Ultrahigh-speed micromachining of sapphire by enhancing laser absorption

Abstract

Fine micromachining of sapphire using ultrafast lasers via nonlinear absorptions has been extensively studied. However, severe damage, along with the low material removal rate, limits the precision and machining speed. Here we use transient and selective laser processing for sapphire by coaxially delivering a single femtosecond laser pulse and a single microsecond laser pulse that are temporally synchronized. It shows that the micromachining speed was improved 10⁴ times, and cracks in the base material are mitigated, compared to femtosecond laser percussion processing with a repetition rate of 1 kHz. The ultrafast electron excitation dynamics induced by the femtosecond laser are captured using pump-probe imaging, revealing a rapid relaxation process with a decay time constant on the order of picoseconds. The machining process is further visualized using a high-speed camera and compared with numerical simulations to elucidate the underlying mechanism. We find that the increased absorption coefficient of sapphire for the microsecond laser pulse, owing to the bandgap narrowing and thermal ionizations, along with high-temperature regions expanding from the sample surface into deeper areas along the laser propagation path, drives the machining process. These results advance high-efficiency and precision micromachining for sapphire and other hard and brittle transparent materials.

Guoqi Ren and colleagues demonstrate a synchronized dual-pulse laser technique for high-speed microprocessing of sapphire. This method can be used for high-efficiency and precision machining of hard, transparent materials.

Introduction

Sapphire, a typical transparent dielectric material, has attracted considerable attention across diverse fields such as electronics, optics, and medical science, owing to its exceptional physical, chemical, mechanical and optical properties^1–4. Its high melting point, remarkable chemical inertness, and superior hardness make it appropriate for applications in harsh conditions⁵. In addition, its broad transmission spectrum makes it ideal for optical applications⁶. However, these properties also pose considerable challenges for conventional processing methods: chemical etching and mechanical machining techniques such as cutting, grinding, and polishing are both difficult and costly^7,8.

In recent decades, ultrafast lasers have been widely studied for the micromachining of hard and brittle transparent materials due to their ultra-high intensities, which enable fine machining through nonlinear absorptions^9,10. The ablation threshold of sapphire under both single-pulse and multi-pulse irradiation conditions was determined¹¹. The quality and morphology of the sapphire surface ablated by a femtosecond laser, as well as its ablation threshold were evaluated¹². Surface morphologies and structural modifications of sapphire under femtosecond laser irradiation were investigated, and the formation of spherical nanoparticles was analyzed¹³. Two-dimensional micro-resolution array patterns on the sapphire surface were fabricated by direct scanning with a femtosecond laser¹⁴. Polarization-dependent nanogratings with a period of ~250 nm were demonstrated on the sapphire surface using femtosecond laser scanning¹⁵. The influence of sapphire crystal orientations on ablation morphology, crater dimensions, damage threshold, and material removal rate was investigated¹⁶. Moreover, a deep ultraviolet (206 nm) femtosecond laser was obtained by generating 5th harmonic of an ultrashort-pulsed Yb:KGW laser operating at 1030 nm, and used for sapphire ablation studies, demonstrating improved processing quality compared to the fundamental 1030 nm wavelength¹⁷. In addition, laser-induced plasma-assisted ablation (LIPAA) of sapphire was also proposed, which shows a reduced ablation threshold and enhanced quality of the fabricated structures^18,19. However, these studies primarily focus on ablating sapphire surface regions with shallow processing depths.

To achieve deep microstructures, it is necessary to increase the fluence of ultrafast lasers. However, using high laser intensities often generates severe cracks around the machining regions^12,20, which greatly degrades the precision of the fabricated structures and hinders the fabrication of small-pitch features. The mechanism of crack generation in ultrafast laser micromachining of transparent dielectrics has been revealed as strong tensile stress around the ablation surface^21,22. To address this issue, several laser machining methods have been developed. Ultrafast laser GHz-burst mode ablation, taking advantage of thermal accumulation, has demonstrated precise material removal^23,24. Reducing the applied pressure on the sample through temporally shaping the ultrafast laser achieved crackless ablation²⁵. However, the machining speed remains low because generating a microhole deeper than 100 µm requires multiple pulses, making the process time-consuming.

A method called transient and selective laser (TSL) processing has been proposed for high-speed and precision machining of glass²⁶. In this approach, free electrons were first excited by a femtosecond laser pulse, and then these electrons absorbed a continuous-wave laser to heat the material. This allows selective removal of material in the excitation region without damaging the surrounding areas. Using this method, crack-free holes were produced at a speed 5000 times faster than conventional femtosecond laser machining. Since sapphire is a highly transparent material like glass, TSL method holds potential for achieving high-speed, precision micromachining of sapphire²⁷. However, sapphire has a larger bandgap and refractive index than glass, which may lead to different electron excitation phenomena. Additionally, sapphire’s much higher thermal conductivity could result in a distinct heating process. Therefore, it is necessary to investigate the fundamental laser–sapphire interactions and reveal the mechanism of laser absorption and material removal in TSL processing through deep analyses of machining dynamics.

In this work, we study the ultrafast dynamics of femtosecond laser irradiation on sapphire, revealing that the excited electrons in the plasma filament decay rapidly with a time constant on the order of picoseconds. A 1070 nm microsecond laser pulse, which normally exhibits high transmittance in sapphire, is absorbed into sapphire after femtosecond laser irradiation, resulting in high-speed micromachining. The processing speed is 10⁴ times faster compared to conventional femtosecond laser percussion micromachining with a laser repetition rate of 1 kHz, and crack formation is mitigated. The machining process is analyzed using high-speed imaging. Further, the underlying mechanism is investigated through experiments and simulations based on thermal diffusion and laser propagation. Results show that the enhanced absorption coefficient of sapphire to the 1070 nm microsecond laser caused by bandgap narrowing and thermal electrons at high temperature, and the expansion of high-temperature regions along the laser propagation direction are key factors driving the micromachining process.

Methods

Experimental setup for ultrafast dynamics detection

Figure 1a shows the schematic of the pump-probe imaging setup. A single laser pulse from a Yb:KGW laser (Light Conversion, Pharos) having a wavelength of 1030 nm and a pulse duration of 170 fs is split into pump and probe pulses using a beam splitter (BS). The pump pulse is focused onto the ($11\overline{2}0$) surface of a single-crystal sapphire sample (Kyocera, SA100) using an objective lens (Mitutoyo, M Plan Apo NIR 10×, NA = 0.26). The ($11\overline{2}0$) plane corresponds to the 50 mm × 0.3 mm surface of the sample, which has a size of 20 mm × 50 mm × 0.3 mm. The probe pulse is frequency-doubled to 515 nm by a beta barium borate (BBO) crystal, and then passes through the sample perpendicularly to the pump pulse, as shown in the inset. The transmitted probe images are magnified by an objective lens (Mitutoyo, M Plan Apo NIR 20×, NA = 0.4) and a tube lens (TL), and subsequently recorded by a cooled charge-coupled device (CCD) (Bitran, BU-55LN). A short-pass filter (SPF) and a bandpass filter (BPF) are employed to eliminate unwanted light components, such as the remaining 1030 nm laser and plasma emission. To synchronize the laser pulse with the CCD, the electronic signal from the laser is fed into a delay generator (DG) (Stanford Research Systems; DG645), which outputs a delayed trigger signal to the CCD. Ultrafast phenomena at different time delays are captured through adjusting the optical path length between pump and probe pulses using an optical delay line.

Fig. 1. Experimental setup.

a Pump-probe imaging setup. b Laser micromachining setup. BS beam splitter, BBO beta barium borate, SPF short pass filter, M mirror, OL objective lens, BPF bandpass filter, TL tube lens, CCD cooled charge-coupled device, PD photodetector, Fs femtosecond laser, µs microsecond laser, HSC high-speed camera.

Experimental setup for laser micromachining

Figure 1b illustrates the laser micromachining setup, which includes an ultrafast laser (Light Conversion, Pharos) and a microsecond laser (SPI Lasers, redPOWER R4 500 W) operating at a wavelength of 1070 nm. A single pulse with a duration of 170 fs from the ultrafast laser and a single pulse having adjustable durations from the microsecond laser are aligned coaxially using a beam splitter and focused onto the ($11\overline{2}0$) surface of sapphire sample. The focal spot diameters are 8.6 µm for the ultrafast pulse and 12.0 μm for the microsecond pulse, achieved using an objective lens (Mitutoyo, M Plan Apo NIR 10×, NA = 0.26). A pulsed diode laser (Cavitar, CAVILUX HF) with a wavelength of 646 nm provides illumination for imaging. After passing through the sample, the light is magnified by an objective lens (Mitutoyo, M Plan Apo NIR 50×, NA = 0.42) and a tube lens. A high-speed camera (HSC) (Shimadzu, HPV-X2) with a frame rate of 5 million frames per second and an exposure time of 200 ns is employed to capture the rapid dynamics during laser machining. The three lasers and the HSC are synchronized by a DG. To precisely measure the timing between the ultrafast and microsecond laser pulses, two photodetectors are positioned equidistant from the sample. In this work, the microsecond laser pulse is intentionally irradiated 10 μs before the ultrafast laser pulse to eliminate the influence of electronic jitter in synchronization, as illustrated in the inset.

Results and discussion

Irradiation dynamics of a single femtosecond laser pulse

Figure 2a shows the ultrafast dynamics under the irradiation of a single femtosecond laser pulse on the sapphire sample, captured using pump-probe imaging. The laser pulse has an energy of 10 μJ, corresponding to a fluence of 17.22 J·cm⁻². By changing the optical path length between the pump and probe pulses, the temporal evolution of the phenomena from 0 ps to 5 ps after pump pulse irradiation is obtained. The 0 ps pump-probe delay is determined when very weak electron excitations are observed. As the delay increases, a filament begins to appear, becoming darker and longer in the initial stage. This is attributed to free-electron excitation from the valence band to the conduction band via nonlinear and cascade ionization processes during the propagation of the pump pulse inside the sample. Around 0.8 ps, a secondary, weak filament appears, which is not continuous with the initial dark filament. This phenomenon, known as filamentation, results from a dynamic balance between the Kerr effect and plasma defocusing²⁸. Subsequently, the dark filament gradually fades, due to the recombination of excited electrons and electron holes. The evolution of filament length prior to the onset of plasma defocusing is quantified in Fig. 2b. The filament length remains stable after ~0.2 ps when the pulse energy is 10 μJ, as the energy is insufficient to induce further electron excitations in deeper regions. The measured speed of filament elongation is 1.73 × 10⁸ m·s⁻¹, 1.70 × 10⁸ m·s⁻¹, 1.70 × 10⁸ m·s⁻¹, and 1.70 × 10⁸ m·s⁻¹ for pulse energies of 10, 30, 50, and 70 μJ, respectively. The speed is consistent with the light propagation speed in sapphire having a refractive index of 1.76.

Fig. 2. Pump-probe results.

a Ultrafast dynamics under a single femtosecond laser pulse irradiation. b Filament length changes. The inset shows the dataset and the fitted line for a pulse energy of 10 μJ. c Absorbance variations.

To quantitatively study the laser-induced free electrons, the absorbance of the probe pulse by the electron plasma is calculated using $A=-\ln \left(T\right)$, where T is the transmittivity of the probe pulse, equaling the ratio of probe intensity after and before passing through the plasma filament region²⁹. A larger absorbance indicates a higher plasma density. The absorbance measured at a depth of 30 μm in the filament center is shown in Fig. 2c. As the increase of delay, the plasma density first increases rapidly and then decreases with a relatively smaller speed. When the pulse energy increases from 10 to 70 μJ, the maximum absorbance occurs at 30 μJ, because too strong surface excitations induced by higher pulse energies inhibit the laser propagation into the sample. The decay stage is fitted with an exponential curve, having a decay time constant of 1.48 ps, 17.04 ps, 23.46 ps, 29.35 ps as the pulse energy increases. The plasma filament eventually disappeared without causing noticeable damage in the excitation region, with only a small crater ablated on the sample surface.

Machining dynamics using a single femtosecond pulse and a single microsecond pulse (TSL processing method)

The machining setup is shown in Fig. 1b. A pulse energy of 10 μJ is used for the ultrafast laser pulse having a duration of 170 fs. A microsecond laser pulse, with a pulse duration of 60 μs and an average power of 90 W, corresponding to a pulse energy of 5.4 mJ, is delivered 10 μs prior to the femtosecond laser pulse, but no machining occurs at this interval due to the high transparency of sapphire at 1070 nm. The effective pulse duration and energy for machining are 50 μs and 4.5 mJ, respectively. The machining process is recorded using the HSC, as shown in Fig. 3a. The time corresponding to the irradiation of the single femtosecond laser pulse is defined as the processing time of 0 ns. A plasma filament is observed at 0 ns, induced by the ultrafast laser pulse, but it disappears in the subsequent frame, corresponding to a processing time of 200 ns, due to the decay of excited electrons. With the continuous irradiation of the microsecond laser pulse, drilling becomes evident after 2 μs. During the drilling process, the hole depth increases, and material is removed from the hole edge in the form of a melting flow that moves from the sample to the air. The hole depth change is measured, shown in Fig. 3b. The depth continues to increase to  189 μm as the processing time reaches 39 μs, due to the sustained absorption of the microsecond laser. The machining continues beyond 39 μs, but it is not recorded in the HSC. The drilling speed is calculated using depth and processing time, which rapidly increases to 7.55 m·s⁻¹ at the beginning stage, and gradually decreases to less than 5 m·s⁻¹. The diameter is measured at a depth of 25 μm, using the width of the dark region, which gradually increases to over 16 μm, as shown in Fig. 3c. The speed of hole widening firstly increases to 1.74 m·s⁻¹ and then gradually decreases to 0.42 m·s⁻¹. The rates of depth increase and diameter growth exhibit a rapid rise during the initial stage, implying the presence of a heat-accumulation effect during this period. The decrease in speed along both the depth and radius directions can be attributed to the attenuation of laser intensity, caused by absorption and divergence during propagation in the depth direction, and the reduction in intensity of the Gaussian beam along the radius direction, respectively. The average drilling speed is 4.86 m·s⁻¹. Furthermore, during laser irradiations, no noticeable cracks are observed at the sidewall region.

Fig. 3. Laser micromachining of sapphire using TSL processing method.

a High-speed observations of the machining process. b Variations of hole depth and processing speed. c Diameter variation and its speed. Error bars represent the standard deviation (n  = 4).

The femtosecond laser micromachining is conducted for a comparison. A femtosecond laser pulse train having 3000 pulses with a repetition rate of 1 kHz from the Yb:KGW laser is focused onto the sapphire sample ($11\overline{2}0$) using an objective lens (Mitutoyo, M Plan Apo NIR 10×, NA = 0.26). The pulse energy is 100 μJ, corresponding to a laser fluence of 172.2 J·cm⁻². This relatively large energy is chosen to create a deep hole, making it comparable to the machining using a femtosecond and a microsecond laser. The Yb:KGW laser, the image intensifier (II) (Hamamatsu Photonics, C10880-03C), and the complementary metal-oxide-semiconductor (CMOS) sensor (Keyence, VW-9000) are synchronized at a repetition rate of 1 kHz using a DG. An image is recorded onto the CMOS after the irradiation of each femtosecond laser pulse based on the pump-probe setup, as shown in Fig. 4b, where pump-probe delay is set to 10 ps. The recorded image is shown in Fig. 4a. A long plasma filament is generated by the first pulse, because of the strong laser intensity. As the increase of pulse numbers, severe damage occurs near the sample surface, and many cracks appear at the sidewall of the hole. Meanwhile, the material ejection in the air is captured although the delay is 10 ps. These ejections are caused by the preceding pump laser pulse, as the ablated material from the base can persist for microseconds in the air near the interface³⁰. Drilling reaches near saturation after ~400 pulses. The evolution of hole depth and processing speed are measured, shown in Fig. 4c. The depth rapidly increases to 170 μm with the first 400 pulses, and then rises to 176 μm with the subsequent 400 pulses, indicating a saturation of the drilling process. The maximum drilling speed appears at the beginning of the machining process, which is 1.55 × 10⁻³ m·s⁻¹, due to the strongest laser intensity near the sample surface. The average speed at the first stage is 0.43 × 10⁻³ m·s⁻¹. Therefore, compared with the conventional femtosecond laser micromachining, no cracks are observed during laser irradiations using the TSL processing method that combines a single femtosecond laser pulse and a single microsecond laser pulse. Additionally, when compared to a femtosecond laser operating at a repetition rate of 1 kHz, this approach achieves a drilling speed that is 10⁴ times faster.

Fig. 4. Conventional femtosecond laser micromachining of sapphire.

a Machining dynamics. b Imaging setup. OL objective lens, BPF bandpass filter, TL tube lens, II image intensifier, RL relay lens, CMOS complementary metal-oxide-semiconductor sensor. c Hole depth and machining speed. Error bars represent the standard deviation (n  = 4).

Machining results

Minor cracks appear in holes after machining using the TSL processing method that combines a single femtosecond laser pulse and a single microsecond laser pulse. For example, the microscope images of drilled holes are shown in Fig. 5c, d, where the microsecond pulse has effective durations of 20 µs and 30 µs, respectively, but no cracks are observed during laser irradiations at processing times of 20 µs and 30 µs (Fig. 5a, b), indicating that these cracks should form during the cooling stage. Figure 5e, f shows the scanning electron microscope (SEM) images of the sapphire surface after laser machining described in the previous section. The tilt angle for the observation is 70°. The molten structure in Fig. 5e indicates that the material is thermally removed in TSL processing. Microcracks appear in the resolidified layer of the molten structure, whereas no cracks are observed in the surrounding unmachined area. However, severe cracks are generated near the machined region when femtosecond laser multi-pulse percussion processing is used, as shown in Fig. 5f. Moreover, the cross-section image of the sample drilled using the TSL processing method is shown in Fig. 5g. The hole is blocked near the surface likely due to the resolidification of molten materials. Minor cracks and resolidified layers are observed inside the hole, which form during the cooling stage after laser irradiations. To solve the issue of blockage and minor cracks, and to control the resolidification dynamics, optimizing the laser heating strategy and carefully managing the subsequent cooling process are needed. The cross-section image of the hole drilled using the conventional method is shown in Fig. 5h. Only a partial cross-section of the hole is obtained, but the remaining cracks in the base material are still clearly visible and comparable in size to the hole diameter. Overall, cracks in the base material surrounding the processed area are mitigated in the machining using the TSL processing method.

Fig. 5. Machining result analyses.

Transient machining characteristics using the TSL processing method at processing times of a 20 µs and b 30 µs. Microscope images of holes fabricated using the TSL processing method with a single microsecond pulse having effective durations of c 20 µs and d 30 µs. SEM images of the surface after laser machining, described in the previous section, using e the TSL processing method and f a femtosecond laser. SEM images (g) and (h) of the cross-section of drilled holes, corresponding to (e) and (f), respectively. The insets are microscope images of the cross-sections.

Additionally, the relationship between drilled-hole characteristics and laser parameters is investigated. As the pulse energy of the femtosecond laser increases from 10 to 100 µJ, the depth and diameter of the holes remain nearly unchanged, as shown in Fig. 6a, where the microsecond laser has an average power of 90 W and an effective pulse duration of 50 µs. Figure 6b displays the dependence of hole depth on femtosecond pulse energy and the effective pulse duration of the microsecond laser. The pulse energy of the femtosecond laser has no apparent effect on the hole depth or its variation behavior. It should be noted that no machining occurs if the pulse energy of the femtosecond laser is too low, because of the insufficient electron excitations. The depth increases from 77 to 226 μm as the effective microsecond duration increases from 10 to 60 µs, with a gradually decreasing growth rate. Figure 6c shows the microscope images of drilled holes, where the femtosecond laser has a pulse energy of 10 µJ and the microsecond laser has an effective duration of 50 µs. The hole characteristics change as the average power of the microsecond laser increases from 90 to 225 W. The hole depth initially increases and then reaches saturation, while the hole diameter continues to grow. The depth increases with the effective microsecond pulse duration from 10 to 60 µs, but the rate of increase gradually diminishes, as shown in Fig. 6d. When the power of the microsecond laser exceeds 180 W, both the depth and its variation remain nearly constant. These results indicate that the hole characteristics can be controlled by adjusting the parameters of the microsecond laser. They also demonstrate that the femtosecond laser pulse, which excites free electrons, acts as a trigger for machining, while the drilling is achieved by the microsecond laser.

Fig. 6. Dependence of drilled holes on laser parameters.

a Optical microscope images of drilled holes with femtosecond laser pulse energy set to 10, 30, 50, 70, and 100 µJ, and a microsecond laser with an average power of 90 W and an effective duration of 50 µs. b Dependence of hole depth on femtosecond laser pulse energy and microsecond laser effective duration, where the average power of the microsecond laser is 90 W. c Optical microscope images of drilled holes with microsecond laser average power of 90, 135, 180, and 225 W, and an effective duration of 50 µs. The femtosecond laser pulse energy is 10 µJ. d Dependence of hole depth on average powers and effective durations of the microsecond laser, with the femtosecond laser pulse energy set to 10 µJ. Error bars represent the standard deviation (n  = 3).

Discussion of the machining mechanism

No machining occurs when the sapphire sample is irradiated solely by the microsecond laser pulse due to the ultralow absorption coefficient of sapphire at 1070 nm. However, drilling begins and persists for tens of microseconds after the femtosecond laser pulse is applied, indicating that the absorption coefficient of sapphire to the microsecond laser has been enhanced by the effect of the femtosecond laser pulse. Free electrons are first excited by the femtosecond laser pulse through multiphoton ionizations, and then the electron-phonon relaxation happens at picosecond timescale after electron excitation^31,32, which generates heat in the material. For the improvement of absorption coefficient of sapphire for the microsecond laser pulse, four potential hypotheses can be proposed: (1) Inverse bremsstrahlung absorption by free electrons in the conduction band excited by the femtosecond laser pulse; (2) Defects induced by the femtosecond laser such as color centers and excitons contribute to the absorption of the microsecond laser pulse^33–36; (3) Thermal electrons generated by the high temperature after the electron-phonon relaxation increases the laser absorption. (4) The reduced bandgap caused by the high temperature results in an improved absorption for the microsecond laser pulse.

Free electrons do absorb the microsecond laser pulse through inverse bremsstrahlung absorption. However, free electrons in the plasma filament induced by the femtosecond laser return to the valence band within tens of picoseconds, as shown in Fig. 2, yet the microsecond laser is still absorbed for machining at a deeper region of the sample where the plasma filament has totally disappeared. This indicates that the absorption based on the free electrons induced by the femtosecond laser is not the main reason for the continuous micro drilling. Delivering the microsecond laser pulse with a several-second delay after the irradiation of the femtosecond laser pulse cannot achieve the machining, indicating that the defect and impurities are not the essential reasons for microsecond laser absorption improvements. High temperature induced thermal electrons have been considered as one of the factors for improving the laser absorption into transparent materials^37–39, as expressed in Eq. (1), where ${\alpha }_0$ is the absorption coefficient at a wavelength of 1070 nm, around 0.24 m⁻¹ at room temperature; $E_{gap}$ is the bandgap of sapphire; ${\sigma }_c$ is the cascade ionization coefficient; ${\rho }_{therm}\left(T\right)$ is the density of thermal electrons, calculated by Eq. (2); ${\rho }_{bound}$ is the valence electron density; $k_B$ refers to the Boltzmann constant; $T$ is the temperature. The temperature-dependent absorption coefficient is obtained, shown in Fig. 7a. Even though the temperature increases to 2300 K, just below the material’s melting point, the absorption coefficient only increases by 0.0167%, resulting in negligible improvement of the absorption. Therefore, only the thermal-electron effect cannot achieve substantial absorption improvement of the microsecond laser.

$$\alpha \left(T\right)={\alpha }_0+\frac{3}{2}{E}_{gap}{\sigma }_c{\rho }_{therm}\left(T\right)$$ 1

$${\rho }_{therm}\left(T\right)={\rho }_{bound}\frac{3\sqrt{\frac{\pi }{2}}{\left(\frac{k_{B}T}{E_{gap}}\right)}^{\frac{3}{2}}\exp \left(-\frac{E_{gap}}{2k_{B}T}\right)}{1+3\sqrt{\frac{\pi }{2}}{\left(\frac{k_{B}T}{E_{gap}}\right)}^{\frac{3}{2}}\exp \left(-\frac{E_{gap}}{2k_{B}T}\right)}$$ 2

Fig. 7. Absorption coefficient for 1070 nm light.

a Different temperatures. b Different bandgaps.

The most possible mechanism of the absorption improvement for 1070 nm light in this study is bandgap narrowing caused by the high temperature^27,40. A higher density of thermal electrons can be generated if the bandgap is reduced at a high temperature, calculated using Eq. (2), which results in a great improvement of the absorption coefficient, as shown in Fig. 7b, where the relations between the absorption coefficient and the bandgap are calculated at three higher temperature conditions, for example. Based on the above analysis, the mechanism of microsecond laser absorption and machining process are proposed, as illustrated in Fig. 8. A plasma filament is first induced in the sapphire sample under irradiation of the femtosecond laser pulse (Fig. 8a), which absorbs the microsecond laser through free-electron linear absorption (Fig. 8b). As electron-phonon relaxation proceeds, the material temperature increases, which narrows the bandgap and induces thermal electrons, so that the microsecond laser is greatly absorbed (Fig. 8c). The absorbed laser energy further increases the temperature and maintains the high absorption. Once the temperature reaches the melting point, the material is removed. Due to the continuous irradiation of the microsecond laser and the thermal diffusion, the high-temperature area expands downward along with material removal (Fig. 8d). Finally, a deep hole is formed after tens of microseconds of machining (Fig. 8e).

Fig. 8. Illustration of machining mechanisms.

a Plasma filament induced by the femtosecond laser in sapphire sample. b Absorption of the 1070 nm microsecond laser starts on the sample surface region. c A high-temperature area is formed within the material. d Drilling proceeds along with the high-temperature area expansion. e A deep hole is formed.

To verify the proposed machining mechanism, a simulation model is developed based on thermal diffusion and laser propagation. The temperature changes along with the absorption of microsecond laser are expressed as

$${\rho }_{mass}C\frac{\partial T}{\partial t}=k\left(T\right){\nabla }^{2}T+\alpha \left(r,z\right)I\left(r,z\right),$$ 3

$$I\left(r,z\right)=I_0{\left(\frac{w_0}{w\left(z\right)}\right)}^2\exp \left(-\frac{2r^2}{{w\left(z\right)}^2}\right)\exp \left(-{\int }_0^z\alpha \left(r,z\right)dz\right),$$ 4

where ${\rho }_{mass}$ represents the mass density; $C$ is the specific heat capacity; $k\left(T\right)$ is the thermal conductivity, which is sensitive to temperature; $\alpha \left(r,z\right)$ is the absorption coefficient; $I\left(r,z\right)$ is the laser intensity of the microsecond laser; $z$ is the depth from the sample surface along the central axis; $r$ is the radial distance from the central axis; $I_0$ is the peak intensity of the microsecond laser; $w_0$ is the waist radius, which is the spot radius on the sample surface; $w\left(z\right)$ is the beam radius at the depth of $z$, which can be calculated by

$$w\left(z\right)=w_0\sqrt{1+{\left(\frac{z}{z_R}\right)}^2},$$ 5

where $z_R$ represents the Rayleigh length, related to the laser wavelength and the waits radius.

For simplification, electron ionizations induced by the femtosecond laser pulse and the subsequent temperature increase process are not included in this model. We directly calculate the stage of microsecond laser irradiation with an improved absorption coefficient at a high temperature. The absorption coefficient of sapphire for the microsecond laser is assumed to be 1200 m⁻¹ increased from 0.24 m⁻¹ due to the effect of the femtosecond laser pulse. The material properties used in the simulation are as follows: a density of 3.98 g·cm⁻³, a specific heat of 0.75 J·g⁻¹·K⁻¹, a melting point of 2323 K, and a refractive index of 1.76. The temperature-dependent thermal conductivity is shown in Fig. 9, in which it is assumed to remain constant for temperatures exceeding 1600 °C.

Fig. 9. Thermal conductivity.

Temperature-dependent thermal conductivity of sapphire used in the simulation.

The simulation results are shown in Fig. 10a, where 0 µs is defined as the onset of high absorption of the microsecond laser pulse. Under continuous irradiation of the microsecond laser, the material temperature increases, and the high-temperature region expands from the sample surface toward the sample bottom. The material is considered to be removed once the temperature reaches the melting point of 2323 K. The 2323 K temperature contour is indicated by a curve at each step. As the laser irradiation continues, the blue contour curve reveals the formation of a small hole that gradually deepens and widens. The changes of hole depth and drilling speed are given in Fig. 10(b). The trends of depth increasing and drilling speed are consistent with the experimental results shown in Fig.3(b). The hole depth (at 39 μs) and the maximum drilling speed in the simulation are 193 µm and 6.26 m·s⁻¹, respectively, close to the experiment values of 189 µm and 7.55 m·s⁻¹, indicating that the proposed laser machining mechanism based on temperature increase and high-temperature area expansion is reasonable. The difference is attributed to the simplification of the absorption coefficient. In the simulation, drilling starts at 7.8 µs, later than that in the experiment, where drilling is observable from ~1.4 µs. This difference implies that the absorption coefficient used in the simulation is smaller than the actual value at the initial stage. The simulation could be further improved by getting the bandgap change at high temperatures in the future. Nevertheless, this simulation model effectively demonstrates that the increased absorption coefficient and the expansion of high-temperature areas are the essential mechanism of laser machining in this method.

Fig. 10. Simulation results.

(a) Color indicates the temperature distribution. The curve represents the contour of 2323 K, corresponding to the melting region and the hole edge. (b) Hole depth and processing speed in simulations.

Conclusion

In this study, high-speed micromachining of sapphire has been achieved by combining a single femtosecond laser pulse with a single microsecond laser pulse. The cracks in the base material surrounding the processing regions are mitigated, and the drilling speed is improved by a factor of 10⁴ compared to conventional femtosecond laser percussion drilling with a repetition rate of 1 kHz. Pump-probe imaging is used to visulize the ultrafast phenomena induced by the femtosecond laser pulse. It reveals that free electrons are excited to form a plasma filament which has a very fast relaxation speed. A high-speed camera is employed to record the machining process by delivering a single microsecond laser pulse to the irradiation area of the femtosecond laser pulse. It shows that machining continues after the disappear of the plasma filament generagted by the femtosecond laser pulse. The machining speed quickly increases at the initial stage, and then gradually decreaes. Moreover, once the femtosecond laser pulse generates sufficient electron excitation to initiate the machining process, its energy has minimal effect on the characteristics of the drilled hole. The depth and diameter of the hole can be controlled by adjusting the parameters of the microsecond laser. Furthermore, a simulation model is developed based on thermal diffusion and laser propagation, which reveals that the machining mechanism in the proposed method is attributed to the improvement of the absorption coefficient and the expansion of high-temperature area. This work is expected to facilitate the precision and high-efficiency machining of hard brittle transparent materials, and also contribute to fundamental research of laser-matter interactions.

Author contributions

The research was conducted by G.R. under the supervision of Y.I. G.R. and Y.I. performed the experiments, analyzed the data, established the simulation model, and wrote the manuscript. H.S. helped with data collection. C.W. helped with simulations. All authors discussed the result.

Peer review

Peer review information

Communications Engineering thanks Xiaoming Yu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: [Philip Coatsworth].

Funding

Y.I. discloses support for the research of this work from Japan Science and Technology Agency PRESTO [JPMJPR22Q1], Japan Society for the Promotion of Science [25H00704] and MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) [JPMXS0118067246]. G.R., H.S., and C.W. declare no relevant funding.

Data availability

The data in this work are available from the corresponding author upon reasonable request.

Code availability

The codes used in this work are available from the corresponding author upon reasonable request.

Competing interests

The authors declare no competing interests.