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Abstract
In this study we explore optical absorptance of single-layer hafnia dielectric coatings deposited on fused silica by ion beam sputtering technique. We investigate both linear and nonlinear absorptance by varying the laser intensity of 10 ps pulses at a 1 MHz repetition rate across wavelengths of 1064 nm, 532 nm, and 355 nm. Significant differences were observed between the as-deposited and thermally treated coatings. The as-deposited sample exhibited diminishing absorptance, while the thermally treated coatings showed an increase in absorption. Furthermore, our study delves into the strong impact of the pump wavelength on the nonlinear response. These findings bear potential significance in enhancing our understanding of the long-term effects in optical coatings. This understanding could prove crucial in the context of fatigue or laser-induced damage.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The advancement of highly intense light sources has been propelled by the emergence of new applications, such as high harmonic generation, table-top particle accelerators, and nuclear fusion [1,2]. Nevertheless, the intense light generated within these lasers also imposes a significant strain on their integrated optical components. Consequently, the coatings on these elements tend to absorb light and emit heat, which ultimately constrain the durability and the maximum achievable focused power of the entire optical system. Since the absorption of dielectric coatings is influenced not only by the wavelength but also by the intensity, careful attention must be given to these effects when developing coatings for cutting-edge lasers. This has driven scientists to closely examine these effects on various optical surfaces, leading to a multitude of performed nonlinear absorption measurements. One of the first and most popular techniques to measure the nonlinear absorption is using a Z-scan method [3–9] implementing the transmission-reflection technique. Z-scan is a convenient method used to evaluate the nonlinear refractive index and multiphoton ($\beta$) as well as linear absorption ($\alpha$) constants from the absorption measurements [3]. Ganeev et al. [4] reported $\beta$ values for various media (such as semiconductors, metals, crystals) using 1064 nm and 532 nm wavelength laser radiation. Correa et al. proposed theoretical formulae to fit two-, three-, four- and five-photon absorption processes with Z-scan [6]. Nagaraja et al. studied nonlinearity of ZnO thin films of various annealing temperatures on quartz substrates [5] using CW He-Ne laser radiation with a Z-scan method. Nonlinear coefficient was calculated from linear absorption measurements. It was noted that the nonlinear coefficient increases with increasing annealing temperature and decreases with increasing intensity. Zeyada et al. noticed that $\beta$ of $\alpha$-PbO$_2$ increases with photon energy and, in contrast to [5], decreases with annealing temperature [8]. Razskazovskaya et al. measured and calculated 2-photon-absorption (2PA) coefficients for dispersive dielectric multilayer coatings (HfO$_2$/SiO$_2$, Ta$_2$O$_5$/SiO$_2$) [7]. They found that the multilayer coating structure influences significant nonlinear absorption response. Chen et al. measured 2PA and 3PA for HfO$_2$, SiO$_2$ and Al$_2$O$_3$ thin films and bulk material of various thickness [9] with 515 nm and 343 nm wavelengths. They noticed that 2PA and 3PA constants vary depending on the coating/material thickness. It was also noted that the nonlinear response of a substrate influenced the coating response. The influence of a substrate using Z-scan method to measure the coating absorption has been also recorded in [10]. The Z-scan measurements hardly account for the thermo-optical effects arising from cumulative heating with a high enough repetition rate. Furthermore, extinction coefficients obtained by Z-scan contain both scatter and absorption contributions because it is difficult to separate these losses by simply measuring transmission and reflection spectra [11]. Apel et al. reported nonlinear absorptance for Al$_2$O$_3$ films of different thickness using an ArF laser calorimeter at 193 nm wavelength [12]. It was noted that the nonlinear absorption constant cannot be defined by a single value for different thickness coatings. Additionally, this method acquires absorption of the sample after few minutes of laser exposure, which effectively measures inaccurate properties of an affected sample. Papernov et al. measured absorption-based annealing of HfO$_2$ coated on a 500 nm thick SiO$_2$ film [13] using a photothermal heterodyne imaging (PHI) technique. It utilizes pump-probe measurement method. With this technique absorption change in time and surface absorption was measured. It was noticed that the sample absorption signal was decreasing with time and this change was attributed to a local annealing on the exposed area. However, this method takes a lot of time to measure the surface absorption in comparison to other known absorption techniques. The annealing of the sample using absorption measurement techniques was also observed in [14]. Another pump-probe-like absorption measurement method is the laser-induced deflection method [11]. Even though it is an accurate measurement technique able to determine nonlinear absorption constant, it is time-consuming.
While the fundamental principles of nonlinear absorption phenomena are understood, there remain certain aspects of optical coatings that lack clarity. This is attributed to several reasons. Firstly, due to their limited thickness, coatings tend to exhibit minimal losses, necessitating extended integration times for measurable thermal responses in most absorption measurement techniques [11,12]. The exploration of nonlinear effects demands the application of both high intensity and high average power. Consequently, acquiring a single data point involves subjecting the sample to laser irradiation for several minutes, potentially inducing changes in the sample or coating properties over that duration. Secondly, optical coatings are not uniformly homogeneous - they contain defects and impurities [4,8,15] and are composed of multiple layers of distinct materials. This inherent complexity makes systematic absorption studies intricate [7,16–18].
To investigate the influences of thermal and laser annealing, as well as the pump wavelength on nonlinear absorption, we opted to undertake a case study involving single-layer hafnia coatings in both their as-deposited and thermally treated states. To achieve this, we employed a sensitive photothermal common-path interferometry technique (PCI [19]). We utilized a high-power laser source that operated at wavelengths of 1064 nm, 532 nm, and 355 nm, with repetition rates of 1 MHz and 400 kHz with a pulse duration of 10 ps. The experimental findings are supplemented by an analysis of the nonlinearity order and are accompanied by in-depth discussions to provide a thorough understanding of the observed phenomena.
2. Materials and methods
2.1 Preparation of samples
For this study we investigate three HfO$_2$ single layer thin-film coatings deposited on fused-silica substrates (6QWOT @355 nm, AOI=0), grown at the company Optoman in Vilnius, Lithuania. The coatings were deposited using ion beam sputtering (IBS) technique on 6.35 mm thick fused-silica (UV-grade) substrates from the same polishing batch. An IBS coating plant from Cutting Edge Coatings GmbH was used for deposition. The apparatus was equipped with two vacuum pumps: a combination of a cryopump with a mechanical pump resulted in a base pressure of 6 - 8 $\times$ 10$^{-6}$ mbar. During the process, oxygen gas was supplied toward the substrate to ensure a complete oxidation of the growing coating. The resulting working pressure was 3 - 4 $\times$ 10$^{-5}$ mbar. A radio-frequency grid-system-based ion source was used to strike a plane metal zone target of hafnium at an angle of incidence of 55 deg. Typical parameters of the main ion source, using argon gas, were set to 1650 V, 230 mA, resulting in deposition speeds of 0.75 - 0.8 Å/s. The thicknesses of growing films were monitored by an integrated broadband transmission optical monitoring system in the wavelength range of 400 – 1000 nm. All films were of the same physical thickness (261 nm) with the same initial optical thickness, namely 6QWOT @355 nm - 6$\lambda$/4$\textit {n}$, where $\textit {n}$ is the refractive index. After deposition one coating was left as-deposited (room temperature - RT) while the other two were thermally annealed using two different temperatures (low - 350$^{\circ }$C and high - 500$^{\circ }$C) for 1 hour. The coatings after annealing were still amorphous. According to a recent study by Abromavičius et al. [20], hafnia tends to undergo crystallization at temperatures of 600$^{\circ }$C or higher.
2.2 Analysis of spectrophotometric data
To determine both the physical thickness and refractive index of the coatings under investigation, we first conducted reflectance and transmittance measurements within the spectral range of 185 - 1500 nm. These measurements were carried out using an RT Photon spectrophotometer (Essent Optics) at a near-normal angle of incidence. The next step involved fitting the experimental spectra by employing numerical simulations of reflectance-transmittance spectra. This simulation was performed within a substrate/single-layer optical system, specifically within a spectral region with low absorptance. To accomplish this analysis, we utilized Optichar, a powerful optical characterization software developed by Optilayer. Numerical simulation process uses a combination of the transfer matrix method, the Sellmeier model for refractive index dispersion formula, and the Fresnel reflectance formulae. In our analysis, we assumed that the refractive index remains constant throughout the entire layer of the coating. Subsequently, the best fitted values from the Sellmeier dispersion model provided a detailed representation of the refractive index at various wavelengths within the coating material. Finally, the physical thickness of the coating corresponding to the best spectral fit was identified as the physical thickness of the sample.
Extinction coefficient k and absorption coefficient $\alpha$ were also deduced from an energy conservation relation for light by taking into account substrate losses, coating thickness, and neglecting the scattering part:
where $\textit {R, A, S}$ and $\textit {T}$ are fractions of reflected, absorbed, scattered, and transmitted light, respectively. The absorption bandgap values for the samples were determined from calculated extinction k spectra [8]. The summarized mean values of physical coating thicknesses, refractive indices at investigated wavelengths as well as bandgaps are in Table 1.
Table 1. Spectral and physical parameters of HfO$_2$ coatings.
2.3 Photothermal common-path interferometry
Figure 1 shows PCI measurement setup. In our experiments in the pump arm we use modulated Ekspla Atlantic 80 laser radiation with 1064 nm, 532 nm and 355 nm wavelengths at 1 MHz and 400 kHz repetition rates delivering 10 ps pulse duration as the pump source. The pump beam spot varied for different wavelengths from 59 $\mu$m to 71 $\mu$m at 1/e$^2$ level. In the probe arm we use continuous-wave (CW) He-Ne laser at 633 nm with the 200 $\mu$m beam spot at 1/e$^2$ level.
The measurement is conducted as follows: pump and probe beams are overlapped on the surface of the sample. The pump beam is modulated at 390 Hz creating a periodically alternating thermal lensing which is being sensed by the probe. The distorted wavefront in the central part of the probe beam interferes with its unaffected part during the propagation and then reaches the imaging unit where it is recorded using a lock-in amplifier. The absorption of the coating sample is calculated using calibrated data of reference sample with a known absorption.
For the experiments we use two measurement protocols: transverse-scan (T-scan) and temporal measurement (time-scan). T-scan is a fresh surface absorption measurement obtained on a moving sample. In this case we measure the absorption of the coating in a line of 1 mm length without significant coating degradation. Each fresh site is exposed to the laser radiation for 100 ms (fastest integration speed of the system) with the overlap of 50${\% }$ of the beam diameter. Time-scan is a temporal absorption measurement type where we measure one site on the sample surface for 10 min and register the changing absorption signal over time. The absorption was measured as a function of laser radiation intensity using both protocols. For each new scan previously unexposed area was chosen. The minimum distance between test sites for each protocol was kept of three beam diameters.
2.4 Analysis of nonlinear response
For the absorption data interpretation we consider a linear and intensity-dependent multiphoton absorption (MPA) [4,9,11,12]:
where $\alpha _0$ is linear absorption coefficient, $\beta _n$ is m-th order nonlinear absorption coefficient, $m = \lfloor \frac {E_g}{h\nu } \rfloor$ is the number of photons needed for the MPA (E$_g$ - bandgap of the material, h$\nu$ - photon energy), I - laser intensity, h - coating thickness. Since it is know that the absorption coefficients vary depending on the coating thickness, we evaluate the absorption including the thickness into the equation [11,12]. The multiphoton absorption process in a material takes place when the combined N-photon excitation energy is equal or higher than the material bandgap. However, as it will be shown in the following section, lower than N-th order of absorption was sufficient to cause nonlinear response in some cases, thus indicating the possible role of sub-bandgap states. In our case, photon energies are: 1.17 eV (1064 nm), 2.33 eV (532 nm) and 3.49 eV (355 nm). To fit the data we first determined the order of the multiphoton process for each sample at each wavelength. Then we fit our data using Eq. (2) with every component to the highest order of the MPA. In later analysis we define the MPA process by the highest order of it. $\alpha _0$ and $\beta _n$ are the free parameters while I and h are fixed. The $\alpha _0$ in the model defines the linear absorption in the material. The nonlinear coefficients $\beta _n$ define the slope of the curve.3. Results and discussion
3.1 Spectral analysis
We initiated our investigation by assessing the linear absorptance through the analysis of reflection and transmission data for all three coatings. Determination of the bandgaps was accomplished by applying tangential fitting to the linear segment of the absorption edge spectrum, as illustrated in Fig. 2. The acquired values for $\textit {E}_g$, which represent the bandgap of HfO$_2$, closely aligned with those previously reported in in [9,21]. Notably, subjecting the coating to thermal annealing at a temperature of 350$^{\circ }$C led to a significant increase in the bandgap by 1 eV, as indicated in Table 1. Elevating the annealing temperature to 500$^{\circ }$C resulted in only marginal further enhancement of the bandgap, while concurrently inducing a reduction in the refractive index at ultraviolet wavelengths. The fact that the absorption spectrum bends towards lower energy optical gap, means that there are some impurities in the coating that lower the bandgap [8,22]. This characteristic feature is known as the Urbach tail or Urbach energy. In the context of this study, its existence might signify the occurrence of mid-gap states in the as-deposited sample due to an incomplete oxidation process. A similar increase in bandgap as well as reduction of the absorption with annealing temperature have been reported in [5,21].
Fig. 2. Spectral characteristics of HfO$_2$ thin films: (a) refractive index dependence on the wavelength, (b) bandgap evaluation using Tauc method at different annealing temperatures according to [8].
Interestingly, the apparent end of Urbach tail in thermally annealed coatings coincides with the optical bandgap of as-deposited coating. When considering nonlinear absorption, the presence of the Urbach tail can potentially exert an influence on the genuine multiphoton processes, thereby leading to a potential reduction in its m-th order, which is estimated based on the bandgap.
3.2 Temporal absorption characterisation
As detailed in Section 2.3, two distinct measurement protocols were employed to assess the absorption within the sample coatings. To provide a clearer illustration, let us initially delve into the examination of time-scan data. Figure 3 presents the absorption outcomes from the time-scan analysis for each sample at the highest applied intensity level corresponding to each respective wavelength. The beginning of the measurement is indicated by a peak or dip in the absorption signal, which is attributed to the sample being repositioned to a fresh location. The increase in absorption with shorter wavelength is attributed to the hafnia spectral characteristics discussed in Section 3.1. With low energy photons (or 1064 nm wavelength) the absorption is minimal, however, with increasing photon energy, we approach the absorption spectrum edge where a significant increase in absorption can be seen. The difference in intensities with each wavelength showcases that with longer wavelengths we need stronger intensities in order to observe the nonlinear absorption.
Fig. 3. Raw time-scan data for HfO$_2$ RT, 350$^{\circ }$C and 500$^{\circ }$C samples at 1064 nm, 532 nm and 355 nm. The initial peak indicates the measurement start by moving the sample to the fresh site.
A general trend for RT coatings is the highest initial absorptance and its slow decrease in time at all investigated wavelengths. Such absorption decrease might be attributed to a laser annealing where the source of heat is localized shallow defect levels in the bandgap [5,8,13,14]. The decrease in absorption is likely associated with elevated local temperature: by irradiating the defect in a shallow state with low laser intensity, bound electrons are linearly excited to the conduction band (CB). As the intensity is not high enough to cause optical breakdown, the electrons relax by releasing heat. Thus, completion of oxidation process is possible at higher temperatures where interstitial metals join oxygen atoms upon repetitive irradiation.
Annealed samples show an opposite trend - the absorption signal is lowest at the beginning of irradiation, however, slowly increasing over time. This suggests the co-existence of the cumulative processes happening simultaneously. The energy from an intense laser pulse is absorbed by a solid via multiphoton absorption. In case the electrons, in a covalent bond they are excited to CB, that bond is broken by creating electron and hole pair. These pairs tend to form self-trapped excitons (STEs) that provide the energy necessary for localized lattice rearrangements and thus the creation of defects. STEs are long-lived and can accumulate during illumination by a sequence of pulses. In the oxide films shallow traps are typical and can manifest themselves as small tails in the transmission spectrum near the bandgap [23–26]. New defect states are created as a result of bond breaking and formation of STEs [27,28] which relax and lose their energy inside the solid through both delocalized and localized charge carrier channels [23]. This process is also known as color center formation and tends to increase the overall absorption of the irradiated area.
Another interesting observation is the fact that even though we see a strong annealing for RT sample at the beginning, the cumulative color center creation is also happening: it is very weak and is screened by linear absorptance. Nevertheless, it becomes apparent only after extended exposure time when absorption signal starts to rise again (not shown here). Laser annealing is reducing the absorption values to those similar of annealed samples, however, the latter samples are showcasing accumulation and an increase in absorption during the same exposure time. In simpler words, at lower intensity levels, multiphoton absorption exhibits inefficiency, leading primarily to the laser annealing process. This process is conditional to the applied laser intensity as well as linear absorption at respective wavelength. On the other hand, MPA becomes strongly dominant once the laser intensities are high enough. This process is the driving mechanism behind the formation of the color centers, inducing mid-band gap states and steadily increasing the absorptance due to its cumulative nature. As a result these factor contribute for substantial alterations in the temporal absorption characteristics at higher laser intensities and shorter wavelengths.
3.3 Nonlinear absorption and laser annealing
To exemplify the difference between time-scan and T-scan as well as the effect of repetition rate we firstly discuss the absorption results obtained for 355 nm wavelength. Figure 4 depicts T- and time-scan absorption as a function of intensity for two different pulse repetition rates.
Fig. 4. Comparison of absorption at 1 MHz and 400 kHz at 355 nm. (a) T-scan comparison, (b) time-scan comparison.
Firstly, let us analyze RT sample absorption behaviour. When measuring surface absorption (see Fig. 4(a)) at 1 MHz rep. rate, we noticed that with increasing intensity a decreasing absorption until a certain minimum value is observed. We attribute it to linear absorption that is changing due to laser annealing. When a plateau is reached laser-annealed linear absorption is minimal. The same behaviour can be observed for time-scan data (see Fig. 4(b)). However, in this case it is evident that the absorption value is significantly lower than that of T-scan. Another interesting observation is that at highest T-scan intensities at 400 kHz nonlinear absorption increase is not significantly pronounced. In this case we have two processes happening simultaneously - both nonlinear absorption as well as very fast laser annealing. However nonlinear part is screened by annealing and high linear absorption. A different absorption behaviour can be observed for the thermally processed samples. In this case there is no laser annealing at low intensities and we do not even observe linear absorption - in the whole intensity range we notice the nonlinear absorption increase. Furthermore, when the absorption values on the time-scan exceed those of the T-scan, it suggests a highly efficient cumulative process.
As can be seen from the data the repetition rate has no strong effect on T-scan data of annealed samples. Time-scan indicates faster annealing of RT samples at 1 MHz in comparison to 400 kHz. Furthermore, the accuracy of PCI system is very sensitive to the average power, thus, a higher repetition rate allows higher accuracy of measurement due to reduced noise. Hence, the following measurements were performed with 1 MHz repetition rate.
3.4 Effect of the pump wavelength
Figure 5 shows summarized T-scan and time-scan data for every sample at three wavelengths. Time-scan absorption results are reported after 10 minutes of irradiation. Here we see that the general behaviour discussed earlier in Fig. 4 follows the same trend with all used wavelengths.
Fig. 5. Absorption data for HfO$_2$ thin films at 1064 nm, 532 nm and 355 nm for each measurement protocol: (a) room temperature, (b) low temperature annealing, (c) high temperature annealing. Solid lines represent T-scan data fit and dashed lines represent time-scan data fit using Eq. (2). Grey lines represent an empirical power-law fit of nonlinear absorption at 355 nm.
The absorption behaviour at 1064 nm wavelength is, however, different: in the whole intensity range it is dominated by linear absorption and effect of laser-annealing is rather weak in comparison to other wavelengths. When measuring T-scans, we could not reach nonlinearity due to limited maximum laser output power. However, with the maximum applied laser output we start to notice nonlinear absorption in thermally processed samples after temporal exposure. Weak thermal annealing at infrared spectral region indicates the role of linear absorptance. As overall absorption level remains in ppm level, annealing is not efficient. Laser annealing is much more pronounced for 355 nm and 532 nm wavelengths respectively, where local temperatures can be elevated by hundreds or thousands of degrees.
At 355 nm wavelength of RT sample the last two data points corresponding to highest intensities for T-scan deviated from the general trend (see Fig. 5(a)). This is likely an artifact of the measurement due to the slow of a response of the system as well as a fast of an annealing at the high intensity (shortest integration time of the lock-in amplifier was 100 ms which resulted in 10$^4$ pulses passed during the integration period). These two data points are exempt of further analysis. However, this indicated that laser annealing as well as cumulative process can be very fast.
Interestingly enough, for thermally processed coatings we do not observe absorption difference between T-scan and time-scan values except for 355 nm. With 355 nm wavelength a substantial increase of absorption is observed after temporal exposure. This is most likely attributed to the very strong and effective creation of color centers and requires further investigations. At the highest intensities, however, T-scan and time-scan absorption do not differ. This result indicates that nonlinear absorption starts to dominate the absorption process and linear absorption becomes negligible.
The multiphoton absorption order m provides insight into the number of photons involved in the absorption process. Moreover, it is important to note that the probability of multiphoton absorption is directly related to the intensity of the incident light, with the intensity being raised to the power of the multiphoton absorption order m. In simpler terms, as the multiphoton absorption order increases, the intensity response exhibits "sharper" nonlinear growth. The specific multiphoton absorption order observed can vary depending on several factors, including the material bandgap and the wavelength of the incident light. To determine the dominant absorption order for the coatings under investigation, we employed polynomial fitting techniques (from Eq. (2)) on absorption data collected at varying intensities. This analysis allowed us to extract the prevailing absorption order that best characterizes the interaction between the incident light and the coating material. In the provided graphs the dominating multiphoton absorption orders (labeled as XPA) are illustrated, where "X" represents two-, three-, four-, or five-photon absorption. Notably, the consideration of five-photon absorption case was based only on factors such as the material’s bandgap and proton energy. These findings offer valuable insights into how the coating material interacts with incident light depending on applied laser intensities and wavelengths. The results of numerical analysis for each sample and all investigated wavelengths are summarized in the Table 2.
Table 2. Linear and nonlinear coefficients according to the absorption model, $\alpha _0$ = [cm$^{-1}$], $\beta _m$ = [cm$^{2m-1}/W^m$].
We see similar trends regardless of the annealing temperature: there exists a linear absorption region (usually also affected by annealing) followed by a nonlinear absorption of respective order to the wavelength. To fit nonlinear part we had to exclude lowest data points affected by laser annealing. As we can see, the polynomial model has no contradictions to absorption data. At 532 nm we observe mixed nonlinear response corresponding to 2 and 3 photons simultaneously. However, after analyzing the nonlinear absorption for 500$^{\circ }$C sample at the highest intensities at 355 nm, we noticed that the data deviated from the general 2PA trend that predicted linear response with respect to intensity.
Since we noticed that for 500$^{\circ }$C sample the 2PA process does not fully fit the deviated data points, we decided to empirically fit the nonlinear absorption with a power-law $A = xI^y$ function (x and y are fitting parameters). This resulted in the exponents of $y_{\mathrm{T-scan}}$ = 0.54 and $y_{\mathrm{Time-scan}}$ = 0.47. Interestingly enough, 1.54 and 1.47 of photon energy is needed to excite electrons from the VB to the CB (bandgap and photon energy ratio $E_g/h\nu$).
In scientific literature the data for nonlinear constants for dielectric coatings is quite scarce, for this reason it may be difficult to make direct comparisons. Chen et al. [9], however, found 2PA and 3PA constants for HfO$_2$ are 1.95 - 2.39 cm/GW and 5.05 $\times 10^{-5}$ - 5.11 $\times 10^{-5}$ cm$^3$/GW$^3$ respectively. In studies which took the coating thickness into account [11,12], even though different material coatings were investigated, the nonlinearity order of magnitude corresponds well with our results. From this analysis it is evident that the nonlinear response differs depending on the coating manufacturing conditions as well as post-production processing. There is also a rather large difference among linear absorption coefficients for RT and annealed samples. The general trend for nonlinear coefficients is that with annealing temperature the coefficients may decrease. Similar behaviour has been noticed in [8].
4. Conclusion
Within this study, we undertook an examination of the nonlinear characteristics inherent in single-layer coatings of hafnia fabricated with IBS. These coatings were subjected to the influence of high-intensity laser irradiation at three distinct wavelengths. At lower intensities, the predominant influence is that of linear absorptance, effectively obscuring the underlying nonlinear response. However, it is noteworthy that all the examined samples exhibited analogous nonlinear behavior when subjected to high laser intensities. A notable observation is the strong correlation between higher linear absorptance and an intensified laser annealing effect, manifesting as a gradual reduction in absorptance over time.
Studies of nonlinear absorption at different wavelengths indicate the different orders of magnitude with respect to intensity: weakest nonlinear response $\sim$ I$^1$ (two photon absorption) is observed for 355 nm wavelength, stronger response $\sim$ I$^1$+$\sim$ I$^2$ (two and three photon absorption at the same time) is for 532 nm. For 1064 nm intensity was not sufficient to observe significant nonlinear response due to limited laser output power.
Significantly, our analysis revealed the absence of a distinct correlation between linear and nonlinear absorptance. This underscores the conclusion that these quantities cannot serve as predictive indicators for each other. As expected, thermal annealing led to reduced linear absorption of hafnia coatings across all investigated wavelengths. No laser annealing neither laser-annealed linear absorption was observed in the thermally treated samples. Time-scan analysis suggested the occurrence of two simultaneous processes during the laser exposure: laser annealing, which reduced overall absorptance, and bond breaking followed by color-center creation, which increased absorptance. Overall, this study shows the complex behavior of hafnia coatings under intense laser light. The findings might contribute to a better understanding of nonlinear properties, which have important implications for various applications in the field.
Funding
European Regional Development Fund (Project No. 01.2.2-LMT-K-718-03-0004) under grant agreement with Research Council of Lithuania.
Acknowledgments
The authors acknowledge the support of UAB Optomenas for a donation of experimental samples. The authors acknowledge Martynas Keršys contribution to this work under agreement (P-SV-23-369) with the Research Council of Lithuania (LMTLT).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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