1. Introduction

2-photon active materials such as dyes, chromophores and photoinitiators (PI) have found broad applications in 3D nanolithography, 2-photon induced fluorescence microscopy (2PIF) and photodynamic therapy [1–5]. The 2PA cross section is given in Goeppert-Mayer Units (1 GM = 10⁻⁵⁰ cm⁴ s photons⁻¹ molecule⁻¹). It indicates the wavelength-dependent 2-photon absorbance behaviour of the compound and is considered high for values above 100 GM [6].

The z-scan technique, introduced in 1990, has become a standard method to characterize higher order nonlinearities such as the 2-photon absorption (2PA) cross section. Using a motorized stage, a thin sample (sample length L smaller than the Rayleigh length ${z_{R}}$ of the focused laser beam) is moved in and out of a focal plane of a laser beam along the z-axis (hence the name of the technique) [7]. The sample can be liquid or solid, as long as it is transparent to the excitation laser wavelength. Ideally, the beam waist is positioned around the middle of the translation stage range. A photo diode at the end of the stage collects the light transmitted through the sample. The discussed open aperture setup detects changes in transmission, which can then be used to calculate the 2PA cross section. The setup can be modified to measure the nonlinear refractive index of a material by adding an aperture before the measurement diode so that the change in beam divergence is detected [8].

There is an increasing need to characterize the 2PA spectra to optimize the performance of 2-photon active PIs for 2PP [9]. This is especially true for water soluble PIs required for biomedical applications [10,11]. On one hand, when such z-scan measurements are performed at the same wavelength used for 2PP, the obtained results might be sufficient for comparison of the expected practical performance of different PIs. On the other hand, the true potential of a certain molecular PI design remains unrevealed, if its complete nonlinear absorption spectrum is not characterized. Matching the laser wavelength to the peak of the 2PA spectrum of a particular compound can result in a few fold increase of the PI’s performance [12]. Most z-scan setups capable of spectral characterization are based on optical parametric amplifiers (OPA). The central wavelength of an OPA can be tuned in a very wide range but this is a time-consuming and cumbersome procedure [13]. Z-scan setups based on white light continuum (WLC) are able to determine absolute cross section values in a wide spectral range, but also require a complex optical path [12,14,15]. Femtosecond laser oscillators offer an alternative approach to amplified systems due to their wide tuning range. However their high repetition can cause thermal effects, which have to be eliminated [16]. The use of femtosecond laser oscillators also allows direct comparison between results from z-scan measurements and 2PP experiments, as the same high repetition rate lasers are used for 2PP. While the absolute cross sections can be determined, it is also possible to measure 2PA relative to a reference substance. However, calculating the absolute cross sections using the exact parameters of the z-scan system allows for a greater degree of control and reproducibility without the need of a reference substance.

To determine the absorption cross section ${\sigma _{2}}$ from the measured data, a variety of system parameters must be known. For the open aperture case, the change in transmission for a given sample position z can be described numerically by Eq. (1) [8].

Table 1. Uncertainties in the setup parameters can significantly affect the calculated 2PA cross section (${\sigma _{2}}$) by up to 30%. Change in ${\sigma _{2}}$ calculated by taking reference data for a 2PA absorbing compound with ${\sigma _{2}} = 150$ and Eq. (1) for a focused laser beam with 20 µm diameter, 70 fs pulse duration and power of 500 mW.

View Table

Exposing a sample to a high-powered laser beam can cause thermal effects, which affect the measured data [17–19]. The heating persists over a characteristic thermal time ${t_{c}} = {\omega _{0}}^2/4D$ [20] after which the sample returns to thermal equilibrium. This coefficient depends on the beam waist ${\omega _{0}}$ and the thermal diffusion coefficient D typically in the range of ${10^{ - 3}}$ to $6 \cdot {10^{ - 3}}$ cm² s⁻¹ for liquids. For lasers with a repetition rate higher than 0.1 kHz the time between exposure is shorter than ${t_{c}}$ causing cumulative heating. This effect has been documented for many z-scan setups measuring the nonlinear refractive index [17,21]. In this case, the absorbed light heats up the sample and the resulting temperature gradient causes a local variation in the sample density. This in turn changes the refractive index and leads to a lens-like behavior of the sample. By introducing a beam chopper, the material can return to equilibrium after being exposed to the laser source [17,19]. As increased energy can also cause higher ordered responses due to excited state absorption [12,22], a beam chopper was installed in the presented setup to allow the sample to return to thermal equilibrium similarly as in systems measuring the nonlinear refractive index [16–18].

The molecular structures of compounds analyzed in this study are displayed in Fig. 1. A common laser dye rhodamine B was chosen as the primary reference substance to calibrate the setup since its ${\sigma _{2}}$ at different wavelengths is well documented in literature [23]. The organosoluble PI M2CMK is typically used for 2PP using acrylate resins [24,25]. DAS is a water-soluble cleavable diazosulfonate-based initiator, which is a promising candidate as a biocompatible PI for 2PP of hydrogels in the presence of living cells [11].

 

Fig. 1. 2PA compounds used in this study. Rhodamine B is a laser dye, which was chosen as a reference standard for the setup [23]. M2CMK has been used in various 2PP applications [24,25]. The water-soluble PI DAS is used for 2PP structuring of biocompatible hydrogels [11,26].

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2. Methods and materials

2.1 Z-scan setup

The z-scan setup is powered by a high power femtosecond laser oscillator (MaiTai DeepSee, Spectra Physics, Santa Clara, USA) with a tuning range of 690-1040 nm and a repetition rate of 80 MHz. The beam passes through a number of optical components and a focusing lens onto the sample. A positive and negative achromatic doublet lens with a focal length of 200 mm is used (AC254-200-B, Thorlabs , Newton, United States), with achromatic coating (650 to 1050 nm). The setup is shown in Fig. 2. A motorized stage (LCS16-025-2(4)5, SMAC, Carlsbad, USA) operated by a one-axis controller (LCC-10, SMAC, Carlsbad, USA)) moves the sample through the focus. A photodiode (PDA100A-EC, Thorlabs, Newton, United States) measures the transmitted light and a reference photodiode helps to compensate signal fluctuations. An oscilloscope (DS4024, Rigol, Beaverton, USA) records the signals from both diodes. A custom-built beam chopper reduces the exposure time of the sample to eliminate effects due to accumulation of multiple pulses [16,19]. A variable adapter allowed to increase the voltage to drive the chopper motor, thereby increasing the rotation frequency while at the same time reducing the on-time of the laser beam.

 

Fig. 2. Beam path from the tunable fs-laser to the sample. A waveplate and polarizing beam splitter attenuate the input laser power. After the chopper and before mirror 2, the beam is expanded by 4x. The expanders consists of two parabolic mirrors. A lens focuses the beam. A motorized stage moves the sample in and out of focus. Two diodes record the measurement- and reference signal while a mechanical chopper allows to adjust the on/off duration of the signal. A flip mirror allows to redirect the beam to an auto correlator to measure the pulse duration.

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Rhodamine B was purchased from Sigma-Aldrich (Merck KGaA, Darmstadt, Germany) and used as received. M2CMK and DAS were synthesized as previously described [11,24]. Solutions of 10 mM were prepared by dissolving rhodamine B in methanol, M2CMK in tetrahydrofuran (THF) and DAS in phosphate buffered saline (PBS). All solvents were bought from Sigma-Aldrich (Merck KGaA, Darmstadt, Germany) and used as received. The respective sample solutions were then filled into a quartz-glass cuvette of 1 mm thickness (120 µl volume, 170-000-1-40, Hellma-Analytics, Müllheim, Germany). The cuvette was placed onto the motorized stage using a 3D-printed socket. Z-scans were performed under static conditions.

Using a chopper, the data were acquired by triggering the oscilloscope to the rising flank of the signal. As the chopper causes partial blocking of the laser beam upon opening and closing, the oscilloscope was required to select the area where a stable signal was recorded. This way, the average signal for a given stage position is recorded. Four different chopper settings with increasing frequency and therefore a shorter on-time (when the sample was exposed to a train of pulses from the oscillator) were compared. The diffusivity of solvents used in this work is in the range of 10⁻⁷, which yields ${t_{c}} < 0.5$ ms for a focused beam of 24 µm diameter [27]. For the final z-scan 90 Hz rotation frequency was selected, resulting in an on-time of 78 µs and 11.9 ms off-time, which was deemed sufficient for the sample to return to equilibrium after exposure.

2.2 Spectral calibration

A custom-programmed Graphical User Interface (GUI) allows the user to collect all system parameters required for the spectral z-scan. The comprehensive database is necessary to both reliably calculate the 2PA cross section from the fit parameter ${q_{0}}$ without any input by the user. Even a large amount of data is easily handled and correctly evaluated without the need to manually evaluate each measurement. The necessity for recalibration depends mostly on the stability of the used laser source. After a complete calibration, the system parameters were measured at 800 nm to determine if beam stability was given or if recalibration was required. A flip mirror directs the beam into an auto correlator to measure the pulse duration. The PreComp unit of the MaiTai allows dispersion optimization for optimal pulse duration. From 700 to 980 nm the compressor was optimized in 10 nm steps. For each wavelength eight different compressor positions were used to calculate the minimum pulse duration. At wavelengths below 700 nm and above 980 nm the output power was too weak to generate a detectable second harmonic signal required for an autocorrelator measurement.

Due to the possibility to tune the wavelength range in the visible to near infrared spectrum (690 - 1080 nm) a CMOS camera (UI-1492LE, IDS, Obersulm, Germany) could be used to determine the parameters of the laser beam. The camera approach was preferred over the knife edge method since it allowed live imaging without the need for an additional automated component like a moveable razor blade [28]. In addition, the high resolution of the camera chip (1.67 µm per pixel, taken from manual) is sufficient to extract the correct beam shape from the image. To extract the characteristic data from the 2D Gaussian beam registered by the camera chip an algorithm was developed.

Since in numerical analysis the rounding error is lower for numerical integration compared to differentiation the integrated Gaussian (error function) was used for our calculations [29]. Calculating the second order moments M₂₀ and M₀₂ and fitting with least-square algorithms (Levenberg-Marquardt algorithm) allows to extract the distribution parameters [29–31]. The process of extracting the characteristic data from the Gaussian beam was repeated for multiple stage positions (0-24 mm,1 mm steps). The obtained results enabled fitting of the beam waist $\omega (z)$, given by Eq. (5), extraction of the Rayleigh length ${z_{R}}$ and determining the focal position ${z_{0}}$ along the stage according to EN ISO 11146-1:2005 [32].

A motorized half-wave plate and a Glan-Taylor polarizer were used to regulate the average laser power P following the law of Malus which describes the power dependence on the polarization angle $\vartheta $. Using a powermeter (Fieldmax II, Coherent Inc, Santa Clara, USA) the average laser power was measured before passing the focusing lens for each wavelength in intervals of 5 nm. Due to the periodic nature of the waveplate retarder we selected rotation angles between 0 and 120 ° (measurement steps of 3 °). The values are stored both as textfiles, as well as a database within the operating software. This allows the user to select the power range for measuring. To automatically select the optimum measurement window for a given laser power the conversion factor from mW to V has to be known. This factor is also depending on the chosen wavelength due to the change in transmission of the optical filters and the quantum yield of the photo diode. The system automatically records signals for each wavelength in a given range and step size. The measurement diode triggers the oscilloscope to a minimum signal using the maximum measurement range (2.4 V) to evaluate the optimal signal range for each wavelength. This list of conversion factors guarantees optimal resolution for any given power and wavelength and eliminates a long and cumbersome manual calibration routine. A single Python based interface controls all hardware, eliminating waiting times due to multiple interfaces used. Once calibrated, a complete spectrum (3 measurements per wavelength in 10 nm steps) can be obtained within an hour, including delay times due to change of wavelength, pulse compressor and waveplate.

2.3 2PA compounds and 2PP

The 2PA components were dissolved in the respective solvent (rhodamine B in methanol, DAS in PBS and M2CMK in THF) at a concentration of 10 mM. These solutions were used for the z-scan measurements. After the individual 2PA spectra were obtained using the z-scan setup we used a concentration of 2 mM DAS in 10 wt % gelatin-methacrylamide hydrogel precursor (GelMA) for 2PP experiments with a degree of substitution of 95%, dissolved in PBS [33]. Using a 10x objective with NA of 0.3 (Plan-Apochromat” 10x/0.3 M27, Zeiss, Oberkochen, Germany) cubes of $100 \times 100 \times 100$ µm³ were structured at a constant scanning speed of 1000 mm s⁻¹ with an average laser power varying from 10 to 100 mW. 2PP structuring was performed at four different wavelengths (700, 720, 750 and 800 nm) to study the dependence of the polymerization threshold from the laser wavelength.

3. Results

Using our custom algorithm, the parameters ($z,{z_{R}},{\omega _{0}}$ and P) required for the fitting of ${q_{0}}$ were collected in a spectral range from 700 to 1000 nm (see Methods and Materials). To study the effect of wavelength dependence on the beam collimation a Galilean beam expander and a reflective beam expander were compared. As one would expect, without manual readjustment for each wavelength, the focal position of the laser beam shifted substantially for the Galilean beam expander while it remained constant for the reflective expander, as can be seen in [Fig. 3(a)].

 

Fig. 3. (a) Focal position for over the laser tuning range. Using a Galilean beam expander caused large shifts in the focal position if the collimation was not manually adjusted for each wavelength. In contrast, a reflective expander collimates the beam over the entire laser spectrum, causing only negligible shifts in focus. (b) Thermal z-scan comparison of Rhodamine B (10 mM in methanol at 800 nm) measured with and without chopper. The signal drop without chopper (straight line) was four times larger than when a chopper was used (squares). The measurement intensity was 37.1 GW cm⁻². A notable sharpening of the transmission curve for continuous exposure resulted in 89% of the signal change within $\pm 1.13 \cdot {z_{R}}$, compared to 69% for the chopper signal.

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Good beam quality for the reflective expander was indicated by the M² factor, which was almost exclusively below 1.2 [34]. No chromatic aberrations were observed. After acquiring the output laser powers for each wavelength, the conversion factors were determined. These factors calculate the signal range in mV for a given laser power. They are especially important, as the change in signal for the z-scan can be below one percent. This narrow window has to be carefully selected before the measurement to ensure the highest possible signal resolution and measurement accuracy. The conversion factors were recorded in 5 nm intervals for the entire laser spectrum. To determine the systematic uncertainty of measurements three laser powers (0.6, 0.8 and 1.0 W) were selected at 800 nm and 100 signals were recorded without any 2PA compound in the beam path. Uncertainty decreased from 0.11% at 0.6 W, to 0.02% at 1.0 W. This trend is a logical result as higher laser powers lead to a higher diode current and therefore the diode noise does not affect the signal as much.

Using a pulse compressor, the pulse duration was minimized to an average 70 fs from 750 to 950 nm. The pulse duration increased towards the edges of the laser spectrum to 110 fs at 700 nm and 95 fs at 1000 nm. Due to this pulse broadening the peak intensity was insufficient to generate a second harmonic signal required for auto correlator measurements above 1000 nm and below 700 nm. After a complete calibration, the system proved stable over several weeks. The most relevant factors influencing stability were determined to be the misalignment of the mirrors due to the fact that the laser was also used for 2PP experiments and the power stability of the provided laser source.

To illustrate the effects of heat accumulation due to the high repetition rate laser, measurements of a 10 mM solution of rhodamine B in methanol at 800 nm were performed under continuous exposure without a chopper and are summarized in [Fig. 3(b)]. These measurements exhibited a significantly larger drop than previously reported values [23]. Upon closer inspection, a notable sharpening of the transmission curve was registered. Under continuous exposure, the peak-to-valley distance of the transmission was smaller. 89% of the signal change occurred within $\pm 1.13 \cdot {z_{R}}$ [17], compared to 69% when using a chopper. This sharpening of the transmission curve could not be described with the beam parameters obtained from the beam profiling. A Rayleigh length 50% smaller than the measured Rayleigh length would have to be assumed, in order to fit the measured data points with R² > 0.9. In contrast, when using a chopper, the data could be reliably fitted with the measured Rayleigh length. To optimize the system four different chopper on-times (470, 210, 90 and 78 µs) were compared at two different laser power values (1.0 and 1.4 W, corresponding to 74 and 104 GW cm⁻², respectively). Each scan was repeated three times. Varying the power should not affect the calculated ${\sigma _{2}}$ and an increase of ${\sigma _{2}}$ with increasing intensity indicates that the observed absorption is no longer just caused by 2PA but potentially due to effects such as thermal heating or excited state absorption (ESA) [22]. For the longest exposure time the cross section at 104 GW cm⁻² was 20% larger than the measured cross section at 74 GW cm⁻². This was not the case for higher chopper frequencies at which an increase of average laser power resulted in fluctuations below 2.5%. [Fig. 4(a)] and corresponded to previous findings [12,23]. Spectral studies of rhodamine B were also independent of the laser power used for scanning. The laser intensities were 37 and 52 GW cm⁻² and a wavelength interval of 10 nm was selected. Rhodamine B showed high absorption close to 700 nm, a secondary maximum between 790 and 850 nm and a low 2PA cross section above 900 nm [Fig. 4(b)]. The spectral data were in good agreement with reference values from literature [12,23].

 

Fig. 4. (a) Four different chopper exposure times were selected to study the impact of heat accumulation due to the high laser repetition rates on the extracted cross section. For each exposure time the cross section was measured at 74 and 104 GW cm⁻² and the relative change in cross section was calculated. At 450 µs exposure time the change in extracted cross section was more than 20% indicating thermal effects. In contrast at chopper on times of 210 µs and below such behavior was not observed. (b) 2PA-spectrum of rhodamine B. The solid blue squares show data measured using the presented tunable z-scan setup with standard deviation below 5%. Black triangles are reference values measured using an OPA-based system [23], whereas dash-dotted data were measured using a z-scan setup based on white light continuum (WLC). No error bars for WLC are provided in source [12]. The data follow similar trends exhibiting high absorption in the region between 760 and 840 nm and lower absorption for longer wavelengths. Close to 700 nm the values obtained with the tunable system and the referenced amplified setup increase.

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For M2CMK at 22.5 GW cm⁻² onwards, the fit parameter ${q_{0}}$ - which corresponds to the 2PA coefficient $\beta $ - increased exponentially with the laser power [Fig. 5(a)]. Under pure 2PA conditions ${q_{0}}$ is expected to scale linearly to the laser power used, as described by Eq. (2). Higher laser powers also lead to a notable sharpening of the transmission curve, with 76% of the signal drop within $\pm 1.13 \cdot {z_{R}}$ compared to 65% [Fig. 5(b)], similarly to the results observed for rhodamine B under continuous exposure [Fig. 3(b)]. Likewise, the Rayleigh length measured via beam profiler, was insufficient to describe the shape of the transmission curve. For 37.5 GW cm⁻² a Rayleigh length of ${z_{fit}} = 0.5 \cdot {z_{R}}$ would have to be assumed in order to describe the results in accordance with Eq. (1). This was further indication, that the change in transmission was not caused by 2PA processes only [8]. Therefore, the intensity was reduced to 18.5 GW cm⁻² for each wavelength to obtain ${\sigma _{2}}$.

 

Fig. 5. (a) 2PA studies of M2CMK (10 mM solution in tetrahydrofuran) at 800 nm. In the pure 2PA case ${q_{0}}$ is expected to follow a linear trend, which was observed for measurement powers up to 18.5 GW cm⁻² (solid line). From 22 GW cm⁻² on ${q_{0}}$ followed an exponential trend (dashed line). (b) This exponential increase was also visible in the recorded transmission signal, where a notable sharpening of the curve can be seen between 15.0 GW cm⁻² and 37.5 GW cm⁻². While at 15.0 GW cm⁻² 65% of the signal drop occurs within a distance of $\pm 1.13 \cdot {z_{R}}$ around the focus, at 37.5 GW cm⁻² 77% of the signal drop is happening within this section. A Rayleigh length of ${z_{fit}} = 0.5 \cdot {z_{R}}$ was required to describe the signal curve at 37.5 GW cm⁻², indicating that the material response was not limited to 2PA processes only.

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The 2PA values obtained for the spectrum of M2CMK were higher than the reference spectrum measured by WLC z-scan. Due to the lower laser powers used the measurement error increased compared to the results for rhodamine B. However, the trend of WLC z-scan and the tunable setup was comparable with a maximum absorption between 720 and 800 nm and a decrease in 2PA cross section below 50 GM above 900 nm [Fig. 6(a)].

 

Fig. 6. (a) 2PA-spectra of 10 mM M2CMK in methanol and 10 mM DAS in PBS. M2CMK z-scans results obtained with the tunable system (blue squares) were compared to the referenced WLC z-scan measurements (solid line)) [12]. While higher than the values obtained by WLC z-scan the spectral behavior of ${{\boldsymbol \sigma }_{2}}$ followed a comparable trend with the absorption maximum between 720 and 800 nm and a decrease above 900 nm. The 2PA spectrum of 10 mM DAS in PBS exhibits a maximum absorption of 90 GM at 700 nm (triangles) and was comparable with the WLC z-scan (dash-dotted line) [11]. No error bars for WLC are provided in sources. (b) Matching the wavelength used for 2PP to the absorption peak resulted in a significant reduction of the polymerization threshold for GelMA (95% degree of substitution, dissolved in PBS) with 2 mM DAS as PI.

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The spectrum of DAS correlates well with the previously reported findings, showing an absorption maximum of 100 GM at 700 nm [12]. To compare 2PA with polymerization efficiency 2 mM DAS was used in the presence of a gelatin methacrylamine (GelMA) with a degree of substitution of 95%, dissolved in PBS [33] to produce structures using a 2PP setup based on the same tunable laser. The structuring was performed at four different wavelengths to compare the minimum power required to yield visible structures, which can be correlated to the polymerization threshold. As can be observed from the array of cubes produced by 2PP in [Fig. 6(b)], the required laser power was 40 mW for 700 and 720 nm, whereas it increased to 60 mW for 800 nm. This result indicates a clear correlation between the absorption maximum of the PI and its performance during 2PP structuring.

From these results a measuring routine was established, which was implemented in the machine and allows for automated data acquisition. In addition to the spectral range and spectral resolution ($\Delta \lambda$), an intensity interval ($\Delta I$) is selected to evaluate the effect of higher ordered effects. For each measurement, the Rayleigh length is fitted using least square algorithm [30]. If the difference in ${z_{fit}}$ and ${z_{R}}$ is above 25%, the measurement is not accepted. This criterion was based on the findings from M2CMK, where a difference above 25% could be related to the nonlinear region of ${q_{0}}$. In a second loop, the linear correlation between ${q_{0}}$ and I is verified. If this relation is violated, the intensity interval is reduced. This procedure is visualized in [Fig. 7].

 

Fig. 7. Measurement algorithm. Illustration of the automated measurement algorithm used in this setup. For a given wavelength an intensity range is selected. For each intensity, the z-scan is carried out m-times. As a first criterion the sharpening of the transmission curve is judged by comparing ${z_{fit}}$ from direct fit and ${z_{R}}$ obtained via beamprofiler. If results get rejected due to this process, the available ${q_{0}}(c)$ are fitted using linear regression. If this behavior is met, the measurement is accepted. If not, the power range is reduced by one increment ($\Delta I$). This procedure is repeated until the criteria are met or the minimum intensity has been reached. To increase measurement efficiency, measurements for ${I_{c}} = {I_{0}} + c \cdot \Delta I$ with $c \in \{ 1,2\ldots ,n\} $ can be used from the previous iteration.

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4. Discussion

Developing a custom algorithm with a variety of hardware implementations (beam profiler, powermeter, autocorrelator, oscilloscope, laser) in a consistent Graphical User Interface (GUI) allows for a convenient calibration of all required parameters with minimal user involvement. A complete calibration routine (autocorrelator, beam profiler, power measurement, diode calibration) in 5 nm steps over the entire available laser spectrum (690-1040 nm) requires more than 10 000 measurement points, which would be an extremely time consuming and error-prone routine, if carried out manually. By automating this process, the setup is capable of handling this huge workload and reliably establish a comprehensive parameter database, which is then used to calculate the 2PA cross section for each z-scan. The collimation of a laser beam using lenses is wavelength dependent, showing a 12 mm total shift in focus position for the spectral range used in this study. Therefore, a setup using lenses for collimation would require manual readjustment between the wavelengths and defy our aim of full automation. Implementation of a reflective expander [Fig. 3(a)] guarantees a collimated beam over the available tuning range of the laser. While such a shift would not affect the fitting procedure as it automatically fits the focal position from the obtained z-scan data, both the available stage distance and measurement efficiency must be considered. A shift of 12 mm would necessitate a travel distance of 34 mm, thereby increasing the measurement time by 30%. Furthermore, lenses introduce additional dispersion into the system, broadening the pulse, which is not the case for metallic coated mirrors. Due to the low dispersion introduced by the optical components the pulse measured with the autocorrelator can be used to fit the 2PA behavior, reducing fluctuations caused by erroneous fitting variables, as discussed in Table 1.

The use of a high repetition rate laser significantly affects the transmitted light detection due to the occurrence of thermal lensing. Using a chopper with 78 µs on-time allows to extract ${q_{0}}$ with a linear dependence on the laser power as described by an established model [7]. For both analyzed compounds rhodamine B and DAS an increase in laser power did not affect this predicted behavior. The determined spectra of rhodamine B and DAS correlated to results previously reported results in literature [11,23]. For M2CMK ${q_{0}}$ increased exponentially for intensities of 22.5 GW cm⁻² and higher [Fig. 5(a)].

Measuring at intensities below 11.1 GW cm⁻² was not possible due to the resolution limit of the setup since the signal drop and diode noise were of similar orders of magnitude. As a result of the limited working window, the measurement error was significantly higher in case of M2CMK. A closer inspection of M2CMK revealed a notable sharpening of the transmission curve at higher powers. Models describing thermal lensing effects for high repetition rate lasers postulate that the peak to valley distance of the signal drop of the z-scan transmission happens within a distance of $\pm 1.13 \cdot {z_{R}}$ from the laser focus in case of 2PA [17]. As can be seen in Fig. 5(b), only 66% percent of the signal drop is occurring within this limit at 15 GW cm⁻². In this power range ${q_{0}}$ scales linearly to the laser power, as described by Eq. (2). At 22.5 GW cm⁻² and above, where ${q_{0}}$ is no longer behaving linearly, the sharpening of the signal leads to an increase of signal area within $\pm 1.13 \cdot {z_{R}}$ from the laser focus.

For closed aperture z-scan setups high repetition rate lasers have been reported to broaden of the peak-to-valley distance of the recorded transmission curve due to thermal lensing effects [17,35]. In the case of the presented open aperture setup, we observed a sharpening of the curve caused by the accumulation of energy due to the high repetition rate. The recorded transmission curves could no longer be reliably fitted to the Rayleigh length measured with the beam profiler, indicating that the measured signal was no longer affected by 2PA processes only [22,36]. The behavior of the transmission curve is comparable to studies reporting on higher order nonlinear responses affecting the measured 2PA cross section [37,38]. As this was detectable by a change in fitted Rayleigh length of up to 50%, it was used as one of the main criteria for the measurement procedure [Fig. 7]. Individual measurements could be fitted with a coefficient of determination of R² > 0.97. As the setup allows to record at different intensities, extraction of the 2PA behavior via linear fit is also possible for measurements where the transmission curve is not as clearly defined [39]. For the described procedure it proved beneficial to initially select the optimal intensity range (${I_{c}} = {I_{0}} + c \cdot \Delta I$) at a single wavelength using the routine displayed in [Fig. 7]. This optimal range was then used for the entire spectrum to reduce the total measurement time.

Using the spectral absorption data of DAS allowed us to compare the polymerization behavior of the PI for 2PP structuring at different wavelengths. The necessary laser power required for observable polymerization was 40 mW at 700 nm compared to 60 mW at 800 nm [Fig. 6(b)]. These results emphasize that matching the 2PP structuring wavelength to the 2PA maximum of the PI can dramatically improve the efficiency of the polymerization process due to the more efficient 2PA.

5. Conclusion

A completely automated z-scan setup for spectral characterization of 2PA cross-sections in a wide wavelength range was developed. An extensive calibration routine is implemented in a custom software, automatically gathering large amounts of data and storing it in a comprehensive library. This database enables reliable and thorough calculation of the respective cross-section values at different wavelengths. The use of an optical chopper eliminates thermal effects and a reflective mirror expander guarantees a collimated beam over the entire spectral range without the need to readjust the setup between measurements. A sharpening of the measured transmission curve was used as indication that the observed material response was no longer caused by 2PA processes only. Therefore, it was essential to have a completely characterized setup, as sharpening of the curve was easily detectable by a reduction of the Rayleigh length used by the fitting algorithm. Using both shape of the curve as well as the behaviour of ${q_{0}}$ led to reproducible and reliable measurement of 2PA cross sections without being affected by the high repetition rate of the laser. After determining the optimal intensity window in accordance with the presented routine [Fig. 7], a complete spectrum (3 measurements per wavelength in 10 nm steps) can be obtained within an hour.

As the same laser source was used for both z-scan and 2PP experiments, the results could be directly compared. Due to its simplicity, the presented z-scan setup is a cost-efficient alternative to complex amplified systems and the fully automated software makes it a user-friendly tool for 2PA characterization of various compounds.