Evolution mechanism of subsurface damage during laser machining process of fused silica

Yichi Han; Yichi Han; Yichi Han; Songlin Wan; Songlin Wan; Songlin Wan; Songlin Wan; Xiaocong Peng; Xiaocong Peng; Xiaocong Peng; Huan Chen; Huan Chen; Huan Chen; Shengshui Wang; Shengshui Wang; Shengshui Wang; Hanjie Li; Hanjie Li; Hanjie Li; Pandeng Jiang; Pandeng Jiang; Pandeng Jiang; Chaoyang Wei; Chaoyang Wei; Chaoyang Wei; Chaoyang Wei; Jianda Shao; Jianda Shao; Jianda Shao; Jianda Shao; Jianda Shao

doi:10.1364/OE.519053

1. Introduction

Fused silica, due to its excellent physical and chemical properties, is currently the prior choice material for lenses, windows, and diffractive optics in high-power laser systems such as the National Ignition Facility, Megajoule Laser Project, and SG-III [1–3]. However, SSD generated during the manufacturing process will strongly absorb sub-band-gap light, resulting in surface damage at low fluence [4]. Therefore, SSD becomes the bottleneck to restrict the development of high laser-induced damage threshold fused silica optics, and removing SSD is of great importance.

Nowadays, the elimination and suppression of SSD to improve the damage resistance of fused silica surfaces consists primarily of improving traditional process techniques. The improvement methods are mainly focused on the effective management of the SSD during the grinding process. LLNL employed a standard finishing strategy to remove the SSD, whereby smaller abrasives are used in subsequent grinding steps to remove SSD generated in the previous step [5]. However, when brittle and abrasive particles come into contact with the fused silica surface, the generated SSD inevitably penetrates deep below the surface [6]. Despite decades of research into ultra-precision grinding methods, such as electrolytic in-process dressing [7], and chemical action-assisted ultra-precision grinding [8], it has not been possible to eradicate SSD. Thus, the removal of SSD requires an accurate assessment and characterization of the distribution of SSD introduced during the grinding process.

To date, there are a number of measurement methods for SSD, including destructive and non-destructive evaluation [9]. While non-destructive techniques such as optical coherent tomography [10] and total internal reflection microscopy [11] provide valuable insights into SSD characterization, they can only quantitatively assess specific optical surfaces using expensive measuring equipment [12]. In contrast, destructive methods, such as magnetorheological finishing (MRF) taper polishing, can provide reliable and precise information on SSD [4,13]. However, this method has low efficiency and cumbersome procedures, restricting its application to inspecting localized areas and inevitably causing damage to the tested substrate; hereafter, it can only be measured indirectly through the test piece. Currently, there is no efficient method available to accurately assess the 3D-space morphology of SSD across the entire optics, while also integrating into the rapid grinding process. The absence of efficient 3D-space full aperture characterization methods for SSD during the grinding process makes the complete removal of SSD difficult, and it is necessary to develop novel methods to solve this challenge.

Due to non-contact and wear-free processing, there is growing concern over the laser radiation processing of fused silica [14]. Due to the minimal thermal damage during material removal process, short wavelength laser and ultrashort pulse laser are very suitable for processing fine features [15–18]. However, the processing efficiency limits their application in large-region processing [19,20]. In contrast, the high absorption of 10.6 µm CO₂ laser by fused silica glass increases the processing efficiency by more than an order of magnitude under the same energy fluence [21,22]. With great potential of 10.6 µm CO₂ laser in reducing process time and manufacturing cost, many works have been focused on ablating forming fused silica optics with CO₂ laser. However, most researchers are concerned about forming accuracy and efficiency, as well as thermal-induced cracking problems, and few reports have been made on the characterization and removal of SSD using CO₂ laser [23,24]. In our recent work, we used pulsed CO₂ laser ablation to remove materials and expose the microscale SSD generated during the grinding process [25]. This method demonstrates the feasibility of SSD removal and characterization in the three-dimensional (3D) space. However, it is unknown whether thermal strain and stress during the ablation process can lead to the formation of extended microcracks. Thus, it is necessary to verify the accuracy of characterization of SSD through theoretical simulation and experimental study.

In this work, the evolution behaviors and properties of representative radial SSD with different characteristic structural parameters during pulsed CO₂ laser layer-by-layer ablation are explicated by multi-physics simulated model and experimental investigation. This research provides a significant contribution to understanding the SSD removal process by laser layer-by-layer ablation strategies.

2. Model and theory

2.1 Simulation model

To accurately describe the SSD evolution using pulsed CO₂ laser layer-by-layer ablation, a multi-physics finite element model is established to study the coupling process between laser and fused silica with SSD. The schematic diagram of pulsed CO₂ laser layer-by-layer ablation of SSD on fused silica optics is shown in Fig. 1. The interaction between CO₂ laser and fused silica is a complex multi-physics coupling process, including different stages of heating and softening of material, viscous flow, evaporative ablation, cooling and freezing. The calculation of material temperature involves laser energy deposition, heat transfer, heat dissipation through convection and radiation, and recoil pressure. The calculation of micro-flow must take factors such as material interface, phase change, surface tension, Marangoni effect and viscosity coefficient into consideration. Although three-dimensional (3D) models provide more comprehensive simulations, their computational cost can be prohibitive. By comparing the simulated processing of fused silica without SSD using 2D and 3D models, it is found that the simulated results of the 2D model are very close to those of the 3D model. Therefore, a 2D model is established to study the evolution process of SSD.

Fig. 1. Mathematical model and boundary condition of laser layer-by-layer ablation.

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The mathematical model in this paper is established based on the following assumptions: (1) The material is isotropic and homogeneous, (2) Material flow in molten pool region is the laminar flow of incompressible Newtonian fluid, (3) Fused silica vapor is treated as the ideal gas, ignoring the absorption of laser energy by vapor plume.

The conduction process of laser energy inside the material can be described by the following heat conduction equation:

(1)$$\rho {C_p}(T)\frac{{\partial T}}{{\partial t}} + \nabla \cdot ( - K(T)\nabla T) = Q,$$

where ρ is the density, C_p(T) and K(T) are the specific heat capacity and thermal conductivity respectively, and Q represents the laser heating source, which is described as [26]:

(2)$$\left\{ \begin{array}{l} {Q_1} = {A}\frac{{2(1 - R)P}}{{\pi \omega_0^2}}\exp ( - \frac{{2{{(x - {v_s}t)}^2}}}{{\omega_0^2}})\exp ( - \alpha z)f(t)\\ {Q_2} = {A}\frac{{2(1 - R)P}}{{\pi \omega_0^2}}\exp ( - \frac{{2{{(x - {v_s}t)}^2}}}{{\omega_0^2}})\exp ( - \alpha z)f(t)\Gamma (h)\\ \alpha = \frac{{4\pi {n_k}(T)}}{\lambda }\\ R = \frac{{{{({n_i} - 1)}^2} + {n_k}{{(T)}^2}}}{{{{({n_i} + 1)}^2} + {n_k}{{(T)}^2}}} \end{array} \right.,$$

where A is the absorption rate, R is the reflectivity, P is the peak power of the rectangular pulse laser, ω₀ is the laser beam radius, v_s is the scan speed along the x direction, n is the ablation numbers, α is the absorption coefficient, Q₁ represents the heat source at the upper surface, Q₂ represents the heat source at the SSD position, f(t) is the time distribution function of the rectangular pulse, Γ(h) is the energy modulation function changing with depth (discussed in Section 2.2), n_i and n_k(T) are the real and imaginary components of the refractive index, respectively, and λ denotes the wavelength of the CO₂ laser.

When the temperature T of the material heated by the laser exceeds the vaporization temperature T_v of the material, the material is evaporated from the surface, and part of the heat is taken away by the vaporized particles. The evaporative heat flux is the product of vaporized mass flow rate M_v and latent heat of vaporization L_v, which can be expressed as [27]:

(3)$$\left\{ \begin{array}{l} qevap = {M_v} \times {L_v}\\ {M_v} = {P_{sat}}(T)\sqrt {\frac{M}{{2\pi {R_c}T}}} \\ {P_{sat}}(T) = {P_{atm}}\exp (\frac{{M{L_v}}}{R}(\frac{1}{{{T_v}}} - \frac{1}{T})) \end{array} \right.,$$

where M is the molecular weight of the molecules in the vapor phase, R_c is the ideal gas constant, P_sat is the vapor pressure, and P_atm is the standard atmospheric pressure. The deformed geometry method is used in the numerical simulation to simulate the erosion of the boundary by laser ablation. Since the solid-liquid phase transition process of the material is not considered, the ablation morphology of the material is mainly determined by the evaporation process. The material removal rate can be expressed as [28]:

(4)$$v = \frac{{{M_v}}}{{\rho {L_v}}}.$$

The fluid flow of fused silica is described by the Navier-Stokes equation [29]:

(5)$$\rho \frac{{\partial \vec{u}}}{{\partial t}} + \rho (\vec{u} \cdot \nabla )\vec{u} ={-} \nabla p + \rho \vec{g} + \eta (T){\nabla ^2}\vec{u}.$$

On this surface, the thermal capillary force (Marangoni effect) acts in the tangential direction, which is related to the temperature gradient. Meanwhile, the capillary force acts in the normal direction and its strength is proportional to the curvature of the surface profile. In this work, surface tension is a function of temperature that can be expressed as [30]:

(6)$$\left\{ \begin{array}{l} {{\vec{\sigma }}_n} = k\sigma \\ \sigma = {\sigma_0} - \gamma (T - {T_m}) \end{array} \right.,$$

where k is the curvature of surface profile, σ₀ is the surface tension coefficient, and γ is the temperature derivative of surface tension. The Marangoni effect is expressed as [29]:

(7)$${\vec{\sigma }_t} = \frac{{\partial \sigma }}{{\partial T}}{\nabla _s}T \cdot \vec{t}$$

In the simulation process, the fused silica parameters of thermal conductivity, specific heat capacity, and viscosity are considered and taken from Refs. [31–33], other parameters are listed in Table 1.

Table 1. Simulation parameters of this model

View Table

2.2 Modulation theory of SSD on light transmission

To get a comprehensive description of the light transmission process in SSD, a scalar diffraction theoretical study is carried out. The modulation effect is derived from the wavefront interaction between the transmitted beam and SSD, and the light transmission is divided into local amplitude and phase modulations. The amplitudes and phase of the initial plane change with the coordinate plane position (x, y). We focus on the changes to study the SSD light transmittance on light field modulation. Fused silica has a strong absorption rate of CO₂ laser at 10.6 µm wavelength. Therefore, when the planar light wave passes through the SSD area, the light is completely obscured in the theoretical model, and the amplitude A of light intensity quickly decreases to zero. The downstream light field diffraction due to amplitude variation is defined as amplitude-type diffraction. Similarly, it is assumed that when the light wave passes through the SSD area, the phase offset of the outgoing beam from the SSD region occurs due to the difference in light path. The downstream light field diffraction due to this phase offset is defined as phase-type diffraction [39].

Figure 2 shows the schematic diagram for the theoretical calculation of downstream light field diffraction for cases where the fused silica with SSD is placed in the laser path. The SSD is located on the surface of fused silica. It is worth noting that a planar wave front is chosen only to calculate the light modulation curves of different SSD types, not to simulate the real process. Light diffraction occurs at a distance Z from the fused silica surface, and the electric vector E is regarded as scalar U(x, y, z).

Fig. 2. Sketch of the light field modulation caused by SSD on fused silica surface during laser layer-by-layer ablation process.

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When the plane light wave is emitted from the fused silica surface, a path difference arises in the light due to the effects of SSD depth. Through derivation, the phase of the light wave can be expressed as:

(8)$$\varphi (x,y,0) = \left\{ {\begin{array}{cc} {k(1 - {n_{si{o_2}}})\frac{{{h_0}}}{{{r_0} - {r_1}}}}&{{x^2} + {y^2} < {{({r_1} + ({r_0} - {r_1}) \cdot \frac{{{h_0} - h}}{{{h_0}}})}^2}}\\ {k(1 - {n_{si{o_2}}})\frac{{{h_0}}}{{{r_0} - {r_1}}} \cdot exp(\frac{{{r_0}^2 - ({x^2} + {y^2})}}{{{r_0}^2}})}&{{{({r_1} + ({r_0} - {r_1}) \cdot \frac{{{h_0} - h}}{{{h_0}}})}^2} \le {x^2} + {y^2} \le {r_0}^2}\\ 0&{{x^2} + {y^2} > {r_0}^2} \end{array}} \right.,$$

where n_sio2 is the refractive index of fused silica, k is the wave number of the light, h represents the SSD depth, h₀ is the maximum depth of SSD, r₀ is half the opening width of the SSD, and r₁ is half the bottom width of the SSD.

However, due to the absorption of the incident light on the fused silica surface and SSD inside, the amplitude of the input light will decrease to 0 V/m. Assuming that the input light amplitude is 1 V/m, the amplitude can be expressed as:

(9)$$A(x,y,0) = \left\{ {\begin{array}{cc} 1&{{x^2} + {y^2} < {{({r_1} + ({r_0} - {r_1}) \cdot ({h_0} - h)/{h_0})}^2}}\\ 0&{{x^2} + {y^2} \ge {{({r_1} + ({r_0} - {r_1}) \cdot ({h_0} - h)/{h_0})}^2}} \end{array}} \right.$$

Then, the complex amplitude at different positions can be expressed as [40]:

(10)$$U(x,y,0) = |A(x,y,0) \cdot {exp}[{j \cdot \varphi (x,y,0)} ]|.$$

At all passive points, U satisfies the Helmholtz equation, and U(x, y, 0) must be a particular solution to the equation corresponding to z = 0. According to the Fourier transform and the angular spectrum theory of light propagation, the general solution of the equation can be obtained as follows [41]:

(11)$$U(x,y,z) = {{{\cal F}}^{-1}}\left\{ {{{\cal F}}\{{U(x,y,0)} \}\cdot exp\left[ {jkz\sqrt {1 - {{(\lambda {f_x})}^2} - {{(\lambda {f_y})}^2}} } \right]} \right\},$$

where ${\cal F}$ and ${{\cal F}}^{-1}$ denote the Fourier transform and the inverse Fourier transform, respectively. f_x and f_y are the coordinates of the plane wave in the x and y directions of the frequency domain, respectively.

Then, we obtained a relation for the complex amplitude change of the light field from z = 0 to a point in any downstream plane. The result of light propagation in the z-direction is represented in the frequency domain as the spectrum of the initial plane light wave field multiplied by a z-dependent phase delay factor.

For the solution of Eq. (11), the discrete Fourier transform can be solved by computer assistance. With the initial plane sampling width as L₀, and the sampling number as N × N, this expression can be rewritten into the following form [40]:

(12)$$\begin{array}{{c}} {U(p\Delta x,q\Delta y) = IFFT\left\{ {FFT\{{{U_0}({m\Delta {x_0},n\Delta {y_0}} )} \}\cdot exp\left[ {jkz\sqrt {1 - {{(\lambda p\Delta {f_x})}^2} - {{(\lambda q\Delta {f_y})}^2}} } \right]} \right\}}\\ {(p,q,m,n ={-} N/2, - N/2 + 1,\ldots ,N/2 - 1)} \end{array},$$

which includes Δx₀=Δy₀= L₀/N as the initial planar discrete Fourier transform, before the corresponding spatial sampling interval. Due to linear system theory, the phase delay factor in Eq. (11) is a transfer function of diffraction in the frequency domain. This shows that the diffraction problem can be viewed as a set of light field waves in a transformation process with a linear space-invariant system.

The above are the conditions that need to be satisfied for the diffraction model for fused silica with SSD. The modulation M is defined as the ratio between the maximum light intensity on the diffraction plane and the initial light intensity at different positions on the downstream light field. As the light intensity is at the spatial position, the modulation can be obtained by the amplitude function. Light intensity I is expressed as [42]:

(13)$$I \propto {|E |^2} = U \cdot {U^\ast }.$$

The light modulation M is defined as the ratio of the maximum light intensity on the observation plane to the initial input light intensity, which is defined as [42]:

(14)$$M = \frac{{{I_M}}}{{{I_0}}},$$

where I_M is the maximum light intensity induced by SSD in the diffracted field image, and I₀ is the intensity of the empty field without SSD.

In previous study, representative radial SSD with different characteristic structural parameters was mainly observed [43], shown in Fig. 3. The depth of SSD is basically in the range from 5 to 100 µm [44], and the width of the etched SSD is in the range from 1.5 µm to 8.1 µm [4]. Therefore, we calculated the downstream light field modulation behind fused silica surface with representative SSD I (with parameters of depth h₀= 20 µm, opening width d₀= 10 µm, and bottom width d₁= 0.5 µm) and SSD II (with parameters of depth h₀= 30 µm, opening width d₀= 15 µm, and bottom width d₁= 10 µm), respectively. Notably, the width of SSD is larger than the real SSD morphology, and the lateral dimension of SSD geometry used in simulations is simplified and modified to verify the experimental evolution process. The above equations are solved by running the program using MATLAB R2021a. Figures 4,5 show the distribution and intermediate section curves of input light amplitude, input light phase, and output light intensity with respect to propagation distance caused by SSD I and SSD II. As the propagation distance from the surface increases, the region of the input light field decreases due to the whole absorption of inner walls of SSD, and the input light phase keeps the same variation tendency with the morphology of SSD. According to the scalar diffraction theory, the output light intensity distribution is obtained, and the maximum output light intensity is at the center of the diffraction pattern.

Fig. 3. Schematics of SSD induced in a scratching process of polished fused silica optics.

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Fig. 4. Distribution and intermediate section curves of input light amplitude, input light phase, and output light intensity caused by SSD I with depth h₀ of 20 µm, opening width d₀ of 10 µm, and bottom width d₁ of 0.5 µm.

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Fig. 5. Distribution and intermediate section curves of input light amplitude, input light phase, and output light intensity caused by SSD II with depth h₀ of 30 µm, opening width d₀ of 15 µm, and bottom width d₁ of 10 µm.

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To obtain the modulation function Γ(h), the output light intensity at the center of the diffraction pattern is extracted, and light modulation M of two types of SSD is calculated under different SSD position according to Eq. (14). In Fig. 6, the light modulation decreases sharply first, and then decreases to a stable value with the increase of propagation depth. Then, the modulation function Γ(h) is fitted to describe the relationship between light modulation and propagation depth. Moreover, this modulation function proves the difference of light intensity between fused silica surface and SSD position, and the light intensity can be calculated precisely by scalar diffraction theory for further SSD evolution analysis during laser layer-by-layer ablation process.

Fig. 6. Light modulation curves of two types of SSD changing with propagation depth. (a) SSD I with depth h₀ of 20 µm, opening width d₀ of 10 µm, and bottom width d₁ of 0.5 µm; (b) SSD II with depth h₀ of 30 µm, opening width d₀ of 15 µm, and bottom width d₁ of 10 µm.

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3. Experimental setup

To verify the simulated results, we used femtosecond laser to prefabricate SSD on fused silica top surface. Femtosecond laser processing can control the morphology and size of prefabricated SSD from 5 to 100 µm in depth and from 5 to 45 µm in width. It is worth noting that chosen the sizes of prefabricated SSD are due to limited processing capabilities for manufacturing defects with higher aspect ratio or smaller diameter when using femtosecond laser processing, and not to known SSD morphology. Then, we conducted laser layer-by-layer ablation to achieve 3D-space SSD characterization, as shown in Fig. 7. For a sample with SSD, we first removed a layer of material on the top surface by laser ablation. The SSD was exposed to the surface and could be directly observed with a microscope at side surface. Then, layers were removed until no SSD was observed on the side surface. At this point, according to the total number of layers removed (N layers), the maximum SSD depth (Δz) was recorded.

Fig. 7. Schematic diagram of SSD prefabrication and removal process.

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The subsurface defects were prefabricated by the femtosecond laser (PH1-15W, PHAROS) processing system with a wavelength of 1030 nm and pulse duration of 290 fs, as shown in Fig. 8(a). A lens with a focal length of 150 mm was used to focus the beam to a diameter (1/e²) of about 0.03 mm. The air-bearing stage assembled in the system was used for sample translating. The prefabricate process of femtosecond laser processing was carried out in the air, and subsurface defects of different sizes were processed by changing the pulse energy with a repetition rate of 200 kHz. The laser layer-by-layer ablation experiments are conducted using CO₂ laser processing equipment, which was independently built by ourselves, as shown in Fig. 8(b). The Gaussian beam wavelength is 10.6 µm, and the signal generator (FY6900, FeelElec) adjusts the output of the CO₂ laser (Diamond Cx-10, Coherent). In our experiments, the signal generator modulates the laser to operate at a high modulation frequency (95 kHz) and duty cycle to reach quasi-continuous output with an average power of 26.5 W. Then, the quasi-CW laser beam is modulated into a rectangular pulse beam with a frequency of 1 kHz by an acousto-optic modulator. By changing the duty cycle through the acousto-optic modulator (AOM), ablation pulses with different pulse durations can be obtained, shown in Fig. 8(c). The focused CO₂ laser beam moves on the fused silica surface by the F-theta lens with a radius of 83.5 µm (1/e²). A unidirectional raster-scanning strategy was used in the laser layer-by-layer ablation experiments (Fig. 8(d)). In order to achieve homogeneous ablation, the laser pulses overlap in both scan and feed directions. The pulse distance d_x in scan direction is determined by dividing the scan speed v_scan (25.5 mm/s) by the pulse frequency f_rep (1 kHz). The pulse spacing d_y in feed direction describes the distance between two parallel scan vectors. To ensure that the spatial resolution is the same in scan and feed direction, pulse overlap in x and y direction was set to be the same in all cases (d_x = d_y= 25.5 µm). The sample with SSD is positioned on the precision three-dimensional mobile platform and ablated layer-by-layer to achieve SSD removal (Fig. 8(e)). The initial samples are ground and polished before experiments. Before every experiment, all samples (Heraeus Suprasil 311) with sizes of 20 mm × 20 mm × 6 mm were submerged in an ultrasonically agitated deionized water bath for 5 min, sprayed with deionized water for 5 min, and carefully air dried.

Fig. 8. Schematic diagram consisting of (a) femtosecond laser processing equipment; (b)CO₂ laser layer-by-layer ablation equipment; (c) pulse modulation principle; (d) procedural principle of scanning path; (e) SSD removal process.

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Subsequently, SSD images were obtained using an Olympus microscope (OLYMPUS BX53). The depth of SSD evolution is observed at the SSD position, and the images of SSD position were recorded at a magnification of 50× (NA = 0.8). The ablation depth per layer is obtained by comparing the height differences inside and outside the ablation fields at the edge position and the images were recorded at a magnification of 20× (NA = 0.5) The uncertainty of the side-view measures with the microscope is about ±0.1 µm.

4. Results and discussion

4.1 Simulated analysis of SSD evolution process

Based on the simulated model established in Section 2, the evolution process of SSD on the surface of fused silica with different sizes was numerically analyzed under laser layer-by-layer ablation. Two representative SSD evolution processes were simulated as follows. The first SSD evolution process is shown in Fig. 9(a) with depth h₀ of 20 µm, opening width d₀ of 10 µm, and bottom width d₁ of 0.5 µm. The depth of SSD decreases with increasing the ablation numbers until the SSD is completely removed. However, healing phenomenon occurs at the bottom position of the SSD at the 6^th ablation and subsequently the bottom position begins to extend at the 8^th ablation. By extracting the surface profile, the morphology at different ablation layers is illustrated in Fig. 9(b). When the fused silica is ablated 20 µm, the SSD depth is extended by 1.03 µm. The SSD is not completely removed until the fused silica surface has been ablated to 11 layers of 22.1 µm, which demonstrates that extension due to evaporation is produced during the ablation process.

Fig. 9. (a) SSD evolution processes with depth h₀ of 20 µm, opening width d₀ of 10 µm, and bottom width d₁ of 0.5 µm; (b)Top surface morphology at different ablation numbers.

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Through the model simulation, we compared the maximum top surface temperature at 6060 µs under different ablation numbers (Fig. 10(a)). There is an obvious temperature difference at the SSD location due to the difference in laser energy, and the temperature difference decreases with the increase of ablation numbers (Fig. 10(b)). Plus, the maximum thermodynamic temperature of the top surface without SSD and the bottom position of SSD at different ablation numbers are exhibited in Figs. 10(c-d). In Fig. 10(c), the maximum temperature of top surface under different ablation numbers had little difference and maintained a similar trend during each processing cycle. However, the maximum thermodynamic temperature of the bottom position of SSD is different under different ablation numbers (Fig. 10(d)). For the first ablation, the maximum temperature is under the melting temperature, and the SSD will not extend. For the sixth and seventh ablation, the maximum thermodynamic temperatures are between melting temperature (1800 K) and evaporation temperature (2200 K), which ensures that the material undergoes melting process successively. The bottom position of SSD will melt flow due to the Marangoni effect and surface tension [30]. When the tenth ablation occurs, the maximum thermodynamic temperature has exceeded the evaporation temperature and the bottom position of SSD is removed leading to extension due to evaporation.

Fig. 10. (a) Maximum thermodynamic temperature of top surface without SSD; (b) Maximum thermodynamic temperature of the bottom position of SSD; (c) Maximum top surface temperature at 6060 µs under different ablation numbers; (d) Temperature difference of the 1^st, 6^th, 7^th, 10^th, and 11^th ablation at 6060 µs.

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Plus, we studied the velocity field and temperature distribution at 6060 µs under three representative ablations, which represent three stages of SSD evolution (Fig. 11). This time point (t = 6060 µs) is at the end of the seventh pulse duration. It represents the time when the material has just finished heating at the SSD position and is ready to cool. During the first ablation process, the direction of flow at the bottom position is straight down. However, the temperature at the bottom position of SSD is below melting temperature, and the material will not flow. In the process of the sixth ablation, the temperature at the bottom position of the SSD is between 1800 K and 2200 K. The melted material flows from both sides along the bottom of the molten pool to the center and then moves upward, and the bottom position of SSD is filled and healed. For the tenth ablation, the temperature at the bottom position of the SSD is above 2200 K and the flow field flows from the center region of the SSD to the edge. Therefore, the bottom position of SSD is removed and the SSD depth will extend.

The second evolution process is related to the SSD with broad bottom width d₁. Figure 12 shows the SSD evolution process with characteristic structural parameters of h₀= 30 µm, d₀= 15 µm, and d₁= 10 µm. Similarly, during the ablation process, the SSD depth gradually decreases. The SSD began to extend from the 8^th ablation and continued to extend 4.07 µm before being completely removed. Since this type of SSD has a broad bottom width d₁, more mass is needed to fill it. The molten material is unable to fill up the SSD downwards during the laser layer-by-layer ablation process, while the movement at the bottom position of SSD is relatively slow, thus no SSD healing occurs.

Fig. 11. Velocity field and temperature distribution at 6060 µs under the (a) 1^st ablation, (b) 6^th ablation, and (c) 10^th ablation with characteristic structural parameters of h₀= 20 µm, d₀= 10 µm, and d₁= 0.5 µm. The black dotted lines represent isotherms of 1800 K and 2200 K.

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Fig. 12. (a) SSD evolution processes with depth h₀ of 30 µm, opening width d₀ of 15 µm, and bottom width d₁ of 10 µm; (b)Top surface morphology under different ablation numbers. The white number represents the total ablation depth after the n^th ablation.

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Figure 13 shows the flow field distribution around the SSD under different ablation numbers at 6060 µs. For the first ablation, the depth of SSD exceeds that of the molten pool. Therefore, the flow trend formed by the property of the molten pool is the same as the surface tension. The SSD is so deep that temperature at the bottom does not reach the melting temperature. As a result, the viscosity coefficient at the bottom is very large, and the SSD is unable to extend. During the 6^th ablation process, although the temperature at the SSD bottom is between 1800 K and 2200 K, the SSD is not healed because more material is needed to fill, resulting in the healing speed to be slower. For the 10^th ablation, the bottom of the SSD reaches the evaporation temperature, and the velocity field goes straight down, resulting in the extension of the SSD.

Fig. 13. Velocity field and temperature distribution at 6060 µs under the (a) 1^st ablation, (b) 6^th ablation, and (c) the 10^th ablation with characteristic structural parameters of h₀= 30 µm, d₀= 15 µm, and d₁= 10 µm. The black dotted lines represent isotherms of 1800 K and 2200 K.

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4.2 Model verification and SSD evolution mechanism

To verify the correctness of simulation model, SSD with the same original morphologies of the simulated model is prefabricated using femtosecond laser. Then, a laser layer-by-layer ablation experiment was carried out on fused silica surface with SSD. Figure 14 represents the evolution process of SSD I (with characteristic structural parameters of h₀= 20.2 µm, d₀= 9.8 µm, and d₁= 0.6 µm) during CO₂ laser layer-by-layer ablation experiments. The actual SSD depth can be directly observed by microscope at the side view, and the ablation depth per layer is measured at the edge position of the ablation region. The actual SSD depth is compared with the ideal SSD depth during the layer-by-layer ablation process, and the difference represents the SSD depth variation. When the fused silica is ablated by 20.2 µm, the SSD depth is extended by 0.9 µm. The SSD is not entirely removed until the fused silica surface has been ablated to the 7th layer of 21.9 µm. The trend and value of SSD evolution are consistent with the model simulation.

Fig. 14. SSD position and edge position morphology of ablation region after laser layer-by-layer ablation. The SSD characteristic structural parameters are h₀= 20.2 µm, d₀= 9.8 µm, and d₁= 0.6 µm.

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Figure 15 represents the evolution of the simulated and experimental SSD depth and SSD depth variation as a function of the ablation depth. The graph reveals three stages in the SSD evolution, which are indicated by three different linear fits in Fig. 15(a) and schematically illustrated in Fig. 15(b). The first stage corresponds to the red linear fit in Fig. 15(a) and stage 1 in Fig. 15(b). The temperature of the bottom position of SSD is below the melting temperature, and the SSD depth variation remains unchanged. The second stage corresponds to the blue linear fit in Fig. 15(a) and stage 2 in Fig. 15(b). The temperature of the bottom position of SSD is between the melting temperature and the evaporation temperature, and the SSD depth variation decreases to less than 0 µm due to the healing process caused by melt flow of molten fused silica. In the third stage (brown linear fit in Fig. 15(a), stage 3 in Fig. 15(b)), SSD depth variation increases gradually to more than 0 µm with the increase of ablation times, where the ablation plume can expand freely in the ambient air above the SSD. Thus, the material of the SSD bottom is removed and the SSD depth extends.

Fig. 15. (a) Comparison of the simulated and experimental SSD depth and SSD depth variation with characteristic structural parameters of h₀= 20.2 µm, d₀= 9.8 µm, and d₁= 0.6 µm; (b) Schematic view of the three stages in the SSD evolution.

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Figure 16 shows the experimental images of SSD II (with characteristic structural parameters of h₀= 29.8 µm, d₀= 15.1 µm, and d₁= 10.0 µm) evolution process. The SSD depth decreases with the ablation numbers, and the SSD depth variation maintains at 0 µm at first, and then extends at the 3^rd ablation. When the fused silica is ablated by 29.9 µm, the SSD depth is extended by 2.0 µm. The SSD is not entirely removed until the fused silica surface has been ablated to the 7^th layer of 33.6 µm, which also shows a similar trend with the simulated results in Fig. 12.

Fig. 16. SSD position and edge position morphology of ablation region after laser layer-by-layer ablation. The SSD characteristic structural parameters are h₀= 29.8 µm, d₀= 15.1 µm, and d₁= 10.0 µm.

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Figure 17 represents the comparison of SSD depth and SSD depth variation between experiment and simulation. In the first stage (red linear fit in Fig. 17(a), stage 1 in Fig. 17(b)), the SSD bottom is below the ablation threshold, and the reduction in SSD depth is consistent with the layer-by-layer ablation depth. The second stage corresponds to the blue linear fit in Fig. 15(a) and stage 2 in Fig. 15(b). The temperature of the SSD bottom is above the evaporation temperature. However, the ablation plume is confined by the inner walls of SSD, leading to a slow extension rate of SSD depth variation (slope of the fit line). According to previous literature, this is supported by assuming a beam propagation inside the hole where the laser beam is subject to reflection under grazing incidence on the inner walls and multiple scattering [45,46]. At each reflection, a part of the energy is lost by material absorption, and supplementary losses are also caused by multi-directional scattering. In the third stage (brown linear fit in Fig. 17(a), stage 3 in Fig. 17(b)), the ablation plume can expand freely to the SSD bottom leading to an increase in the extension rate of SSD depth variation. Based on the above experimental results, the reliability of the laser layer-by-layer ablation model can be verified, and the evolution mechanism of fused silica with SSD is further revealed.

Fig. 17. (a) Comparison of the simulated and experimental SSD depth and SSD depth variation with characteristic structural parameters of h₀= 29.8 µm, d₀= 15.1 µm, and d₁= 10.0 µm; (b) Schematic view of the three stages in the SSD evolution.

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4.3 Influence of characteristic structural parameters on extended SSD depth

In order to develop the manufacturing strategy to suppress the extended SSD and improve the accuracy of SSD characterization after laser layer-by-layer ablation, it is necessary to find out the extension law of different original SSD. Thus, three characteristic parameters (SSD depth h₀, SSD opening width d₀, and SSD bottom width d₁) were selected to study their effects on the laser layer-by-layer ablation process via the multi-physics simulated model.

Figure 18 shows the extended SSD depth with different initial parameters after the initial SSD depth has just been ablated. The d₀ and d₁ here refer to the original parameters of the SSD before ablated. In Fig. 18(a), it is noticed that the initial extended SSD depth first decreases when increasing initial SSD depth and then maintains stable at 1.1 µm when the initial SSD depth reaches 30 µm. Plus, when the opening width gradually increases, the initial SSD depth at less than 30 µm increases, while the initial SSD depth at more than 30 µm remains almost unchanged. In Figs. 18(b-c), as the bottom width d₁ increases, the value of extended SSD depth shows a trend of increasing, and the stable initial SSD depth point gradually becomes larger from 30 µm to 40 µm. Based on the above analysis, the characterization correctness of laser layer-by-layer ablation is closely related to the characteristic structural parameters of SSD, and this method is more suitable for deep SSD with narrow widths.

Fig. 18. The simulated results of extended SSD depth varied with different characteristic structural parameters (h₀, d₀ and d₁).

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5. Conclusion

In this work, a model of the CO₂ laser layer-by-layer ablation process of SSD is established by taking energy deposition, heat transfer, microflow, light field modulation and defect morphology into consideration, and the effects of SSD on light field modulation were theoretically investigated based on scalar diffraction theory. Based on the simulated model, we analyzed two types of radial SSD evolution with different characteristic structural parameters. For the first type of SSD with narrow bottom width, the SSD depth variation keeps unchanged at first, then decreases due to the melt flow of material, and increases finally when the bottom position of SSD reaches the evaporation temperature. For the second type of SSD with wide bottom width, the SSD depth variation keeps 0 µm firstly, then increases slowly at the second stage confined by the inner walls of SSD, and extends quickly at the third stage. Through the comparison between laser layer-by-layer ablation experiment and simulation, experimental measurements demonstrate that the proposed model can precisely predict the SSD depth, and three stages of SSD depth variation are further proposed and elaborated. The influence of characteristic structural parameters on SSD is also elaborated, which provides the theoretical basis for characterizing SSD based on laser layer-by-layer ablation. In future work, more surface microstructures such as scratches, as well as their characteristic parameters will be taken into consideration, and reasonable compensation formula for the characterization of SSD depth will be introduced to further ensure the correctness of this laser layer-by-layer ablation strategies.

Funding

National Funded Postdoctoral Researchers Program (GZC20232816); Member of Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022246); Key projects of the Joint Fund for Astronomy of National Natural Science Funding of China (U1831211); Natural Science Foundation of Shanghai (21ZR1472000); National Natural Science Youth Foundation of China (62205352); Shanghai Sailing Program (20YF1454800); National Key Research and Development Program of China (2022YFB3403403).

Acknowledgements

The authors would like to thank the referees for their valuable suggestions and comments that have helped improve the paper.

Disclosures

The authors declare no competing interests.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter (Symbol)	Value	Unit
Laser peak power P	26.5	W
Laser beam radius ω₀	83.5	µm
Laser frequency f	1	kHz
Scanning speed v_s	25.5	mm·s^-1
Ideal gas constant R_c	8.314	J·mol^-1·K^-1
The absorption rate A	0.8 [34]	/
Melting temperature T_m	1800 [35]	K
Vaporization temperature T_v	2200 [36]	K
Latent heat of vaporization L_v	1.14e⁷ [27]	J·kg^-1
Molecular weight M	40 [37]	g·mol^-1
Radiation emissivity ε	0.8 [27]	/
Density ρ	2201 [26]	kg·m^-3
Imaginary part of refractive index n_k	1.82e⁻²+ 10.1e⁻⁵(T-273.15) [27]	/
Surface tension coefficient σ₀	0.38 [38]	N·m^-1
Temperature derivative of surface tension ∂σ/∂T	-6e^-5 [38]	N·m^-1·K^-1

Evolution mechanism of subsurface damage during laser machining process of fused silica

Abstract

1. Introduction

2. Model and theory

2.1 Simulation model

2.2 Modulation theory of SSD on light transmission

3. Experimental setup

4. Results and discussion

4.1 Simulated analysis of SSD evolution process

4.2 Model verification and SSD evolution mechanism

4.3 Influence of characteristic structural parameters on extended SSD depth

5. Conclusion

Funding

Acknowledgements

Disclosures

Data availability

References

Data availability

Cited By

Figures (18)

Tables (1)

Equations (14)

Optics Express