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Abstract
The mechanical properties of tissues and cells are increasingly recognized as an important feature for the understanding of pathological processes and as a diagnostic tool in biomedicine. Impulsive stimulated Brillouin scattering (ISBS) is promising to overcome shortcomings of other measurement methods such as invasiveness, low spatial resolution and long acquisition time. In this paper, we present for the first time ISBS measurements of hydrogels, which are model materials for biological samples. We demonstrate ISBS measurements discriminating hydrogels of different stiffness. ISBS measurements with lateral resolution close to cellular level are presented. These results underline that ISBS microscopy has a high potential for biomedical applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The measurement of mechanical properties offers an exciting view on samples in the field of biomedicine [1]. Enormous progress in the treatment of diseases, especially in cases where early diagnosis is essential for successful therapy is expected [2]. The investigation of mechanical properties is already used in clinical practice, for example in the diagnosis of liver fibrosis [3] and breast cancer [4]. Measurement techniques described in the literature are manifold [5–12]. An established method is the classical ultrasonic technique in which a transducer is used to deduce the mechanical properties from the propagation of shear waves [13,14]. This technique has an advanced state of development, but due to its low resolution in the millimeter range it is only suitable for macroscopic investigations. More recent research aims at the measurement of mechanical properties with higher spatial resolution employing new methods. Particularly in biology, the measurement of mechanical quantities provides insight into the interaction of individual cells with surrounding tissue and processes within the life cycle of a cell. Aiming for cellular or sub-cellular spatial resolution atomic force microscopy (AFM) is a suitable measurement method. However, only surface measurements are possible [15] and the measurement is contact-based, very time-consuming and requires a complex and invasive sample preparation for biological tissue samples. This sample preparation leads to lesions and can influence the measured properties. Furthermore, the observation of time-varying processes such as healing processes is an important field of application in biomedicine [16], which requires contact-less, non-destructive measurements, which can be provided by optical methods.
A particularly emerging optical measurement method able to perform three-dimensional non-contact high spatial resolution measurements on in vivo samples is spontaneous Brillouin microscopy [17–21]. In spontaneous Brillouin scattering, an incident photon generates or destroys a coherent sound wave through a photon-phonon interaction. The interacting photons gain (anti-Stokes) or lose (Stokes) energy. This energy change corresponds to an equivalent wavelength shift of the backscattered photons [22]. The energy that can be gained or lost is coupled to the speed of sound via the wavelength of the phonons and thus to the mechanical properties of the material [23]. The wavelength shifts can be determined by spectroscopic evaluation. The spontaneous Brillouin microscopy enables a high spatial resolution of about 0.5 µm [24] as it is based on a confocal microscope. However, one drawback of the technique is the low effectiveness of the scattering process which leads to a small signal-to-noise ratio (SNR) of the Brillouin-scattered component, which is hard to detect due to the strong background close-by. Especially in biological samples, the amount of Mie and Rayleigh scattering increases enormously [25]. In order to achieve a spatial separation of the components, sophisticated spectroscopic setups [26] are used, which results in a long measurement duration. Successful approaches towards acceleration of the detection [27,28] and the combination with other measurement methods such as Raman spectroscopy were described [29–31].
A promising technique to overcome the shortcomings in acquisition duration of spontaneous Brillouin microscopy, is the impulsive stimulated Brillouin scattering (ISBS). This potential improvement is important, as the long measurement duration of spontaneous Brillouin microscopy is a significant factor limiting its usability on biological samples. This is particularly the case with imaging, for example for the measurement in the work of Schlüßler et al. [16], where a measurement duration of one second per pixel was required for optimal measurement uncertainty. This results in a total measuring duration of several minutes. Many changes in samples and biomedical processes take place on shorter time scales. This long established, ISBS based measurement technique [32–34] is also known as transient grating spectroscopy. Initially, the main focus was on the investigation of physical processes such as phase transitions in different materials [35–39]. Today it is getting more popular due to its focus on biomedicine. It is important to distinguish the impulsively stimulated technique (ISBS) from stimulated Brillouin spectroscopy methods, which require tunable highly wavelength-stable lasers [40–42]. The pioneering work to transfer ISBS microscopy from materials science to biomedicine was done by researchers from the Department of Biomedical Engineering at Texas A&M University [17,43–45]. The information obtained by ISBS microscopy is comparable to that obtained by spontaneous Brillouin microscopy. ISBS thus offers the potential for non-contact high spatial resolution measurements of in vivo samples but with a significantly shorter measurement duration. In this work we present for the first time ISBS measurements on the biological model material hydrogel and an investigation on shrinking the measurement volume towards cellular resolution. The principles of the ISBS microscope are described and the experimental setup is presented. Finally, the results of the experiments are discussed.
2. Principle of ISBS microscopy
ISBS microscopy is based on the generation of a transient density grating with a ultra-short pulsed laser and probing by Bragg diffraction with a cw laser (see Fig. 1).
Fig. 1. Principle explanation of the function of the ISBS microscope. From left to right: excitation by the excitation beam and generation of the fringe pattern; oscillation of the acoustic standing wave; readout of the acoustic standing wave by the probe beam.
The pulsed laser beam is split into two coherent beams using an achromatic Mach-Zehnder interferometer setup [46,47] (see Fig. 2). The superposition of the coherent laser beams leads to the formation of an interference fringe system [48] with the fringe spacing $d$, depending on the wavelength of the excitation beam ${\lambda _{\textrm {pump}}}$ and the half crossing angle ${\varphi _{\textrm {pump}}}$:
Fig. 2. Sketch of the ISBS microscope: PUL excitation laser (pulsed 12 ps, 532 nm); L2 L3 cylindrical lenses (optional); L1 L4 L5 L6 L7 achromatic lenses; PRL probe laser (cw, 895 nm); COL collimator; DM dichroic mirror (long-pass); GT grating; SC sample container; LP long-pass; ID iris diaphragm; FC fiber connector with long-pass; DET detector; OC oscilloscope.
The impulsive excitation of a standing acoustic wave is caused by an electrostrictive or thermal coupling of the laser pulse to the material in the measurement volume. The variation of the density also results in a change of the refractive index. A part of the probe beam is therefore diffracted at a temporally changing refractive index grating under the Bragg condition and is intensity modulated. For electrostrictive excitation a modulation frequency of
with the sound velocity in the probe $c_{\textrm {S}}$ is expected. If the signal is generated by thermal excitation, the expected frequency is [38,49]. Electrostriction produces a force on matter along the gradient of the absolute electric field strength [50]. This results in a displacement of matter in the direction of the regions of high light intensity. Thermal excitation results in a heating of the matter at regions with higher light intensity. And thus an impulsive expansion of the matter there. The resulting temporal change of matter is governed by the thermodynamic material equations.It is also possible to use a heterodyne detection in ISBS microscopy [51]. In this case, the probe beam reflected by the standing wave and a further coherent part of the probe beam are superimposed on the photo detector. This further part can be deliberately generated but can also arise involuntarily in the setup. For purely electrostrictive excitation combined with a heterodyne detection the frequency $f_1$ is expected. Both frequencies can be used for the measurement of sound velocity and thus for the deduction of the mechanical properties.
3. Setup of the ISBS microscope
The implementation of the impulsive stimulated Brillouin microscope is shown in Fig. 2. The pulsed ps laser (InnoSlab PX200-2, EdgeWave) is focused via the lens L1 onto the optical grating (GT) with a constant $g$ of 8 µm. The pulsed laser is operating at a wavelength of 532 nm and has a pulse length of 12 ps. The continuous probe laser (DL100, Toptica Photonics) is focused onto the grating via the lens L7. The probe laser emits at a wavelength of 895 nm and has an maximum output power of about 1 W. The two beams, excitation and probe, are combined by the dichroic mirror (DM). The focused beams are imaged into the sample container via a 4f setup consisting of achromatic lenses L4 ($f_{\textrm {L4}}$ = 75 mm, AC254-075-A-ML, ThorLabs) and L5 ($f_{\textrm {L5}}$ = 250 mm, AC254-250-A-ML, ThorLabs). All but the $\pm$1st diffraction orders for the excitation beam and the -1st order of the probe beam are blocked in the Fourier space between lenses L4 and L5. The formation of the interference fringe system takes place in the sample container. The probe beam automatically fulfills the Bragg condition regarding the resulting refractive index grating in the sample container due to the optical setup used. Likewise, the resulting fringe spacing in the sample container is independent of the refractive index of the sample for plane refractive index transitions and small beam angles. Therefore, in contrast to spontaneous Brillouin microscopy, the measured frequency is independent of the refractive index. The reflected part of the probe beam is directed to the detector (DET). To filter out unwanted light components - especially the pulsed laser peak - a spatial and wavelength-selective filtering is performed in front of the detector. The output voltage of the detector is measured with an oscilloscope and transmitted to a PC for further evaluation. Using parameters of the setup, the focal lengths $f_{\textrm {L4}}$ and $f_{\textrm {L5}}$ of the lenses L4 and L5 and a small angle approximation, the fringe spacing $d$ can be expressed as:
This results in the expected frequency for electrostrictive excitation:4. Experiments with ISBS microscopy
4.1 Measurement on methanol
As a first step measurements on methanol were carried out. A camera (uEye UI-1492LE, Imaging Development Systems) is placed at the intersection of the excitation beams in order to observe the characteristics of the fringe pattern and to estimate the size of the excited measurement volume. For this the sample container is removed from the setup and the camera is moved to the z-position of intersection of both excitation beams. After the measurement with the camera, the sample container is reinserted and no further changes to the optical setup are necessary. The resulting intensity distribution of the excitation beams is shown in Fig. 3(c). The fringe spacing is about 13 µm. The size of the cross-section was determined to be 107 µm times 48 µm (full width at half maximum, FWHM). These values provide an estimate of the lateral resolution of the measurement system. The excitation by the pulsed laser took place with a repetition rate of 1.5 kHz, which was matched to the used data acquisition hardware. For the time signal shown in Fig. 3(a), 512 individual signals were averaged. The avalanche photodiode (APD) detector used (HCA-S, FEMTO Messtechnik) had a conversion gain of 1 MV/W (at 800 nm) and a cutoff frequency of 220 MHz, which was sufficient for the expected frequencies. The detector voltage was measured with an oscilloscope (DPO 4054, Tektronix) and averaged internally. The sampling rate was chosen to be 1.25 GS/s to allow a compromise between acquisition duration and sufficient sampling. The averaged signal was transferred to a PC where it was evaluated with a Matlab script. The evaluation is based on a Fourier transformation of the windowed time signal. In the frequency domain, a regression with a Lorentzian function is performed (see Fig. 3(b)). The center frequency is derived from the parameters of the regression. The power of the probe laser was 20 mW. The energy of a single pulse was 8.8 µJ. Based on an elliptical Gaussian beam profile determined from Fig. 3(c), the maximum peak fluence results to 0.15 J/cm$^2$. According to Eq. (5) a frequency $f_2$ of about 160 MHz results for measurements with this setup on methanol at room temperature and electrostrictive excitation. The center frequency determined by the regression is in good agreement with the expected frequency.
Fig. 3. Measurements on methanol: (a) Time signal for 512 averaged signals; (b) Windowed Fourier transform of the time signal with regression function; (c) Intensity distribution of excitation beams at beam intersection captured by a camera.
In order to investigate the influence of the excitation energy and the number of averaged signals, a series of measurements was carried out. Figure 4 shows the time signals for increasing excitation energy (Fig. 4(a)) and for increasing averaging numbers (Fig. 4(b)). As with the measurement in Fig. 3, the probe beam has a power of 20 mW. For variation of the excitation energy, the number of averaged signals was kept constant at 512 and for variation of the number of averaged signals, the excitation energy was kept constant at 3.1 µJ. For a more in-depth examination, the signal strength was determined for both cases. The respective time signal was Fourier transformed and fitted with a regression (see Fig. 3(b)). An integral over the determined regression results in a signal strength equivalent. The resulting signal strength curve for variation of the excitation energy and for variation of the number of averaged signals is shown in Fig. 4(c) and 4(d) respectively.
Fig. 4. (a) Time signals for different excitation energies (512 averages); (b) Time signals for different numbers of averaged signals (3.1 µJ excitation pulse energy); (c) Signal strength equivalent based on integral in frequency domain over excitation energy; (d) Signal strength equivalent based on integral in frequency domain over number of averaged signals
As expected, the signal strength increases for increasing excitation energy. In contrast, the signal strength remains approximately constant as the number of averaged signals increases. However, it is recognizable in the time signals that the noise is significantly reduced with increasing number of averaged signals. For uncorrelated noise, the amplitude of the noise decreases with the inverse of the square root of the number of averaged signals. This means uncorrelated measurement values can be assumed [52,53]. Due to the higher SNR, a lower measurement uncertainty of the center frequency is possible. Deviations in signal strength for lower numbers of averaged signals in Fig. 4(d) are likely to be due to random variations causing an issue in the algorithmic evaluation of the signal strength. For small numbers of averages the regression and thus the estimation of the signal strength is not always accurate. Especially single signals with unfavorable noise can cause a wrong estimation of the signal strength. Since these signals are part of the set for all larger averaging numbers, there is a decaying influence on the signal strength with increasing averaging numbers. By this effect the curve in Fig. 4(d) can be explained.
In summary, the series of measurements shows that both an increase in the excitation energy and an increase in the number of averaged signals results in a smaller measurement uncertainty of the center frequency and therefore a trade-off between both parameters can be made. The results of the measurements on methanol (Figs. 3 and 4) are in accordance with the experiments described in the literature [43,44]. In those instances heterodyne detection was used and therefore the measured frequency was $f_1$. Furthermore, the results are supported by additional previously performed ISBS microscopy measurements with a nanosecond laser and a similar setup.
With regard to the potentially greatest advantage of ISBS microscopy over spontaneous Brillouin microscopy, it is reasonable to take a look at the measurement duration. The theoretical limit for temporal resolution strongly depends on the decay-time of the signal, which in this example amounts to about 150 ns. Thus, a pulsed laser with a repetition rate of about 6 MHz could be used, resulting in a theoretical measurement duration of 100 µs, when an averaging of 600 measurements is applied. This could bring about a paradigm shift in the measurement of mechanical properties for biomedicine, especially in imaging applications towards clinical studies and high-throughput screening.
4.2 Measurement on hydrogels
As a first step towards biologically relevant samples, we used polyacrylamide (PAA) hydrogels as a relevant model material, which was already studied with spontaneous Brillouin microscopy [16,54,55]. Three hydrogel samples of different stiffness were prepared (see Fig. 5(c)). The cross-linking of the liquid hydrogel mixture took place in the sample container (CV10Q3500FS, ThorLabs).
Fig. 5. Measurements on hydrogel: (a) Time signals for 512 averaged signals; (b) Windowed Fourier transform of time signals with regression; (c) Prepared samples of three different stiffness; (d) Statistical analysis of 60 measurements (each 512 averages) for each sample in the form of a box plot.
The expected stiffness (Young’s modulus) of the samples are ’soft’ at 800 Pa, ’intermediate’ at 2.5 kPa and ’stiff’ at 30 kPa respectively. These values were determined on samples of the same mixture with indentation-type atomic force microscopy. Due to deviations in the manufacturing process, small deviations in stiffness are possible. The variations in stiffness between the three Hydrogels are similar to variations found in biological samples, for example in the examination of a zebrafish larva [16]. The power of the probe laser was still set to be 20 mW. The energy of a excitation pulse was 10 µJ. This results in a maximum peak fluence of 0.07 J/cm$^2$, for an elliptical Gaussian beam profile. The pulse energy was chosen in such a way that a clear signal could be obtained after averaging of 512 signals during test measurements. The time signal of a single measurement (512 averages) for the three samples is shown in Fig. 5(a). The waveform of the signal differs from the measurements on methanol in the previous section. A DC component and a signal amplitude of similar magnitude for all three hydrogels are obtained. However, the oscillation takes place above and below this constant component, which indicates a heterodyne detection. The curves determined from the time functions in the frequency domain with their corresponding regression can be seen in Fig. 5(b). The increasing center frequency with increasing stiffness of the sample is clearly visible. The center frequency is the frequency $f_1$ which supports the assumption of a heterodyne detection.
On each sample container, 60 measurements consisting of 512 averaged single pulse measurements each were taken over a period of one minute. The center frequencies for each of the 60 measurements were determined and statistically evaluated. The measurements result to a center frequency of 112.3 $\pm$ 0.6 MHz, 116.1 $\pm$ 0.4 MHz and 118.1 $\pm$ 0.4 MHz (mean value $\pm$ standard deviation) for the hydrogels with the stiffness ’soft’, ’intermediate’ and ’stiff’ respectively. The results are shown in Fig. 5(d) in the form of a box plot. It is clearly visible that the three hydrogels can be discriminated. However, it can also be seen that the individual measurements are strongly scattered. A comparison with measurements from spontaneous Brillouin microscopy on hydrogel samples shows strong similarities. Measurements by Schlüßler et al. on samples with the same composition (see supplements [16]) showed a linear relationship between spontaneous Brillouin frequency and longitudinal modulus. Between Young’s modulus and longitudinal modulus a logarithmic relationship was found. Corresponding to the differences in the measuring principle, the spontaneous Brillouin microscope operates at a significantly higher center frequency of several GHz. The relative differences of the center frequency are however comparable to ISBS microscopy measurements. In order to make detailed statements about the quantitative values, it is necessary to carry out a series of measurements using spontaneous Brillouin microscopy, ISBS microscopy and a reference method (e.g. AFM) on the same samples.
4.3 Enhancement of spatial resolution
Applications in biomedicine mostly require cellular resolution in the range of 10 µm. For the ISBS microscope presented in this paper, this means that the size of the signal generation volume must be reduced. As the most important change, the imaging ratio of the 4f setup consisting of the L4 and L5 lenses was adapted (compare Fig. 2). The lens L4 ($f_{\textrm {L4}}$ = 75 mm, AC254-075-A-ML, ThorLabs) was not changed. For the lens L5 an achromatic lens (AC254-060-A-ML, ThorLabs) with a focal length of 60 mm was used and thus the imaging ratio changed from 10:3 to 4:5. In addition, the collimator (COL), the lens L7 and L1 were slightly adjusted. The aim was to maintain the separability of the individual beams between L4 and L5 and to make optimum use of the available space in x-direction. As in the experiments on methanol, cylindrical lenses L2 and L3 were used to squeeze the excitation beam in the measurement volume along the y-direction. This results in an increased spatial resolution in the y-direction and a higher overall energy density. The separability between lenses L4 and L5 remains unaffected. An image of the interference pattern at the intersection of the excitation beams is shown in Fig. 6(a). Here the camera is at the Nyquist limit and hinders a good resolution. However, there is a good agreement with a simulation of the interference fringe pattern (see Fig. 6(b)). This simulation is based on a calculation of the electric field of two elliptical Gaussian beams on a gridded 3D volume in Matlab. The intensity was calculated by superposition of the intersecting beams under the given crossing angle. The simulation was verified by a comparison of FWHM derived from the camera measurements and simulation. The size of the cross-section can be determined on the basis of the FWHM to be 23 µm times 10 µm. Based on the determined FWHM and the simulation, the factor of reduction of the measurement volume can be determined to be about 477 (from $19.3 \cdot 10^{-3}$ mm$^3$ to $40.3 \cdot 10^{-6}$ mm$^3$). The resulting fringe spacing $d$ is 3.1 µm. Due to the significantly smaller fringe spacing, a higher expected modulation frequency results according to Eq. (2), so that a new detector (APD210, ThorLabs, cutoff 1 GHz) and a new oscilloscope (WavePro 7100A, LeCroy) have to be used. The energy of a single pulse in front of the sample container was estimated to be about 12 µJ. Based on an elliptical Gaussian beam profile determined from Fig. 6(a), the maximum peak fluence results to 4.4 J/cm$^2$. For the time signal shown in Fig. 6(c), 2000 single pulse signals were averaged. A clear decaying signal is apparent. Using the new hardware (detector and oscilloscope), the rearming of the trigger is prolonged after each acquisition of a single pulse measurement. The signal is shown in the frequency domain with a regression in Fig. 6(d). Thus the center frequency can be determined and corresponds to the calculated frequency $f_1$. This proofs a successful measurement with an immensely reduced measurement volume.
Fig. 6. Measurement on methanol with shrunk measurement volume: (a) Intensity distribution of excitation beams at beam intersection captured by a camera; (b) Intensity distribution resulting from a simulation of the excitation beams; (c) Time signal for 2000 averaged signals; (d) Windowed Fourier transform of time signal with regression function.
As discussed in the section 2. there are two main causes for the occurrence of frequency $f_1$ instead of frequency $f_2$. One is an electrostrictive excitation which generates the frequency $f_1$ by a heterodyne detection on the detector due to scattered light of the probe beam. The second is thermal coupling of the excitation beam causing a sound wave.
5. Discussion
An important requirement for the applicability of ISBS microscopy in biomedicine is an improvement of the spatial resolution and thus a reduction of the measurement volume. The method used in this work to shrink the measurement volume (see section 3) reduces the spot size of the excitation beam at the beam intersection and the fringe spacing uniformly. The smaller fringe spacing results in an increase of the signal frequencies. High frequencies ($\geq$ 1 GHz) result for viable measurement volume sizes and place high demands on the detector and the acquisition hardware. To meet the condition of impulsive excitation, the pulse duration of the excitation must be short compared to the period duration of the standing acoustic wave. Thus the requirement on the excitation laser is higher with smaller fringe spacing. Furthermore, the larger crossing angle of the excitation beams leads to a steeper angle of incidence of the probe beam. The steeper angle can result in reduced diffraction efficiency at the standing acoustic wave and thus a lower intensity of probe beam on the detector.
Higher repetition rates of the excitation laser are used in order to accelerate the measurement, which represents the greatest advantage of ISBS microscopy. It is important that the damage threshold of the sample material is not exceeded and the material properties themselves are not influenced by the measurement. A balance must be found between the size of the measurement volume, the pulse energy of the excitation laser, its repetition rate, the power of the probe laser and the number of averaged signals. This larger number of parameters for adjustment gives ISBS microscopy more control over the SNR than spontaneous Brillouin microscopy. An example for such an optimization potential is the comparison of excitation energy and number of averaged signals in Fig. 4.
Another challenge for measurements on biological samples with the ISBS microscope are their optical properties. For biological samples stronger scattering, absorption but also light distortion at refractive index inhomogeneities compared to pellucid liquids is expected. These effects can lead to a disturbance of the probe beam but foremost the fringe pattern of the excitation can be disturbed. Since stronger scattering and refractive index inhomogeneities can be observed with hydrogel, the successful measurement on hydrogel is a good indicator for the suitability of the measurement method for biological samples. Adaptive optical methods [56] can be used to compensate for aberrations on biological samples. Such techniques have already been used for measurements with spontaneous Brillouin scattering [57].
The hurdles presented here show the still developing status of ISBS microscopy with regard to its application in biomedicine. However, the successful measurements also show the potential of the technique. This is of particular interest as the question as to which material property is actually measured by Brillouin elastography has recently been raised. Wu et al. [58] has shown that there is a strong cross sensitivity of the measurement method to the water content of the samples. These results were obtained by measurements with spontaneous Brillouin on samples with high water content (> 90 %). The correlation of the Young’s modulus with the bulk modulus is relevant for the measurements of stiffness with Brillouin measurement techniques. Biomedicine, is particularly interested in the Young’s modulus, which can also be measured with other reference methods such as AFM. There is a well-known connection between the speed of sound determined by Brillouin measurement methods and the bulk modulus. Accordingly the speed of sound is directly proportional to the square root of the bulk modulus. There is an empirical correlation between the Young’s modulus and the bulk modulus also on biological samples [59]. Measurements of stiffness with ISBS microscopy on samples with typical water content and water content changes are expected to be possible based on this chain of dependencies [60].
6. Conclusion
ISBS microscopy enables very fast non-contact measurements of the mechanical properties of cells and tissues. A comparison of ISBS microscopy with the spontaneous Brillouin microscopy, shows that ISBS microscopy allows significantly shorter measurement durations but faces greater challenges regarding spatial resolution. A theoretical measurement rate of 10 kHz was estimated for the assumed constraints. The lateral spatial resolution has been improved to about 23 $\times$ 10 µm$^2$, which allows cellular structures to be resolved. With the realized ISBS microscope hydrogels of different stiffness were discriminated successfully. ISBS microscopy is still in its infancy for biomedicine, but there is enormous potential, especially in high-throughput screening.
Funding
Deutsche Forschungsgemeinschaft (DFG Cz 55\44).
Acknowledgments
The authors would like to thank Raimund Schlüßler (Biotechnology Center, TU Dresden), Jochen Guck (Max Planck Institute for Physics of Light, Erlangen) and Lars Büttner (Laboratory of Measurement and Sensor System Technique, TU Dresden) for fruitful discussion and support. We thank Andres Fabian Lasagni (Institute for Manufacturing Technology, TU Dresden) for support with ultrafast laser sources. J. W. C. is appreciating the valuable discussions with Vladislav Yakovlev (Texas A&M University). We thank the DFG for their funding.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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