Figures 2(a2–e2), (a3–e3); Figures 2(a4–e4) present SEM images showing the Ti surface morphology produced by the GHz burst mode fs laser pulses with P-values of 1, 3, 5, 7 and 9 at average laser powers of 8, 16 and 20 mW. These values correspond to peak burst pulse fluences, F _bp, of 0.49, 0.98 and 1.22 J/cm², respectively. Note that, in these experiments, the intensity of the intra-pulses in the burst pulse was essentially constant for all F _bp, as indicated in Figures 2(a1–e1).

It is evident from Figures 2(a2–a4) that the single-pulse-mode fs laser pulses (P = 1) created 1D-LIPSS having periodicities of 730–840 nm (equivalent to 0.71–0.82λ). These structures were formed perpendicular to the laser polarization direction for all F _bp, in agreement with results previously reported by many groups (Okamuro et al., 2010; Bonse et al., 2012; Oya et al., 2012; Nathala et al., 2015; Shinonaga et al., 2015; Shinonaga et al., 2016). The GHz burst mode with P = 3 also formed 1D-LIPSS Figures 2(b2–b3) but with less nanoparticle deposition on the ridges compared with the single-pulse mode. The periods of the structures obtained using F _bp values of 0.49, 0.98 and 1.22 J/cm² were determined to be approximately 810–920 nm (0.79–0.89λ), 810–970 nm (0.79–0.94λ) and 860–1,010 nm (0.78–0.98λ), respectively. Prior studies indicated that the period of 1D-LIPSS fabricated on Ti using single-pulse mode fs laser pulses becomes smaller as the number of pulses increases (Bonse et al., 2012; Nathala et al., 2015; Shinonaga et al., 2016). The period has also found to decrease with decreasing laser fluence (Okamuro et al., 2010; Bonse et al., 2012; Nathala et al., 2015). These experimental observations are in good agreement with a theoretical model proposed by Sakabe et al. (Sakabe et al., 2009) and are also supported by experimental work by Okamuro et al. (Okamuro et al., 2010). In contrast, in the present study, although the total number of intra-pulses was three times the number applied in single-pulse mode and the laser peak fluence for each intra-pulse, F _ip , was one-third that associated with single-pulse mode, the period of 1D-LIPSS formed by the GHz burst mode was larger than that generated using single-pulse mode. This discrepancy suggests that the period of 1D-LIPSS fabricated by the GHz burst mode process may be significantly affected by unique phenomena resulting from consecutive exposure to multiple pulses with an extremely high repetition rate. These phenomena may include transient changes in physical properties, such as the absorption coefficient and permittivity, due to heat accumulation. These changes could be maintained during subsequent intra-pulse irradiation and, in turn, affect the wavelength of the surface plasma wave to increase the period (Sakabe et al., 2009; Okamuro et al., 2010). Interestingly, some central parts of the ridges of the present 1D-LIPSS were found to have been ablated to produce shorter periods of 430–500 nm (0.42–0.49λ) at F _bp values of both 0.98 and 1.22 J/cm² (as indicated by the red arrows in Figures 2(b3, b4). This effect has not yet been reported and may also be related to transient changes in physical properties. The ongoing intra-pulse irradiation of 1D-LIPSS following transient variations in properties could generate SPPs having shorter wavelengths. These SPPs could be responsible for creating LIPSS exhibiting shorter periods (Bonse and Krüger, 2010; Miyaji et al., 2012; Miyazaki and Miyaji, 2013; Tjy et al., 2014; Iida et al., 2021), although further investigation is necessary.

It should also be noted that, in the case of P-values of 5 or greater [see Figures 2(c2–e2), (c3–e3); Figures 2(c4–e4)], the application of GHz burst mode fs laser pulses created 2D-LIPSS consisting of periodic structures both perpendicular and parallel to the laser polarization direction. This outcome was similar to the results of prior work with Si substrates by our group (Kawabata et al., 2023). Observations also showed that the period perpendicular to the laser polarization direction was smaller than that in the parallel direction for all conditions. As an example, the periods perpendicular and parallel to the laser polarization direction for P = 7 and F _bp = 0.98 J/cm² Figure 2(d3) were found to be approximately 840–970 nm (0.82–0.94λ) and 1,510–1840 nm (1.47–1.79λ), respectively. Additionally, melting and resolidification of the processed area became more prominent as P was increased, producing smoother surfaces on the ridges. These melting and resolidification processes likely resulted from the accumulation of excess heat as a consequence of the GHz repetition rate of the intra-pulses. The minimum P-values necessary for the creation of 2D-LIPSS on Si and Ti substrates were evidently 3 and 5, respectively. This difference may be related to the different physical characteristics of these elements, such as their optical properties, photon absorption processes and electron-phonon coupling times. Nevertheless, the appearance of 2D-LIPPS on Ti in a manner similar to the results obtained with Si suggests that hot spots may have been induced by the GHz burst pulses. Nanostructured Ag and Au are known to generate hot spots associated with greatly enhanced electric fields due to the LSPR effect (Anker et al., 2008). In addition, Jung and Choi confirmed experimentally that the intensity of peaks in the Raman spectra of Ti nanodots with native oxide layers was enhanced, presumably due to the stronger electric field of the incident laser beam, although the degree of enhancement was much smaller than that observed in the case of Au (Jung and Choi, 2021). In the nanogrooves with finite length, the hot spots are a type of standing wave that occurs during the resonance, and are therefore generated periodically. Periodical generation of hot spots in the nanogrooves, which should be responsible for formation of 2D-LIPSS, has been also confirmed by finite-difference time-domain simulations (Bai et al., 2018; Kawabata et al., 2023). The geometry of 1D-LIPSS, such as the depth and width of the nanogroove created by preceding intra-pulses in a burst, is an important factor to determine the periodicity of hot spots. For further discussion of formation mechanism of 2D-LIPSS, detailed measurements of the geometry will be our future work. Another important factor is the permittivity of Ti surface. As described above, transient changes in the physical properties of the substrate including the permittivity could contribute to the generation of hot spots. We consider that the former part of intra-pulses cannot contribute to generation of the hot spots, because 2D-LIPSS cannot be created when P = 3 Figures 2(b2–b4). Meanwhile, the transient changes could be maintained during irradiation of the latter part of intra-pulse irradiation to generate the hot spots. To assess this possibility and discuss the formation mechanism of 2D-LIPSS, the periodic enhancement of electric fields associated with 1D-LIPSS on Ti will be examined by our group in the future using simulations combined with further experiments including measurement of the 1D-LIPSS geometry and identification of the permittivity change during GHz burst pulse irradiation. The melting and resolidification exhibited by the 2D-LIPSS produced in this work suggest that hydrodynamic effects contributed to the formation of these structures, which should also be investigated. Although the physical properties of Ti are significantly different from those of Si, the GHz burst mode method was also able to form 2D-LIPSS on the former metal, providing helpful insights into the 2D-LIPSS formation mechanism.

In the present study, a laser beam was scanned over the Ti surface to fabricate 2D-LIPSS having relatively large areas. As such, essentially homogeneous structures were created over the entire laser-irradiated region. This large-area texturing is critical for allowing the characterization necessary to identify practical applications for LIPSS. In the future, our group will carry out additional characterizations of these structures, such as by assessing cell growth behavior and wettability.

Assuming a formation mechanism based on hot spots, the present work attempted to create more well-defined 2D-LIPSS by tuning the energy distribution of the intra-pulses in each burst pulse. It was expected that the resulting structures would be degraded by melting and resolidification as a result of overly strong electric fields generated at hot spots. To optimize this process, the envelope of the burst pulse was tailored to give a negatively sloped energy distribution. In these experiments, P and F _bp were fixed at 7 and 0.98 J/cm², respectively, and three different envelope shapes having negatively sloped distributions were employed Figures 3(a1, b1, c1). For comparison purposes, a positively sloped distribution was also employed Figure 3(d1). SEM images of the LIPSS obtained from these trials are presented in Figures 3(a2–d2) while enlarged images are shown in Figures 3(a3–d3). The morphologies of these specimens were found to be significantly affected by the distribution of the burst pulse. If the formation mechanism of 2D-LIPSS based on hot spots, which was proposed for Si, is effective for Ti, degree of the enhancement of electric field at the hot spots should be an important factor to determine the final shape of 2D-LIPSS (Kawabata et al., 2023). Since the electric field enhancement is induced by the latter part of intra-pulses, the energy distribution in the burst pulse influences the degree of enhancement. If the enhancement is too strong by relatively high energy of the latter part of intra-pulses, melting occurs at the hot spots and the resultant structure is deteriorated due to the hydrodynamic effects. In contrast, if it is too weak by relatively low energy of the latter part of intra-pulses, the electric field is insufficient to induce ablation for creation of 2D-LIPSS. Specifically, a lower negative slope value [see Figure 3(b1)] gave a 2D-LIPSS morphology Figures 3(b2, b3) that was very similar to that obtained using a flat distribution Figure 2(d3). These results are ascribed to the relatively high energy contained in the latter part of the intra-pulses, which was still able to greatly increase the electric field. In contrast, an overly high slope Figure 3(c1) did not provide 2D-LIPSS but rather generated 1D-LIPSS with a period of 900–1,000 nm (0.87–0.97λ) Figures 3(c2, c3). This morphology was similar to that obtained at P = 3 with a flat distribution shown in Figures 2(b2–b4). This change can be understood by considering that the energy contained in the latter part of the intra-pulses was insufficient to enhance the electric field. In trials in which the slope was adjusted to have a positive energy distribution, as shown in Figure 3(d1), 2D-LIPSS exhibiting significant melting and resolidification exceeding those seen in Figure 2(d3) were created (Figures 3(d2, d3)). This effect was likely due to the generation of hot spots together with greatly increased electric fields by the intense latter part of the intra-pulses. These data confirm that appropriate tuning of the burst pulses as demonstrated in Figure 3(a1) can cause melting and resolidification to be significantly suppressed, resulting in the creation of much more well-defined 2D-LIPSS Figures 3(a2, a3). The sizes of the periodic structures perpendicular and parallel to the polarization direction in this case were approximately 930–1,000 nm (0.90–0.97λ) and 1,160–1750 nm (1.13–1.70λ), respectively. To quantitatively evaluate the homogeneity of 2D-LIPSS, we analyzed spatial frequency distributions by 2D Fourier transformation using the SEM images of 2D-LIPSS formed by the flat distribution Figure 2(d1) and the appropriate energy distribution with negative slope Figure 3(a1) with P = 7 and F _bp = 0.98 J/cm² (16 mW). For more precise analysis, the wider areas of SEM images than those shown in Figure 2(d3); Figure 3(a3) were used, which are given in Supplementary Figure S2 along with information on analyzing direction. Since the periodic structures formed by the latter part of intra-pulses are parallel to the laser polarization direction, the periodicity perpendicular to the polarization direction was analyzed. Figures 4A, B present the spatial frequency spectra of periodic structures formed by the flat and negatively sloped distributions, respectively. The sharp peaks are observed around 1 μm^-1 for both spectra. However, the full width at half maximum of 0.14 μm^-1 for the negatively sloped distribution is significantly narrower than 0.20 μm^-1 for the flat distribution, which quantitatively indicates that the negatively sloped GHz burst pulse can form more homogeneous 2D-LIPSS compared to the flat distribution. Therefore, these results indicate that the latter part of the intra-pulses may play an important role in determining the extent to which the electric fields at hot spots are enhanced. Furthermore, tailoring the energy distribution in the burst should be effective to reduce melting and resolidification, resulting in creating more homogeneous 2D-LIPSS. Assuming our model based on the periodic generation of hot spots, we think that 2D-LIPSS similar to those presented in this work can be formed on some other metals and metal oxides as long as the hot spots can be generated in 1D-LIPSS. For generation of the hot spots, geometry of 1D-LIPSS and the transient physical property such as permittivity, both of which are induced by former part of intra-pulses, are important factors as discussed above. In order to make these factors fulfill the conditions for 2D-LIPSS formation, control of energy, number, and repetition rate of intra-pulses is important. In fact, the minimum P-value necessary for the creation of 2D-LIPSS on Ti was 5, while it is 3 for Si (Kawabata et al., 2023). Additionally, for the almost same kind of stainless steel, a high repetition rate of burst pulses (42–667 GHz) forms 1D-LIPSS (Giannuzzi et al., 2019), while a low repetition rate of burst pulses (50 MHz) can fabricate 2D-LIPSS (Wang et al., 2018). Meanwhile, it may be difficult to form 2D-LIPSS on metals with high heat conductivity such as Au, Ag, and Cu, because the irradiation of burst pulses may further cause significant melting and resolidification. Exploring the materials on which 2D-LIPSS can be formed is our future work, which will provide better insight into understanding the formation mechanism.