## 1 Introduction  
Laser-induced breakdown spectroscopy (LIBS) is a versatile technique for the analysis of the chemical composition of many classes of materials. Solids, liquids, gases, powders, biological, and organic material, aerosols, and micro and nanoparticles are investigated and the type and abundance of chemical elements in such materials is determined by LIBS [1, 2, 3, 4, 5, 6, 7, 8]. This laser-based analytical method is fast and robust, enables multi-element detection, does not require laborious sample preparation, and can be employed for field measurements under harsh conditions. For these reasons, LIBS is becoming one of the key techniques for element analysis of complex materials besides X-ray fluorescence spectrometry (XRF), spark optical emission spectrometry (spark OES), prompt gamma neutron activation analysis (PGNAA), and others [9]. LIBS has enormous potential for various applications and LIBS-based sensors are employed in many areas: industry (e.g., for materials analysis on-site or in-line with production processes), security (e.g., for remote detection of hazardous materials such as CBRNE threats [10]), mineralogy and geological materials [11, 12], cultural heritage [13, 14], biomedicine (e.g., identification of bacteria [15, 16, 17, 18]), deep-sea inspection [19, 20], space exploration (e.g., for analysis of Martian rocks using the LIBS sensors in ChemCam and SuperCam on board of the NASA Mars rovers Curiosity and Perseverance [21, 22, 23, 24]), environmental measurements [25, 26, 27, 28], and many others. The number of scientific papers on LIBS that are published per year is increasing rapidly (Figures A1 and A2 in Appendix A).  
In LIBS, material is pulsed-laser ablated from the surface of a sample and the optical radiation of the laser-induced plasma (LIP) is analyzed by optical emission spectroscopy [29; 30]. Short nanosecond laser pulses are employed for the sampling of material, typically, as stable and robust nanosecond laser sources operating at various wavelengths, pulse energies and repetition rates are available. However, ultrashort femtosecond lasers offer several advantages for LIBS compared to conventional nanosecond lasers and femtosecond-LIBS experiences a growing number of applications (e.g., [31; 32; 33; 34; 35; 36; 37; 38]). In most studies, the optical emission of atomic and molecular species in the plasma is analyzed spectroscopically. Furthermore, recent studies have successfully demonstrated the remote isotope analysis by LIBS-based molecular isotope spectroscopy [39; 40].  
For the quantitative analysis of the chemical composition of plasma and sample calibration-based methods are frequently employed. Certified reference materials (CRM) are measured with the LIBS system and calibration curves for the analyte species are derived by univariate or multivariate regression procedures. With chemometric methods and machine learning techniques, large spectral data sets can be evaluated and the extraction of information from multidimensional data cubes can be automated [41; 42]. The calibration-based approach enables quantifying trace concentrations (ppm range). However, matrix-matched reference materials have to be measured under the same conditions as the sample materials. With laboratory-based analytical methods such as laser-ablation inductively coupled plasma mass spectrometry/optical emission spectroscopy (LA-ICP-MS/OES) much smaller element concentrations (ppb range) can be resolved [43; 44; 45; 46; 47]. Calibration-free (CF) LIBS is complementary to calibration-based LIBS and can be employed to quantify the major elements in a sample material without measuring CRMs. In CF-LIBS, the concentration of major components is derived directly from measured LIBS spectra by modeling the laser-induced plasma and the optical plasma emission [48; 49]. This approach is of interest as matrix-matched calibration samples are not required and constraints regarding the control of experimental parameters are less stringent.