Laser diagnostic measurements have become the standard for noninvasive characterization of complex combusting flows. In particular, laser-induced fluorescence (LIF) provides a straightforward single-input-beam diagnostic approach for determination of both temperature and species number density [1]. Traditionally, nanosecond-duration pulsed lasers have been used as excitation sources for LIF detection. However, these laser sources typically operate at repetition rates of $10–50\mathrm{Hz}$, whereas the turbulent nature of many complex reactive-flow environments—particularly those associ ated with propulsion via fuel combustion—requires the continued development of high-repetition-rate optical probes to allow time-series measurements of high- frequency events.

Recent technological advances have resulted in commercially available amplified ultrafast laser systems that operate at repetition rates of $1–10\mathrm{kHz}$, and much progress has been made toward the development of single-shot diagnostic techniques using broadband femtosecond laser sources. For example, single-shot coherent anti-Stokes Raman scattering probes have been developed using ultrafast lasers for high-repetition-rate thermometry of stable gas-phase species, such as ${\mathrm{N}}_2$ in reacting-flow environments [2, 3]. Nevertheless, the extreme environments associated with many real-world combusting flows are often challenging to access with optical methods, necessitating the use of simplified optical geometries [4]. Furthermore, the quadratic signal- level dependence of nonlinear optical probes on number density makes them prohibitively difficult to generalize to minor species detection.

These considerations have led us to begin development of an LIF optical probe of important minor species within combusting flows using a high-repetition-rate femtosecond laser system. In fact, Laurendeau and coworkers have developed the picosecond time-resolved LIF (PITLIF) technique into a powerful tool to make high- repetition-rate measurements of minor species. For example, time-series measurements of the hydroxyl radical, OH, using PITLIF have been carried out at repetition rates of $10\mathrm{kHz}$ and greater [5]. Developing analogous LIF detection schemes using subpicosecond pulses holds the added promise of time-gated detection on time scales that are faster than typical collisional lifetimes, even in high-pressure environments. Such quenching effects in the presence of myriad combustion intermediates make the modeling of an LIF signal initiated by ns-duration sources difficult. Future directions of this approach include the development of a subpicosecond time-resolved LIF probe for single-shot detection of important species in complex combusting flows with $10\mathrm{kHz}$ repetition rate and the extension of this method to two-dimensional measurements via planar LIF.

Described here, therefore, is the LIF detection of OH radicals within reacting flows following TPE into the $(0,0)$ band of the OH $A^2{\sum }^{+}-X^2\mathrm{\Pi }$ transition using a high-repetition-rate femtosecond pulsed laser source. This work particularly addresses several unique characteristics of subpicosecond pulsed sources—including large peak intensities and broad bandwidth—that provide both benefits and disadvantages for LIF detection. For example, typical OH LIF schemes involve single-photon excitation to the $v=1$ state of the $A^2{\sum }^{+}$ excited electronic state (generally using excitation wavelengths near $285\mathrm{nm}$), which allows observation of redshifted emission in the $(1,1)$ and $(0,0)$ bands ($\lambda \sim 310\mathrm{nm}$) that is readily filtered from scattered excitation-laser light [6]. In contrast, the use of broadband ultrafast pulses with wavelengths near $620\mathrm{nm}$ allows direct excitation in the $(0,0)$ band of the OH A–X transition via far-from-resonance TPE (i.e., no intermediary electronic state is resonant with single-photon $620\mathrm{nm}$ excitation) without concern for excitation-laser scatter. This TPE scheme is experimentally feasible by virtue of the strong peak intensities associated with ultrafast laser pulses, allowing exploitation of the stronger $(0,0)$ transitions. Although two-photon absorption (TPA) cross sections are typically small relative to one-photon transitions [7], broadband femtosecond pulses provide a multiplexed source of two-photon excitation frequencies. In particular, for a given two-photon optical transition energy, ${\omega }_{\mathrm{TPE}}$, multiple pairs of frequencies contained within the optical pulse, detuned by $\pm \mathrm{\Delta }$ relative to ${\omega }_{\mathrm{TPE}}/2$, contribute simultaneously.

The experimental apparatus consists of a Ti:sapphire oscillator/amplifier system (Spectra Physics Solstice) operating at a $1\mathrm{kHz}$ repetition rate. Approximately $1.1\mathrm{mJ}/\text{pulse}$ of the $800\mathrm{nm}$ output is used to pump an optical parametric amplifier (OPA) (Spectra Physics Topas), which produces tunable light from $600–670\mathrm{nm}$ [bandwidth: $12–16\mathrm{nm}$ full width at half-maximum (FWHM) over this tuning range]. Pulse characterization and shaping, used in some of the experiments described below, are facilitated by the use of a MIIPS Box 640 (Biophotonics Solutions, Inc.) pulse shaper [8]. The LIF excitation beam passes through an $f=+300\mathrm{mm}$ spherical lens that focuses the beam within the sample, which consists of a near-adiabatic, laminar, premixed fuel—air flame that is produced by a Hencken calibration burner; either ethylene (${\mathrm{C}}_2{\mathrm{H}}_4$) or hydrogen (${\mathrm{H}}_2$) is used as the fuel. Following bandpass filtration (Semrock FF01-320/40), fluorescence collection optics are used to image the signal emanating from the focal volume of the excitation beam into the detector. For dispersed-fluorescence experiments, a $0.25\mathrm{m}$ spectrometer coupled to an intensified charge-coupled device is used to collect the signal. For all other experiments, a photomultiplier tube (Hamamatsu R9110) is employed to collect the total emission.

Dispersed-fluorescence experiments were first carried out following TPE by a broadband subpicosecond pulse centered at $622\mathrm{nm}$. During these measurements a $15\mathrm{ns}$-duration gate was used to discriminate against steady-state background OH fluorescence that was emanating from the reacting flow. Moreover, broadband background fluorescence signal resulting from a multiphoton laser-induced breakdown (LIB) process was observed at high intensities. Since this latter background emission was difficult to separate from the $(0,0)$ emission band of OH, care was taken to eliminate LIB background by reducing the excitation energy to $<30\mathrm{\mu J}/\text{pulse}$ under these focus conditions. Figure 1 depicts the dispersed-fluorescence spectrum resulting from TPE of species in a ${\mathrm{C}}_2{\mathrm{H}}_{4-\text{air}}$ flame (equivalence ratio: $\mathrm{\Phi }=1.2$) measured $20\mathrm{mm}$ above the burner surface and averaged over 30,000 pulses. Simulated OH emission spectra, calculated assuming a thermalized excited-state population at $2400\mathrm{K}$ [9] and convolved over the experimental instrument response function, are also shown in Fig. 1. Excellent agreement is observed, which is consistent with the observation of excited-state OH that is thermalized at an adiabatic flame temperature [10] during its fluorescence lifetime.

The two-photon fluorescence excitation spectrum of this observed species was also collected by tuning the broadband excitation-laser spectrum over the $(0,0)$ absorption band. Figure 2 shows the total fluorescence intensity that was observed following TPE of OH in a ${\mathrm{H}}_{2-\text{air}}$ flame ($\mathrm{\Phi }=1.0$) as a function of the average spectral wavelength, which is calculated from the first moments of the measured TPE laser spectra. Each data point represents an average over 512 laser pulses, and error bars depict the variance observed for three replicate measurements. Although this approach does not yield a high-resolution TPE spectrum, it provides further confirmation that the observed signal results purely from OH present within the reacting flow. Also included in Fig. 2 is a simulated high-resolution TPA spectrum, assuming an initial $2400\mathrm{K}$ Boltzmann distribution [11] and using relative TPA cross sections (${\sigma }_{\mathrm{TPA}}$) calculated by explicitly considering products of transition-dipole- (μ) allowed one-photon transitions that couple rota tional (J) levels, between the vibrationless ground ($|X,(v^{\prime \prime }=0),J^{\prime \prime }〉$) and first excited ($|A,(v^{\prime }=0),J^{\prime }〉$) states of OH [12]. Summation according to

To confirm that differences observed between the experimental and calculated fluorescence excitation spectra are consistent with the use of pulses that are not transform-limited (TL), additional experiments were carried out in which the second-order frequency domain phase [${\varphi }^{\prime \prime }$, where $\varphi (\omega )={\varphi }_0+{\varphi }^{\prime }·\omega +1/2{\varphi }^{\prime \prime }·{\omega }^2+\cdots$; i.e., “linear chirp”] of the pulse was varied. Pulse compression was first carried out using MIIPS on an excitation pulse centered at $625\mathrm{nm}$ (bandwidth: $16\mathrm{nm}$ FWHM) to compress the pulse to within 0.2% of the Fourier transform limit ($\sim 35\mathrm{fs}$); the compensating phase mask suggests an uncompressed pulse FWHM duration of $\sim 160\mathrm{fs}$. Second-order phase, ${\varphi }^{\prime \prime }$ (range: $\pm 20000{\mathrm{fs}}^2$), was subsequently applied to this nearly TL pulse while the corresponding total TPE LIF signal intensity was measured for OH in a ${\mathrm{H}}_{2-\text{air}}$ flame ($\mathrm{\Phi }=1.0$). Figure 3 depicts the observed OH fluorescence intensity (512 pulse average) as a function of ${\varphi }^{\prime \prime }$. A plot of simulated TPE intensity versus ${\varphi }^{\prime \prime }$ is also shown for comparison purposes; this simulation incorporates the calculated $2400\mathrm{K}$ TPA spectrum and integrates over all pairs of frequencies ($1/2{\omega }_{\mathrm{TPA}}(J^{\prime },J^{\prime \prime })\pm \mathrm{\Delta }$) that can contribute to a given two-photon transition. Differences between the calculated and observed results for nearly TL pulses likely arise from small amounts of uncompensated phase variation across the pulse. The LIF intensity is strongly dependent on the degree of chirp associated with the TPE pulse, since the observed experimental signal decreases more than a factor of 2 relative to that of the nearly TL pulse with a second-order phase application of ${\varphi }^{\prime \prime }=+2000{\mathrm{fs}}^2$ (this corresponds to a pulse duration of $\sim 140\mathrm{fs}$ for this experimental pulse bandwidth, which is not unreasonable for an uncompressed pulse from an OPA).

These experiments confirm the potential for detection of fluorescence, free of background scatter from the excitation source, from a transient radical species (OH) in a combusting flow following efficient TPE by a high-repetition-rate ultrafast laser. Future work in our group will extend this broadband TPE approach toward other species (H atom, O atom, etc.) that are inaccessible if combustion environments via single-photon excitation. Since the emphasis of these initial experiments was on exploration of the advantages and challenges associated with the use of broadband, ultrafast TPE pulses, this work does not directly address the potential for detection of fluorescence on subpicosecond time scales. Moreover, no single-shot experimental results are presented here, and experiments are currently underway in our laboratory to address those experimental issues that limit detection sensitivity. Most importantly, background emission associated with LIB requires significant atten uation of TPE pulse energies, and pulse shaping experiments will be carried out to optimize the observed ratio of TPE LIF signal to background resulting from breakdown. Such modifications are expected to allow single- shot measurements of OH concentrations that are typical in air-breathing reacting flows.

Funding for this research was provided by the Air Force Research Laboratory under contract FA8650-10-C-2008 (Ms. Amy Lynch, Program Manager), and by the Air Force Office of Scientific Research (USAFOSR) (Drs. Tatjana Curcic and Julian Tishkoff, Program Managers).

 

Fig. 1 Comparison of experimental and simulated dispersed-fluorescence signal from OH following broadband TPE at $622\mathrm{nm}$. Symbols, experimental signal obtained from a ${\mathrm{C}}_2{\mathrm{H}}_{4-\text{air}}$ flame. Curves, calculated $A\to X$ emission spectrum (high-resolution stick spectrum and spectrum convolved with a $3.0\mathrm{nm}$ instrument response function) from thermalized ($2400\mathrm{K}$) OH.

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Fig. 2 Comparison of experimental and simulated two-photon (TP) OH spectra (${\mathrm{H}}_{2-\text{air}}$ flame). Experimental data (symbols), LIF TPE spectrum obtained by scanning the broadband TPE wavelength. Simulations (curves), high- resolution and Gaussian-broadened TPA OH spectra, assuming an adiabatic flame temperature ($2400\mathrm{K}$).

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Fig. 3 Effect of chirp on TPE fluorescence signal from OH (${\mathrm{H}}_{2-\text{air}}$ flame). Simulations were carried out using the experimental spectral envelope and the calculated TPA intensities at $2400\mathrm{K}$, as described in the text. The corresponding calculated pulse duration (FWHM) is shown on the upper axis.

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