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Abstract
A femtosecond frequency-doubled erbium-doped fiber laser with an adjustable pulse repetition rate is developed and applied in two-photon excited fluorescence microscopy. The all-fiber laser system provides the fundamental pulse at 1560 nm wavelength with 22 fs duration for the second harmonic generation, resulting in 1.35 nJ, 60 fs pulses at 780 nm. The repetition rate is adjusted by a pulse picker unit built-in within the amplifier chain, directly providing transform-limited pulses for any chosen repetition rate between 1 and 12 MHz. We employed the laser source to drive a scanning two-photon excited fluorescence microscope for ex vivo rat skin and other samples’ imaging at various pulse repetition rates. Due to compactness, ease of operation, and suitable pulse characteristics, the laser source can be considered as an attractive alternative for Ti:Sapphire laser in biomedical imaging.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Femtosecond lasers are the enabling technology in the field of biophotonics, including non-invasive diagnostics, optical imaging, and multiphoton microscopy (MPM) [1,2]. In the latter group, two-photon excited fluorescence (TPEF) – a process in which two photons are absorbed simultaneously by a single fluorophore – is an important example of such a technique [3]. Currently, state-of-art TPEF imaging systems primarily utilize commercially-available femtosecond Ti:Sapphire lasers delivering femtosecond pulses in the 700-1000 nm window [4–7]. However, due to their architecture, Ti:Sapphire lasers have certain disadvantages hindering, or in many cases prohibiting real-life applications outside the laser physics laboratory. A Ti:Sapphire laser is based on a free-space resonator pumped by an expensive green laser (532 nm), besides active water cooling and an optical table are often required. As a result, the entire setup becomes complex, bulky, and expensive. Working with Ti:Sapphire lasers might be bothersome since they often require re-alignment or some adjustments to initiate a pulsed operation. Considering real-life applications in biological or medical research laboratories, clinics, and hospitals, the TPEF imaging system should be as simple as possible, while daily operation of a Ti:Sapphire laser requires knowledge about laser optics. Moreover, intrinsically Ti:Sapphire lasers operate at relatively high pulse repetition frequencies (frep), often above 70 MHz. However, some applications require much lower frep, which implies using an external pulse-picker (based on a bulk crystal) to reduce the repetition rate. A pulse-picker introduces unwanted chromatic dispersion and further increases the size, cost, and complexity of the setup.
The development of femtosecond lasers is often driven by the needs of particular applications in biology and medicine. One such example is a need for low and adjustable frep femtosecond sources, especially important for multiphoton microscopy. It has been shown that reducing the pulse frep is beneficial for increasing the TPEF signal during the imaging of biological tissues. One example is the imaging of skin and a few other pigment-containing tissues, where thermal-mechanical damage can be mitigated by using a pulse picker [8]. The origin of this damage is strong one-photon absorption of melanin at the wavelength of excitation [9]. For this reason, the average excitation power cannot be increased, as this will result in tissue damage. On the contrary, while picking pulses, the average laser power is reduced, but the peak power is maintained. Moreover, it also allows sufficient time for heat dissipation between pulses. As a consequence, when allowed by biochemical damage threshold, it gives room to increase further the pulse peak power resulting in increased TPEF signal [10]. This has also been exploited in deep-tissue brain imaging, where the optimal repetition rate was determined to be within 1 and 10 MHz [11]. The optimal repetition rate depends on imaging depth, highlighting the need for an arbitrarily tunable source. In another example, it was shown that reduced frep increases fluorescence yield through dark state relaxation. Increasing time between pulses to >1 µs ensures that transient molecular dark states with a long lifetime will relax between two absorption events [12]. Finally, pulse pickers are commonly used in two-photon fluorescence lifetime imaging microscopy (FLIM) to adjust the pulse separation to the specific fluorophore’s lifetime [13–15]. For those reasons, the ability to reduce and control the repetition rate is very important.
Currently, there is a demand for compact lasers with ultrashort pulse duration, but not necessarily high average power, especially in in vivo imaging of, e.g., human retina. As an alternative to Ti:Sapphire lasers, compact frequency-doubled Erbium-doped fiber lasers can be used [16]. Fiber lasers, compared to solid-state Ti:Sapphire lasers, are more compact and simple, robust, maintenance-free, and cost-effective. However, achieving few-cycle pulses directly from Erbium-fiber oscillators is challenging. Sub-50 fs pulses were obtained from the setup utilizing free space optics [17], while in the case of all-fiber Erbium-lasers, pulse duration was limited to ∼50 fs by high order dispersion and nonlinear effects in optical fibers [18,19]. Another approach to achieve fs pulses is external amplification and compression, using non-standard fibers with precisely adjusted length, which allows to achieve even sub-20 fs pulses [20–24]. The pulse duration of 14 fs was achieved from an amplified carbon nanotube mode-locked fiber laser; however, the setup includes at its output a highly nonlinear fiber (HNLF) and a prism pair [25]. Generation of 22.7 fs pulses with 2.8 nJ energy was reported in [26], by single-stage soliton compression using a standard single-mode fiber (SMF) for both pre-stretching pulses from the oscillator, and their compression after amplification. All-fiber and polarization-maintaining (PM) setup presented in [27] allowed to achieve 24 fs pulses with the energy of 3 nJ. The presented setup utilizes only three commercially available PM fiber optic components and two types of PM fibers (also commercially available – SMF and active fiber), providing linear polarization of the output pulses and stable operation. Further power scaling is possible by using conventional chirped pulse amplification (CPA) scheme, in which the seed pulses are stretched, amplified, and finally compressed in a linear compressor (e.g., based on diffraction gratings). Such an approach enables amplification even to µJ energy levels and MW/GW peak powers [28–30], but for the cost of the dramatically increased complexity of the system and significantly longer output pulse (>400 fs), which is too long for in vivo TPEF imaging of delicate biological tissues.
Femtosecond pulses at 1560 nm wavelength can be converted to ultrashort 780 nm pulses, to ideally match the two-photon absorption spectra of many fluorophores of interest, by adding a frequency-doubling stage for the second harmonic generation (SHG). As an example, a high-power frequency-doubled laser with 520 fs pulses at 85 MHz repetition rate, resulting in pulse energy of 10.3 nJ and peak power of more than 19.8 kW was used for in-vivo TPEF spectroscopy and imagining [31]. However, the relatively long pulse duration and high repetition rate exclude such sources from, e.g., retinal imaging [4]. Another system for two-photon microscopy, generating 191 fs pulses with a 156 MHz repetition rate and 1 W of average power, was demonstrated in [32]. The generation of much shorter pulses - about 40 fs at 796 nm was presented in [33], which was achieved by converting 50 fs pulses at the central wavelength of 1600 nm by the SHG module. The average power of the signal at ∼800 nm was 140 mW, corresponding to 3.5 nJ pulse energy at a frep of 40 MHz. The system does not contain any frep control and requires three amplification stages. Moreover, configuration based on nonlinear frequency conversion creates a possibility for dual-wavelength operation for simultaneous two- and three-photon imaging in a multimodal instrument. In [34], 80 fs pulses at 790 nm wavelength (61 mW of average power) were generated and used simultaneously with residual, unconverted 80 fs pulses at 1580 nm (117 mW of average power). The residual 1580 nm pulses were used for third-harmonic generation (THG) skin imaging, while 790 nm pulses for TPEF and SHG imaging. However, none of the configurations presented so far has provided an adjustable frep, required in many biomedical applications.
In this work, we report a frequency-doubled Er-fiber laser system for TPEF imaging, which addresses the main shortcoming of the previously reported setups: it enables pulse repetition rate tuning by means of a fiber-coupled pulse-picker integrated with the amplifier chain. The system delivers sub-65 fs pulses with >1.3 nJ energy preserved in the entire frep tuning range. The applicability of the source for two-photon excited fluorescence microscopy was confirmed by imaging of ex vivo samples at various pulse repetition rates. We show that reducing the pulse repetition rate allows us to increase fluorescence intensity from rat skin samples.
2. Design of the frequency-doubled Er-fiber laser source
Figure 1 shows the experimental setup of the frequency-doubled Er-doped fiber laser source. As a seed source, a ring cavity Er-doped fiber laser (EDFL) mode-locked via semiconductor saturable absorber mirror (SESAM) was used (Batop GmbH). The seed generated 325-fs pulses at a 35.7 MHz repetition rate and average power of 1.1 mW at 1561 nm central wavelength. Next, the pulses were pre-amplified in an in-house made Erbium-doped fiber amplifier (EDFA) based on a 1.5 m-long segment of highly-Erbium doped fiber (Liekki Er80-4/125-PM, EDF). After amplification, the pulses entered a pulse-picker (PP) based on a fast acousto-optic modulator (Gooch & Housego Fibre-Q 200 MHz, AOM). The details on the PP design were already presented in our previous work [35]. After frep reduction, the pulses were amplified in a final amplification stage, based on the same 1.5 m-long EDF as in the previous stage. An additional band-pass filter (BPF) with 10 nm width (centered at 1560 nm) was placed before the power amplifier (PMBP-1560-10-2-B-Q-2-C, Advanced Fiber Resources). The BPF limited the spectral width prior amplification and enabled achieving a clean pulse shape at the output, with minimized sidebands (the role of the BPF is explained later in the text).
Fig. 1. Scheme of the frequency-doubled, fiber laser: EDF – Erbium-doped fiber; OC – 70/30% output coupler; WDM – 980/1550 nm wavelength division multiplexer; SESAM - semiconductor saturable absorber mirror; TC – 99/1% tap coupler; AOM – 200 MHz acousto-optic modulator; BPF – 10 nm band-pass filter.
The setup was entirely fiberized and spliced using a standard arc-fusion splicer. All fibers and components used in this setup were single-mode and polarization-maintaining (PM-SMF), providing polarization stability, which is crucial for frequency doubling. The entire system was built using only two types of fibers (the EDF and PM-SMF). All components are standard, off-the-shelf PM fiber components (Advanced Fiber Resources).
The source is capable of generating pulses with duration down to 22 fs at any chosen repetition rate from 1 to 12 MHz. The evolution of the optical spectrum and pulse shape in the system is depicted in Fig. 2. The optical spectra (recorded with an optical spectrum analyzer, Yokogawa AQ6370B, OSA) and autocorrelation traces (APE PulseCheck) were measured at three different stages of the setup and the pulse picker frequency set to 1 MHz: after the seed oscillator, i.e. before entering the preamplifier (a,b), after the preamplifier and AOM (c,d), and after the BPF (e,f). The spectrum after the second amplifier is depicted in Fig. 3(a). It can be seen that the relatively narrow spectrum from the seed (a) is significantly broadened during amplification via nonlinear effects, mostly self-phase modulation (SPM) [36,37]. The pulse propagation can be described by an interplay of SPM, gain narrowing, second-order and higher-order dispersion [38]. Due to the normal dispersion of the EDF, the pulses experience parabolic amplification [25] and are positively chirped. After the gain fiber, the pulse propagates through a segment PM-SMF with anomalous dispersion; therefore it is again compressed, which results in a 225 fs pulse recorded after the AOM (d). Due to the broad spectrum, the pulse duration after amplification is shorter than generated from the oscillator. Next, the spectrum is intentionally limited to 10 nm using a BPF (e). Spectral narrowing leads to significant elongation of the pulse (f). Such pulse is then amplified in the second amplification stage, where again SPM co-exists with normal dispersion, leading to significant spectral broadening [Fig. 3(a)], which enables compression down to 22 fs [Fig. 3(b)]. Achievement of a pedestal-free, nearly transform-limited pulse at the output of the system was possible due to the use of spectral filtering (i.e. BPF) prior amplification. This is related to the amount of accumulated nonlinear phase (described by the B integral [37]). It has been shown that gain narrowing in fiber amplifiers leads to a spectral shaping, which degrades the pulse shape [39]. Pre-compensation of the gain narrowing by a spectral amplitude filter results in a lower overall nonlinearity due to the larger initial pulse duration. Proper spectral filtering prior amplification can dramatically improve the pulse shape and minimize unwanted side-wings, as shown e.g. in [39]. We have found experimentally that removing the BPF has indeed a negative impact on the pulse shape after the power amplifier.
Fig. 2. Evolution of the optical spectrum and pulse shape in the system: spectrum and autocorrelation traces recorded after the seed laser (a,b), preamplifier with the AOM (c,d), and the bandpass filter (e,f).
Fig. 3. (a) Optical spectrum after amplification at 1 MHz repetition rate and (b) FROG temporal intensity of the pulse (solid red line) together with the calculated transform-limited intensity (dotted green line) and temporal phase (solid blue line).
Figure 3 shows the optical spectrum and the temporal intensity of the pulse together with the temporal phase, measured via frequency-resolved optical gating technique (Mesa Photonics FS-Ultra2, FROG). Both measurements were taken at frep set to 1.02 MHz at the output of the power amplifier (second amplifier stage). In this setting, the obtained average power was 6.5 mW, which corresponds to pulse energy of approx. 6.37 nJ, more than twice than reported previously [26,27]. The energy is lower than in [33]; however, our setup has only two amplification stages in comparison to three [33], and the peak powers are comparable. The pulse duration is nearly transform-limited (22 vs. 18 fs). Further compression down to the transform limit would require additional bulk components, like prisms [25] or dispersive mirrors [16].
The ultrashort 1560 nm pulses were afterward frequency-doubled in the SHG module. The amplifier output was collimated by an aspheric lens (C220TME-C, Thorlabs) and focused by an achromatic lens (19 mm focal length, AC127-019-C-ML, Thorlabs) on a MgO:PPLN crystal (FSHNIR-ER, HC Photonics Corp.) with a 19.65 µm quasi-phase matching period and 0.3 mm poling length (Lpoled). The SHG efficiency is at the level of 23.3%, comparable to [33]. Further optimization of the setup and increasing the conversion efficiency might be possible by using fiber-coupled PPLN crystals. The frequency-doubled beam was collimated by an aspheric lens (C560TME-B, Thorlabs) and directed through two filters: a dichroic mirror which reflects the unconverted 1560 nm pump (Thorlabs DMSP1000, Filter 1) and a band-pass filter with a cut-off at 700 nm (Thorlabs FELH0700, Filter 2) which blocks higher harmonics below 700 nm. The optical spectrum of the second harmonic and the temporal pulse intensity at frep = 1.02 MHz are presented in Figs. 4(a) and 4(b), together with the measured and retrieved FROG spectrograms (c). The spectrum is centered at 782.6 nm with a full width at half maximum (FWHM) of 19 nm. The pulse duration is 60 fs and the average power (measured after both filters) equals 1.4 mW, corresponding to a pulse energy of 1.37 nJ. It is noteworthy that the FROG measurement revealed a clean pulse shape without any pronounced sidebands and a flat temporal phase.
Fig. 4. (a) Generated second harmonic spectrum, (b) FROG temporal intensity of the 780 nm pulse (solid red line) together with the temporal phase (solid blue line), (c) measured and retrieved FROG spectrograms.
The used PP allows for easy repetition frequency tuning by dividing the fundamental frep by a chosen factor [35]. Figure 5(a) presents the average output power and pulse duration characteristic of the second harmonic versus repetition rate. The optical powers plotted in Fig. 5(a) are the maximum powers that could be achieved at the given repetition rate setting (i.e., they were recorded at different amplifier pump settings). By increasing the frep from 1.02 MHz up to 11.9 MHz, we observed a linear increase of the average power (i.e., preserved pulse energy) and small changes of the pulse duration in the range of only 2 fs, which indicates that the source can be used in a wide range of frequencies with preserved pulse energy and duration, enabling optimization for specific experimental requirements (like a lifetime of fluorophores, etc.). The output power and pulse energy remain stable over long periods of time. Figure 5(b) presents the pulse energy stability measured over 6 hours without any active stabilization (only passive thermal stabilization of the oscillator, amplifiers, and PPLN crystal). It is worth noting that there is no warm-up time required to achieve the desired parameters - the system is fully turn-key operated, and the obtained stability is 0.7% rms.
Fig. 5. (a) Measured average power and pulse duration of the 780 nm pulses as a function of the pulse repetition rate. (b) Long-term energy stability measurement over 6 hours, indicating the stability of 0.7% rms.
The pulse parameters (energy, power, pulse duration) measured at each stage of the system are summarized in Table 1.
Table 1. Summary of the pulse parameters at different stages of the laser setup.
3. Application to TPEF microscopy
To verify the laser applicability to nonlinear imaging and confirm the expected effect of decreasing the pulse repetition rate, the laser was coupled to a home-build TPEF microscope schematically shown in Fig. 6(a). A variable neutral density (ND) filter placed in front of the microscope allows us to adjust the average power level at the sample. Next, the beam is directed to the galvanometer scanning system (Thorlabs GVS002), then through a scan lens (Thorlabs AC254-50-B-ML) and tube lens (Thorlabs AC254-100-B-ML) to a microscope objective (Olympus LUCPlanFL 40x/0.6 NA). The microscope objective was slightly underfilled to compromise the resolution and power efficiency. The emitted fluorescence is collected in epi-mode in a descanned manner. We use a dichroic mirror (Semrock HC 705 LP) to separate fluorescence from excitation light and a set of two additional optical filters (Semrock 694/SP BrightLine HC). The fluorescence light is collected and processed by a photon-counting GaAsP photomultiplier module (Hamamatsu H7422-40P), photon counting module (Hamamatsu C9744), data acquisition card (National Instruments USB-6212), and a custom-written LabView software. In most cases, the autofluorescence was used as a contrast. To facilitate imaging with low excitation power, the images were acquired with 40 µs dwell time and 512 × 512 pixels, resulting in 0.1 frames/s. To improve the signal to noise ratio, 10 frames were typically collected for averaging; however, this was not mandatory to obtain high-quality, informative images. In the case of stained samples, 10 µs dwell time was used, resulting in a 0.4 frame rate. The fluorescence intensity is quantified as a mean count of photons per pixel (mpc) within the image.
Fig. 6. (a) Experimental setup of a home-built TPEF microscope. VF – variable neutral density filter, DM – dichroic mirror, GS – galvanometer scanning unit, SL – scan lens, TL – tube lens, OBJ – objective lens, S – sample, F – cut-off filter, PC-PMT – photon-counting photomultiplier. (b) Fluorescence of test target in mean photon counts per pixel (mpc) as a function of average excitation power for 1, 3, and 9 MHz pulse repetition rates. Slopes of linear regression lines through the data points on the log-log plot indicate a two-photon process for all pulse repetition rates.
The fluorescence intensity depends on the number of absorbed photon pairs per second (Na) in the two-photon process [8,10]:
where frep is the pulse repetition rate, δ is the two-photon absorption cross-section, A is the spot size of the beam in focus, τ is the pulse duration (in the sample plane), and Pavr is the average excitation power. According to this relationship, it is possible to increase the fluorescence signal by decreasing the pulse repetition rate, if the average power at the sample is maintained at the same, unchanged level. We tested this relation by measuring the fluorescence of a fluorescence test target (Edmund Optics, #57-894) as a function of power for pulse repetition rates of 9, 3, and 1 MHz. In all cases, slopes of linear regression in log-log plot are ∼1.8 [see Fig. 6(b)], indicating a second-order nonlinear process with a small contribution of linear absorption, possibly originating from a broad absorption spectrum of the test target. It is also visible that the fluorescence intensity gradually increases with decreased pulse repetition rate (with respect to 9 MHz – 2.73 times for 3 MHz and 9.34 times for 1 MHz repetition rate).Next, we applied the developed laser and two-photon microscope for ex vivo imaging the cross-section of the unstained albino rat skin sample. Figures 7(a)–7(f) shows six representative TPEF images recorded at various pulse repetition rates and two average power levels. The variable ND filter was adjusted to obtain desired average excitation power for a given pulse repetition rate, i.e., to have sufficiently bright images and yet not to saturate the PMT or the photon counter. Each image is showing the same location within the sample displaying oval structures of hair follicles. It is apparent that reducing the repetition rate to 1 MHz results in a brighter image. For quantitative analysis, we recorded the fluorescence intensity as a function of power for 9, 3, and 1 MHz repetition rates and plotted in Fig. 7(g). A quadratic function (y = C·x2) was fitted to each measurement series. We obtained 3.56 times higher value of C parameter for 3 MHz repetition rate with respect to 9 MHz, while 9.40 times higher when reducing to 1 MHz. This means that it is possible to obtain the same fluorescence intensity with 1 MHz excitation using 9.401/2 = 3.07 times less power when compared with 9 MHz excitation, which reduces the thermal damage probability [8]. Minor deviation from theoretically expected values of C parameters (3 and 9 for 3 MHz and 1 MHz pulse repetition rates, respectively) is caused by small differences in pulse duration for different repetition rates, as seen in Fig. 5. For further analysis, we recorded the fluorescence intensity as a function of the repetition rate without adjusting the variable ND filter. In this experiment, a constant pulse energy of 65 pJ in the sample plane is maintained, while the average power increases with the repetition rate. The fluorescence intensity grows linearly, as expected, and is shown in Fig. 7(h). Figure 7(i) shows the TPEF image of the sample obtained with 1 MHz and 440 µW of excitation power in the larger field of view of 600 × 600 µm. Summarizing, this demonstrates that the laser is performing according to expectations and can be used for imaging with various pulse repetition rates.
Fig. 7. Reducing the pulse repetition rate while maintaining the average excitation power allows increasing fluorescence intensity from ex vivo rat skin samples. (a)-(c) Imaging with 220 µW excitation power and 9, 3, and 1 MHz repetition rates. (d)-(f) Imaging with 440 µW excitation power and 9, 3, and 1 MHz repetition rates. (g) Fluorescence intensity of ex vivo rat skin in mean photon counts per pixel (mpc) as a function of average excitation power for 1, 3, and 9 MHz repetition rates; the last point in 1 MHz data series deviates from fit function due to saturation of photon counting electronics. (h) Fluorescence intensity of rat skin as a function of pulse repetition rate (excitation power) and maintained pulse peak power. (i) Image with a larger field of view obtained with 1 MHz repetition and 440 µW excitation power; selected ROI indicates sample region where (a)-(f) images were taken.
As another example, various biological samples were imaged with 1 MHz pulse repetition rate excitation using their endogenous autofluorescence or staining. Figure 8(a) shows the cross-section of a frog liver on a prepared microscope slide obtained with 380 µW excitation power. A characteristic structure of hepatocyte cells is visible. An example of stained sample is shown in Fig. 8(b). A cross-section of Epipremnum scindapsus stalk stained with rhodamine B was imaged with 750 µW of excitation power. Figures 8(c) and 8(d) show the autofluorescence image of freshly picked plant leaf of Chamaedorea elegans and Epipremnum scindapsus, respectively. In both cases, the excitation power was less than 200 µW in the sample plane. The fluorescence is originating from chlorophyll stored in the chloroplasts. All in all, it demonstrates that it is possible to benefit from an adjustable repetition rate of the laser source for low excitation power imaging of biological samples.
Fig. 8. Exemplary TPEF images of biological samples obtained with 1 MHz pulse repetition rate. (a) Ex vivo frog liver cross-section imaged with 380 µW excitation power. (b) Cross-section of Epipremnum scindapsus stalk stained with rhodamine B imaged with 750 µW excitation power. (c) Chamaedorea elegans leaf imaged with 115 µW excitation power. (d) Epipremnum scindapsus leaf imaged with 154 µW excitation power.
4. Summary
In conclusion, we report an exceptionally simple and compact system for low power, efficient two-photon excited fluorescence microscopy with a fiber laser source of ultrashort pulses at 780 nm wavelength. The light source is based on a frequency-doubled Er-doped fiber laser with a built-in pulse-picker for an easy repetition rate adjustment. New set-up enables easy repetition rate tuning in the range of 1 to 12 MHz, with preserved sub-65 fs pulse duration (60 fs at shortest) and energy exceeding 1.3 nJ. The performed experiments at various biological samples confirm that the light source meets the requirements of two-photon excited fluorescence microscopy, and it is possible to benefit from an adjustable pulse repetition rate. As an example, we showed that it is possible to increase the TPEF signal by 9.4 times by reducing the repetition rate from 9 to 1 MHz with maintained average power level. Moreover, our laser system can be an excellent platform for the development of an adaptive excitation source for high-speed imaging of neuronal activity [40]. We believe that such robust and reliable fiber-based sources can replace Ti:Sapphire lasers as excitation sources in outside-laboratory applications.
Funding
Fundacja na rzecz Nauki Polskiej (First TEAM/2017-4/39, MAB/2019/12, POIR.04.04.00-00-3D47/16-00); Horizon 2020 Framework Programme (666295); Ministerstwo Nauki i Szkolnictwa Wyższego (International co-financed project 2016-2019 no. 3544).
Acknowledgments
We thank Maciej Popenda and Bogusław Szczupak from Wrocław University of Science and Technology for providing the 780 nm pulse autocorrelator for preliminary measurements. We acknowledge the invaluable help of Piotr Ciąćka in LabView programming, also Jadwiga Milkiewicz and Łukasz Kornaszewski (Institute of Physical Chemistry PAS) for helpful discussions. We thank Hubert Doleżyczek from Nencki Institute of Experimental Biology for the preparation of rat skin samples.
Disclosures
The authors declare no conflicts of interest.
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