# Laser-Assisted Etching of EagleXG Glass by Irradiation at Low Pulse-Repetition Rate
## 3 Experimental Results
### Role of Thermal Effects  
In the experimental study discussed in the previous Section, we chose the 25 kHz repetition rate as a reasonably low value to avoid thermal accumulation. In fact, the absence of thermal effects, in general, is not an absolute requirement in the laser-assisted etching technique, as convenient sets of irradiation parameters that provide good selectivity may also be found in the presence of these phenomena, with irradiation performed at high repetition rates [23; 24]. However, the non-thermal regime can provide more versatility in adjusting the irradiation parameters, as the material modification is substantially independent of the timing of the pulses impinging in the focus. Namely, in this case, the same kind of modification can be obtained by keeping the pulse energy fixed, and by scaling both the repetition rate and the translation speed in such a way that the number of pulses per unit length of the irradiated track remains constant. Alternatively, the effect of a slower speed may be emulated by multiple overlapped laser scans. In addition, the absence of pulse-to-pulse cumulative effects makes the laser-matter interaction process simpler, and possibly facilitates its microscopic modelling.  
To assess how widely the repetition rate can be varied, while maintaining the same non-thermal irradiation regime, we irradiated several tracks keeping the pulse energy \(E_{p}\) constant, varying the repetition rate of the femtosecond laser from 5 kHz to 200 kHz, and scaling the translation speed \(v_{t}\) proportionally. Two optimal sets of parameters, identified in the previous analysis at 25 kHz repetition rate, were chosen as references; in detail, \(E_{p}\) = 2.2 \(\upmu\)J and \(v_{t}\) = 1 mm/s, \(E_{p}\) = 8.6 \(\upmu\)J and \(v_{t}\) = 1 mm/s. All the tracks were written with orthogonal polarisation, as in the previously described results.  
Figure 4a reports the cross-section of the irradiated tracks, imaged at the optical microscope after polishing the lateral facets of the glass substrate. Material modification from heat build-up is identified from the pictures as an elliptical white crown, which appears and then enlarges as the repetition rate increases. At the lowest pulse-energy explored (\(E_{p}\) = 2.2 \(\upmu\)J), this feature is barely visible up to the highest repetition rate. On the other hand, for the highest pulse energy (\(E_{p}\) = 8.6 \(\upmu\)J) it becomes evident already at 50 kHz.  
After laser irradiation and polishing, the glass sample was immersed for 15 min in HF solution, and the A.R. of the etched cones was finally measured. Results are plotted in Figure 4b. We note that up to 25-kHz repetition rate the A.R. of the cones is almost constant for both values of \(E_{p}\), consistently with the observation of no visible heat build-up. On the other hand, for higher repetition rates the A.R. changes, as thermal accumulation is altering the etching selectivity.  
In the light of these results, we can conclude that, at the chosen repetition rate of 25 kHz, thermal accumulation effects are indeed small or negligible. In case it is needed for the application, it should be possible to further scale down the repetition rate together with the translation speed, down to 5 kHz, and reliably reproduce the results obtained at 25 kHz for a given pulse energy. Once in the single pulse regime, we expect that this scaling can be extended to even lower repetition rates, further reducing the translation speed. On the contrary, caution should be used in performing an analogous scaling by increasing the repetition rate above 25 kHz. In fact, the onset of thermal accumulation effects may alter the laser-modification process and affect the etching selectivity. The results obtained in this work cannot be extended to repetition rates higher than 200 kHz in a straightforward fashion and dedicated experimental investigations should be performed to assess the etching selectivity in those regimes.