1. Introduction

The few cycle pulse (FCP) laser-solid interaction has paved ways to unique phenomena like unprecedented attosecond control in relativistic plasmas [1], novel attosecond lighthouse generation [2], and promises world changing future technology of petahertz electronics [3] based on driving sub-optical cycle electron dynamics in solids. Fundamental studies and applications involving FCPs require design and construction of FCP laser systems with ever increasing energy and repetition rates [4,5], which necessitates the development of next-generation ultra-broadband high damage threshold optics [6]. Some recent works have addressed current state-of-the-art performances [7] of such optics, and also discovered anomalous FCP-induced mechanical saturation effects [8] causing failure in complex optical thin film systems like ultra-broadband chirped mirrors. In the light of these works, it is abundantly clear that at present, ultra-broadband optics have nearly an order of magnitude lower laser induced damage threshold (LIDT) interacting with FCP lasers than those of the best broadband optics used for 40 fs laser pulses and beyond [9]. Therefore, it is apparent that there is significant room for improvement in the damage performance of FCP optics. However, we believe that this is impossible without adequate understanding of the FCP ablation physics of thin optical films, which is currently lacking. As a logical first step towards the understanding of FCP-induced damage and ablation of complex multi-layer thin film optics, a study of the interaction with a single layer thin film is necessary.

Studying FCP ablation of a single layer thin film systems is also interesting from a fundamental perspective since the uniformity of the interaction across the thickness of the film could help in understanding physical processes of the interaction, including the non-equilibrium effects due to extremely fast creation of a high density of excited electrons. So far, there have not been many rigorous studies of single pulse laser ablation of thin film optics in the femtosecond regime [10,11], and FCP ablation studies in general are rare [12]. To the best of our knowledge, there have been no time-resolved studies of FCP ablation of thin films prior to this work.

In this work, we present experimental observations of pulse duration dependence (9 to 150 fs) of single shot ablation crater morphology on two single layer TiO₂ thin films (a reflection optimized sample and the other transmission optimized), and compare the time-resolved ablation dynamics between the two films with sub-ps resolution in a temporal range from 0 to 9.6 ns after the damaging pulse arrives. A one-dimensional model based on the finite-difference time-domain infrastructure is used towards understanding a mechanism for the observed crater morphologies, as well as to estimate the excited electron density prior to ablation.

2. Experimental methods

Single layer TiO₂ thin films on a SiO₂ substrate (custom fabricated by Spectra-Physics Vienna using a deposition method similar to that of chirped mirrors tested in [7]) were irradiated by single pulses with 150, 100, 50, and sub-10 fs pulse durations at an angle of incidence of 45° with p-polarization. Two film thicknesses were tested: an enhanced reflectivity “λ/4” thickness of 91.65 nm (∼ 18% reflectance at 800 nm) and an anti-reflective “λ/2” thickness of 183.3 nm (< 1% reflectance at 800 nm), optimized for 800 nm light incident at 45°. Both of the films were deposited using electron beam deposition under the same conditions. Figure 1 shows spectra of the sub-10 fs pulses and the longer pulses (top), and the reflectance spectra of the films provided by the manufacturer (bottom). Note that the variation of the reflectance over the pulse bandwidth is minimal, as shown by transmitted FCP spectrum calculated from the reflectance data in Fig. 1 (dotted red line in the top plot). Sub-10 fs FCPs with a nominal central wavelength of 760 nm were generated with a Ar-gas filled hollow core fiber and chirped mirror compressor system. A more detailed description of the laser system and laser-induced damage setup can be found in [7,8]. To measure the FCP pulse duration, the full-width half-maximum of the autocorrelation trace is measured from a home-built dispersionless scanning autocorrelator, and a Gaussian deconvolution factor of $\sqrt{2}$ is assumed to calculate a pulse duration of 9 ± 1 fs. The uncertainty is due to slow fluctuations in the pulse spectrum and energy, leading to fluctuations in the measured autocorrelation width. To achieve longer pulse durations, the hollow-core fiber is evacuated and the grating pulse compressor before the fiber is adjusted to vary the pulse duration. A single-shot autocorrelator is used to measure the longer pulse duration. Damage morphology was studied using an atomic force microscope (AFM, Flex Axiom, Nanosurf), which provides precise depth and lateral size information about the damage craters.

 

Fig. 1 Pulse spectra (top) and reflectance spectra (bottom) for p-pol. light incident at 45 degrees. The dotted red line (top) shows the calculated transmitted FCP spectrum through the λ/2 film.

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To study ablation dynamics, a time-resolved microscopy setup similar to [13] was used. A weak probe pulse is used to back-illuminate the sample at a given delay time after the strong pump pulse induces damage, forming an image of the surface in the in situ imaging setup, as shown in Fig. 2. Probe pulses are generated by frequency-doubling a pick-off of the strong pulses in a 250 μm thick BBO crystal followed by a 390 ± 20 nm bandpass filter (Semrock BrightLine FF01-390/40-25). An identical filter was used on the triggered in situ camera to block out scattered pump light as well as most of the flash due to plasma recombination during the laser ablation process. The probe pulses are delayed between 0 and ∼ 9.6 ns via an optical delay line before being weakly focused and transmitted through the sample surface into the in situ imaging setup. The bandwidth of the probe pulses is roughly 15 nm centered on 403 nm, and after passing through several mm of glass before reaching the sample surface, the pulse duration is estimated to be ∼200 fs. As mentioned above, the sample was moved after every laser shot so that the probe images correspond to single pulse damage. Zero delay between pump and probe pulses was determined to within the probe pulse duration by iteratively changing the delay while watching for signal to appear in the probe images. The sample is translated after every shot so that all probe images correspond to single pulse irradiation.

 

Fig. 2 Time-resolved transmission microscopy setup. Weak probe pulses back-illuminate the thin film, and an image of the surface is formed on a triggered CCD camera. An image of a crater is shown (top right), with a corresponding AFM depth profile (bottom right). The beam-normal focal spot profiles for 9 fs and 100 fs pulses are shown in the bottom left.

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3. Results and discussion

3.1. Crater morphology

A comparison of AFM images of ablation craters for the two film thicknesses and two pulse durations (9 and 100 fs) are shown in Fig. 3. The crater morphology for 9 fs pulse ablation on the thicker λ/2 sample exhibits a shallow region (<10 nm deep; region “A” in Fig. 3) surrounding a much deeper hole at the center of the site (∼130 nm deep; region “B”). The crater morphology of the λ/4 sample only exhibits a deep region, reaching the substrate. For 100 fs pulses with a similar fluence, craters on both sample thicknesses exhibit no shallow region. Note that the focal spot beam profiles for 9 fs and 100 fs pulses are nearly identical, as shown in Fig. 2. For slightly lower fluence shots on the λ/2 sample, a similar two-region morphology is exhibited for 100 fs pulse craters, but the size of the shallow region is small relative to the entire crater, in contrast to the 9 fs pulse craters. The range of fluences for which the two-region morphology is exhibited with 100 fs pulses is small compared to that for craters generated by the shorter pulses. For 100 fs pulses this range is comparable to the shot-to-shot fluence variations due to energy and focal spot size fluctuations, whereas for 9 fs pulses we could consistently generate craters that only exhibit a shallow region. Figure 4 shows AFM images of craters generated with 9, 50, 100, and 150 fs on the λ/2 sample, showing that for a fluence where the FCP generates a two-region morphology, the shallow region becomes smaller as the pulse duration is increased. We have observed the same two-step morphology generated by FCP on λ/2 single layer thin films (and absence of it in the case of λ/4 films) made from different materials and deposited using a different deposition method. A detailed discussion of this comparison is left for future work. The observed crater morphologies for the 9 fs pulses when the experiment was conducted at a vacuum pressure of roughly 1 mbar are the same as at atmospheric pressure. This indicates that non-linear interactions with the air, such as self-focusing, have little to no effect on the crater formation.

 

Fig. 3 Schematic of mechanism for two-region crater morphology on λ/2 thickness TiO₂ thin film. In the part of the beam that has high enough intensity, the approximately flat electron density distribution near the back of the film surpasses the threshold density, causing an abrupt change in depth in the crater.

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Fig. 4 AFM images comparing the crater morphology for the λ/2 thickness film for 150, 100, 50, and 9 fs pulses. The area of the shallow region of the crater is larger for shorter pulse durations.

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The difference in crater morphology between the two film thicknesses suggests that the thickness-dependent field distribution within the thin film plays a role in the damage process. For low intensity 760 nm light incident on the λ/2 film (183.3 nm thick), the cycle-averaged field has maxima at the front and back of the film and a minimum in the middle. The λ/4 film (91.65 nm) has a minimum at the front and a maximum at the back. If we assume for the moment that the field distribution maps in a straightforward way to the distribution of excitation of the lattice, then the fact that the λ/2 field distribution has maxima at the front and back could explain the two-region crater morphology: in the moderately intense wings of the beam, only the front part of the film ablates, but the back of the film is not excited enough to ablate since there is a “cold” layer of material corresponding to the minimum of the field distribution that must be surpassed. This corresponds to the shallow region of the crater. At the center of the beam where the intensity is largest, the back of the film is energetic enough to ablate through the “cold” middle layer, or the middle layer is excited enough that it ablates, giving rise to the deep region of the crater. However, determining the distribution of excitation of the film is not trivial since the pulse generates free carriers via non-linear photoionization and subsequently interacts with those carriers, which modifies the field distribution.

In order to get a better idea of the distribution of excitation across the thickness of the films, we performed one-dimensional finite-difference time-domain (FDTD) simulations similar to [14,15] to determine the density of excited electrons as a function of depth in the films. The simulations inherently capture thin film interference, and take into account nonlinear photoionization using the Keldysh model [16] and dynamic modifications to the refractive index due to excited electrons with the Drude model. For the electron momentum relaxation time in the Drude model we used 0.2 fs in accordance with [10]. The film thickness associated with normal incidence was used since the simulations are one-dimensional (λ/2 film has a thickness of 161.7 nm for normal incidence). Figure 5 shows excited electron density vs. depth for 9 fs pulses (left) and 100 fs pulses (right) on a λ/2 film. For 100 fs pulses, the excited electron density has a qualitatively similar distribution to the low intensity field distribution, showing a minimum in the center and maxima at the front and back. The electron density is slightly larger at the front of the film because the field is attenuated by free-carrier absorption before it reaches the back of the film. For 9 fs pulses, the bias towards the front of the film is much more pronounced since the intensity gradient across the film is much larger for shorter pulses, and the peak intensity is larger than for 100 fs pulses. This means that the generation of free carriers at the front of the film during the rising edge of the pulse is much larger than at the back, which subsequently leads to much greater attenuation of the rest of the pulse at the front of the film, resulting in a final electron distribution that is heavily biased towards the front. Note that the electron density has a minimum near the middle of the film and increases towards the back, but that the density at the front is larger by roughly an order of magnitude. Assuming that the criterion for ablation is that the excited electron density must exceed a threshold value [17,18], the shape of the electron density distribution could explain the abrupt depth change of the two-region crater morphology. Figure 6 shows a schematic of how the beam profile maps onto the crater depth profile. For the low intensity wings of the beam (position a in Fig. 6), only a thin layer near the front of the film has a final excited electron density that surpasses the threshold density, resulting in the shallow region of the crater. Treating the electron density distribution as approximately independent of depth past the depth of the shallow region, there is a position on the beam profile where the intensity is large enough to make the electron density in this part of the film equal to the threshold density (position b). This position corresponds to the sharp change in depth of the crater, and points on the beam profile closer to the center (e.g. position c) correspond to the electron density distribution being entirely above the threshold, resulting in the deep central crater. It must be noted that the FDTD simulations do not take into account avalanche ionization, which could lead to an even more biased electron distribution towards the front of the film.

 

Fig. 5 FDTD simulation results: final excited electron density (on a logarithmic scale) as a function of depth in the λ/2 thickness film for 9 fs (left) and 100 fs (right) pulses. The excitation distribution for 9 fs pulses is heavily biased towards the front of the film relative to that for 100 fs pulses.

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Fig. 6 Schematic of mechanism for two-region crater morphology on λ/2 thickness TiO₂ thin film. In the part of the beam that has high enough intensity, the approximately flat electron density distribution near the back of the film surpasses the threshold density (b and c), causing an abrupt change in depth in the crater.

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Thin film optics are typically designed to have strongly wavelength-dependent properties such as a high reflectance over a specific bandwidth, so it is important to consider how the spectral distribution of the broadband 9 fs pulses plays a role in the observed damage of the single layer thin film samples. The reflectance of the two samples is relatively flat over the FCP bandwidth (see Fig. 1), so any dependence of the damage morphologies on the spectral distrubition would most likely not be due to the wavelength-dependent thin film interference. Note that since the thin film interference is inherent in the FDTD simulations, the wavelength dependent interference properties are taken into account in our model. The FCP spectrum probably plays a much larger role in how the nonlinear ionization dynamics affect the damage of the single layer thin films. To first order, if the spectral distribution were changed so that the instantaneous frequency within the envelope of the pulse is changed, the photoionziation rate will change according to multiphoton/tunneling ionization models, which could change the distribution of free-carrier excitation within the films. It is also worth noting that the use of the Keldysh model for photoionization may not be a valid approach for FCP-solid interactions [19,20]. In [20], Zhokhov et al. suggest that for two-cycle pulses interacting with a material with a given bandgap, the Keldysh model signifcantly underestimates the final excited electron density, and Gruzdev et al. show that the rapidly changing envelope of a FCP leads to transient dynamics to the effective bandgap in [19], leading to significant changes in the ionization rate during the pulse. However, the 9 fs pulses used in the current work are wide enough in duration that the transient effects specific to FCP are not significant, according to [19], and the Keldysh model is most likely a good approximation in this case. It is also important to note that our model to explain the FCP generated two stage ablation crater for λ/2 films do not depend on specific photoionization model; all that is required is that the rate is large enough to create high free-carrier (electron in the conduction band) densities on the near-surface atomic layers to dynamically modify/attenuate the laser field as a function of depth inside the thin film layer. For example, were we to use the photoionization rates from [20] in our FDTD simulation instead of Keldysh rates, the density distribution would still be biased towards the front of the λ/2 film due to free carrier absorption and attenuation of the pulse. In fact, the effect could be even more extreme. Therefore, our qualitative arguments for the proposed mechanism of the two-step morphology formation should remain valid.

3.2. Ablation dynamics

Ablation dynamics were studied for 9 fs and 100 fs pulses on both film thicknesses. The four experimental configurations show similar dynamics over the 0 to ∼9.6 ns delay range tested to what would be expected from the generally accepted picture of femtosecond laser ablation [21,22]. Figure 7 shows a typical example for 9 fs pulse ablation on the λ/4 sample. During the first ∼10 ps after the pump pulse hits the surface the irradiated site looks dark and blurry in the probe transmission image, which most likely corresponds to pump pulse-generated excited electrons thermalizing among themselves and beginning to transfer energy to the “cold” lattice via electron-phonon interactions [21,22]. After 10 ps, concentric interference rings, or “Newton’s rings”, form, marking the onset of material removal [23,24]. The rings increase in number and become more closely spaced until ∼1300 ps, when they are no longer resolvable in the image. After the rings disappear, the damage site appears dark and sharp crater borders begin to develop as well as bumpy ripple-like structures at the center of the crater. These structures could be due to void formation that is thought to occur in the “spallative” regime of ablation where an intact layer of material is removed from the surface as a result of rapid material expansion after ultrafast heating [22].

 

Fig. 7 Time-resolved transmission microscopy images of evolution of single pulse ablation on the λ/4 film with 9 fs pulses. From left to right, the damage site initially appears dark and blurry (0 < Δt < ∼ 10ps), then concentric ring fringes form due to material removal (∼ 10 < Δt <∼ 1300ps), followed by what appears to be voids in the center of a crater (∼ 1300ps < Δt <?). The rightmost image shows the final damage crater.

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The Newton’s rings that appear between 10 and 1300 ps have been observed by other groups for single pulse ablation of metals, semiconductors [13, 25, 26], and dielectrics [27, 28]. The rings are thought to arise from reflections off of two optically sharp interfaces: an intact ablating layer and the interface between the laser-excited region and the rest of the bulk [23, 25]. The formation of the intact layer can be explained when considering the rapid (isentropic) expansion of the laser-heated material that has a temperature comparable to the critical temperature. As the material expands away from the bulk, the material around the low density tail of the corresponding rarefaction wave is in the liquid-gas coexistence regime and the sound speed is significantly lower than for high density material near the head of the wave. This discontinuity in sound speed causes a plateau of nearly uniform density to form (corresponding to the density at the boundary of the liquid-gas coexistence region in p − ρ space), as well as a sharp density gradient at the expanding front. The head of the rarefaction wave reflects off of the cold bulk and meets up with the plateau, causing a region of uniformly decreasing density between the bulk boundary and the plateau, which forms the ablating layer [24,29].

The evolution of the height profile, h(x, t), of the ablating layer can be determined by tracking the positions of the bright fringes at each delay time, and also requires information about the index of refraction, n, of the material between the bulk boundary and ablating layer. Without knowing the index n, we can extract the “optical height”, n × h(x, t), from the fringe evolution. The “optical velocity”, $\frac{d}{dt}\left(n\times h(x,t)\right)$, was calculated to be ∼1050 m/s at the center of the irradiated spot, comparable to what Garcia-Lechuga et. al. measured for bulk LiNbO₃ [27], which has similar optical properties to TiO₂.

When comparing the ablation dynamics between the two film thicknesses, the formation time and optical velocity of the ablating layer are essentially the same. The visibility of the fringes for the λ/2 sample is lower than for the λ/4 sample, especially for the 9 fs pulse excitation, as shown in Fig. 8. For 9 fs ablation on the λ/2 film, the fringes are only visible in the part of the site corresponding to the shallow region of final crater, and the center of the site where the deep region forms appears dark and blurry at these delays. On the λ/4 film, the fringes have a higher contrast and are visible throughout the entire irradiated site for 9 and 100 fs pulses. Since the fringes on the λ/2 sample are only visible in the shallow region of the crater, the ablating layer there consists of a small amount of material, which could be consistent with the low fringe visibility there. After the fringes disappear (Δt ≳1300 ps), the center of the site for the λ/2 film with 9 fs pulses remains dark and blurry, while void-like structures appear in the shallow region. These structures don’t appear in the center of the site until several ns later, as shown in Fig. 9. For 100 fs ablation on the λ/2 film, the void-like structures appear at the center of the site at a similarly long delay time, but because the area of the shallow region of the final crater is so small compared to that of the deep region, it is difficult to tell whether the ablation dynamics in this range of delays are similar to the 9 fs pulse ablation. In contrast to the λ/2 film, the void-like structures appear much sooner after the fringes disappear on the λ/4 film for the both pulse durations. This suggests that for the λ/2 film, where the field distribution has maxima at the front and back of the film and a minimum in the middle, the ablation occurs in two stages, where a thin layer of material at the front is removed first, causing interference rings, followed by the material in the deep region of the crater that is removed in a less orderly fashion.

 

Fig. 8 A comparison of the interference fringe contrast between four experimental configurations during the spallative ablation of the λ/4 (left column) and λ/2 (right column) films. The top row corresponds to 9 fs pulses; the bottom to 100 fs pulses. The fringe contrast for the λ/2 film with 9 fs pulses (top right) is very low, and fringes are only resolvable in the region corresponding to the shallow part of the final crater (region A in Fig. 3))

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Fig. 9 Comparison of formation time of void-like structures between the two film thicknesses for 9 fs pulse ablation. For the λ/2 film, the structures appear at roughly the same delay as they do for the λ/4 film, but only in the shallow region (region A, Fig. 3) of the crater (center frame, bottom row). The structures only become visible in the central deep region (region B, fig. 3) roughly 2 ns later (bottom left frame).

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3.3. Estimation of excited electron density

An estimate of the excited electron density from the transient optical properties of the interaction region for early delay times was made from the TRSM measurements using the Drude model. The shape of the electron density distribution as a functnion of depth within the film was extracted from the FDTD simulation (e.g. Fig. 5) and was used with the Drude model to model the depth dependent index of refraction of the film that the probe pulse experiences. The peak value of the electron density distribution, N_e,0, was used as a free parameter and was varied until the calculated change in transmission of the excited film at the probe wavelength matched the measured value. For the λ/2 film with 9 fs pulses, the relative change in transmission decreases from 0 to $\frac{\mathrm{\Delta }T}{T}\approx -0.75$ in about 250 fs, which is roughly the temporal resolution of the setup determined by the probe pulse duration. The transmission increases steadily until reaching $\frac{\mathrm{\Delta }T}{T}\approx -0.7$ at Δt = 10 ps, when the interference fringes due to ablation begin to form. For $\frac{\mathrm{\Delta }T}{T}\approx -0.75$, the peak electron density at the center of the interaction region is estimated to be between N_e,0 = 5 × 10²² and 12.5 × 10²² cm⁻³, which is between 10% and 25% of the valence electron density of TiO₂ (∼ 5 × 10²³ cm⁻³), respectively. Note that these values are roughly an order of magnitude larger than the plasma critical density $N_{\mathit{crit}}=\frac{4{\pi }^2{n}_{{\mathit{TiO}}_2}^2{∊}_{0}m{c}^2}{{\lambda }_L^2{e}^2}\approx 1.1\times {10}^{22}$ cm⁻³, where n_TiO2 = 2.35 is the unexcited index of refraction of TiO₂ at the pump pulse central wavelength λ_L = 760 nm. The estimated range of excited electron densities prior to ablation are higher than the plasma critical density, which is consistent with the threshold criterion used by Austin et. al. [18] based on the level of ionization of the valence band.

4. Conclusion

We have systematically performed time-resolved studies of few cycle pulse laser ablation of two types of single layer thin films of TiO₂, each thickness optimized for maximizing either reflection (λ/4) or transmission (λ/2). We found qualitative differences in ablation dynamics and crater morphology of the two types of films. We also found that the dependence of the dynamics and crater morphology on the pulse duration is only exhibited by the λ/2 film. For a fixed fluence, the FCP-generated crater exhibits a deep crater surrounded by a shallow region that is large in area. As the pulse duration is increased, the area of the shallow region shrinks until it is almost gone for pulses longer than 100 fs. Our time-resolved surface microscopy observations suggest that the two concentric regions of the crater are created by different mechanisms: first, a thin layer of material corresponding to the shallow region undergoes spallative ablation, remaining relatively intact as it expands away from the surface, resulting in interference rings in the TRSM images; and second, the material in the deep region takes longer to ablate and does not remain as intact, with void-like structures appearing much later in the deep region and with no associated interference rings. Our 1-D FDTD model seems to corroborate this by showing that for 9 fs pulses the excited electron density distribution is largest in a shallow region at the front of the film due to a large intensity gradient across the film during the rising edge of the pulse, as well as free-carrier absorption. The ablation threshold is satisfied only in this shallow region in the moderately intensity wings of the pulse, and is satisfied over the entire film thickness near the center of the beam, resulting in shallow and deep regions of the crater. For longer pulses, the intensity gradient during the rising edge is not as great, and the resulting excited electron distribution is not heavily skewed towards the front of the film, which results in almost no shallow region in the final crater. For the case of the λ/4 film, the entire crater is formed spallatively by the removal of a intact layer, since the interference rings are visible throughout the interaction region. From the evolution of the fringes, we measured optical velocities of the ablating layer that are consistent with previous ablation dynamics measurement of ultrashort pulse interaction with dielectrics [27]. We also estimated the excited electron density from the relative change in probe transmission at early time delays, and found values that could be consistent with a threshold criterion based on the degree of valence band ionization rather than on the plasma critical density [18]. In the future, we plan to extend this study to two layer systems and beyond to gain an understanding of damage mechanisms of complex optical systems interacting with few cycle laser pulses.