magnitude of the longitudinal field, which is normal to the interface, varies according to the ratio of the dielectric constant ($\varepsilon$), i.e., the ratio of the square of the refractive index ($n$), between the two media [11]. As for the incidence from the atmosphere ($\varepsilon$ = $\sim$1) to the material (|$\varepsilon$|>1), the longitudinal field significantly weakens within the material, even under tight-focusing conditions [12]. Nonetheless, some previous experimental results suggest that the presence of a longitudinal field induces the light–matter interaction, possibly improving the spatial resolution of laser processing for dielectric materials using radially polarized beams [13,14]. Despite these findings, the impact of the boundary condition on the longitudinal field has not been fully elucidated in the context of laser processing characteristics. Moreover, a recent study reveals that a longitudinal field exhibits a material-dependent behavior during the single-shot laser ablation of metal surfaces [15]. Therefore, a more detailed study on laser processing with a radially polarized beam is required to understand its characteristics under high-NA conditions in the presence of an interface.

In this Letter, we examined the single-shot laser ablation of a glass surface using a radially polarized beam under high-NA conditions to elucidate the role of the interface in the generation of a longitudinal field at the focus. Focusing a radially polarized beam on the back surface of the glass from the inside can remarkably enhance the longitudinal field even inside the material, directly inducing the light–matter interaction. Owing to the small focal spot formation by the longitudinal field, we presented a condition that produced a fine, spot-shaped crater sized 67 nm, corresponding to $\sim \lambda$/16, through total internal reflection. This result demonstrated the shrinkage of the processing scale, offering a novel approach to laser nanoprocessing using a radially polarized beam.

First, we investigated the influence of the interface on the focusing of a radially polarized beam under high-NA conditions. Numerical simulations were conducted using the vector diffraction theory [8,16,17] while considering the interface of two media having different refractive indices ($n_1$ and $n_2$). Figure 1 illustrates three cases where a radially polarized beam ($\lambda$ = 1040 nm) with a homogeneous amplitude distribution is focused without an interface in free space ($n_1$ = $n_2$ = 1), focused on the front surface of a borosilicate glass surface ($n_1$ = 1 and $n_2$ = 1.52), and focused on the back surface of the glass from the inside using an oil immersion lens ($n_1$ = 1.52 and $n_2$ =1). We assumed the use of objective lenses with NA = 0.95 [Figs. 1(a) and 1(b)] and NA = 1.4 [Fig. 1(c)]. The glass interface was placed at the focus. We calculated the intensity distribution on the $xz$ and $xy$ planes. The one-dimensional intensity profile along the $x$ axis and its polarization components were also calculated.

 

Fig. 1. Focusing of a radially polarized beam (a) in free space (NA = 0.95), (b) on the front surface (NA = 0.95), and (c) on the back surface of a glass plate (NA = 1.4, oil immersion) for an incident wave with $\lambda$ = 1040 nm. The calculated intensity distributions on the $xz$ and $xy$ planes [inside the glass for (b) and (c)] at the focus are in the middle panels. The scale bar in each panel is 1 $\mathrm{\mu}$m. The corresponding intensity profiles and the transverse $|E_r|^2$ and longitudinal $|E_z|^2$ components are in the right panels.

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As shown in Fig. 1, the presence of the interface substantially altered the intensity distribution at the focus, resulting in variations in the spot shape and size. Without the interface [Fig. 1(a)], a radially polarized beam produced a circular spot with an intensity peak at the center, originating from the strong longitudinal field under high-NA conditions. This spot shape changed to a doughnut-like shape with a reduction in intensity at the center when the beam was focused on the glass interface in air [Fig. 1(b)]. This was because the boundary condition weakened the longitudinal field inside the glass [12]. By contrast, for the third case (with the oil immersion lens) [Fig. 1(c)], a radially polarized beam was focused inside the glass without the impact of the boundary condition on the front surface when the immersion oil and the glass had the same refractive index. We produced a narrow spot on the back surface within the glass due to the generation of the strong longitudinal field. Note that focusing on the back surface without the immersion oil is accompanied by the refraction at the front surface, which results in lowering the effective NA, thus significantly weakening the longitudinal field.

To verify the influence of the interface on laser processing, we performed single-shot ablation on a glass surface. A laser source with a wavelength of 1040 nm and a pulse width of 311 fs was used in our experiment. We introduced a phase-only spatial light modulator (SLM) for aberration correction, which was needed for high-NA focusing. To generate a radially polarized beam, we used a segmented half-wave plate (SHWP) to convert linear polarization into radial polarization [9]. In this setup, azimuthal polarization could also be generated by rotating the incident polarization direction at 90° by inserting a half-wave plate before the SHWP. Subsequently, the laser beam was focused on the surface of a borosilicate glass plate with a thickness of 0.17 mm using an objective lens. Taking into account the possible focal shifts caused by self-focusing, the focal position was finely adjusted using the SLM for each condition.

We used three objective lenses with NAs of 0.25, 0.85, and 1.4 (oil immersion with $n$ = 1.52) for irradiation using radially and azimuthally polarized beams. An azimuthally polarized beam produces a doughnut-shaped focal spot with no longitudinal field, even under high-NA conditions; we tested this in comparison with the radially polarized beam. Figure 2 shows scanning electron microscopy (SEM) images of the fabricated ablation craters on the surfaces after laser irradiation. In each figure, the calculated intensity distribution of the focal spot inside the glass is also shown. Under each condition, we evaluated the ablation threshold energy by gradually increasing the pulse energy from zero until the ablation signature was observed using a microscope setup composed of the objective lens and imaging optics. Under all experimental conditions, laser irradiation was performed at a pulse energy slightly greater than the threshold (see the value in each panel of Fig. 2 for the pulse energy, measured at the focus).

 

Fig. 2. Single-shot ablation using (a) and (b) a radially polarized beam and (c) and (d) an azimuthally polarized beam on the front and back surfaces of a borosilicate glass plate using lenses with NAs = 0.25, 0.85, and 1.4. (a) and (c) Calculated intensity distributions inside the material under each condition. (b) and (d) SEM images of the fabricated craters. The pulse energy used is written in each panel. Each scale bar is 1 $\mathrm{\mu}$m.

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Under the NA = 0.25 and NA = 0.85 conditions, doughnut-shaped craters were fabricated on the front and back surfaces via a single-shot irradiation using both the radially and azimuthally polarized beams. These crater shapes were attributed to the intensity distribution of the focal pattern, as expected by the calculation under these conditions. By contrast, the irradiation of the back surface at NA = 1.4 using the radially polarized beam produced a spot-shaped ablation crater; the azimuthally polarized beam generated a doughnut-shaped crater. This difference was due to the formation of a small, circular focal spot attributed to the generation of the strong longitudinal field inside the glass and verified the direct contribution of the longitudinal field to the laser ablation process. Under this condition, the crater fabricated using the radially polarized beam was a small hole with a diameter of approximately 200 nm. We estimated the size of the ablated crater by defining a region whose brightness was darker than the surrounding area from the SEM images.

For focusing on the back surface, we needed to consider the interference between the incident and reflected waves on the back surface, which significantly contributed to the generation of the longitudinal field. To investigate this aspect in detail, we explored the focusing of a radially polarized beam with an annular-shaped amplitude mask with different inner and outer radii ($R_{\mathrm {i}}$ and $R_{\mathrm {o}}$, normalized to the pupil radius), as illustrated in Fig. 3(a). The insertion of the annular mask restricted the angle of the convergent wave. Thus, by changing the annular diameter and width, we could examine the angle-dependent behavior of the focal spot formation in the presence of the interface.

 

Fig. 3. Effect of the annular mask design on the focal spot fabricated on the back surface of a glass sample using an oil immersion lens with NA = 1.4. (a) Schematic diagram of the focusing condition. (b) FWHM values of the focal spot just inside the surface, calculated by changing $R_\mathrm {o}$ and $R_\mathrm {i}$ ($<R_\mathrm {o}$) with a step size of 0.01. Conditions I–IV correspond to $(R_\mathrm {i}, R_\mathrm {o})$ = (0, 1), (0.75, 0.85), (0.9, 1), and (0.4, 0.6), used in the later experiment (see main text). (c) Peak intensity ratio of the longitudinal field to the transverse field at the focus. (d) Intensity profile and its polarization components at $R_\mathrm {i}$ = 0.71, $R_\mathrm {o}$ = 0.72 [“A” in the magnified view in (c)].

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Figure 3(b) presents the full-width at half-maximum (FWHM) values of the focal spot inside the surface, calculated by changing $R_\mathrm {o}$ and $R_\mathrm {i}$ (where $R_\mathrm {i} < R_\mathrm {o}$) with a step size of 0.01. Similar to the case in Fig. 1(c), the annular-shaped radially polarized beam was focused on the back surface of the borosilicate glass using the oil immersion lens. In the colored region in Fig. 3(b), the intensity distribution at the focus shows a spot shape with the intensity peak in the center. By contrast, the white areas with $R_\mathrm {i}<R_\mathrm {o}$ indicate the region where a doughnut-shaped intensity distribution formed because of the weak longitudinal field. Figure 3(c) shows the variation in the peak intensity ratio of the longitudinal field to the transverse fields (radially polarized component) of the intensity distribution at the focus.

Figure 3(b) shows that the minimum spot size of 380 nm was obtained using an annular mask with $R_\mathrm {o}$ = 0.72 and $R_\mathrm {i}$ = 0.71, which was the closest condition to the annulus corresponding to the critical angle for the total reflection ($R_\mathrm {o}$ = $R_\mathrm {i}$ = $\sim$0.714). At this point [“A” in Fig. 3(c)], the longitudinal field was remarkably enhanced (with a peak intensity ratio of 140), resulting in a steep intensity profile almost perfectly composed of the longitudinal field at the focus [Fig. 3(d)]. This was a distinct feature caused by the interference between the incident and reflected waves, which is hard to realize in free space. In principle, without an interface, focusing an extremely thin annular beam with a diameter equal to the pupil size ($R_\mathrm {o}$ = $R_\mathrm {i}$ = $\sim$1) produces the smallest spot size [18]. However, in the presence of an interface with $n_1>n_2$, laser irradiation induces a total internal reflection through a proper annular mask design, remarkably enhancing the longitudinal field at the interface.

To reveal the influence of the total reflection on the generation of the longitudinal field in detail, we further calculated the intensity distribution near the focus of a radially polarized beam with an extremely thin annular mask ($R_\mathrm {o}$ $\simeq$ $R_\mathrm {i}$). The diameter of the thin annular mask at the pupil plane corresponds to the maximum convergence angle ${\theta }_\mathrm {max}$, also represented as the effective NA (= $n_1$ sin${\theta }_\mathrm {max}$). We considered three cases of an annular mask with NA = 1.4, 1, 0.7 for $n_1$ = 1.52 and $n_2$ = 1, corresponding to ${\theta }_\mathrm {max}>{\theta }_\mathrm {c}$, ${\theta }_\mathrm {max}$ = ${\theta }_\mathrm {c}$, and ${\theta }_\mathrm {max}<{\theta }_\mathrm {c}$, respectively, where ${\theta }_\mathrm {c}$ is the critical angle [= $\mathrm {sin}^{-1}(n_2 / n_1)$].

Figures 4(a)–4(c) show the calculated intensity distribution on the $xz$ plane inside the glass when the focus was on the back surface of the glass under the three annular mask conditions. In all cases, the intensity distribution inside the glass showed apparent interference fringes along the axial direction due to the reflection at the interface. The node (antinode) of the transverse (longitudinal) field was on the surface only at ${\theta }_\mathrm {max}$ = ${\theta }_\mathrm {c}$ [Fig. 4(b)], thus maximizing the intensity of the longitudinal field on the surface. Under the critical angle condition, the transverse field on the surface completely vanished. This was also confirmed by the intensity profile and its polarization components along the $x$ axis [Fig. 4(d)]. Otherwise [Figs. 4(a) and 4(c)], the antinode (intensity peak) of the longitudinal field formed away from the surface, resulting in a doughnut-shaped pattern on the surface due to the emergence of the transverse field. Thus, the total reflection near the critical angle played a central role in enhancing the longitudinal field just inside the back surface of the glass under high-NA conditions.

 

Fig. 4. Calculated intensity distributions on the $xz$ plane when a radially polarized beam with an extremely thin annular mask having different annular diameters corresponding to effective NAs of (a) 1.4, (b) 1, and (c) 0.7 is focused on the back surface of the glass using an oil immersion lens. Each scale bar is 1 $\mathrm{\mu}$m. The intensity profile and its polarization components along the $x$ axis on the surface just inside the glass for (a)–(c) are shown in (d).

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To examine the applicability of the enhanced longitudinal field mediated by total reflection to laser processing, we performed a single-shot ablation on the back surface of a glass sample using an annular-shaped radially polarized beam. The annular beam was generated using the spatial light modulator by displaying an annular mask pattern with the desired inner and annular radii. As with the preceding experiments, the converted beam was focused on the back surface of a borosilicate glass plate using the oil immersion lens with NA = 1.4. To explore the influence of the total reflection, we tested four annular masks with ($R_\mathrm {i}$, $R_\mathrm {o}$) = (0, 1), (0.75, 0.85), (0.9, 1), and (0.4, 0.6); these conditions are labeled I, II, III, and IV in Fig. 3(b). These conditions were chosen by considering the laser power available in this experiment that ensured the ablation process despite the low transmittance of the thin annular masks.

Figure 5 shows the SEM images of the ablation crater under each condition and the expected intensity profile at the focus. The observed crater shape reflected the feature of the expected focal spot. Spot-shaped craters were observed under conditions I–III, whereas a doughnut-shaped crater was seen under condition IV. These results demonstrated that the intensity distribution of the focal spot was successfully controlled by changing the annular mask design, directly affecting the ablation crater shape. Particularly, the annular mask obtained by condition II provides the focusing close to the critical angle on the back surface [see Fig. 3(b)]. Indeed, this condition resulted in a small, spot-shaped crater sized approximately 67 nm, corresponding to $\sim \lambda$/16. This implies the potential applicability of the present approach to improve the spatial resolution in laser processing, realizing nanometer-scale processes.

 

Fig. 5. Single-shot ablation of the back surface of the glass using an annular-shaped radially polarized beam. The observed craters under annular conditions I–IV in Fig. 3(b) are shown in (a)–(d). The pulse energies used are written in the panels. Each scale bar is 500 nm. The normalized intensity profile and the polarization components of the focal spot inside the glass calculated for each condition are shown in the bottom panels.

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The present experimental results verify that the ablation crater fabricated on the surface reflects the intensity distribution of the focal spot inside the material. In other words, the longitudinal field of a radially polarized beam contributes directly to the laser ablation process provided that strong longitudinal fields exist at the focus. However, whether both longitudinal and transverse fields lead to identical ablation threshold energies during the laser ablation of glass is not obvious at present. Furthermore, our previous study suggested the presence of an additional mechanism associated with the longitudinal field that can promote the ablation process on highly reflective metal surfaces [15]. Therefore, further comprehensive studies with more thorough consideration of the polarization-dependent light–matter interaction in laser ablation should be conducted. This will be clarified by a quantitative evaluation (experimental and theoretical) of ablation threshold energies depending on the polarization direction in our future work.

The strength of the longitudinal field is largely affected by the boundary condition. It can be significantly enhanced compared with that of the transverse field using total reflection. In this manner, the presence of an interface plays a significant role in the focal spot formation on the interface. The present ablation condition may be highly applicable to various laser processing techniques, including laser-induced forward transfer [19] and laser-induced backside wet etching [20], where the laser beam is focused on the back surface of a transparent medium. Though these techniques are only suitable for transparent materials, the appropriate choice of laser wavelength will extend its applicability to various materials including semiconductors (e.g., >1.1 $\mathrm{\mu}$m for silicon with a solid immersion lens). Along with the total reflection under high-NA conditions, the use of a radially polarized beam with an appropriately designed annular mask can enhance the spatial resolution in these techniques.

In summary, we explored the single-shot laser ablation of a transparent glass sample where a radially polarized beam was tightly focused on the surface. The impact of the boundary conditions at the interface under high-NA conditions was carefully examined. Using an oil immersion objective lens, we produced a small focal spot attributed to the enhanced longitudinal field on the glass surface. This condition enabled direct laser processing using the longitudinal field, resulting in the fabrication of a small hole sized 67 nm. The present findings will advance the development of laser ablation processes using radially polarized beams under high-NA conditions.