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Abstract
Optical aberrations are a critical issue for tight focusing and high precision manufacturing with ultrashort pulsed laser radiation in transparent media. Controlling the wave front of ultrashort laser pulses enable the correction of low order phase front distortion and significantly enhances the simplification of laser-based manufacturing of 3D-parts in glass. The influence of system-inherent, dominating aberrations such as spherical and astigmatic aberrations affect the focal area, the beam caustic and therefore the focus intensity distribution. We correct these aberrations by means of a spatial light modulator (SLM) for various processing depths in glass thickness of up to 12 mm. This flexible aberration correction significantly simplifies the process control and scanning strategies for the selective laser induced etching process. The influence on the selectivity is investigated by comparing the three different focus conditions of the intrinsic microscope objective aberration corrected, the aberrated and the SLM aberration corrected beam profile. The previously necessary pulse energy adjustment for different z positions in the glass volume is compensated via SLM aberration correction in the end. Furthermore, the spatial extend of the modified and etched area is investigated. In consequence, a simplified scan strategy and depth-independent processing parameters can be achieved for the selective laser induced etching process.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The so-called selective laser induced etching (SLE) process is a two-step process for fabrication of transparent materials micro components. In the first step, modifications are inscribed inside the bulk material of the transparent material, like glass or sapphire, with ultrashort pulsed (USP) laser radiation. Subsequently, the sample is etched along these structures. The fabrication of complex microstructures of micrometer precision with SLE requires high control of tightly focused laser pulses with respect to pulse energy, pulse duration, focus volume and the resulting intensity. The uniformity and control of these laser parameters during the process is required. The current state of the SLE process is limited to depth-dependent pulse energies and depth-dependent aspect ratios (width to length) of the focus volume and the resulting modification. This must be considered for the design of scan strategies for each structure. A constant modification volume, constant modification threshold and a constant pulse energy for different z-positions would be a great simplification of process design. In consequence, a reduction of complexity in designing scanning strategies will lead to a significant simplification of the SLE process, which is of utmost importance for its acceptance and economic use.
USP laser radiation provides the ability to structure and modify all materials. Ultrashort laser pulses and strong focusing conditions lead to high peak intensities > 1013 W/cm2. The high intensities lead to ionization due to non-linear absorption mechanisms in transparent dielectrics like glasses for visible and near-visible wavelengths [1–3]. The highly localized absorption zone generates in-volume modifications in transparent dielectrics. In fused silica, these modifications lead to reduced resistance to etching agents such as aqueous KOH or HF. Thus, etching channels in fused silica with selectivities of more than 1400:1 can be achieved by direct laser writing with a subsequent wet chemical etching process [4–12]. The SLE process can be applied for the fabrication of complex microstructures in glass components. Prominent applications are microfluidics [6,13–17], sensors [8,18], optics [19–21] and opto-couplers or quantum components [22,23].The SLE process is a combined process of in-volume USP laser modification and subsequent wet-chemical etching. The initial step of the SLE process chain is the conversion of a CAD file of the final 3D-part into a 2.5-D part and the layer wise calculation of scan vectors. Scanning of the USP laser radiation in the fused silica bulk material along the scan vectors is realized via microscanner.
For transparent materials like glasses the absorption mechanisms are quite complex. The high peak intensity initially causes non-linear absorption effects like multiphoton and tunnel ionization. Subsequently, ionized electrons are able to absorb incident photons via inverse Bremsstrahlung. The absorbed optical energy is transferred to the lattice via impact ionization. The ionized electrons form a localized plasma in the focus volume. Due to electron phonon coupling the absorbed optical energy is transferred from the electronic subsystem to the lattice of the bulk material. Here, the transferred energy generates in-volume microstructures with increased etching rates. Different phenomena and dependencies such as non-linear absorption and accumulative processes are stated in literature due to the dielectric properties of the processed material and are of paramount importance for the occurrence of the process regime. [2,9–11,24–32]
The main origin of the increased etching rates of fused silica modified by USP laser radiation are so-called nanogratings and changed chemical bonds. The nanogratings are self-organized periodic structures which result from local plasma micro-explosions due to the electron plasma [11]. The change of chemical bonds and an increased penetration speed of aqueous KOH or HF in the modified nanogratings are attributed to increased etching rates compared to intrinsic fused silica [5,11,29,33,34]. The change of hexagonal chemical bonds to trigonal rings in fused silica may be another contribution for increased etching rates [35]. Also, the dissociation of SiO2 to SiO and O2 is predicted to increase the etching rate in fused silica [36]. The etching rate and therefore the selectivity of etching channels depends on the orientation of the polarization of incident laser pulses towards the feed velocity direction. Polarization perpendicular to the feed velocity direction yields highest selectivities [5,11,37].
The nanogratings and therefore etchable structures are created in a certain pulse energy range at a defined depth beneath the workpiece surface [9]. For constant focusing conditions the intensity profile changes in dependance of the focusing depth due to spherical aberrations [38–42]. This effect is especially important for the SLE process and has to be compensated. One way to eliminate this effect is the utilization of spherical aberration corrected optical systems for a fixed depth [42]. Another way to account this is to adjust the pulse energy as a function of focusing depth. Aberrated beams cause an increased focus volume which leads to a spatially increased modification, reduced precision and also affects etching selectivities [30]. Furthermore, higher pulse energies are necessary to reach the modification threshold for an extended volume to generate the modification.
A technical solution for the customized correction of spherical aberrations for USP processing is the use of spatial light modulators (SLM). The basic principle to maintain the process windows of USP in-volume structuring for transparent materials up to a depth of $2.4\; \textrm{mm}$ have been demonstrated [40,41,43–45]. Salter et al. applied a phase correction function to correct spherical aberrations up to $2.4\; \textrm{mm}$ in fused silica with a focusing condition of $NA = 0.5$ and up to $1\; \textrm{mm}$ with $NA = 0.75$ [40]. Kotenis et al. used Zernike coefficient based phase corrections to correct spherical aberration with focusing conditions of $NA = 0.9$ in soda-lime glass in focusing depth up to 1 mm [41]. Mauclair et al. wrote waveguides inside BK7 glass up to 3 mm in depth, using a SLM for dynamic aberration correction [43]. Huang et al. demonstrated the aberration correction for laser-written waveguides in depths up to $1.2\; {\mathrm{\mu} \mathrm{m}}$ [46]. Alimohammadian et al. applied conical-phase fronts with an SLM to elongate the focal volume for generating nanostructures with subsequent chemical etching [44,45]. The applied conical-shaped phase front is limited suitable to correct spherical aberrations due to the linear nature of the correction polynomial.
In this study, a concept for the simplification of the SLE scanning strategy and depth-independent process parameters is presented. In this context, we demonstrate the dynamic correction of spherical aberration and astigmatism in fused silica of up to $12\; \textrm{mm}$ thickness. We apply Zernike polynomial-based phase masks on a Liquid Crystal on Silicon (LCoS) SLM to compensate beam distortions, which leads to a depth-independent modification and in consequence to a simplification of the SLE process. In contrast to Salter et al. [40] and in accordance to Kotenis et al. [41] we utilized Zernike polynomial based phase masks to correct the spherical aberrations. The advantage of this approach is that we are also able to correct other optical aberrations such as coma and astigmatism. Furthermore, we expect that the Zernike coefficients are predictable for each depth in the glass volume, once the system is calibrated for at least two glass thicknesses. This aspect is necessary for the capability of changing the modification depth continuously in standard fabrication environment. The phase correction method, the utilized setup and the sample processing are explained in section 2. The aberration correction is verified by beam caustic measurements in section 3. Afterwards, three different processing regimes of the SLE process are demonstrated: 1.) intrinsic microscope objective aberration corrected case, 2.) aberrated case and 3.) SLM aberration corrected case. The evaluation of the successful correction of aberrations for the SLE process is based on the analysis of the observed selectivities in combination with images of the laser induced, pre-etched and etched microstructures. Based on this, a depth independent process window with a constant pulse energy can be defined. Due to this decoupling of scan strategy and pulse energy a significant simplification of CAM/CAD design is achieved as discussed in section 4.
2. Phase correction and experimental setup
In this section the application of Zernike polynomial-based phase masks is explained, and the utilized setup is described. Since the SLE process requires tightly focused USP laser radiation, the difference between normal incidence of the central part of the beam and the outer part of the beam under a small incidence angle of approximately 24° in air is not neglectable. If the laser radiation is focused into a glass sample, the refractive index mismatch between air (${n_1}$) and glass (${n_2}$) causes refraction, which is described by Snell’s law. [47] This leads to wavefront aberrations due to differences in the optical path length. The theoretical background for the application of Zernike polynomials for aberration correction can be found in [48–52].
The resulting phase difference can be written in the following form:
To study the aberration correction a system for processing fused silica consisting of an USP laser system TRUMPF TruMicro2000 with a central wavelength of $\lambda = 1030\; \textrm{nm}$, ${M^2} < 1.2$, a pulse duration of $\tau = 1\; \textrm{ps}$, a repetition rate of ${f_{\textrm{rep}}} = 700\; \textrm{kHz}$ and an average power of $\bar{P} = \; 20\; \textrm{W}$ is utilized. The aberration correction is accomplished with an LCoS SLM (Hamamatsu, Modell: X11840-09) with a spatial resolution of $800 \times 600$ pixels. The SLM is utilized in SVGA operation mode and calibrated with the method described by Ronzitti et al. [53]. The laser radiation is guided from the laser source over the SLM through a microscanner with a microscope objective (Mitutoyo LCD Plan APO NIR 20x/0.4 NA). The microscanner is a galvoscanner (Scanlab intelliScan 14) with an advanced optical system to direct the laser pulses through a microscope objective. A quarter wave plate is used to apply circular polarization. The microscope objective has a fixed spherical aberration correction for a nominal depth in glass of $1.1\; \textrm{mm}$. The SLM plane is projected into the microscanner. An xyz-axis system (AEROTECH Pro165LM, Pro225, Pro115) is utilized for sample positioning (Fig. 1).
Fig. 1. Schematic utilized setup consisting of a USP laser source, LCoS SLM, microscanner, microscope objective and $xyz$-positioning system.
Beam caustic measurements are conducted to analyze the aberrations in the focus region. Therefore, a magnifying optical system consisting of a microscope objective (Olympus, LMPLFLN20X), a plano-convex lens (Thorlabs LA1509) and a beam profile camera (Spiricon SP620U) is placed under the sample. The beam profile camera is not depicted in Fig. 1. The beam profile is recorded in multiple z-planes with a step size of $10\; \mathrm{\mu} \textrm{m}$ around to the focal plane. All images are recorded with equal camera settings. Thus, the intensity distributions for all cases are directly comparable. The recorded beam profiles are analyzed with regard to beam radius $r(z )$ and maximum intensity $I(z )$ by fitting a Gaussian beam profile to the horizontal, vertical and both diagonal cross sections. For each z-position 16 images are recorded. The standard deviation of the beam radius $r(z )$ and the maximum intensity $I(z )$ indicates the precision of the measurement in terms of repeatability. The focus beam diameter ${r_0}$, the focus peak Intensity ${I_0}$ and the Rayleigh length ${z_\textrm{R}}$ are determined by fitting
to the beam radius and by fitting to the peak intensity of the different z-planes.To receive the phase front correction for a certain depth, the focus peak intensity is maximized while the beam radius and the Rayleigh length are minimized. The Zernike coefficients for astigmatism, coma and spherical aberration are determined. The aberration corrections are executed for the overall optical system. For this case we assume that the imaging optics as well as the thin layer of glass material behind the in-volume focus have neglectable effect on this value. The sample is processed $200\; {\mathrm{\mu} \mathrm{m}}$ above the rear side. The feed rate of $150\; \textrm{mm}/\textrm{s}$, the repetition rate of ${f_{\textrm{Rep}}} = 700\; \textrm{kHz}$ and the pulse duration of $\tau = 1\; \textrm{ps}$ are constant for all experiments. These parameters are based on the parameters described by Gottmann et. al [10]. Circular polarization avoids polarization effects in dependence of the scanning direction. To neglect effects of the so-called pulse front tilt [54–56], which is relevant for the SLE process, the samples are processed in forward direction only. Thus, the pulse front tilt might be different from 0, but constant for all experiments. A set of five lines is structured, etched and analyzed for every parameter. For the wet etching process the sample is separated orthogonally to the modification direction. One part is etched in aqueous KOH ($8\; \textrm{mol}/\textrm{l}$) for 24 hours. The etched and unetched modifications are analyzed microscopically with respect to width and modification structure, and the channel length of the etched samples is determined. The ratio of channel length and etching duration is the etching rate $\rho $. The characteristic property of parameters for a successful SLE processing is the selectivity:
with the etching rate ${\rho _{\textrm{unmod}}}$ of the unmodified glass volume and the etching rate ${\rho _{\textrm{mod}}}$ of the modified glass volume. The etching rate ${\rho _{\textrm{unmod}}}$ is determined via the change of the glass thickness by measuring the glass thickness before and after the etching process.3. Wave front manipulation
In this study the beam profile measurement for aberration analysis is preferred over other methods like wavefront measurements to directly compare the focus intensities. Due to the quadratic terms in the radial Zernike polynomial for the spherical aberration ${Z_{11}} = \sqrt 5 ({6{\rho^4} - 6{\rho^2} + 1} )$ and the defocus Zernike polynomial ${Z_4} = \sqrt 3 ({2{\rho^2} - 1} )$ the wavefront analysis with a Shack-Hartman wavefront sensor leads to mixed outputs of the Zernike coefficients ${c_4}$ and ${c_{11}}$. Thus, the beam profile measurements are more suitable for demonstrated application. To analyze the influence of aberrations on the SLE process, the phase of the laser beam is manipulated with the SLM. For fused silica with thicknesses of $1\; \textrm{mm}$, $3\; \textrm{mm}$, $5\; \textrm{mm}$, $8.5\; \textrm{mm}$ and $12\; \textrm{mm}$, the beam profile is measured in vicinity of the focal position. The beam profile measurements are performed as follows: To avoid absorption effects the focus is shifted approximately $1\; \textrm{mm}$ below the fused silica sample. Hence, the effect of aberrations can be investigated in isolation without being affected by absorption effects of laser radiation in the focus volume. The focus position relative to the sample does not affect the aberrations if the sample surface is placed in normal incidence. To minimize aberrations, the Zernike coefficients of the phase mask on the SLM are adjusted. The adjustment is realized by maximizing the peak intensity in the focal plane.
The approach to analyze the present aberrations is divided into two steps. First, the focal region of the non-corrected case, ${c_\textrm{i}} = 0$, is analyzed. In the second step, the astigmatism and the spherical aberration are corrected with suited values for the coefficients ${c_4}$, ${c_6}$ and ${c_{11}}$. Here, ${c_4}$ and ${c_6}$ correspond to the oblique and vertical astigmatism, respectively. For each thickness of fused silica, the beam radius and the peak intensity along the beam propagation axis are recorded. The beam intensity is normalized for direct comparison of the intensity of the measured beam profiles with and without spherical aberrations and astigmatism. From the caustic measurements, the beam radius ${w_0}$ in the focal plane and the Rayleigh length ${z_\textrm{R}}$ are determined. In the following, the analysis of aberration correction is performed for a fused silica sample with thickness of $12\; \textrm{mm}$. Afterwards, the aberration effects for different glass thicknesses are discussed.
3.1 No correction (ci = 0)
Figure 2(a) shows a homogeneous phase shift on the SLM, which leads to spherical aberrations in $12\; \textrm{mm}$ fused silica. For this case transversal beam profiles in a range from $- 30\; {\mathrm{\mu} \mathrm{m}}$ to $30\; {\mathrm{\mu} \mathrm{m}}$ are recorded. A Gaussian beam profile is measured as depicted in Fig. 2(b)-(d). In each beam profile the central intensity peak is enclosed by a lower intensity ring, which indicates spherical aberrations [41,57]. The beam radii for the planes $z \le 8\; {\mathrm{\mu} \mathrm{m}}$ are plotted in Fig. 2(e). The difference in the beam radius for $z > 0$ is attributed to the low intensity rings due to spherical aberrations. Therefore, the determination of the beam radius by a Gaussian fit is valid for beam profiles in planes $z < 8\; {\mathrm{\mu} \mathrm{m}}$. For z < 20 µm, a difference between the extent of the ring around the center in the intensity distribution in positive diagonal direction d(+) (from lower left to upper right) and negative diagonal direction d(-) (from upper left to lower right) is observed, which is attributed to astigmatism.
Fig. 2. Calculated phase mask on the SLM (a). Camera images to determine beam radius and peak intensity at different z-positions (b-d). Measured beam radius (e) and peak intensities (f) (x, y and both diagonal cross sections) in dependence on different focus positions in $12\; {\rm{mm}}$ fused silica with maximum aberration.
A minimum beam radius of ${r_0} = 2.36 \pm 0.03\; {\mathrm{\mu} \mathrm{m}}$ is determined. The peak intensity in z direction is depicted in Fig. 2(f). The fit of Eq. (3) yields a maximum peak intensity of ${I^{\textrm{max}}} = 844 \pm 2\; \textrm{cts}$ and a Rayleigh length of ${z_\textrm{R}} = 39.5 \pm 0.6\; {\mathrm{\mu} \mathrm{m}}$. Both, minimum beam radius and Rayleigh length, exceed the measured values of the utilized microscope objective in air of $r = 1.96 \pm 0.02\; {\mathrm{\mu} \mathrm{m}}$ and ${z_\textrm{R}} = 14.9 \pm 0.6\; {\mathrm{\mu} \mathrm{m}}$. The focus elongation and expansion of the beam radius due to aberrations is detected.
3.2 Spherical aberration and astigmatism correction
The correction of astigmatism and spherical aberrations leads to Zernike coefficients of ${c_4} ={-} 0.2$, ${c_6} ={-} 0.2$ and ${c_{11}} ={-} 1.35$. The resulting phase mask is depicted in Fig. 3(a). The phase mask is slightly elliptic due to astigmatism correction. The number of phase shifts is increased outside the center due to the quadratic influence of the beam radius in the corresponding Zernike polynomial. The intensity ring from the case without correction (Fig. 2(b)-(d)) vanished due to the spherical aberration correction. The beam profiles have a single intensity region. The coefficients ${c_4}$ and ${c_6}$ cause an elliptic shape along the diagonal axes. All resulting beam profiles exhibit radially symmetric beam profiles (see Fig. 3(b)-(d)). The beam radii along z direction are similar for all four cross sections (X, Y, d(+) and d(-)). This indicates the absence of astigmatism.
Fig. 3. Calculated phase mask on the SLM (a). Camera images to determine beam radius and peak intensity at different z-positions (b-d). Measured beam radius (e) and peak intensities (f) (x, y and both diagonal cross sections) in dependence on different focus positions in $12\; {\rm{mm}}$ fused silica with spherical aberration and astigmatism correction.
The minimum beam radius is determined by a fit of Eq. (2) to ${r_0} = 1.60 \pm 0.03\; {\mathrm{\mu} \mathrm{m}}$. The resulting maximum peak intensity and Rayleigh length by a fit of Eq. (3) to the intensity curve from Fig. 3(f) are ${I^{\textrm{max}}} = 3555 \pm 134\; \textrm{cts}$ and ${z_\textrm{R}} = 7.6 \pm 0.5\; {\mathrm{\mu} \mathrm{m}}$. Thus, both beam radius and Rayleigh length decrease significantly below the case ci = 0 without correction. Consequently, the maximum intensity increases. The shift of the minimum beam radius and maximum intensity in the focal plane corresponds to the quadratic term in the Zernike polynomial for astigmatism and spherical aberration which has a defocusing effect. The smaller beam radius and Rayleigh length compared to focusing in air result due to the used microscope objective, which is intrinsically aberration corrected for a glass thickness of $1.1\; \textrm{mm}$.
The results show a strong dependence of the beam profile on the spherical aberration and astigmatism. The observed distortion is mainly determined by the spherical aberrations. The ring profile around the central intensity peak and the elliptic beam profiles outside the focus region as evidence of the presence of spherical aberrations and astigmatism vanish for the applied phase mask. The flexible correction of beam radius extension and focus elongation is demonstrated by applying Zernike distributed phase masks on a SLM.
3.3 Beam caustic measurements for different glass thicknesses
In the following, the impact of the glass thickness on the measured beam radius and the Rayleigh length is investigated. The minimum beam radii and the Rayleigh length for all glass thicknesses and the two steps of correction are shown in Fig. 4. The standard deviation of ${r_0}$ and ${z_\textrm{R}}$ is determined by the fit of Eq. (2) and Eq. (3), respectively.
Fig. 4. Minimum beam radius ${r_0}$ (left) and Rayleigh length ${z_R}$ (right) in dependency on glass thickness without correction (red) and with spherical aberration and astigmatism correction (blue).
The results of the non-corrected beams with a phase mask for constant phase shift (red curves) exhibit a minimum beam radius of ${r_0} = 1.74 \pm 0.03\; {\mathrm{\mu} \mathrm{m}}$ and a minimum Rayleigh length of ${z_\textrm{R}} = 9.7 \pm 0.6\; {\mathrm{\mu} \mathrm{m}}$ for glass thicknesses of $3\; \textrm{mm}$. For the $1\; \textrm{mm}$ sample the beam radius and the Rayleigh length are ${r_0} = 1.91 \pm 0.04\; {\mathrm{\mu} \mathrm{m}}$ and ${z_\textrm{R}} = 12.3 \pm 0.7\; {\mathrm{\mu} \mathrm{m}}$. For $d > 3\; \textrm{mm}$ both, beam radius and Rayleigh length, increase nearly linear.
For the correction of astigmatism and spherical aberrations, the Zernike coefficient ${c_{11}}$ is determined to 0.15, -0.05, -0.35, -0.9 and -1.35 for thicknesses $1$, $3$, $5$, $8.5$ and $12\; \textrm{mm}$ respectively (see Fig. 5). The coefficient decreases linearly with the glass thickness as expected from Eq. (1). The linear behavior allows the prediction of the Zernike coefficients for all depths in the glass volume after a calibration for the specific optical systems for at least two glass thicknesses. The Zernike coefficients for the astigmatism correction of ${c_4} ={-} 0.2$ and ${c_6} ={-} 0.2$ remain constant and are depth independent. The beam radii and Rayleigh length for all thicknesses are reduced significantly to a constant level compared to the non-corrected step. The minimum beam radius and minimum Rayleigh length are measured for $d = 3\; \textrm{mm}$ to ${r_0} = 1.56 \pm 0.02\; {\mathrm{\mu} \mathrm{m}}$ and ${z_\textrm{R}} = 7.1 \pm 0.2\; {\mathrm{\mu} \mathrm{m}}$. The independence of the beam radius and the Rayleigh length indicates the absence of spherical aberrations and astigmatism. Furthermore, the absence of intensity rings and elliptic shapes outside the focus position is observed for the corrected beam profiles of all thicknesses. Thus, the flexible spherical aberration and astigmatism correction in the beam profile is demonstrated for all thicknesses. In the following, details of the observed results are discussed.
Fig. 5. Zernike coefficient for correction of spherical aberrations ${c_{11}}$ in dependence on the glass thickness.
Since the used focusing microscope objective is aberration corrected for a glass thickness d = $1.1\; \textrm{mm}$, the beam radius and the Rayleigh length are expected to be minimized. Our experiments show the minimum beam radius and Rayleigh length at $d = 3\; \textrm{mm}$. The shift of the position of the optimized beam is attributed to a change of spherical aberrations caused by the optical system. In our setup, the optics of the Relay system in the setup of the SLM and the microscanner are spherical lenses. Therefore, the shift of the minimized spherical aberrations towards greater glass thicknesses is attributed to the overall optical system. The minimum aberrated glass depth of the whole optical system is estimated between $1\; \textrm{mm}$ and $3\; \textrm{mm}$ due to the flatter slope between $d = 1\; \textrm{mm}$ and $d = 3\; \textrm{mm}$ than between $d = 3\; \textrm{mm}$ and $d = 5\; \textrm{mm}$.
For $d = 3\; \textrm{mm}$ the correction of astigmatism has a higher impact on the beam radius compared to the correction of spherical aberration. In our case, the spherical aberrations have a stronger impact on the beam radius and the Rayleigh length compared to the correction of astigmatism. Since the astigmatism is almost constant, the astigmatism is attributed to be caused mainly by the optical system. The spherical aberration is caused by the glass sample. This is in accordance with theory because for normal incidence of the laser beam on the fused silica sample one does not expect astigmatism. These experimental results confirm the assumption that Zernike polynomials without an angular dependency are sufficient to describe the observed aberrations.
4. Aberration correction for SLE process
The impact of the non-corrected beam profiles and the spherical aberration and astigmatism corrected beam profiles is investigated for the SLE process. For this purpose, three cases are investigated (see also Fig. 9):
- 1. The SLE process is performed with the non-corrected beam profile. A single line is structured in 1.1$\textrm{mm}$ depth which is attributed to the nominal aberration free or at least minimum aberrated depth of the microscope objective (Mitutoyo LCD Plan APO NIR 20x/0.4 NA). In the following, we call this case ‘microscope objective corrected aberration’.
- 2. The focus is shifted $0.2\; \textrm{mm}$ above the backside of the sample with $12\; {\mathrm{\mu} \mathrm{m}}$ thickness without active correction of the SLM. At this depth the measured aberrations of the whole thickness are present. In the following, we call this case ‘maximum aberration’.
- 3. The spherical aberration and astigmatism corrected beam profile is shifted at the same depth $0.2\; \textrm{mm}$ above the backside of the sample with $12\; {\mathrm{\mu} \mathrm{m}}$ thickness. At this depth nearly no aberration should be present since the beam is corrected. In the following, we call this case ‘SLM corrected aberration’.
These three cases are compared to each with regard to selectivities and modification geometry. For all experiments a repetition rate of ${f_{\textrm{Rep}}}=700\; \textrm{kHz}$, a pulse duration of ${\tau _\textrm{P}}=1\; \textrm{ps}$ and a feed velocity of $150\; \textrm{mm}/\textrm{s}$ are used. The pulse energy under the microscope objective is varied from $150\; \textrm{nJ}$ to $5.6\; \mathrm{\mu} \text{J}$. The conservation of the process regime due to aberration correction, which yields the independence of depth and pulse energy for the SLE process, is discussed first. The maintained extent of the volume in direction of laser propagation and the flexibility of the aspect ratio of the etched channels are analyzed subsequently.
4.1 Development of depth independent process windows
The selectivities of the aforementioned three cases are plotted in dependence on the pulse energy in Fig. 6. The selectivity of the microscope objective corrected aberration case (green) rapidly increases between ${E_\textrm{P}} = 300$ nJ and ${E_\textrm{P}} = 400\; \textrm{nJ}$ from 0 to $S > 150$. In the range of ${E_\textrm{P}} = 400\; \textrm{nJ}$ to ${E_\textrm{P}} = 1.1\; \mathrm{\mu} \text{J}$ the selectivity saturates ($S > 150$). For ${E_\textrm{P}} > 1.2\; \mathrm{\mu} \text{J}$ the selectivity drops rapidly on a selectivity level of $S < 150$ with a minimum at ${E_\textrm{P}} = 1.44\; \mathrm{\mu} \text{J}$. This is consistent with results from other groups for circular polarized laser radiation and the mechanisms which lead to the regime of the high selectivity plateau are attributed to the stated phenomena of nanogratings and changed chemical bondings (refer to [9,30,37]). The maximum selectivity is approximately five times smaller compared to [9] due to the circular polarization used in our experiments, which is chosen to maintain unidirectional processing.
Fig. 6. Selectivities in 12 ${\rm{mm}}$ fused silica sample for minimum aberrated case in 1.1 ${\rm{mm}}$ depth (green), maximum aberrated case in 11.8 ${\rm{mm}}$ depth (red) and aberration corrected case in 11.8 ${\rm{mm}}$ depth (blue).
Selectivities for the maximum aberrated case (red) are obtained for ${E_\textrm{P}} \ge 1.0\; \mathrm{\mu} \text{J}$. The selectivity increases over a range from ${E_\textrm{P}} = 1.0\; \mathrm{\mu} \text{J}$ to ${E_\textrm{P}} = 2.0\; \mathrm{\mu} \textrm{J}$ to $S > 200$. In comparison, the slope of the microscope objective corrected aberration case is approximately eight times steeper than the slope of the minimum aberration case (green). In the range from ${E_\textrm{P}} = 2.0\; \mathrm{\mu} \textrm{J}$ to ${E_\textrm{P}} = 5.0\; \mathrm{\mu} \textrm{J}$ the selectivity saturates on a level $S > 200$ (except ${E_\textrm{P}} = 3.0\; \mathrm{\mu} \textrm{J}$). The selectivity is higher than the maximum selectivity of microscope objective corrected aberration case. The pulse energy range of the aberration corrected case is approximately three times the pulse energy range of the minimum aberration case. For the highest pulse energies, we observe a significantly larger variation of the etching channel length.
The selectivity for the SLM corrected aberration case exhibits a rapid increase from ${E_\textrm{P}} = 200\; \text{nJ}$ to ${E_\textrm{P}} = 400\; \textrm{nJ}$ comparable to the minimum aberrated case. The selectivity plateau at $S \ge 200$ is higher and wider than the plateau of the minimum aberrated case. After a drop for ${E_\textrm{P}} > 1.4\; \mathrm{\mu} \textrm{J}$ the selectivity has a local minimum at ${E_\textrm{P}} = 2.0\; \mathrm{\mu} \textrm{J}$. Afterwards the selectivity increases and reaches a second plateau of $S > 150$ for ${E_\textrm{P}} > 3.2\; \mathrm{\mu} \textrm{J}$.
The increase of selectivity of the maximum aberrated case starts at comparable high pulse energies above $1.0\; \mathrm{\mu} \text{J}$ due to aberrations. A potential explanation is the extended focus volume which leads to lower peak intensities. The non-linear absorption process in glasses is dominated by the local intensity [2]. Hence an intensity loss due to aberrations directly effects the energy deposition and the selectivity, respectively. In first approximation, a threshold intensity must be reached to obtain laser-induced modifications leading to measurable selectivities. The ratio between the peak intensities for the maximum aberration (see Fig. 2(f)) and the SLM corrected aberration case (see Fig. 3(f)) is $4.01 \pm 0.06$. This implies that a pulse energy of the maximum aberration case (red) leads to a lower peak intensity by a factor of $4.01 \pm 0.06$ in comparison to the pulse energy of the SLM corrected aberration case (green) in Fig. 6. In consequence, the start at ${E_\textrm{P}} = 2.0\; \mathrm{\mu} \textrm{J}$ and the end at approximately ${E_\textrm{P}} = 5.0\; \mathrm{\mu} \textrm{J}$ of the high selectivity plateau of the maximum aberration case are obtained at comparable peak intensities from the start and the end of the high selectivity plateau of the SLM corrected aberration case at ${E_\textrm{P}} = 400\; \textrm{nJ}$ and ${E_\textrm{P}} = 1.4\; \mathrm{\mu} \textrm{J}$, respectively. This underlines the impact of the spatial intensity distribution on this process.
For the SLM corrected aberration case the high selectivity plateau is in the same pulse energy regime as for the microscope objective corrected aberration case. The width of the process window is increased by more than 40% with respect to pulse energy. The increase of the selectivity is shifted back to pulse energies of ${E_\textrm{P}} = 300\; \textrm{nJ}$ and the width of the high selectivity plateau decreases. This is attributed to the absence of spherical aberrations and astigmatism. In comparison to the microscope objective corrected aberration case, the plateau is wider. The difference in the plateau width of approximately $350\; \textrm{nJ}$ between microscope objective corrected aberration and SLM corrected aberration case could originate from the shifted nominal minimum aberrated depth of the optical system due to spherical lenses which is discussed above. Furthermore, the present astigmatism for the microscope objective corrected aberration case leads to lower selectivities. Thus, the phase correction with a SLM has the potential to compensate aberrations caused by the complex optical system.
In addition to the measured selectivities, microscope images of the laser-induced modification are depicted in Fig. 7. In the regime of the selectivity plateau of the microscope objective corrected aberration case, the modifications are homogeneous lines, which become more pronounced with increasing energy. At the transition to lower selectivities separated dark features arise. For ${E_\textrm{P}} = 2.0\; \mathrm{\mu} \textrm{J}$, these features occur periodically. With increasing pulse energy, the distance and a heat affected zone around these dots becomes visible at ${E_\textrm{P}} > 2.0\; \mathrm{\mu} \textrm{J}$. For ${E_\textrm{P}} > 3.2\; \mathrm{\mu} \textrm{J}$ the separation of the dots increases. The occurrence of the dark features indicates low selectivities.
Fig. 7. Microscope images of unetched modifications in 12 mm fused silica sample for microscope objective corrected aberration case in 1.1 mm depth (top), maximum aberration case in 11.8 ${\rm{mm}}$ depth (mid) and SLM corrected aberration case in 11.8 ${\rm{mm}}$ depth (bottom) for different pulse energies.
For the maximum aberration case no modifications are observed up to ${E_\textrm{P}} < 1.0\; \mathrm{\mu} \textrm{J}$. This is in agreement with the selectivities of $S = 0$. The modifications at pulse energies at the start of the plateau are broader than the equivalent modifications of the microscope objective corrected aberration case. This is attributed to the greater spot diameter and the intensity ring around the center due to spherical aberrations. Periodic and broader modifications are observed for higher pulse energies. At the decreasing branch the dots become more separated, and a melting zone occurs.
The modifications of the plateau of the SLM corrected aberration case are similar to the microscope objective corrected aberration case. For the selectivity minimum at ${E_\textrm{P}} = 2.0\; \mathrm{\mu} \textrm{J}$, a heat affected zone (HAZ) and inhomogeneous modifications are obtained. The earlier occurrence of HAZs in comparison to the microscope objective corrected aberration case is caused by a tighter focusing due to the aberration correction. This results in accumulation effects which lead to process interruptions and a subsequent restart of the process until heat is accumulated again [32]. For ${E_\textrm{P}} > 3.0\; \mathrm{\mu} \textrm{J}$ the selectivity reaches a second plateau, which is not observed for the minimum aberrated case. We attribute this behavior to the focusing conditions. The modifications exhibit dark periodic features which are connected within a HAZ. This connection is correlated to higher selectivities. Obviously, the SLM aberration correction is advantageous to create these structures.
The effects of aberrations on the in-volume modifications and therefore on the etching channels are observed for the structuring depth of $12\; \textrm{mm}$ fused silica. The observed modification and its dependence on the pulse energy modification structure of the microscope objective corrected aberration case in $1.1\; \textrm{mm}$ is maintained in $12\; \textrm{mm}$ glass depth for the SLM corrected aberration case. The conservation of the selectivity plateau up to $1.0\; \mathrm{\mu} \textrm{J}$ for all depths compared to the microscope objective corrected aberration case shows the capabilities of aberration correction with a SLM for the SLE process. Thus, aberration correction enables depth independent pulse energy processing window for the SLE process.
4.2 Depth independent precision of etch channels
In the following, the influence of the SLM aberration correction on the channel dimensions in direction of the laser propagation is analyzed. In Fig. 8, the extension in z direction is plotted against the pulse energy for the three cases in $12\; \textrm{mm}$ thick fused silica substrates. For all three cases the z extension increases with pulse energy. This yields high selectivities except for ${E_\textrm{P}} > 2.0\; \mathrm{\mu} \textrm{J}$ of the SLM corrected aberration case. The microscope objective corrected aberration and the SLM corrected aberration case show a comparable dependence. An increase of the channel height $> 45\; {\mathrm{\mu} \mathrm{m}}$ for ${E_\textrm{P}} = 1.3\; \mathrm{\mu} \textrm{J}$ and ${E_\textrm{P}} = 1.4\; \mathrm{\mu} \text{J}$ is measured, respectively. For ${E_\textrm{P}} \ge 2.0\; \mathrm{\mu} \textrm{J}$ the height decreases to a constant level between $26 - 37\; {\mathrm{\mu} \mathrm{m}}$. The extension decreases for higher pulse energies. The channel width (expansion in y direction) is nearly constant for all cases and pulse energies.
Fig. 8. Height of etching channels in 12 mm fused silica sample for microscope objective corrected aberration case in 1.1 mm depth (green), maximum aberrated case in 11.8 mm depth (red) and SLM corrected aberration case in 11.8 mm depth (blue).
The entries of the etching channels are larger than the modification cross section of the unetched material. This is due to the significantly lower etching rate for the unirradiated glass of ${\rho _{\textrm{unmod}}} = 0.76 \pm 0.03\; {\mathrm{\mu} \mathrm{m}}/\textrm{h}$. In first approximation, we assume linear increase of the channel width with higher etching durations. The measured channel height h reveals that the correction of aberration leads to the same extension of the etching channels as the microscope objective corrected aberration case. The maximum height is $h = 48.0 \pm 2.4\; {\mathrm{\mu} \mathrm{m}}$ for the microscope objective corrected aberration case and $h = 49.4 \pm 2.6\; {\mathrm{\mu} \mathrm{m}}$ for the SLM corrected aberration case. Compared to the maximum height of $h = 78.4 \pm 8.8\; {\mathrm{\mu} \mathrm{m}}$ for the maximum aberration case the correction of aberration for the SLE process leads to an increase of the precision and smaller aspect ratios, which is important for glass component manufacturing.
The consequences for the depth-independence by applying aberration correction is summarized in Fig. 9. The depth-independence enables uniform scan strategies in all depths of the sample, which reduces the complexity of sample processing significantly.
Fig. 9. Comparison of pristine and etched modifications for the three cases of nominal microscope objective corrected aberration in 1.1 mm depth (green), maximum aberrated case in $11.8$ mm depth (red) and SLM corrected aberration case (blue) to demonstrate pulse energy conservation and uniform etch channel precision in laser propagation direction for all glass thicknesses.
4.3 Consequences for SLE process
The results of the SLE process with the aberration corrected beam profile are compared to the results of the case without aberration correction and with the nominal aberration correction of the microscope objective in $1.1\; \textrm{mm}$ depth (see Fig. 9). The aberration correction via SLM for the SLE process stands out for the three main results:
- 1. Pulse energy conservation
- 2. Uniform etching channel precision in laser propagation direction for all glass thicknesses
- 3. Depth independent processing due to decoupling of scan strategy and pulse energy
The pulse energy conservation reduces the requirements on the USP laser source and productivity increase by means of processing at higher repletion rates or enables massive parallel processing by dividing the pulse energy into several beamlets. The uniformity of the etched channel precision ensures depth independent quality of the manufactured structures. In combination, both aspects reduce the complexity of the SLE process for the machine operator due to a depth-independent parameter window for scan strategy and pulse energy. This significantly reduces the effort spend for CAM/CAD design for 3D SLE parts.
5. Conclusion
In this study, the influence of aberrations on the SLE process is analyzed and the capability of an aberration compensating technique consisting of a LCOS SLM is demonstrated. Spherical aberrations and astigmatism with a measurable impact on the focus diameter, the beam caustic and the focus intensity distribution are identified for 5 different focus depths in fused silica from $1\; \textrm{mm}$ to $12\; \textrm{mm}$. Since the Zernike coefficient for spherical aberrations ${c_{11}}$ is linear to the glass thickness, the aberration correction can be performed for all depths in the glass volume with prior calibration for the specific optical system. The impact of astigmatism and spherical aberrations are quantified by correcting the aberrations utilizing a SLM with subsequent beam caustic measurements. The use of a SLM for aberration correction significantly increase stability and reduces the used pulse energy and thermal load on the workpiece. A constant processing window resulting in a depth independent pulse energy, uniform etching channel extensions and simplified scan strategy of the SLE process have been demonstrated. The optimized process window enables the reduction of pulse energy in all depths which is mandatory for scaling approaches like multibeam intensity distributions. Furthermore, the demonstrated correction of aberrations for the SLE process enables a depth independent scanning strategy for generation of complex 3D geometries in transparent materials, which leads to a significant simplification of the process.
Funding
Bundesministerium für Wirtschaft und Energie (16KN070939, MB-SLE4MF); Bundesministerium für Bildung und Forschung (13N15423, Forschungscampus Digital Photonic Production).
Disclosures
The authors declare no conflicts of interest.
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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