1. Introduction

Combustion diagnostics is of great importance for rationalizing the combustion process and thrusting the innovative design of the combustion system for high combustion efficiency with low detrimental products [1]. Recently, it was demonstrated that femtosecond laser filament-induced nonlinear spectroscopy (FINS) possesses high potential for combustion diagnostics [2–5 ]. Clean optical emissions from multiple combustion intermediates including free radicals C₂, CH, OH and CN and atomic species C and H were simultaneously observed when a filament was formed in an ethanol-air flame by using a Ti:Sapphire femtosecond laser [3]. The fingerprint nonlinear photoemissions were ascribed to multiphoton excitation of the combustion intermediates due to the high clamped intensity inside the filament, which was implicitly assumed to have the same value as that in air [4].

In air, femtosecond laser filamentation originates from Kerr self-focusing and defocusing of the plasma generated from the ionization of air molecules [6]. Because both the critical power that decides the formation of filamentation and the clamped intensity that are crucial for the nonlinear light-matter interaction are significant for a broad spectrum of applications of femtosecond laser filamentation in areas such as light frequency conversion, pulse compression, remote sensing and so forth, extensive investigations have been performed to measure the two parameters in air [7–11 ]. The critical power for the Kerr self-focusing of a Ti: Sapphire laser pulse at 800 nm was determined to be 5-10 GW depending on the pulse duration [12]. The intensity inside the filament during free propagation is clamped to a constant value by the dynamical balance between the self-focusing and defocusing, which was previously evaluated to be ∼5 × 10¹³ W/cm² from the measured cut-off frequency of high-order harmonic generation or from the assumption of a steady state balance between self-focusing and multiphoton ionization [13, 14 ] and from ionization measurement [15]. More recently, the clamped intensity was directly measured to be ∼1.4 × 10¹⁴ W/cm² by recording the laser energy transmitted through a pinhole drilled by the filament itself on a thin metallic foil [16]. However, both the critical power and clamped intensity of a filament are sensitive to the gas species, which gives different Kerr nonlinear index of refraction. For example, the critical power of helium was estimated to be ~268 GW at atmospheric pressure and the clamped intensity inside an argon filament was measured to be ~3 times larger than that in air under the same focal condition [17, 18 ].

However, femtosecond laser filamentation occurring in a combustion flame is rarely investigated, and, to our best knowledge, the determinations of the two fundamental physical parameters, i.e., the critical power and the clamped intensity of femtosecond laser filament in flames have not been reported yet. In order to better understand the fluorescence mechanisms of combustion intermediates induced by the interaction of femtosecond laser pulse with flames, we experimentally measure in the present study the critical power and clamped intensity of femtosecond laser filaments in an ethanol-air flame on an alcohol burner array. We determine these two parameters respectively by measuring the shift of the focal position of femtosecond laser pulses based on the technique described in [12] and by comparing the difference of the laser energy transmitted through a pinhole drilled by the filament itself on a thin metallic foil placed both in flame and in air. It is found that both of the determined critical power and clamped intensity in flame are much smaller than those in air [12–16 ].

2. Experimental setup

The experiments were performed with a Ti: Sapphire laser system (Spectra physics, Spitfire ACE), which produces laser pulses characterized by a central wavelength of 800 nm, a transform-limited pulse duration of 35fs, a pulse energy of up to 5 mJ and a repetition rate of 1 kHz. The output energies of the laser beam have an uncertainty of ∼2%. The laser pulses were chirped slightly to compensate the dispersion from the laser propagation, and the pulse duration after the lens was measured to be ∼35 fs with an uncertainty of ∼5%. A half-wave- plate and a Brewster window were inserted into the laser beam to modify the pulse energy. In the measurement of the critical power [Fig. 1(a) ], the laser pulses were focused by a fused silica lens (f = 50 cm) into the ethanol-air flame on an alcohol burner array a continuous length of about 5 cm (no gaps between two adjacent flames) to generate a single filament located totally in the flame. The fluorescing filament was imaged by using a periscope and a fused silica lens (50.8mm in diameter, f = 6 cm) onto the entrance slit of a spectrometer coupled with a gated intensified charge coupled device (ICCD, Andor iStar). The fluorescence was then dispersed by a grating of 1200 grooves/mm (blazed wavelength at 500 nm) and recorded by the gated ICCD camera. The ICCD gate was opened 10 ns before the laser pulse arrived and the gate width was set to Δt = 210 ns for all the measurements of the focal positions.

 

Fig. 1 Schematic of the experimental setups for the (a) critical power and (b) clamped intensity measurements. HWF: half wave plate; BW: Brewster window; L1: fused silica lens with f = 50 cm; PSM: periscope mirrors; L2: fused silica lens with f = 6 cm. L3: fused silica lens with f = 100 cm. (c) Typical filament-induced nonlinear spectrum in the ethanol-air flame in ambient atmosphere. Inset: the image of the flame together with the filament.

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In the measurement of the clamped intensity [see Fig. 1(b)], the laser beam was loosely focused by a fused silica lens with a focal length of 1 m. The reason that different focal length lenses was chosen in the two measurements is as follows. Because different external focal conditions can lead to a significant change of the filament plasma density, but only a relatively small change of the clamping intensity inside filament core [19]. Therefore, the use of the short 50-cm focal length lens in the critical power measurement can give rise to a relatively higher plasma density, and thus a stronger fluorescence signal to enable the critical power measurement at low input energies. Whereas in the clamping intensity measurement, the use of the long 100-cm focal length lens can decrease the power density of the photon bath (or background reservoir), and thus reduce the influence of the power density of the photon bath on the measurement. In addition, as shown in [19], when the focal length of the lens is 100 cm, the clamping intensity inside the filament core is comparable to the case of free propagation.

The repetition rate of the laser pulses in the clamping intensity measurement was changed to 100 Hz to allow a mechanical shutter with an opening/closing time precision of 1-2 ms to precisely control the number of the laser pulses irradiating the surface of a piece of 50-μm-thick copper foil, which was inserted into the flame with the surface being roughly perpendicular to the laser propagation direction. The shutter was placed before the 1-m focal length lens. The laser energy was fixed at 0.8 mJ. The laser beam was loosely focused by a fused silica lens with a focal length of 1 m to keep the clamped intensity comparable to the free propagation [19]. The transmitted laser energy through the pinhole drilled by the filament on the copper foil was recorded by a laser power meter placed several tens of centimeters behind the foil. The distance between the filament and the burner wick was about 9 mm. The temperature in this flame zone is about 400 ~500 °C [20], which is much lower than the melting point (~1000 °C) of the copper foil. The fabricated pinholes were measured by a scanning electron microscope (SEM) (JEOL JSM-7500F). For comparison, a similar experiment in air was also performed.

3. Results and discussions

Figure 1(c) shows a typical filament-induced fluorescence spectrum of the laminar ethanol-air flame in the ambient atmosphere in the UV-Vis range of 300-600 nm. The laser pulse energy was about 500 μJ measured after L1, and the distance between the filament and the burner wick was about 9 mm. The data were accumulated over 3.4 × 10⁴ laser shots. As shown in Fig. 1(c), the signals are assigned to molecular bands of CH, CN, N₂, NH, OH, and C₂, which are consistent with our previous observation [3]. In order to avoid the influence of the optical emissions from the flame itself on the measurements, we select the band of N₂ at 337 nm for measuring the shift of the self-focal position. This is because when the laser energy is decreased, the signal intensities of the laser-induced optical emissions from free radicals such as CH, OH, and C₂ would become comparable to those from the spontaneous emission from the flame itself.

As an example, the intensity distributions (dots) of the fluorescence at 337 nm along the laser propagation are plotted for three input energies of Fig. 2(a) 60 μJ, Fig. 2(b) 215 μJ, and Fig. 2(c) 420 μJ in the left columns of Fig. 2, in which the x-axis denotes the ICCD chip pixel converted into the unit of millimeter. In this measurement, the ICCD exposure time was fixed to 20 s which corresponds to 2 × 10⁴ laser shots. The signal in the left columns of Fig. 2 are the sum of the fluorescence in the wavelength range from 336.5 to 337.5 nm, as shown by the images in the right columns of Fig. 2 with the integrated wavelength ranges marked. It can be seen from Fig. 2 that as the laser energy varies the peak of the nitrogen fluorescence signals shifts accordingly. To see closely, we fit the signal profiles in Fig. 2 with a Gaussian profile (solid line). It can be clearly observed that the signals for the energies of Fig. 2(a) 60 μJ, Fig. 2(b) 215 μJ, and Fig. 2(c) 420 μJ are peaked at the positions 12.525, 11.25 and 10.65 mm, respectively, showing that the peak position gradually moves towards the focusing lens as the pulse energy increases (Note that increasing pixel values correspond to further distances from the focusing lens).

 

Fig. 2 On-axis intensity distributions of nitrogen fluorescence at 337 nm in an ethanol-air flame and the images recorded by ICCD with three input energy: (a) 60μJ, (b) 215 μJ, and (c) 420 μJ. The arrow: the laser propagation direction. The kinks at the profiles come from the pixel damage of the ICCD camera and the signal at 336 nm resulting from the combustion intermediate of NH becomes clearer as the input laser energy increases.

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It is well known that when the peak power exceeds the critical power the self-focusing in air follows the relation [21],

Since when the peak power of the laser pulse is smaller than the critical power, the focal position of the laser beam keeps constant at the geometrical focus. The measurement of the shift of the peak position of the filament as a function of the laser power will directly result in the critical power [12].

In Fig. 3 , we plot the peak positions measured with different input laser energies. The error bar of the peak positions may result from several different factors, such as the turbulence of the combustion system, the laser energy and pulse duration uncertainties. It can be seen that the peak position is almost unchanged when the pulse energy is low, but moves towards the lens when the laser energy exceeds a certain value (corresponding to the critical power). We performed two linear fits (solid lines) to the data to show the behaviors. In order to obtain the fit of the high energy data, we temporally removed the data with the energy less than 80 μJ, which have clearly different behavior, that is, we started from 80 µJ towards higher energy points; for fitting in the low energy part, we temporally removed, in a similar way, the high energy data and started from below 80µJ towards the lowest energy. Meanwhile we kept the slope to be zero when fitting the low energy data, which gives a fit uncertainty of ∼2%. The fits clearly show the critical energy of ∼78 μJ for the self-focusing of 800 nm, 35 fs Ti: Sapphire laser in the ethanol-air flame, which corresponds to $P_c=78\mu J/35fs=2.2GW.$ Considering the uncertainties introduced by the pulse duration and the measurements, the uncertainty of the measured critical power is estimated to be about 10-15%, and thus _{$P_c\approx 2.2\pm 0.3$} GW, which is about 4-5 times smaller than that (10 GW for 800nm, 42 fs laser pulses) in air [12]. It should be pointed out that the determination of the critical power in the flame is not influenced by the self-focusing of the laser pulse propagating in air. This is because at around the critical power (∼2.2 GW) of the flame, the laser peak power is much smaller than the critical power (10 GW) of air for self-focusing, that is, no self-focusing occurs in air.

 

Fig. 3 Peak position of the signal intensity at 337 nm as a function of pulse energy of the pump laser.

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According to the relation of $P_c=3.72{\lambda }^2/8\pi n_0{n}_2$ with n₀ and n₂ being the linear index of refraction and second order nonlinear index coefficient of the flame, respectively, the second order nonlinear index coefficient of the flame is deduced to be n₂ = 40 × 10⁻²⁰ cm²/W when assuming n₀ = 1. This value is about 4 times larger than that of air (12 × 10⁻²⁰ cm²/W for 800 nm, 90 fs laser pulses) measured by a polarization technique [23].

Next, we present the measurement of the clamped intensity of the femtosecond laser filament in the ethanol-air flame. We measured the laser pulse energy through a pinhole drilled on the metallic foil by the filament as well as the pinhole areas under the conditions with different laser shots. Shown in Fig. 4(a) is the plot of the transmitted energy versus the laser shot measured in flame. It can be seen from the linear fits (solid lines) of Fig. 4(a) that the transmitted laser pulse energy firstly increases linearly and then slows down linearly at a lower slope after 700 laser shots where the transmitted pulse energy is measured to be ~400 μJ. The data for the linear fittings were treated in a similar way as those in Fig. 3, in which the obviously different data were temporally removed during the fitting processes. The pinhole profile was imaged by the SEM, and an ablated area of 2.05 × 10⁴ μm² was obtained, as shown from the inset of Fig. 4(a). The error bar results mainly from the uncertainties of the measured transmitted energy and the drilled pinhole areas. The not-very-circular profile may result from wrinkles of the thin metallic foil during interacting with the laser pulses, and beam wandering caused principally by the gas motion inside the flame. Meanwhile, we also performed the measurement in air. All the other experimental parameters are kept the same except for the working medium. The results in air are presented in Fig. 4(b), which show similar behaviors as those shown in Fig. 4(a). In this case, when the number of the laser shots reaches 1100, the slope of the transmitted energy versus the number of the laser shots changes resulting in a transmitted energy of 360 μJ. The area of the drilled pinhole is measured from its SEM image to be 8.3 × 10³μm². The larger pinhole size in the copper film in the flame than that in air reflects the larger filament core in the flame than that in air.

 

Fig. 4 The transmitted laser energy versus the number of laser shots under the conditions of (a) flame and (b) air. Inset (a) and (b): the SEM image of the pinhole on the copper foil for the flame (650 laser shots) and the air (1100 laser shots), respectively.

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We assume that in the case of the larger slope the laser energy inside the filament core passes the pinhole, while the energy in the reservoir is blocked by the pinhole. That is, the drilled pinhole results mainly from the high intensity inside the filament core, and thus the area of the drilled pinhole can represent a relative cross sectional area of the filament core. With further increased laser shots, the slow increase of the transmitted energy of the filament may reflect that the wandering of the filament becomes dominant in enlarging the diameter of the drilled pinhole. It should be pointed out that although the contributions from the wrinkling of the metal foil and beam wandering to the area of the drilled pinhole are an accumulation effect, which is more significant for the cases of more laser shots, it still exists in the case of less laser shots. According to the slopes (0.39 and 0.29) obtained from Figs. 4(a) and 4(b) for the cases with more laser shots, the contributions from the wrinkling of the metal foil and beam wandering is slightly larger in the flame than that in air due to the stronger gas motion in the flame.

For the laser pulses with a Gaussian temporal profile, the clamped intensity inside the filament core in the flame is estimated to be 5.24 × 10¹³ W/cm², based on the relation of $I=0.94E/(A\cdot \tau )$ with E being the transmitted laser energy, A the area of the pinhole and $\tau$ the laser pulse duration [16]. Because the length of the filament is short (~1 cm), the self-modulation of the pulse duration in the filament can be neglected, and thus the pulse duration is assumed to be constant in our case. With this special definition, the intensity of the filament in air is estimated to be ∼1.2 × 10¹⁴ W/cm². The latter value is in good agreement with the recently reported value of 1.45 × 10¹⁴ W/cm² [16]. The above definition could be considered as a quick guide towards a ‘feeling’ of the clamped intensity simply because the size of the filament drilled pinhole is material and thickness dependent. We thus adopt the usually quoted clamped intensity of 5 × 10¹³ W/cm² in air [6] for calibration, and obtain the clamping intensity, I _c, in the flame by I _c/(5 × 10¹³ W/cm²) = (5.2 × 10¹³ W/cm²)/(1.2 × 10¹⁴ W/cm²), and thus I _c = 2.2 × 10¹³ W/cm². Considering the contributions from the wrinkling of the metal foil and beam wandering to the area of the drilled pinhole, we introduce a corrected factor, a = 0.39/0.29 = 1.3, where the correction is assumed linear, and thus I _c is corrected to be 2.8 × 10¹³ W/cm². As a consequence, the clamped intensity obtained in the flame is about a half of that in air.

4. Summary

In summary, we have experimentally measured the critical power and clamped intensity of femtosecond laser filamentation in the ethanol–air flame. The critical power and clamped intensity in the flame was found to be much smaller than the usually quoted ones in air. The second order nonlinear index coefficient of the flame has also been deduced from the measured critical power. The determinations of these fundamental physical parameters not only help understand the photoemission mechanisms of combustion intermediates induced by femtosecond laser filament, but also thrust the application of FINS technique for combustion diagnostics in practical combustion system.