# A Review of Femtosecond Laser-Induced Emission Techniques for Combustion and Flow Field Diagnostics
## 2 Femtosecond Two-Photon Laser-Induced Fluorescence (fs-TPLIF)  
Laser-induced fluorescence (LIF) is one of the most common techniques for combustion diagnostics [7], which uses a resonant laser beam to excite a selected transition from a special molecule (or atom) to a higher excited state and detects the induced fluorescence. Various combustion intermediate species can be measured by LIF [14; 15]. Based on fluorescence imaging, two-dimensional visualization can also be achieved by planner LIF [16]. For LIF measurements, one-photon excitation is preferred, since it has a linear response and high absorption cross-section. However, many key combustion intermediates, such as atomic hydrogen (H) [17], atomic oxygen (O) [18] and carbon dioxide (CO) [19], have a large energy gap between the ground and the first excited electronic states, which makes one-photon LIF impossible as the wavelength falls into the region of vacuum-ultraviolet (VUV). To address this complication, researchersdeveloped a two-photon excitation scheme. Two-photon laser-induced fluorescence (TPLIF) was first demonstrated for H and deuterium measurements by [PERSON] et al. [20], and then it was applied to detect many other species, including O [21; 22; 23] and N [22]. A limitation of two-photon excitation is that high laser fluence is required in order to overcome the issue of small absorption cross-section. The high laser fluence could cause significant photo-dissociation. For example, in TPLIF detection of H, a substantial amount of additional H can be produced via photodissociation [24] of some hydrogen-containing radicals, such as H\({}_{2}\)O\({}_{2}\)[25] and CH\({}_{3}\)[26], which makes it difficult to distinguish the natively generated H in the flame and the photolytic H. Even if the photolytic products are different from the species of interest, they may also cause interference. For example, when performing CO-TPLIF measurements in a sooty flame, the ns-laser at 230 nm, which is used to excite CO molecules, will generate photolytic C\({}_{2}\) radicals. Moreover, the so-called Swan-band emissions from C\({}_{2}\) will interfere with the CO detection, since they partially overlap with the CO fluorescence. To circumvent the above-mentioned issues, researchers use fs lasers in place of ns lasers. By assuming that the molecular transitions have a linewidth much narrower than the excitation laser energy distribution [27], the efficiency of two-photon excitation can be expressed as  
\[S_{\text{LIF}}\propto\sigma_{0}\cdot I_{0}^{2}\frac{1}{c_{\omega}\cdot c_{t}}, \tag{1}\]  
where \(S_{\text{LIF}}\) is the fluorescence signal, \(\sigma_{0}\) is the two-photon rate coefficient, \(I_{0}\) is the laser pulse energy of the excitation laser, \(c_{\omega}\) is the laser spectral linewidth of the laser, and \(c_{t}\) is the laser pulse duration, so the relative TPLIF efficiency can be estimated by the product of \(c_{t}\cdot c_{\omega}\) of the excitation laser pulse. For a Fourier transform limited (FTL) laser pulse, \(c_{t}\cdot c_{\omega}\) is a constant and has the smallest value, which is the most favorable for the two-photon excitation. Most fs laser pulses are close to FTL, while for most ns or picosecond (ps) laser pulses, the \(c_{t}\cdot c_{\omega}\) values are generally larger by a factor of around 100. For detection of molecular species, the possibility of a simultaneous excitation of the whole vibration band (or even including some hot bands) forms another extra advantage of fs-TPLIF in contrast to the ns and ps cases, where only a couple of rotational lines can be excited. This effect will be more evident in flames, where much more rotational lines and even hot vibrational bands can be populated. Therefore, even if the pulse energy of an fs laser is two orders of magnitude lower than that of a typical ns laser, the fluorescence intensity is similar to that in ns or ps TPLIF measurements [28; 29].