The formation of LIPSS by laser direct writing is a multi-pulse cumulative process, which greatly depends on the laser fluence and scanning speed [37, 38]. In the following, the formation of LIPSS induced by the 515 nm fs laser and the phase retardance were studied by changing the laser fluence and scanning speed.

Figures 3A–F show the SEM images of the LIPSS formed on the FTO film fabricated by a 515 nm fs laser at a scanning speed of 0.01 mm/s. When the laser fluence was less than 19 mJ/cm², the laser was too weak to ablate the sample. When the laser fluence was increased to 20 mJ/cm², very short and broken ripples formed on a part of the sample surface, and indicating that the ablation threshold of FTO film had been reached. After laser irradiation at 21 mJ/cm², LIPSS appeared on the entire surface, excluding a few spots. Regular LIPSS formed on the entire film as the laser fluence increased to 23 mJ/cm². The LIPSS is perpendicular to the direction of laser polarization, with periods much less than half of the laser wavelength, which is categorized as high-spatial-frequency LIPSS (HSFL) [12]. When the laser fluence was further increased to 27 mJ/cm², some molten debris remained on the surface, indicating that HSFL begin to melt. These molten debris covered nearly one-third of the entire sample surface irradiated by a laser with a fluence of 31 mJ/cm2, as shown in Figure 3F.

Figures 3G–J show the 2D Fourier transformed (FT) images of Figures 3A,B,D,and F, respectively. To clearly demonstrate the regularity of the HSFL, the Fourier spectra for k_y = 0 μm⁻¹ are shown in Figure 3K. When the laser fluence is 23 mJ/cm², the peak of the FT spectrum is at 5.8 μm⁻¹, and the LIPSS period is approximately 172 nm. The FT spectra are much wider, and the peaks are lower for the HSFL irradiated by the other laser fluences, which means that the LIPSS are irregular.

As shown in Figures 3A–F, we measured the size of the grooves and calculated the average values. The ripple periods were obtained according to the FT spectrum, and the duty cycle of the HSFL was calculated as the ratio of the groove width to the ripple period. Figure 4 shows the variation in the duty cycle of the HSFL with the laser fluence. It increases to 0.3 at a laser fluence of 23 mJ/cm², and decreases to 0.25 as laser fluence increases to 31 mJ/cm².

Figure 5 shows the retardance of the FTO film with HSFL varying with the laser fluence. When the laser fluence is 21 mJ/cm², the retardance is 119 nm. When the laser fluence increases to 23 mJ/cm², the phase retardance reaches a maximum of 135 nm. It is three times larger than that of the ITO film owing to the difference in the focusing lens and film thickness [26]. However, the phase retardance decreases with a higher laser fluence. When the laser fluence is 31 mJ/cm², the retardance is only 83 nm.

The SEM images of the nanostructured FTO thin film with increasing scanning speed are shown in Figure 6. The HSFL is very clear, and the duty cycle is as large as 0.3 at a scanning speed of 0.01 mm/s (the corresponding laser shots per area of 14,000, which is equivalent to spatial pulse overlapping of 99.99%), as shown in Figure 6A. As the scanning speed increases, the HSFL becomes shorter and narrower, and the grooves became narrower, as shown in Figures 6B,C. This is because the cumulative laser pulses and deposited laser fluence decrease at each position. The ripples are only partly covered on the film when the scanning speed is larger than 0.08 mm/s. Only some very narrow and shallow short ripples appear on the surface of the FTO film at a speed of 0.2 mm/s (the corresponding laser shots per area of 700, which is equivalent to spatial pulse overlapping of 99.8%).

Figure 7 shows the relationship between the phase retardance and the laser scanning speed. It can be observed that the irradiated FTO thin film exhibits lower retardance at higher scanning speeds. In summary, the experimental results showed that the birefringence effect of the FTO film reached a maximum value of 135 nm when the laser fluence was 23 mJ/cm² and the scanning speed was 0.01 mm/s.

The principle of the birefringence effect of the FTO film with LIPSS is essentially the same as that of a uniaxial anisotropic material. The phase retardance of transmitted light (φ) can be directly determined from the thickness of the LIPSS layer (d) and the birefringence effect (Δn) [19, 36]: φ = d ⋅ Δ n (2) where ∆n = n _e -n _o represents the difference between the refractive indices for ordinary and extraordinary light of the FTO film. In order to calculate ∆n for the FTO film, the LIPSS layer can be considered to consist of a periodic alternating arrangement of the unablated FTO nanoplane with width w ₁ and the ablated nanogroove with width w ₂ [19]. Therefore, the refractive indices for ordinary light and extraordinary light satisfy the following relationship [39]: n o 2 − n e 2 = f ( 1 − f ) ( n 1 2 − n 2 2 ) 2 f n 2 2 + ( 1 − f ) n 1 2 (3) where f = w ₂/(w ₁ + w ₂) is the duty cycle, and n ₁ and n ₂ are the refractive indices of unmodified and modified FTO, respectively [24, 36]. The refractive index n ₁ of FTO is 2.24 for 515 nm light [40]. The modified material was air and n ₂ = 1.0. The ordinary refractive index n _o is approximately equal to the refractive index n ₁ = 2.24 of FTO without nanostructures, so the expression n _e can be obtained according to Eq. 3 n e = n o 2 − f ( 1 − f ) ( n 1 2 − n 2 2 ) 2 f n 2 2 + ( 1 − f ) n 1 2 (4)

The difference of refractive index Δn can be written as Δ n = n o − n e = n o − n o 2 − f ( 1 − f ) ( n 1 2 − n 2 2 ) 2 f n 2 2 + ( 1 − f ) n 1 2 (5)

According to Eq. 5, the birefringence effect of the nanostructured FTO film depends mainly on n ₁, n ₂, and duty cycle f. Figure 8 shows the relationship between n _e, Δn, and the duty ratio f. It can be seen that when duty cycle increases from 0.2 to 0.4, n _e decreases from 2.09 to 1.96, and Δn increases from 0.15 to 0.27 correspondingly. This demonstrates that the birefringence effect increases with the duty cycle, namely, with the difference in refractive index Δn, which can well explain the similar changing trends of the duty cycle and retardance of the FTO film in Figures 4, 5.

The period of HSFL formed on the surface of the FTO film was 172 nm, and the duty cycle w ₂/Λ was 0.3 when the laser fluence was 23 mJ/cm² and the scanning speed was 0.01 mm/s. The difference in the refractive index Δn of the FTO film with HSFL can be calculated to be 0.21, according to periods Λ and w ₂. The retardance of the FTO film with HSFL was 135 nm (quantitatively measured by a 532 nm laser), and the thickness of the LIPSS layer was calculated to be approximately 640 nm using Eq. 2.

To further study the birefringence effect, the thickness of the LIPSS layer in the FTO film was studied. FTO films with regular LIPSS were immersed in a 1% HF solution at 24°C and etched for different times (10, 20, 25, and 30 s). After etching, the samples were washed with deionized water and dried. The surface morphology and depth of the FTO film were measured by SEM and a step profiler, respectively.

Figure 9 shows SEM images of the FTO film with different etching times. When the etching time is 10 s, the etching depth is 322 nm, as shown in Figure 9A. The ripples of HSFL became unclear as the etching time increased to 20 s, and the etching depth reached 600 nm, as shown in Figures 9B,E. When the etching time was increased to 25 s, the ripples almost completely disappeared, and the etching depth reached 700 nm, as shown in Figure 9C. These results indicate that the thickness of the HSFL layer formed on the FTO film was approximately 650 nm. This value is very close to the calculated result of 640 nm owing to the birefringence effect. When the etching time was increased to 30 s, the SEM image showed that the glass substrate was exposed, as shown in Figure 9D.

We have done the variation of retardance at 343, 515, and 1,030 nm with different fluence and scanning speed respectively. After analysis, we can find that the best retardance corresponds to a scan speed of 0.01 mm/s at three laser wavelengths. Therefore, we only discuss the results at 1030 and 343 nm wavelengths at a scanning speed of 0.01 mm/s.

Figure 10 shows the retardance of FTO thin films after irradiation with a 1,030 nm laser at different fluences. The retardance increases from 56 to 96 nm when the laser fluence increases from 77 mJ/cm² to 89 mJ/cm². When the laser fluence continues to increase, the retardance begins to decrease slowly. When the laser fluence is 92 mJ/cm², the retardance of the nanostructured FTO film decreases to 88 nm. The experimental results at a laser fluence of 89 mJ/cm² and scanning speed of 0.01 mm/s were studied in detail. The period and groove width of the HSFL were measured to be 300 and 108 nm, respectively. The duty cycle was 0.36, and the difference in the refractive index Δn was approximately 0.2, according to Eq. 5. The difference in the refractive index Δn is less than that in the case of 515 nm, leading to a smaller retardance. Moreover, the thickness of the HSFL layer was measured to be approximately 480 nm, which is another reason for the smaller retardance with the 1,030 nm laser.

Comparing the birefringence effects of the FTO film after irradiation by the 515 and 1,030 nm fs lasers, it was observed that the widths of the grooves were similar; the duty cycle for the 515 nm laser was larger because the period of the HSFL was smaller. According to the relationship between the birefringence effect (Δn) and the duty cycle in Figure 9, the birefringence effect increases with the duty cycle. Therefore, by using a laser with a shorter wavelength, we predicted that the duty cycle and the birefringence effect would be larger because the HSFL formed on the FTO film would have a shorter period [24, 33]. A femtosecond laser with a wavelength of 343 nm was used to fabricate the HSFL on the FTO film.

Figure 11A shows the SEM image of the laser-induced nanostructures on the FTO film for a scanning speed of 0.01 mm/s. For the 343 nm laser with a fluence of 13 mJ/cm², regular HSFL formed over the entire ablation area. The ripple period is approximately 126 nm, which is less than the value of 172 nm induced by the 515 nm laser. Figure 11B shows the retardance varying with the 343 nm laser fluence. When the laser fluence increases from 9 to 13 mJ/cm², the retardance increases from 35 to 47 nm. The birefringence retardance decreases rapidly to 33 nm as the laser fluence increases to 22 mJ/cm². Surprisingly, the retardation produced by the 343 nm laser is only 47 nm, which is much smaller than the optimal value of 135 nm induced by the 515 nm laser. The width of the groove was measured, and Δn was calculated to be 0.21, which is nearly equal to the value for the 515 nm laser. The thickness of the HSFL layer was measured to be approximately 230 nm, which is much smaller than the value of 650 nm for the 515 nm laser. The very thin HSFL layer is the main reason for the smaller retardation produced by the 343 nm laser.

For the FTO film, the extinction coefficients k are 0.11 and 0.055 for 343 and 515 nm light, respectively [40]. Accordingly, the penetration depth, d = λ/4πk, is only 248 nm for the 343 nm laser, which is much less than the result of 746 nm for the 515 nm laser. As a result, the thickness of the HSFL layer fabricated by the 343 nm laser is much smaller than that for the 515 nm laser, as well as the retardance.

The transmittance and absorptivity of FTO films at 343, 515, and 1,030 nm are very different [41], so the laser fluence required to process LIPSS is different at the same scanning speed. By comparing the experimental results using a femtosecond laser with UV to IR wavelengths, the retardance of the FTO film fabricated by the 515 nm laser is the largest, which is more suitable for fabricating birefringence optical elements.

An HSFL layer with an area of 10 × 10 mm was prepared on the FTO film using a 515 nm fs laser with a fluence of 23 mJ/cm² and a scanning speed of 0.01 mm/s. The spacing between adjacent scans was 1 mm. After laser fabrication, the FTO film was mounted on a rotating mirror frame and placed between two mutually perpendicular polarizers to form a light attenuator, as shown in Figure 2. By rotating the FTO film with HSFL, the relationship between the transmittance and rotation angle was obtained, as shown in Figure 12A. The transmittance changes in the range of 0–50%, which is very consistent with the theoretical prediction for a birefringence element with a phase rate of 135 nm, indicating that the HSFL layer on the FTO film has good birefringence characteristics. Here, light transmission through the unprocessed FTO film was set to 1.

The maximum retardance of the nanostructured FTO film was 135 nm, which was similar to a quarter wave plate for 532 nm light. Rotating the sample so that the ripples of the HSFL are oriented at a 45° angle to the polarizer GP1. As shown in Figure 12B, when analyzer GP2 was rotated from 0 to 360°, the detected light intensity hardly changed, indicating that the linearly polarized light became circularly polarized after passing through the nanostructured FTO film. These experimental results demonstrate that the FTO film with HSFL can function as a quarter-wave plate for 532 nm light.