Optical Gain Switching by Thermo‐Responsive Light‐Emitting Nanofibers through Moisture Sorption Swelling

The development of intelligent photonic systems made of stimuli‐responsive materials, i.e., with features tunable and switchable by environmental signals, is gaining increasing attention. Here, the study reports on switchable optical gain based on complex arrays of nanofibers made of thermo‐responsive poly(2‐n‐propyl‐2‐oxazoline), incorporating a blue‐emitting chromophore. The fluorescent component endows the nanofibers with optical gain in addition to the moisture absorption capability of the polymer. Light amplification is found with temperature‐ and humidity‐dependent excitation threshold. The threshold value is halved close to the polymer cloud point temperature, enabling reversible switching of the emission intensity upon temperature change. Waveguiding analysis by back‐focal plane imaging on individual fibers allows the switching mechanisms to be rationalized, in terms of moisture sorption swelling‐induced morphological changes. These responsive light‐emitting nanofibers may find application in a novel class of lasers with dynamically‐controlled properties, environmentally‐switchable optoelectronics, and smart sensors.


Introduction
The combination of stimuli-responsive materials [1,2] and microand nano-fabrication technologies may lead to new components and devices, that mimic the rich variety of smart and adaptive systems present in Nature. This approach is continuously evolving, boosted by applications in soft robotics, [3,4] intelligent drug delivery and diagnostics, [5,6] smart textiles, [7] impact on the lasing spectrum or intensity while keeping sufficient light amplification and scattering. So far, the capability of modulating the optical gain properties, including amplified spontaneous emission (ASE) of organics has been achieved through various stimuli, including pH, [30] electric fields, [31] heat, and light. [32,33] Moreover, a few studies on thermo-responsive random lasers have been reported, exploiting sintered glass infiltrated with liquid crystals, [34] in which temperature is varied around the nematic-isotropic phase transition. Recently, the tunability of the emission by thermal stimuli has been reported in densely packed metal-organic framework particles doped with intramolecular charge transfer (ICT) laser dyes [35] and in bulk dye-doped hydrogels, [36] through modulation of the energy levels of the ICT dye and of the refractive index and light diffusion properties, respectively. Thermo-responsive polymers, [37][38][39] that are fully soluble at low temperatures while phase-separate upon heating, are other highly suitable candidates in this framework. Their transition temperature, known as the lower critical solution temperature (LCST), represents the lowest phase transition temperature in the polymer phase diagram.
Among other classes of photonic micro-and nano-structures that can be used to embed thermo-responsive polymers, electrospun fibers can be advantageous since they show amplification along the fiber length, and photon scattering through their complex networks. [40,41] In addition, networks of lightemitting nanofibers (NFs) feature a multiscale porosity that, once combined with the phase transition properties of thermoresponsive polymers, would make the overall morphology and photonic features highly controllable through water condensation and swelling. [42] These effects can be exploited both for tuning emission properties, and for achieve switching control. NFs with thermo-responsive polymers have been realized for on-demand drug release, optical sensors, membranes and water harvesting, [43][44][45][46][47][48] whereas polymer NFs with thermo-responsive optical gain are still unexplored.
Here, we introduce thermo-responsive NFs whose optical gain is switchable by two environmental stimuli (i.e., temperature and humidity). Fibers are made of poly(2-n-propyl-2oxazoline) (PnPrOx), whose wetting properties change upon varying temperature, [49] and that is doped with a chromophore to achieve blue light amplification and enhanced moisture sorption properties. Amplification of emitted light is evidenced through line-narrowing, with temperature-dependent excitation threshold resulting from water sorption swelling across the polymer cloud point temperature (T CP ). This behavior is also analyzed by investigating waveguiding in individual fibers. Overall, the emission intensity can be varied reversibly either by temperature or by humidity. These multifunctional, smart optical materials are highly promising components of laser devices that can be dynamically reconfigured by environmental stimuli.

Results and Discussion
PnPrOx NFs are realized by eco-friendly electrospinning (see Experimental Section) of a Stilbene 420 (S420)-doped polymer solution, thereby adding to the polymer matrix a light-emitting organic component (molecular structures in Figure 1a,b). The PnPrOx is a thermo-responsive polymer with T CP ≈21°C in systems at low concentrations, which decreases upon increasing concentration until water-insolubility occurs >100 mg mL −1 . [49] No thermal hysteresis is reported for PnPrOx due to its low glass transition temperature (T g = 40°C) and the absence of intramolecular hydrogen bonding in its collapsed state. [50,51] PnPrOx features LCST-like behavior, i.e., it shows either hydrophilic or hydrophobic character, below or above T CP , respectively. Consequently, PnPrOx NFs show water-stable properties above 21°C, while increasing its hydro-solubility below T CP . Due to the low T g of PnPrOx and its T CP , the nanofibrous structure is not significantly altered upon contact with water at room temperature. [49,52] Uniaxially aligned arrays of fibers are electrospun (Figure 1c), with uniform fluorescence along the filament length, which can be appreciated looking at single fibers (Figure 1d,e). S420 does not alter significantly the morphology of pristine NFs (Figure 1f,g). The average diameter pristine and S420-doped PnPrOx fibers is measured to be (300±90) and (250±50) nm, respectively. Multi-branched fibers are also found in the complex mats (inset of Figure 1f). Given the S420 emission spectrum, few waveguided modes are expected. Indeed, for a wavelength, = 430 nm (S420 emission peak, Figure S1a, Supporting Information) and a refractive index, n p = 1.52 for poly(2-oxazoline)s, [53,54] the cut-off diameter for light propagation, estimated as [55] Dynamic vapor sorption (DVS) analysis of pristine PnPrOx and PnPrOx/S420 NFs shows their capability of absorbing a moisture amount from 7% to 9% of their own weight, respectively (Figure 1h), if the relative humidity (RH) is increased to 80% at room temperature. The small increase in moisture absorption upon S420 addition could be ascribed to an increase in local inter-polymer distances, due to the presence of the bulky, rigid S420 molecules. However, the increase in moisture absorption is more likely, mainly due to the presence of the hydrophilic sulfonate groups in the S420 molecules. [56,57] DVS measurements on pristine PnPrOx NFs, performed at various temperatures to gain information on the maximal moisture uptake at RH = 90% (Table 1), confirm the effect of increasing hydrophobicity of NFs networks at increasing temperatures.
At low (0.5 wt.%) S420 loading within the NFs, the effect of the dye on structural properties, such as the overall T g under dry conditions, as typically measured by differential scanning calorimetry (DSC), is likely minimal and too low to be detected. In fact, the effect of ambient humidity, moisture, on the T g , will outweigh the eventual plasticizing effect of the dye itself. However, the dyeenhanced hydrophilicity may result in an increased plasticizing effect on the fibers, due to a higher moisture sorption. Importantly, such absorption of moisture does not alter the morphology of the NFs (Figure 1i,j).
In the complex, 3D fibrous material, light diffusion through multiple scattering can occur at various length-scales. Photons from S420 molecules can be either emitted into free-space, or coupled to the waveguide modes of the fibers. [58] The component of light emitted by the S420 molecules and propagating along the NFs can then be scattered at the splitting point and interfiber joints or out-coupled to free-space, by scattering of bulk and surface defects of the polymer filaments. Moreover, photons emitted or scattered to free-space can undergo additional scattering by other fibers, leading to 3D diffusion. The guided and the Inset of (f): magnified SEM micrograph of branched fibers. Scale bar: 2 μm. h) Weight change of pristine PnPrOx NFs (continuous line) and PnPrOx/S420 NFs-upon increase in humidity from 0% RH to 80% RH at 25°C. The three subsequent cycles show repeatability of the weight variation. SEM micrographs measured i) before and j) after DVS experiments, which show no significant influence of moist sorption on nanofiber morphology. Scale bars: 5 μm. diffusively propagating light components can be amplified by stimulated emission. All these properties have been investigated in detail, for both single NFs and planar networks encompassing many fibers. [58][59][60] Figure 2a shows the emission spectra from uniaxially aligned PnPrOx/S420 fibers (sample photographed and imaged in its fluorescence in the insets of Figure 2a), upon varying the exci-tation fluence in the interval 0.5-26 mJ cm −2 . These measurements are performed by using a stripe-shaped beam for excitation, with the length of the stripe parallel with the direction of alignment of the NFs (see Experimental Section for more details). While photoluminescence (PL) spectra at low excitation fluences (<6 mJ cm −2 ) feature a broad emission (full width half maximum, FWHM, ≈60 nm, see also Figure S1, Supporting Information), at higher fluences the emission spectrum collapses in a narrow band (FWHM ≅ 10 nm, Figure 2b). [61] Figure 2c shows the intensity in the wavelength range between 425 and 440 nm and the FWHM versus the excitation fluence, highlighting a change of the slope of the Light-in/Light-out (L--L) curve and a six-fold reduction of the FWHM above the threshold of ≈6 mJ cm −2 . Comparing the threshold measured by an excitation stripe with length either parallel or perpendicular to the alignment axis of the NFs, we found a threshold lower by a factor 2 for the parallel configuration ( Figure S2, Supporting Information), due to waveguiding-promoted amplification along the filaments. In the following, we focus on data obtained in such parallel configuration. Moreover, we find that the spectral features of the emission do not significantly vary upon exciting different areas of the sample ( Figure S3a, Supporting Information). Analyzing the visibility of interference fringes generated by such emitted light passing through a double slit evidences a ≈1% intensity contrast ( Figure S3b, Supporting Information), that is indicative of generally low coherence. Finally, a relevant forward emission (i.e., along the direction perpendicular to the sample surface) is found, which displays a broad angular spread. Emission spectra with FWHM of few nm can be detected also at ≈30°collection angles ( Figure S3c, Supporting Information).
To investigate how the thermo-responsive features of PnPrOx can be exploited, NFs are placed in a chamber with controlled relative humidity (variable in the range 3%-90%) and temperature (variable in the interval 15°C ≤ T ≤ 35°C). A scheme of the setup is reported in Figure S4 (Supporting Information). The upper value of the temperature is chosen to be lower than the polymer T g (40°C), as working above T g would irreversibly alter the morphology of the NFs and of the networks formed by them. Figures S5-S7 (Supporting Information) report on the properties of the PnPrOx/S420 NFs for various values of T and RH, evidencing the general presence of line-narrowed emission above an excitation threshold. By measuring this threshold for each couple of parameters, we obtain the overall temperature and humidity dependence of light amplification (Figure 3). Figure 3a shows the temperature dependence of the threshold for RH = 10% and 80%, respectively. A decrease of the threshold is found upon increasing temperature in the range 20-25°C, i.e., near the switch in hydrophilic/hydrophobic character as indicated by the polymer T CP . By considering the average excitation thresholds, A TH,1 and A TH,2 , at 15-19°C and at 31-35°C, respectively, we find that A TH,1 > A TH,2 for the whole range of investigated RH values ( Figure S8, Supporting Information). The dependence of the threshold on RH is presented in Figure 3b, for T = 17°C and T = 33°C. At both temperatures, a continuous increase of the excitation threshold is found upon increasing the humidity. The trends reported in Figure 3a,b are general, and found for other ranges of temperatures and humidity ( Figure 3c). Overall, the threshold can be controlled finely and effectively by both temperature and humidity, with a five-fold decrease of threshold found upon varying the environmental parameters from (RH = 90%, T = 17°C) to (RH = 3%, T = 35°C).
A distinct feature of thermo-responsive polymers is the reversibility of the hydration-dehydration process, as well as the capability to dynamically change their microscopic phase and related properties following a change of the environmental variables. We investigate the switching capability of the PnPrOx/S420 NFs by iteratively varying the relative humidity between RH = 3% and RH = 87%, and measuring the emission intensity for a fixed temperature (T = 15°C) and excitation fluence, namely correspondingly switching the system between above-and belowthreshold conditions (Figure 3d). While line-narrowed emission occurs at RH = 3%, the increase of RH largely suppresses light amplification, as shown in in Figure S9a (Supporting Information) where an example of the spectra measured in a cycle at the two values of RH are shown. The emission intensity can also be changed by varying the temperature of the sample between two values corresponding to a hydrophilic and a hydrophobic behavior, i.e., T = 17°C and T = 33°C, respectively, for a fixed humidity and excitation fluence ( Figure S9b, Supporting Information). The slow decay of the emission intensity upon increasing the number of cycles is attributed to dye photo-bleaching, as also found under continuous optical excitation at fixed fluence and ambient parameters. The photo-stability of the emission could be enhanced by using suitable long-living dyes, as resulting from appropriate design strategies. [62]  To investigate the switching behavior of NF emission more in depth, the waveguiding properties of the light-emitting PnPrOx/S420 NFs are studied in different environmental conditions. To this aim single NFs are deposited on a glass coverslip, and their fluorescence intensity, excited with either a Hg lamp or a focused laser beam, is analyzed by means of an inverted optical microscope. This setup, schematized in Figure 4a, allows the fluorescence image of the PnPrOx/S420 NFs to be collected (inset of Figure 4a) together with the angular distribution of the emitted light. This is accomplished by exciting the S420 molecules with a focused laser beam and by imaging the back-focal plane that is projected on a camera by using a lens. [58,63,64] The emission angular patterns (Figure 4b,c, measured at T = 18°C and T = 28°C, respectively) consist of a circular region that is limited by the air-light line at k = k 0 (k 0 being the wavevector of light in air), and a few lobes in the ranges −NA < k x /k 0 < −1 and 1 < k x /k 0 < NA (here, x is the direction of the nanofiber length and NA is the numerical aperture of the objective), which extend in the direction perpendicular to the fiber longitudinal axis. When excited by a focused laser beam, part of the light emitted by S420 molecules couples to the modes of the thermoresponsive fiber, due to the mismatch between the index of refraction of the polymer and air. This produces the lobes along the k x axis in the angular patterns, similarly to those found for nanofiber-embedded single-photon emitters and organic single crystals. [58,65] The emitted photons propagating along directions that do not satisfy the condition of internal reflection are transmitted into the free-space and detected in the central circular area of the angular patterns (−1<k x,y /k 0 <1). Figure 4d,e shows the line profiles, along k x (k y /k 0 = 0), of the angular patterns shown in Figure 4b,c, respectively, with highlighted peaks corresponding the waveguide modes. These peaks also allow the fiber diameter and refractive index to be estimated, by comparison with the propagation constant , obtained by modeling the nanofiber as a cylindrical dielectric waveguide surrounded by air. [66] Figure 4f shows the dependence of on the waveguide diameter for various linearly polarized (LP) modes, using the resulting values of the refractive index and highlighting the corresponding fiber transversal size. We find: (n S = 1.46, d S = 650 nm) and (n NS = 1.5, d NS = 520 nm) for T = 18°C -hydrophilic behavior-, and T = 28°C -hydrophobic behavior-, respectively (for complete details of the procedure to estimate the refractive index and diameter values in the low-temperature and high-temperature regimes, see Figures S10 and S11 in the Supporting Information and the discussion therein). For T = 28°C (fibers dehydrated), three peaks can be identified in the experimental k x profile (Figure 4e), corresponding to modes LP 01 , LP 11 , and to a combination of LP 21 and LP 02 (which cannot be resolved in our measurements). The corresponding estimated refractive index (n NS = 1.5), agrees with the value for poly(2-oxazoline)s. [53,54] At lower temperature (T = 18°C), the fibers swell and the diameters might increase, resulting in one more band in the back-focal plane image (mode LP 31 appearing in the lowest edge of the interval of accessible k x values). The corresponding refractive index (n s = 1.46) is compatible with a hydration process in the fibers, and is in line with results of previous studies by thin-films of poly(2-oxazoline)s. [53]  Overall, these results show that an effective swelling/deswelling is likely to be induced in PnPrOx/S420 electrospun fibers by varying the temperature across the T CP of PnPrOx. Swelling-induced changes could impact on the emission from embedded fluorescent molecules, [45,67] as well as on the light scattering, waveguiding and amplification in the fibers. Swollen NFs could better guide the light emitted by S420 molecules, which might favor amplification, due to the overlap with the gain medium. In fact, a slight increase (≅9%) of the fraction of the power of the fundamental mode confined in the core is calculated upon swelling ( Figure S12, Supporting Information), which however could be compensated by the corresponding decrease of the fraction of power coupled to the fundamental mode, because of the presence of additional higher-order modes. [58] To better assess light amplification, one can consider the gain, g, of N emitting molecules in a fiber of volume V, given by: g = N/V, where is the transition cross section. [61] For an isotropic swelling behavior, the density of S420 molecules would decrease by a factor 3 ( being the ratio between the size of a swollen fiber, d S , with respect to a dehydrated one, d NS , = d S /d NS ) and a similar decrease would occur for the gain (assuming that is not significantly altered by the swelling process): g S = N/V S = N/( 3 V NS ) = g NS / 3 , where g NS (V NS ) and g S (V S ) are the gain (volume) of pristine and swollen fibers, respectively. From the waveguiding measurements one finds ≈1.25, a value that leads to a decrease of the gain coefficient by about a factor 2 for swollen fibers, in line with the increase of the threshold of line-narrowed emission observed in fibers at low temperature. This effect is highly promising in view of future optical sensing applications, where the swelling-induced gain variation and switching could be exploited for probing environmental parameters, especially in the framework of indoor monitoring. For instance, the increase of excitation threshold found at high RH values could allow monitoring the formation of mold on indoor walls, a process triggered at RH>75%. [68,69] Moreover, NFs are mechanically flexible and conformable to curved surfaces, and can be used to combine optical gain switching with network laser architectures, whose emission wavelengths have been demonstrated to be very sensitive to local variation of optical parameters (e.g., refractive index). [59] In this respect, NFs could be further exploited for enhancing the sensitivity and the robustness of sensing units.

Conclusion
Light-emitting NFs made of a thermo-responsive polymer are introduced, with optical gain properties tunable through temperature and humidity. Line-narrowing of the emission is found in uniaxially aligned arrays of fibers, with threshold excitation fluence of few mJ cm −2 . The excitation threshold can be tailored with both temperature and humidity, enabling reversible switching of the optical gain. The investigation of the waveguiding properties of individual NFs supports swelling effects at low temperature, namely below the polymer T CP . In combination with the high surface-to-volume ratio of nanofibrous networks, these temperature and humidity-sensitive systems are promising materials for creating future components and devices for stimuliresponsive optics, intelligent photonics, and optical sensing.
The nPrOx monomer was synthesized via the Witte Seeliger synthesis method as previously described. [70,71] Ethanolamine (1.2 eq), zinc acetate dihydrate (0.02 eq), and butyronitrile (1 eq) were mixed and stirred for 45 h at 130°C in a reflux setup until all nitrile was reacted as determined by gas chromatography (GC). After a first distillation under vacuum, a second distillation under Ar with addition of ninhydrin, and a third distillation under Ar with addition of sodium, the pure monomer was obtained.
Polymerization was carried out under Ar flow in round bottom Schlenk flasks. [49,72,73] The polymerization mixtures contained the monomer with an [M] of 4 m, dry ACN as the solvent, and the oxazolinium salt HPhOxBF 4 as initiator ([M]/[I] 625/1 for a DP of 500). The reaction mixture was heated to 40°C for 30 min, after which the setup was degassed and statically distilled toward a round bottom flask. This flask was then put in an oil bath at 60°C under Ar atmosphere for seven days (conversion ≈80% according to GC). The polymerization was terminated by addition of an excess of KOH (2.5 times the molar amount of the initiator), dissolved in MeOH, while keeping the reaction mixture at room temperature for 18 h. The reaction mixture was finally precipitated in ice-cold diethyl ether and filtered. The resulting PnPrOx polymer was dried under vacuum, to obtain the polymer as a white-yellow powder. The procedure was performed according to literature. [49] Further characterization information was shown in Figure S13 (Supporting Information).
Electrospinning: NFs were realized by electrospinning, in which a polymer solution was continuously stretched by an electric field. [74] Solutions were prepared by dissolving the dye S420 in ethanol upon heating (50°C), after which water and PnPrOx were added under continuous stirring, until homogenous solutions were obtained. Based on PnPrOx electrospinnability, [49] 25% (wt.%, i.e., ratio of polymer mass and the sum of polymer and solvent mass) of PnPrOx was dissolved in a 30/70 vol.% water/ethanol. The S420 concentration (wt.%), expressed as the ratio of the chromophore-weight to the polymer-weight, was 0.5%.
Electrospinning experiments were carried out using a mono-nozzle setup, including a negatively charged (−7.5 kV) drum collector rotating at 60 Hz to obtain aligned NFs. A KD Scientific (KDS-100-CE) pump was used to inject the spinning solution through the plastic syringe (Henke Sass Wolf Norm-ject) upon which a needle (18 gauge, Terumo mixing needle) without bevel was attached. Around the needle, an auxiliary ring electrode was placed to direct the jet. A flow rate of 0.5 mL h −1 , a tip-to-collector distance of 10 cm, and a voltage between 20 and 30 kV (Glassman Series EH high voltage source) were used to obtain a stable Taylor cone and optimized, reproducible processes. Electrospinning was performed at ambient conditions (T = 25±2°C, and RH = 30±10%).
Nanofiber Characterization: To investigate the morphology of the fibers, both a tabletop SEM (FEI Phenom XL) and a high resolution SEM (FEI Quanta 200 FFE-SEM) were used, with typical accelerating voltages of 15 and 20 kV, respectively. The investigated materials were coated with a thin layer of gold (LOT-Quantum Design or Balzers Union SKD 030 sputter coater). Average diameters and standard deviations were obtained on at least 50 measurements per sample using ImageJ software, or at least 300 measurements per sample using Phenom FiberMetric software.
The water absorption/adsorption/desorption capacity of the material at specific relative humidity and temperature could be measured through DVS analysis. The amount of absorbed/adsorbed water was expressed as a weight change of the material. DVS experiments were carried out with a Q5000SA Dynamic Vapor Sorption apparatus from TA Instruments. Samples of (2.50 ± 0.50) mg were characterized by using metalized quartz sample pans. Following a drying step at T = 30°C and RH = 0%, the samples undergo a relative humidity of 80% at 25°C. Three subsequent cycles were performed. All weight changes were allowed to reach equilibrium (weight change < 0.05% during 60 min).
Optical Properties: To study the dependence of the emission properties on environmental parameters, an apparatus that allowed the sample temperature and the relative humidity to be controlled and monitored was realized ( Figure S4, Supporting Information). Samples of NFs were deposited on a quartz glass (area 1 cm ×1 cm) and mounted on a sample holder, while a temperature sensor (AD590) was placed in contact with the surface of the nanofiber mat. To control the sample temperature, a Peltier module was positioned in contact with the quartz substrate. The sample holder was designed to dissipate the heat generated by the Peltier module. The Peltier module and the temperature sensor were connected to a PID device. The sample holder was placed in a stainless steel chamber connected to a mechanical vacuum pump and to a water reservoir. A nitrogen flow through the water reservoir allowed the moist content in the chamber to be varied. The relative humidity was measured by using a HIH-4000 humidity sensor (Honeywell) placed near the sample. A static condition of temperature and relative humidity was maintained on the timescale of a measurement ( Figure S14, Supporting Information). The investigation of the switching behavior was performed by setting the relative humidity and temperature parameters and waiting a time interval of 10 min before acquiring the emission spectra.
To characterize the NF emitters, the third harmonic of a Nd:YAG pulsed laser system (Quanta-Ray INDI, Spectra-Physics) was used, emitting at 355 nm with a repetition rate of 10 Hz and pulse width <10 ns. The excitation laser beam was stripe-shaped (beam size 0.52×0.03 cm) by using a cylindrical lens. The light emitted from the sample was collected from the sample edge (along a direction perpendicular to the one of the propagation of the excitation beam, Figure S4, Supporting Information) and sent to a spectrometer (iHR320, HORIBA) equipped with a CCD detector (Symphony, Horiba). The set-up schematized in Figure S3b (Supporting Information), similar to the one of Ref. [75], was used for evaluating the coherence features of the devices. NFs were excited through a dichroic mirror with the Nd:YAG laser focused on the sample in order to form a circular spot with 2.2 mm diameter. Two lenses were used to direct the emission from the excited spot onto a double slit (width 150 μm and separation 250 μm). A detector (CMOS camera) was placed on the back focal plane of a lens positioned behind the double slits.
Back-Focal Plane Imaging: To evaluate waveguiding, a few isolated NFs were deposited on a glass coverslip. The fluorescence of a single fiber was first imaged through an optical microscope (Olympus iX71), exciting with a Hg lamp. In order to study the light guided in the fiber, a diode laser (model Lepton IV L4 405M-15-TE, Micro Laser System) with emission at 405 nm was focused (spot diameter ≈6 μm) on the fiber by the microscope objective (NA = 1.42). The emitted light was collected by the same objective and sent to a CMOS camera (DCC1545M, Thorlabs). To obtain an image of the back-focal plane on the camera, a lens with focal length f = 60 mm was placed in front of the camera at a distance, d = f. LP modes were calculated using dedicated functions from a MATLAB library, developed in Ref. [76].

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.