The next generation imaging systems, such as smartphone camera systems, head-up displays, and endoscope systems, require high-precision machining and manipulation to satisfy smaller features and more densely packed commercial components [1]. Therefore, the non-contact, precisely controllable nature of laser pulses is highly advantageous for processing different materials and complex features.

Continuous-wave (CW) CO₂ laser processing, based on thermal melting and surface reflow, has been used for polishing and form correction of optics, achieving surface roughness down to the single-digit-nanometer level [2–4]. However, sub-surface damages and thermal-gradient-induced stresses remain the two main challenges for achieving high processing quality [5]. In addition, the linear-absorption nature of laser energy at 10.6 µm prevents a CO₂ laser from processing brittle materials, limiting its flexibility. In contrast to a CW laser, the higher peak intensity (10⁵ to 10⁸ W/cm²) of a nanosecond pulsed laser increases the processing efficiency while reducing the thermal effect [6–8]. However, the heat-affected zones induced by the thermal aspect of the interaction still cause stress, ripples, cracks, and recast [1,9]. Non-thermal ablation is therefore desired to achieve machining quality and precision. It overcomes the limits of the thermal processing done with CW and nanosecond-pulsed lasers.

Femtosecond (fs) laser processing is becoming an attractive technology for optics-and-photonics fabrication, including polishing [10], bonding [11], waveguide writing [12], laser-ablation-based patterning [13], and nanoparticle creation [14]. Compared to processing with longer pulses, fs-laser processing enables material removal without inducing thermal melting. As fs-laser-material interaction is faster than lattice disorder and thermal diffusion (picosecond and nanosecond time scale, respectively), the lattice is still cold when the thermal energy transfer from the fs-pulse ends [15]. The decoupling of optical absorption and lattice thermalization results in material removal by non-thermal ablation, which is a solid–vapor phase transition rather than a solid–liquid–vapor phase change [16]. In addition, fs-laser processing allows for simultaneous ablation and high-precision thermal control [10].

Currently, different techniques and steps are required for polishing and/or finishing optics, such as grinding, diamond turning, magnetorheological finishing (MRF), and ion beam figuring (IBF) [17]. The starting surface roughness for grinding can reach the millimeter order. The typical ending surface roughness for grinding is in the range of 0.1 µm to 2 µm [18]. It is the appropriate starting surface roughness for IBF which is the state-of-the-art optic finishing technique to achieve sub-nanometer surface roughness. It, however, lacks spatial resolution and requires operation in vacuum. These contact-based polishing techniques often leave mid-spatial-frequency (MSF) errors that are submillimeter-scale periodic patterns, detrimentally affecting imaging quality. Fs-laser finishing is potentially a replacement technique for IBF for surfaces with an initial sub-micrometer surface roughness.

Although laser processing of materials has been proven to produce the finest ablation structures, it is not a trivial task to assess, differentiate, and control the non-thermal ablation and thermal impact. Femtosecond laser ablation of material reported thus far often induces detrimental ripples or leaves micrometer or sub-micrometer level surface roughness [19,20]. Achieving simultaneous surface figuring and finishing without inducing detrimental thermal impact remains challenging and is a hot topic for research [21].

In this Letter, we demonstrate simultaneous material removal and surface finishing of glass, Borofloat 33 (BF33), using femtosecond-laser-based processing. We achieve non-thermal ablation via establishing a dynamic pulse propagation model to guide the selection of laser parameters [11]. We have achieved controllable material-removal depth with nanometer precision and sub-nanometer surface roughness, without inducing ripples. Here, we synonymously use “simultaneous figuring and finishing” and “simultaneous material removal and finishing”. “Finishing” means maintaining nanometer-level surface quality throughout the material removal process.

Laser processing of a BF33 substrate was performed by an ytterbium fiber laser (Satsuma HP3, Amplitude Laser) with 1030-nm central wavelength and 300-fs pulse duration. The laser beam is focused on the substrate surface using a confocal system with 35-mm focal length and 0.34 numerical aperture. The Rayleigh length is 45 µm. The radius of the laser focal spot is 5.9 µm (at 1/e² peak intensity). The focused beam spot radius was determined using the single-pulse ablation experiment, fitting a set of measured crater areas and pulse energies [22]. It was also separately confirmed by measurements using a beam profiler CCD camera. Beam attenuation and scanning were controlled by an integrated beam control module (LS-Shape, LASEA) and high-precision translation stages (Jenny Science, Lxc 80F40), respectively.

Laser processing parameters are specific to materials because each material has different electro- and thermo-responses to the interacting laser pulses having a different wavelength, pulse duration, energy deposition, etc. We have numerically and experimentally determined the ablation threshold of BF33 in the femtosecond regime to be 5.92 J/cm², using the single-pulse ablation method [22]. The ablation threshold is expected to decrease for line-scan-based processing with overlapping laser pulses, which is due to the “incubation effect” [23].

We first carry out line-scan-based processing of BF33 to investigate the influence of laser fluence on ablation and on the thermal effect. The processing was conducted at two different fluences, 4.26 J/cm² and 2.76 J/cm², both of which are lower than the single-pulse ablation threshold. The repetition rate and the scanning speed of the laser were respectively fixed at 10 kHz and 1 mm/s. Figure 1(a) shows that the ablation tracks under microscopy imaging exhibit dramatically different surface morphologies for the two fluences. For the higher fluence, the processed region is a black track with material ejection in the form of micro-particles. Micrometer-scale structures were further observed within the track using scanning electron microscopy (SEM). For the lower fluence, microscopy imaging shows a uniform ablated track that has the same coloration as the unprocessed area. The detailed feature within the track is not observable under SEM due to its resolution limitation (1.2 nm at 30 kV).

 

Fig. 1. (a) Microscopy images of line-scan-based processing, and (b) predicted surface temperature evolution for two laser fluences.

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It is essential to understand the underlying cause of different morphologies and optimize the processing parameters. We established a dynamic pulse propagation model in MATLAB, based on the formulation in Ref. [11], to predict the evolution of free-electron density and surface temperature during the interaction with multiple femtosecond laser pulses that are scanned across the BF33 sample surface. Plasma generation is determined by a rate equation that describes the evolution of the free-electron density when a fs-laser pulse is focused on the surface of the material [24]. The onset of ablation is defined as the laser fluence at which the maximum free-electron density equals the critical density value (1.05 ×10²¹ cm⁻³ at 1030 nm). The instantaneous temperature rise after the arrival of each pulse is calculated from the deposited pulse energy considering beam propagation and plasma generation [11]. The temperature distribution in the bulk material is then obtained by the heat diffusion calculations between pulses [25]. These simulations allow for the prediction of the onset of ablation and thermal melting during femtosecond laser processing. Although severe defects and surface roughness will impact photoexcitation, they do not affect the purpose of our model for acting as a predictive step to guide the understanding of the process and narrow the selection of laser parameter combinations to achieve nonthermal ablation for figuring and finishing. The impact is also negligible during our study because the surface roughness of the unprocessed and the processed areas is within single-digit nanometers.

The evolution of the maximum surface temperature in BF33 is simulated at the two fluences used in the aforementioned experiment. The morphologies of the laser-processed surface are correlated to the simulated temperature. Figure 1(b) shows that the predicted temperatures exceed the softening temperature of BF33 (T_s = 1093 K) for both fluences. However, the surface temperature rises above the melting temperature of T_m = 1923 K for the higher fluence, whereas the surface temperature remains below the melting temperature for the lower fluence. Based on the experimental and simulation results, we determined that the predicted surface temperature can be used as an indicator to control the thermal effects and achieve a smooth surface. A set of model-guided laser parameters was further identified and used to achieve ablation while controlling the thermal effect. With these parameters, the highest surface temperature is between the softening temperature and the melting temperature.

The laser parameters used for line-scan-based ablation were extended to achieve area processing on BF33. A fluence of 2.16 J/cm² was chosen to maintain the predicted peak of surface temperature between the softening temperature and the melting temperature. The other laser parameters are the same as for the line-scan-based experiment. The scanned line overlap is 70% of the linewidth to maintain processing efficiency [26].

Figure 2(a) shows an optical microscopy image of a 1 ×1 mm² laser-polished BF33 substrate surface area using 30 passes of area scans. It demonstrates that there are no laser-induced patterns or microstructures in the processed area. There is a slight color difference between the processed and unprocessed areas, also between the two unprocessed areas on the left and right sides of the image, potentially indicating the impact from a nonuniform lighting condition of the microscope. An SEM image [Fig. 2(b)] confirms that the surface morphologies are indistinguishable across the processed and unprocessed areas. We have further performed a subsurface damage (SSD) test based on the nanoindentation method [27]. No SSD was detected as the measured Young’s modulus in the processed region is the same as that in the unprocessed region. From these measurements, we conclude that the slight color difference shown in the microscopy image is unlikely to have been caused by laser-induced surface defects or SSD. The details of SSD measurements and the continued investigation of the color difference will be reported in a future publication.

 

Fig. 2. (a) Optical microscopy image of area processing on BF33 after 30 passes of area scans. (b) Comparison of the processed and unprocessed areas from an SEM measurement.

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Figure 3(a) shows the surface map across the processed and unprocessed areas, measured by a white light interferometer (Zygo NewView). The overall surface roughness across the 0.8 mm × 0.8 mm processed area is 0.68 nm [root mean squared (rms)], compared to 0.58 nm for the unprocessed area. The difference in height between the two areas is 16 nm. Zoomed-in surface profiles of unprocessed and laser-polished areas are shown in Figs. 3(b) and 3(c), corresponding to the locations of the surface profile in Fig. 3(a). There are no laser-induced ripples in the processed region and its surface roughness is 0.61 nm compared to 0.63 nm in the unprocessed region, both in rms. The lateral spatial resolution of the scanning interferometer is 2.2 µm on the sample surface. The longitudinal resolution of the interferometer is 0.1 nm, and the rms repeatability is 0.01 nm.

 

Fig. 3. (a) Surface profile of the 30-pass laser-processed surface region and zoomed-in (b) laser-processed area and (c) unprocessed area.

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The controllability of material removal was further investigated. Figure 4(a) shows that the material-removal depth linearly increases with the increasing number of area-passes while the measured surface roughness consistently remains less than 1 nm (rms) within the 0.8 mm×0.8 mm processed area. This demonstrates that simultaneous material removal with nanometer precision and subnanometer surface finishing without detrimental thermal impact have been achieved, using model-guided laser parameters.

 

Fig. 4. (a) Influence of the number of area-passes on material-removal depth (left axis) and the resulting surface roughness (rms) (right axis). (b) Removal depth linearly increases with energy density varied by the number of passes (blue dots) and the scanning speed (red diamonds).

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We have identified the total deposited energy density as a metric to quantify the combined contributions from various laser parameters, such as the number of area-passes and the scanning speed. The energy density of a single scan is 3.9 J/mm² using a fluence of 2.16 J/cm², a scanning speed of 1 mm/s, and a repetition rate of 10 kHz. A linear relation between the material-removal depth and the deposited energy density is obtained over this range, as shown in Fig. 4(b). The same removal depth is obtained when the combined contributions from different numbers of area-passes and scanning speeds are equal. Deterministic material removal with nanometer-scale precision has been achieved and can be scaled up to accommodate different processing geometries and tasks.

Laser beam figuring was conducted using the removal depth versus energy density calibration and the same scanning strategy used for area processing. A four-step staircase structure was created to demonstrate high-precision material removal. Each step (0.4×0.4 mm²) was processed with various area scans from 20 to 80 passes. The interval of the area scans between steps is 20 passes. The surface map of the staircase structure is presented in Fig. 5(a). The fourth step was only measured partially due to the limited field of view of the Zygo NewView objective. Figure 5(b) shows the corresponding integrated line profile. The removal depth for each step agrees with the calibrated value shown in Fig. 4(b), and the resulting surface roughness of each step remains within one nanometer (rms) of the initial roughness. The process steps of surface measurement and tunable control over removal depth can be further cyclically repeated until the desired surface geometry is achieved. Thus, controllable fs-laser figuring and finishing demonstrate the potential for freeform optic forming, polishing, and reduction of MSF error, a submillimeter periodic pattern that is often induced by the current polishing methods, such as IBF, diamond turning, and MRF.

 

Fig. 5. (a) Surface profile of the staircase structure and (b) vertically integrated line profile.

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In conclusion, we have demonstrated controllable material removal with nanometer precision and sub-nanometer surface finishing for BF33 using femtosecond laser processing. We have developed a dynamic pulse propagation model to investigate the combined impact of laser parameters on ablation and surface temperature. The model enables deterministic material removal with minimized thermal effects. We further identify energy density as a metric to determine the combined contributions of laser parameters and to achieve high-precision material removal. It will allow one to scale up the material removal toward larger area processing and flexible geometrical features. Thus, controllable fs-laser figuring with optical quality surface demonstrates the potential for advanced freeform optic forming, finishing, reduction of detrimental mid-spatial-frequency errors, and laser-ablation-based patterning used for fabrication of integrated photonics and lasers.