Recent developments in plasma science and technology have opened new areas of research both for fundamental purposes (e.g., description of key physical phenomena involved in laboratory plasmas) and novel applications (material synthesis, microelectronics, thin film deposition, biomedicine, environment, flow control, to name a few). With the increasing availability of advanced optical diagnostics (fast framing imaging, gas flow visualization, emission/absorption spectroscopy, etc.), a better understanding of the physicochemical processes taking place in different electrical discharges has been achieved. In this direction, the implementation of fast (ns) and ultrafast (ps and fs) lasers has been essential for the precise determination of the electron density and temperature, the axial and radial gradients of electric fields, the gas temperature, and the absolute density of ground-state reactive atoms and molecules in non-equilibrium plasmas. For those species, the use of laser-based spectroscopy has led to their in situ quantification with high temporal and spatial resolution, with excellent sensitivity. The present review is dedicated to the advances of two-photon absorption laser induced fluorescence (TALIF) techniques for the measurement of reactive species densities (particularly atoms such as N, H and O) in a wide range of pressures in plasmas and flames. The requirements for the appropriate implementation of TALIF techniques as well as their fundamental principles are presented based on representative published works. The limitations on the density determination imposed by different factors are also discussed. These may refer to the increasing pressure of the probed medium (leading to a significant collisional quenching of excited states), and other issues originating in the high instantaneous power density of the lasers used (such as photodissociation, amplified stimulated emission, and photoionization, resulting to the saturation of the optical transition of interest).

The present study focuses on the application of a picosecond (ps) two-photon absorption laser-induced fluorescence (TALIF) technique in krypton (Kr) at variable pressure (0.1–10 mbar). The laser intensity (I, units W cm⁻²) is tuned between 1 and 480 MW cm⁻², and the depletion of the density of the Kr 5p′[3/2]₂ fluorescing state through photoionization (PIN) and amplified stimulated emission (ASE) is investigated. This is done by combining TALIF experiments with a simple 0D numerical model. We demonstrate that for a gas pressure of 3 mbar and 15 $<I\le$ 480 MW cm⁻², a saturated fluorescence signal is obtained, which is largely attributed to PIN, ASE being negligible. Also, a broadening of the two-photon absorption line (i.e., 4p^{6 1}S₀$\hspace{0.17em}\to \to$ 5p′[3/2]₂) is recorded due to the production of charged species through PIN, inducing a Stark effect. For I $\le$  15 MW cm⁻², though, PIN is significantly limited, the absorption line is noticeably narrowed, and the quadratic dependence of the TALIF signal intensity vs the laser energy is obtained. Thus, in this case, the investigated Kr TALIF scheme, using the 5p′[3/2]₂ $\to$ 5s[3/2]₁ fluorescence channel, can be used for calibration purposes in ps-TALIF experiments. These results are of interest for fundamental research since most ps-TALIF studies performed in Kr do not investigate in detail the role of PIN and ASE on the depletion of the Kr 5p′[3/2]₂ state density. Moreover, this work contributes to the development of ps-TALIF for determining absolute densities and quenching coefficients of H and N atoms in plasmas. The use of ps-TALIF can allow sub-ns measurements of quenching rates that are necessary for absolute atomic densities determination in atmospheric pressure plasmas. Thus, the present study is linked to many experimental works focused on plasma physics and applications. In fact, the investigation of the application of ps-TALIF in Kr and the definition of regimes where the TALIF signal intensity scales quadratically with the laser energy is essential to calibrate H and N atom densities in reactive plasmas.

We present a detailed methodology for (i) correctly configuring a streak camera to capture raw picosecond two-photon absorption laser induced fluorescence signals (ps-TALIF) of H-atom in low- and atmospheric-pressure plasmas, and (ii) properly processing the recorded raw experimental data with a dedicated mathematical signal processing method to infer actual ps-TALIF signals of H-atom. The goal is the accurate determination of the decay time of the recorded ps-TALIF signals of H-atom. A ps-laser is used to excite atomic hydrogen produced in both plasmas and the raw fluorescence signals are detected by the streak camera using different time windows/ranges (TR). It is shown that the choice of the TR affects the shapes and the decay times of the recorded raw TALIF signals. This is defined as the instrumental function of the streak camera and has a Gaussian profile as determined by recording the ultrafast laser pulse at different TR. To remove this instrumental distortion and extract the actual shape of the TALIF signals, the captured raw TALIF signals were fitted using the mathematical procedure developed in this study, which involved an exponentially modified Gaussian function. The application of our methodology leads to more reliable measurements of hydrogen atoms decay times after respecting the following acquisition conditions: (i) the TR of the streak camera should be sufficiently large to capture the complete (raw) TALIF signal, and (ii) the time width of the instrumental function of the streak camera should be as small as possible compared to the actual decay time of the fluorescence, while ensuring an optimal signal-to-noise ratio. This work demonstrates the remarkable potential of the combination of ps-TALIF and streak cameras in state-of-the-art optical plasma diagnostics.

A nanosecond-two-photon absorption laser-induced fluorescence (ns-TALIF) technique was employed to investigate the transients of a strongly emissive, pulsed microwave discharge. We analysed the conditions that have to be fulfilled in order to use the TALIF intensities measured with the laser central frequency tuned to the absorption peak instead of the fully integrated laser excitation spectrum absorption for measuring N-atom densities. We demonstrated the validity of the method under our conditions and applied it to the straightforward monitoring of N-atom densities during the transients of a pulsed ECR plasma. In particular, we demonstrated the existence of an unexpected increase in N( ⁴ S) atom density of about 10% at the early stage of the transition from high- to low-power phase. Using a self-consistent, quasi-homogenous plasma model encompassing a detailed state-to-state kinetics, a thorough analysis of the N-atom and N ₂ (B) kinetics was carried out and enabled this enhancement to be attributed to surface de-excitation of N( ² D) and N( ² P) atoms. The rise of the N( ⁴ S) atom density can serve as an indicator of the concentration of N( ² D) and N( ² P) atoms in the discharge.

One of the major constraints of measurements of atomic hydrogen densities using two-photon absorption laser induced fluorescence in most plasma and combustion environments is the determination of fluorescence decay times ( τ fluo H ), especially when using nanosecond-lasers or slow acquisition systems. Therefore, it is necessary to identify the depopulation processes of the laser excited level in order to correctly estimate τ fluo H . In this study, depopulation mechanisms of atomic hydrogen excited by two-photon absorption to the n = 3 level (H(n = 3)) have been investigated using a picosecond-laser excitation and acquisition of fluorescence by a streak camera, which allowed for direct measurement of τ fluo H and hence, the atomic hydrogen densities, in an H₂ microwave plasma operating in the pressure range 20–300 Pa. By combining these measurements with a detailed H(n = 3) collisional radiative depopulation model, it was found that full mixing amongst the H(n = 3) sub-levels occurs in our discharge conditions, even at a pressure as low as 20 Pa. Moreover, it is also seen that the Lyman β line is only partially trapped, as its escape factor Λ 31 decreases from 0.94–0.98 down to 0.58–0.86 while the measured atomic hydrogen density rises from 8 ± 5 × 10 19 m − 3 to 9 ± 6 × 10 20 m − 3 . This means that the radiative decay rate of H(n = 3) atoms varies with pressure and the classical Stern–Volmer method used to determine the quenching cross-section of excited H(n = 3) in collisions with H₂ molecules, σ Q H n = 3 / H 2 , is not valid for our measurements. We used two different physics-based approaches, and show that the quenching cross-section σ Q H n = 3 / H 2 lies in the range 90– 106 × 10 − 20 m 2 , which can be averaged as 98 ± 8 × 10 − 20 m 2 . This substantially improved estimation of σ Q H n = 3 / H 2 obtained in this work will be useful for the accurate estimation of H(n = 3) fluorescence decay times and therefore the atomic hydrogen densities.