1 Introduction

Femtosecond lasers have developed to be a very important tool for a multitude of different technologies, including material deposition, surface treatment, and bulk processing of transparent materials [1]. Apart from that, laser micromachining with ultrashort laser pulses is an important target fabrication technique for both science experiments and target production in the realm of laser fusion research. One specific approach of laser fusion is proton fast ignition, which aims to ignite a pre-compressed fuel using a pulse of protons [2]. For this fusion scheme, the target is composed of a polymer ablator shell, containing the fusion fuel, and a metallic cone, which is mounted inside the shell pointing toward its center [3]. Since the shell and the cone are made of different materials, one approach to fabricate such a target is to produce both components separately and join them in a second step. In this process, femtosecond laser micromachining can be used to create a hole in the polymer shell for mounting the cone. This hole poses several strict requirements regarding the cleanness and accuracy of the laser machining process. Additionally, the walls of this hole need to be tailored to fit the opening angle of the cone. This is achieved using a combination of laser milling and angle-of-incidence machining, where the sample is tilted relative to the laser beam to machine a straight wall with a defined taper angle. During this process, it is important to keep material change, induced by the femtosecond laser pulses, as localized as possible. Material redeposition around the hole, as well as material change of the bulk caused by pulses propagating into the material, could impair the compression behavior of the capsule [4]. As a consequence, the energy deposition of ultrashort laser pulses in the polymer shell needs to be well understood to meet the fabrication requirements of proton fast ignition targets.

The absorption of ultrashort laser pulses in transparent materials, including polymers and glasses, is based on the free-electron generation in the material. Dominant mechanisms for this free-carrier generation are multi-photon ionization (MPI), tunnel ionization (TI), and barrier suppression ionization (BSI), which are described in detail in Refs. [5,6,7,8,9]. The relative importance of MPI compared to TI or BSI is described by a parameter introduced by Keldysh [10]:

$$\begin{aligned} \gamma = \omega _0\frac{\sqrt{2 m_e I_\text {ion}}}{eE}, \end{aligned}$$
(1)

where e and \(m_e\) are the electron charge and mass, respectively, \(\omega _0\) is the angular frequency of the laser pulse, \(I_\text {ion}\) is the binding energy of the electron, and E is the pulse electric field, corresponding to the intensity of the pulse. For \(\gamma \ll 1\), TI/BSI dominates; while for \(\gamma \gg 1\), MPI dominates [10]. Having created free electrons in the material, these can absorb incoming photons while scattering off an ion in a process called inverse bremsstrahlung (IB) [5,6,7]. Once an electron has experienced enough IB events to have gained an energy larger than \(I_\text {ion}\), it can free another electron in a scattering process. Both resulting electrons can then start gaining energy and eventually each free another electron. This results in an accumulative ionization process called avalanche ionization (AI) [5,6,7, 11, 12]. Since it takes some time for an electron to experience enough IB events, the relevance of this ionization mechanism depends on the intensity and duration of the incoming laser pulse [5, 12].

This ionization behavior, together with the spatio-temporal evolution of the generated free-electron plasma, has been examined in several works before [13,14,15,16,17,18,19,20]. These works were mostly done in the context of volumetric laser machining inside of glass, with the motivation to improve the accuracy with which material change is induced inside the bulk. To image the spatio-temporal evolution of the free-electron plasma, pump-probe shadowgraphy is a common method [13,14,15,16,17,18,19,20]. It uses a pump pulse to induce material change and a probe pulse to create a shadowgraphy of the interaction zone at defined times after the pump pulse has arrived. The short pulse length of the probe pulse enables the high temporal resolution required to image the transient ionization and expansion processes of the free electrons inside the material on a timescale of hundreds of femtoseconds.

To the knowledge of the authors, this method was not yet used to image the spatio-temporal evolution of free electrons created by ultrashort laser pulses in polymers instead of glasses. Additionally, since most of the work conducted in this field focuses on volumetric laser machining, to the knowledge of the authors, no attempts have been made to prevent pulse propagation into the material and the subsequent material change inside the bulk.

Since this is of great interest for target fabrication in laser fusion research, this work presents experimental data on the energy deposition of ultrashort laser pulses in polyvinyl chloride (PVC), a polymer widely used in the context of target fabrication. This includes the analysis of the pulse propagation into the bulk, the ionization of the material, and the subsequent thermalization of the free electrons with the atoms and ions of the material on a time scale of several picoseconds to microseconds. Additionally, these aspects are compared for two different pulse intensities. Furthermore, the pulse propagation into the material is related to ablation craters produced by multiple consecutive pulses.

The findings of this work help to understand the ablation crater topology in PVC and allow optimizing laser micromachining for laser fusion target fabrication, by reducing the amount of unwanted bulk material change.

2 Experimental setup

To image the energy deposition of ultrashort laser pulses in PVC, a two-color pump-probe shadowgraphy setup is used, which is sketched in Fig. 1.

Fig. 1
figure 1

Two-color pump-probe shadowgraphy setup. The beam is split up into a pump beam and a probe beam. The pump beam passes a mechanical shutter (MS) and an attenuator, consisting of a halfwave plate (\(\lambda\)/2), a thin film polarizer (TFP), and a beam dump (BD). It is focused onto the sample using a focusing lens (f). The probe beam passes two delay stages (DS1, DS2) for coarse and fine adjustment, and enters a telescope, composed of two lenses (L1, L2) and an iris (I) in the focus position. Inside this telescope, the second harmonic is generated using a beta barium borate (BBO) crystal in combination with a shortpass filter (SP1). The probe beam illuminates the sample, which is imaged using a microscope objective (MO), a shortpass filter (SP2), a field lens (FL), and a camera (C)

Full size image

The laser used in this work is a chirped pulse amplified Ti:sapphire system composed of a Griffin-3 oscillator by KMLabs Inc. and an Integra-C amplifier by Quantronics Cooperation. For this work, this system is tuned to provide ultrashort laser pulses with a maximum energy of 120 \(\upmu {\textrm{J}}\) and a pulse duration of about 130 fs (Gaussian distribution, FWHM), at a repetition rate of 5 kHz, and a central wavelength of 795 nm. The \(1/e^2\) beam diameter is about 5.8 mm.

Directly after the laser exit aperture, a pulse is split into a probe and a pump pulse, using a thin glass plate. The pump pulse transmits through the glass plate and is used to excite the sample and ablate material. Having passed a mechanical shutter, it is attenuated to an energy of about 40 \(\upmu {\textrm{J}}\) using a halfwave plate and a thin film polarizer. This energy was chosen to minimize the relative error of the pulse energy, caused by energy fluctuations of the laser of about 1 \(\upmu {\textrm{J}}\). After that, the pump pulse is focused onto the PVC sample using a focusing lens with either 500 mm or 100 mm focal length. For the beam parameters mentioned above, the different focal lengths result in spot sizes (\(1/e^2\) beam waist diameter) of about 113 \(\upmu \textrm{m}\) and 23 \(\upmu \textrm{m}\) for 500 mm and 100 mm focal length, respectively. The corresponding peak intensities of the pulses on the sample for the focal lengths of 500 mm and 100 mm are about 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\), respectively. This intensity change was done using different focusing lenses to reach two significantly different intensities. Due to the limited stable energy output range of the laser system used in this work, it was not possible to produce such different intensities by varying the pump pulse energy.

The probe pulse is used to illuminate the region of the sample that is excited by the pump pulse. The effective exposure time of the illumination is defined by the length of the probe pulse, which is 130 fs, similar to the pump pulse. This enables imaging the dynamic processes of ionization and pump pulse propagation in the medium. Two delay stages are used to introduce a defined delay of the probe pulse with respect to the pump pulse. The first delay stage is used to adjust the path length so that pump and probe pulse arrive approximately simultaneously at the sample. With the second precisely adjustable delay stage, a defined delay is introduced to the probe pulse, thus illuminating the interaction zone at defined intervals after the pump pulse has arrived. Furthermore, the probe pulse is frequency doubled using a beta barium borate (BBO) crystal for second harmonic generation, which is aligned within a telescope with magnification factor one. Before the second lens of the telescope, the fundamental beam is filtered out using a shortpass filter with a cut-off wavelength of 650 nm. Additionally, at the focus position of the telescope, an iris is placed as a spatial frequency filter. Finally, the frequency-doubled probe pulse transmits through the sample at the same point at which the pump pulse impinges on it. The interaction zone is imaged using a 20x microscope objective with a numerical aperture of 0.6 (Edmund Optics, 58–373). After the objective, a shortpass filter with a cut-off wavelength of 550 nm is used to block the scattered light of the pump pulse. A 200 mm tube lens focuses the light onto the camera of type U3-3070CP-M-GL Rev.2.2 by IDS Imaging, with a minimum exposure time of 40 \(\upmu \textrm{s}\) and a 12-bit CMOS sensor.

The sample used in this work is a 40 mm wide, 10 mm high, and 200 \(\upmu \textrm{m}\) thick piece of PVC foil from the company Goodfellow, with a refractive index of 1.54 [21]. The sample piece is prepared by polishing one of the long edges using sandpaper with grit sizes of 3200, 4000, and 6000, subsequently. The sample is then mounted on two translational stages with the polished edge being irradiated by the pump pulse and the probe pulse illuminating the interaction zone perpendicularly, thus transmitting through the 200 \(\upmu \textrm{m}\) thick material. To position the sample surface accurately at the height of the laser beam waist, craters at different sample heights were produced and the position that yielded the highest aspect ratio of the laser-induced crater was chosen. According to [22], this corresponds to the beam waist position being on the sample surface. This was particularly important for the small focal length, due to the correspondingly small Rayleigh length of about 400 \(\upmu \textrm{m}\). For the larger focal length, the Rayleigh length is almost 1 cm, which relaxed the alignment requirements significantly.

For each shadowgraph, nine background images without pump pulse are taken to reduce the influence of illumination variances caused by pointing instability of the probe beam. These background images are averaged. Since the feature in the signal image is a shadow, subtracting the background from the signal image would result in a dark image. Instead, the signal image is subtracted from the average background. In the resulting image, regions of full transmission in the signal image are dark and regions with high absorption are bright. The histogram of this image is equalized using OpenCV [23] to enhance image contrast and the image is inverted. As a result, bright areas of the image show regions with high transmission, while absorbing regions are represented by dark areas, as is intuitive for a shadowgraph. After each signal image, the sample was moved, making sure the next pump pulse impinges on a new spot of the sample. This procedure was repeated three–five times for each parameter combination to ensure reproducibility of the results. The coordination of sample movement, delay stage movement, mechanical shutter operation, laser triggering, and delay stage movement was done using the laser machining software Direct Machining Control (DMC) [24].

3 Results

First, the delay of the probe pulse to the pump pulse is calibrated by analyzing the propagation of the pump pulse into the medium. After that, the energy deposition of the pump pulse in the sample is analyzed at different intervals after the arrival of the pump pulse at the sample and with different pump pulse intensities of 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\). Finally, ablation craters produced by multiple consecutive pulses of these intensities are compared and related to the energy deposition behavior.

3.1 Timing calibration and pulse expansion

To calibrate the delay of the probe pulse relative to the pump pulse, shadowgraphs with different delay stage positions are acquired for a single pulse. Such patterns are shown in Fig. 2 for intensities of 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\), and for two different positions of the delay stage each. The images in Fig. 2, as well as the images shown in the rest of this work, are exemplary for their combination of parameters. Further shadowgraphs taken with the same parameters are contained in the data repository provided with this work and confirm the reproducibility of the results.

Fig. 2
figure 2

Shadowgraphs for pump pulse intensities of 6 \(\hbox {TW cm}^{-2}\) in (a) and (b), and 143 \(\hbox {TW cm}^{-2}\) in (c) and (d) at two different positions of the delay stage each. These positions are related to delays of the probe pulse relative to the pump pulse, as described in Sect. 3.1. The probe pulse delays are depicted under the respective image. The surface of the PVC sample is indicated by the green line. The pump pulse impinges on the sample from the top. The energy deposition pattern expands through the sample with increasing probe pulse delay. The pattern created by the higher-intensity pump pulse is significantly narrower compared to the lower-intensity pattern due to the smaller focal spot size

Full size image

For each image in Fig. 2, the pump pulse impinges on the sample from the top. The green line indicates the surface of the PVC sample. In the shadowgraphs with the higher-intensity pump pulse, a bright region directly below the sample edge is visible. This is attributed to plasma glow created by the pump pulse after a few nanoseconds [25, 26] and caught by the camera due to its exposure time of 40 \(\upmu \textrm{s}\). The lower-intensity pump pulse does not create a plasma bright enough to be visible in the images. All of these images show a pattern expanding from the sample edge downwards with increasing probe pulse delay. To relate the delay stage position to the delay between the probe pulse and pump pulse, the distance of the sample edge to the bottom of the pattern is measured as a function of the delay stage position. By adapting a linear function to the data and calculating the zero of this function, the delay stage position of simultaneity is determined. The delay of the probe pulse with respect to the pump pulse is then calculated based on the distance of the delay stage to this reference position. The error of the probe pulse delay results from the error of the reference position and is 66 fs and 167 fs for 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\), respectively. The resulting expansion of the patterns is shown in Fig. 3.

Fig. 3
figure 3

Expansion of the shadowgraphy patterns into the PVC sample as a function of time. The probe pulse delay errors result from the calibration procedure described in the text, while the expansion depth errors are due to defining the bottom edge of the pattern. The lines are linear fits with slopes of \({0.91 \pm 0.09}\) and \({1.2 \pm 0.2}\) times the speed of light in PVC for the blue and green line, respectively. The dashed line indicates the speed of light in PVC

Full size image

For both intensities, the expansion of the pattern follows a linear behavior. Using the method of least squares to adapt a linear function to the measurements, the expansion velocity is determined to be \(({0.91 \pm 0.09})c_\text {PVC}\) and \(({1.2 \pm 0.2})c_\text {PVC}\) for 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\), respectively. Hereby, \(c_\text {PVC}\) is the speed of light in PVC calculated as the fraction of the speed of light in vacuum and the index of refraction of PVC.

For both intensities, \(c_\text {PVC}\) is included in the error margin. The expansion speed for the larger intensity is slightly faster than for the lower intensity. This can be attributed to a larger decrease in the refractive index due to the creation of a free-electron plasma with a higher density, as will be discussed in Sect. 3.2.

For the smaller intensity, after about 1 ps, the bottom of the pattern could not be located anymore, since it has propagated out of the image frame. For the higher intensity, the pattern could not be located anymore after 0.8 ps, because the expanding pattern had faded.

3.2 Ionization

To analyze the ionization of the material caused by a single ultrashort laser pulse, the situation directly after the pump pulse impinges on the sample surface is imaged. Figure 4 shows shadowgraphs with a probe pulse delay of 269 fs and 228 fs for pump pulse intensities of 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\), respectively.

Fig. 4
figure 4

Energy deposition shadowgraphs shortly after the pump pulse impinged on the sample from the top, with intensities of 6 \(\hbox {TW cm}^{-2}\) in (a) and 143 \(\hbox {TW cm}^{-2}\) in (b). The higher-intensity pump pulse causes the PVC sample to absorb significantly more of the probe pulse compared to the lower-intensity pump pulse

Full size image

Both images show different patterns beneath the sample surface. Since these patterns already occur on a timescale of femtoseconds, they are attributed to the electron response of the material to the pump pulse [5, 7, 9, 27]. The shape of these patterns is mostly attributed to the characteristics of the relevant ionization mechanisms. The roughness of the sample surface is particularly relevant for highly reflective materials, such as many metals, where the light is reflected away from the peaks and into the pits, resulting in a modulated intensity distribution on the sample surface. However, for a highly transmissive medium, such as PVC, the light is predominantly refracted at the sample surface while propagating into the material, so that the imprint of the sample surface on the intensity distribution is minimal. Consequently, to explain how these patterns are created, the significance of the different ionization mechanisms in the situation of this study is evaluated in the following.

Applying Eq. (1) to the situation of a hydrogen atom (\(I_\text {ion} = {13.6}\,{\textrm{eV}}\)) and a wavelength of 795 nm, values of \(\gamma \approx 4\) and \(\gamma \approx 0.9\) can be calculated for the intensities of 6 \(\hbox {TW cm}^{-2}\) and 143 \(\hbox {TW cm}^{-2}\), respectively. According to Wang et al. [28], these values do not allow the conclusion that one mechanism dominates for either intensity. Instead, it is assumed that a mixture of MPI and TI/BSI causes the ionization of the material.

In addition to that, the role of AI in the carrier excitation process was examined theoretically by Rethfeld [12], who used a multi-rate equation (MRE) model. The solution of this model yields a characteristic time \(t_\text {MRE}\) for AI, which depends on the probability of an IB event happening and on the number of IB events needed to reach an energy level large enough for collisional ionization. For pulse lengths larger than \(t_\text {MRE}\), AI is relevant during the pulse; while for pulse lengths shorter than \(t_\text {MRE}\), the cascade process needs too much time to be relevant during the pulse. This characteristic time decreases with increasing electric field of the pulse. Explicit values from [12] state that for 7.5 \(\hbox {GVm}^{-1}\), \(t_\text {MRE} = {415}\,{\textrm{fs}}\); while for 10 \(\hbox {GVm}^{-1}\), \(t_\text {MRE} = {233}\,{\textrm{fs}}\). The electric field for an intensity of 6 \(\hbox {TW cm}^{-2}\) is 6.7 \(\hbox {GVm}^{-1}\). Since the 130 fs pulse length used in this work is significantly smaller than the \(t_\text {MRE} = {415}\,{\textrm{fs}}\), it is assumed that AI is not relevant for this intensity. In contrast, the intensity of 143 \(\hbox {TW cm}^{-2}\) corresponds to an electric field of 32.8 \(\hbox {GVm}^{-1}\), which is significantly larger than the 10 \(\hbox {GVm}^{-1}\) with \(t_\text {MRE} = {233}\,{\textrm{fs}}\) from [12]. Consequently, since \(t_\text {MRE}\) decreases with increasing electric field, it is assumed that AI is relevant for an intensity of 143 \(\hbox {TW cm}^{-2}\).

For a pump pulse intensity of 6 \(\hbox {TW cm}^{-2}\), the shadowgraph shows a pattern of darker and brighter vertical lines. These can be attributed to interference and diffraction of the probe pulse on the spatial distribution of free electrons in the material. According to various literature, the propagation of intense laser pulses in dielectrics can result in the formation of filaments [6, 8, 29,30,31]. These filaments are formed by the competing processes of self-focusing and plasma defocusing. Consequently, the critical power of self-focusing has to be exceeded for filamentation to happen. According to [29], this threshold power is given by \(P_c = \frac{3.77\lambda ^2}{8 \pi n_0 n_2}\). For \(\lambda = {800}\,{\textrm{nm}}\), \(n_0 = {1.54}\), and \(n_2 = 3.6 \times 10^{-16}\,\hbox {cm}^{2}W^{-1},\), based on [32], the critical power of self-focusing \(P_c\) resolves to 1.73 MW. With a pulse energy of 40 \(\upmu {\textrm{J}}\) and a pulse length of 130 fs, the peak power of the pulses used in this study is \(P_\text {p} \approx 355 P_c\), thus vastly exceeding the critical power for self-focusing. As a result, it can be assumed that the initially Gaussian intensity distribution evolves into a filamented intensity distribution, which imprints on the spatial distribution of the free electrons. Thus, when the probe pulse propagates through this filamented free-electron distribution, its complex diffraction and interference pattern is imaged by the camera, resulting in the pattern visible in Fig. 4a.

The pattern in Fig. 4b for a pump pulse intensity of 143 \(\hbox {TW cm}^{-2}\) is a result of the same mechanisms. However, due to the higher intensity and the additional relevant ionization mechanism of AI, the free-electron density in the material is higher. Consequently, a larger fraction of the probe pulse is absorbed. Since a larger free-electron density reduces the refractive index, this corresponds well to the slightly larger expansion velocity found for this intensity in Sect. 3.1.

3.3 Thermalization

As soon as free electrons are present in the material, they start colliding with the surrounding atoms and ions. These collisions result in an energy transfer from the free electrons to the atoms and ions, eventually heating the material on a timescale of hundreds of femtoseconds to a few picoseconds [7].

Figure  shows shadowgraphs with a probe pulse delay of about 3 ps and 200 \(\upmu \textrm{s}\), which is both long after the pulse has propagated through the whole image.

Fig. 5
figure 5

Energy deposition shadowgraphs with a probe pulse delay of about 3 ps and 200 \(\upmu \textrm{s}\) for 6 \(\hbox {TW cm}^{-2}\) in (a) and (b) and 143 \(\hbox {TW cm}^{-2}\) in (c) and (d). The pump pulse propagation direction is from top to bottom. For 3 ps, the pattern created by the lower-intensity pump pulse extends vertically through the whole image, while the pattern created by the higher-intensity pulse fades significantly with increasing penetration depth. For both intensities, the patterns have slightly faded but are still visible after 200 \(\upmu \textrm{s}\)

Full size image

The patterns in these shadowgraphs look different from the patterns during the expansion in Fig. 2. Looking at the lower-intensity shadowgraphs (a) and (b) of Fig. 2, the part close to the bottom of the pattern, i.e., at the expansion front, is constituted by an interference pattern with broad bright and dark vertical lines that only exist within a certain range of the image. The higher-intensity patterns in (c) and (d) of Fig. 2 show overall smaller, but similar interference patterns at their expansion front. In contrast to that, the patterns after the expansion in Fig.  have a significantly smaller spacing of the lines. This pattern type can already be observed during the expansion, above the expansion front in image (d) of Fig. 2, while it starts building at the top of image (b) of the same figure.

Additionally, Fig. 5 shows that these patterns prevail up to 200 \(\upmu \textrm{s}\), indicating that they are not created by a transient free-electron plasma, but by a less transient variation of the refractive index. This change can be attributed to the change in temperature caused by the energy transfer from the free electrons to the atoms and ions. For ultrashort laser pulses, the temperature can rise up to several times the melting temperature resulting in extreme overheating of the material [7]. The stripe pattern imprinted by the intensity filamentation largely prevails throughout the energy transfer to the atoms and ions. The consequent temperature distribution in turn causes a similarly distributed change in the refractive index [33, 34].

The timescale on which the heating of the material occurs is defined by the collisions of the free electrons with the atoms and ions. An estimation of the energy exchange time is given by

$$\begin{aligned} \tau _\text {e-ph}^\text {en} \simeq \frac{M}{m_\text {e} \omega _\text {at}}, \end{aligned}$$
(2)

where M is the atomic mass, \(m_\text {e}\) is the mass of the electron, and \(\omega _\text {at}\) is the atomic frequency, which is usually in the order of 2e16  Hz [7]. This estimation was derived for metals with a free-electron plasma and a background of ions. To apply this estimation to PVC, it is assumed that after the interaction of the pump pulse with the sample, the interaction region is similarly composed of a free-electron plasma and a background of atoms and ions. This background is not composed of a single species, but instead of three different species, according to the composition of PVC (\({\hbox {C}_{2}\hbox {H}_{3}\hbox {Cl}}\)). Using this composition, the energy exchange time can be estimated for each composite individually using Eq. (2), and a weighted average, according to the abundance of each composite results in 0.93 ps. Consequently, after about 0.93 ps, the atoms and ions have been heated significantly and the main part of a joint Maxwell distribution is established [7].

This estimation fits well with the shadowgraphs acquired in this work. In Fig. 2, the narrow stripe patterns first start developing at the top of images (b) and (d), i.e., after 970 fs and 768 fs, respectively. After about 3 ps, in Fig. 5a and c, the energy transfer from the electrons to the atoms and ions has continued and the temperature-induced stripe pattern has fully evolved.

Furthermore, Fig. 5 shows that the patterns created by a higher-intensity pump pulse start fading with increasing penetration depth, while the patterns created by a lower-intensity pump pulse extend throughout the whole image. This indicates the higher-intensity pump pulse has a smaller penetration depth compared to the lower-intensity pulse. The reason for this smaller penetration depth is attributed to the larger density of free electrons created by the higher-intensity pulse. As a result, more electrons are available to absorb the pump pulse while propagating through the material.

3.4 Micromachining results

The smaller penetration depth for pulses with larger intensity, as shown in the previous section, directly influences the micromachining results. For the two intensities, the PVC sample is irradiated by 25 consecutive pulses and the resulting ablation crater is imaged using a digital microscope with transmitted lighting. These microscope images are shown in Fig. 6.

Fig. 6
figure 6

Ablation craters of a PVC sample irradiated by 25 consecutive pulses with intensities of 6 \(\hbox {TW cm}^{-2}\) in (a) and 143 \(\hbox {TW cm}^{-2}\) in (b). The pulses impinged on the sample from the top. The crater produced by the lower-intensity pulses is less deep and shows a trail of material change significantly below the crater. The images are created using a digital microscope with transmitted lighting

Full size image

The crater produced by the lower-intensity pulses is much wider and less deep compared to the crater produced by the higher-intensity pulses. This is because the change in intensity was achieved by producing different focal spot sizes.

For 6 \(\hbox {TW cm}^{-2}\), material change significantly below the ablation crater is observed in the form of black dots with sizes of a few  \(\upmu \textrm{m}\). These black dots extend beyond the bottom of the image, more than 500 \(\upmu \textrm{m}\) below the sample surface, and are most likely bubbles of molten and resolidified material, as well as carbonized material. According to [7], phase transitions induced by ultrashort laser pulses are either based on heterogenous or homogenous nucleation. Heterogenous nucleation is energetically favored and occurs on interfaces of the material with vacuum or air. The result of this process is bubbles of resolidified material directly next to the ablation crater, which can be observed in both images of Fig. 6. In contrast to that, homogenous nucleation takes place in the bulk and results in the formation of small bubbles of molten material. Figure 5a and b shows that the pulse with an intensity of 6 \(\hbox {TW cm}^{-2}\) propagates far into the material without visible attenuation. Consequently, on its way, it excites the material and induces localized melting deep inside the bulk.

In contrast, the higher-intensity pulses do not cause visible material change below the ablation crater. This is attributed to the significant attenuation of the pulse on its way into the material, as observed in Fig. 5(c) and (d) and discussed in the previous section.

4 Conclusion

In this study, we analyze the energy deposition of ultrashort laser pulses in polyvinyl chloride using two-color pump-probe shadowgraphy. We show that a laser pulse with an intensity of 143 \(\hbox {TW cm}^{-2}\) causes significantly more ionization compared to a pulse with an intensity of 6 \(\hbox {TW cm}^{-2}\). We further show that this difference in ionization influences the propagation of the pulse into the bulk material. The lower-intensity pulse is not visibly attenuated within the shadowgraph field of view of about 250 \(\upmu \textrm{m}\). In contrast, the higher-intensity pulse is significantly attenuated before reaching the bottom of the shadowgraph. This is attributed to the different amounts of absorption caused by the free-electron plasma in the material. The shadowgraphs after 3 ps and 200 \(\upmu \textrm{s}\) show a temperature-induced shadowgraphy pattern with similar attenuation behavior. Moreover, the ablation craters produced by multiple consecutive pulses are compared for the two different intensities. The lower-intensity pulse causes significant material change deeply below the surface of the sample due to its propagation into the material. In contrast, no deep bulk material change is observed for the higher-intensity pulse, attributed to the significant attenuation.

These findings help to optimize laser micromachining for target fabrication in laser fusion research by localizing material change to the sample surface.