Single-mode scannable nanosecond Ti:sapphire laser for high-resolution two-photon absorption laser-induced fluorescence (TALIF)

Abstract

A pulsed Ti:sapphire laser has been developed so as to operate over a wide range of frequencies, even far from the optimum wavelength (790 nm), as a narrow-band light source for TALIF experiments on O, Cl, N and H. The coupling of the optical cavity, both to its injection seeder and to the laser output beam, relies on a reflecting plate, which makes it fundamentally easier to control the coupling coefficient over a wider spectral range than with an ordinary transmission coupler. Two intra-cavity prisms are used to bring the green pumping light longitudinally coincident with the cavity axis, inside the Ti:sapphire crystal. Seeding by a CW Ti:sapphire laser has made it possible to obtain single-mode emission over the whole range of tunability, thanks to the spectral selection of the prisms and to a specifically developed digital/analog controller. Experiments carried out with the system on oxygen atoms inside an oxygen plasma show that the experimental bandwidth is limited essentially by the collisional dephasing rate and the finite pulse duration.

1 Introduction

For spectroscopic applications, nanosecond pulsed lasers can cover a wide spectral range from the IR to UV. The high peak power allows frequencies to be easily converted by suitable non-linear crystals and provides access to multiphoton transitions and photo-ionization. The Ti:sapphire (or $\hbox {Ti:Al}_2\hbox {O}_3$) laser [1] is particularly interesting because it is an all solid-state laser system with a broad gain curve, from 690 nm to $1~\upmu \hbox {m}$. However, nanosecond lasers, even in homogeneous-broadening crystals, are not longitudinally single-mode lasers because their behavior is governed by the high gain transitory regime where the coexistence of many axial modes is possible.

To have narrow-band emission, one possibility is pulsed amplification of a narrow-band CW laser. But for the low gain Ti:sapphire crystal, a multipass configuration is necessary [2]. Single-mode emission can also be achieved when the cavity of a pulsed laser is seeded by a narrow-band continuous-wave (CW) laser, such as a dye laser [3], a $\hbox {CW Ti:Al}_2\hbox {O}_3$ laser [4] or a diode laser [5]. When the seeded frequency is matched with a resonant mode of the pulsed cavity and if its amplitude greatly exceeds the spontaneous emission noise, all of the fluorescence can be channeled into this mode. Up to 99.8 $\%$ of the pulsed emission intensity has been measured at the seed frequency under optimum matching conditions [6]. This condition requires good adjustment of the seed beam inside the cavity (beam waist position and dimension) and the cavity length has to be kept in resonance with the frequency of the injected beam. In the Fourier transform limited regime, with injection seeding, spectral linewidth of the pulsed laser is only limited by the inverse of the pulse’s finite duration.

Injection seeding of the pulsed laser however may be challenging when implemented far from the spectral peak of Ti:sapphire gain curve ($\approx 790 \hbox { nm }$). We have already developed a injection-seeded Ti:sapphire laser devoid of any wavelength selective element [7], it was impossible to obtain a single-mode emission beyond 850 nm, without parasitic light appearing around 790 nm. A way to solve this difficulty is to insert a frequency-selective element in the cavity: one or more dispersive prisms [8], or birefringent quartz plates [9]. In the past, specifically developed and characterized pulsed Ti:sapphire laser systems have been utilized for a wide variety of experiments: such as LIDAR [10, 11], differential absorption measurement systems [6, 12], atmospheric spectroscopy [9], high-resolution molecular spectroscopy [2, 13, 14], spectroscopy of anisotropic helium [15], resonance ionization spectroscopy [16], and for cooling trapped antihydrogen [17].

Optical diagnostics in plasmas can also make use of the wide tunability of Ti:Sapphire. In this field, the TALIF technique (two-photon absorption laser-induced fluorescence) is very often used to obtain information on the temperature, collision processes (quenching rate) and density of some atomic species present in the plasma, with high temporal and spatial resolution, and high sensitivity. The principle is as follows. Upon excitation of a two-photon allowed transition, the fluorescence due to spontaneous radiation is detected at a different wavelength. This technique spectrally separates the excitation light from the emitted light. Generally, this type of diagnostics is applicable to atoms used in plasmas such as: H [18, 19], O [18, 20], N [21, 22] and Cl [23]. For these diagnostics, the TALIF method is also regularly used on rare gases, such as Kr and Xe. This then allows, by comparing the signals collected for a given quantity of rare gas atoms, to determine the density of the species present in the plasma, provided that the ratio of the two-photon absorption cross sections is well-known [24,25,26]. The transitions used, located in the VUV and UV spectral region, have often been addressed using pulsed dye lasers. These transitions are also accessible by non-linear optical conversion from the more versatile Ti:sapphire lasers.

This article is organized as follows: in the first section, we describe the laser design, the pulsed cavity and an overview of the laser setup. We then present an electronic control system well-adapted for the seeding of pulsed lasers. The energy performance and tuning bandwidth of the system are measured. The beam is spatially characterized. Finally, we present an example of a Doppler-free two-photon absorption spectrum on O obtained with seeded operation.

2 Laser design

2.1 Slave-pulsed ring cavity

Figure 1 shows the pulsed slave laser. In the case of Ti:sapphire crystal pumped by a nanosecond pulse beam, the cavity works in the gain-switched regime [1] because the pump pulse is shorter than the buildup time of the Ti:sapphire laser pulse and thus the initial condition for the oscillating mode is identical to that of Q-switched lasers. The $5 \hbox { mm } \times 7 \hbox { mm }$ and 15 mm long Ti:sapphire laser material (0.15 % Ti by weight providing an absorption coefficient of $2.1 \hbox { cm }^{-1}$ at 532 nm, FOM > 200 [27]) was cut by the manufacturer (Saint-Gobain / Roditi) to Brewster’s angle. We have built a cavity with planar mirrors and the gain-guiding effect [28], induced in a solid-state laser longitudinally pumped by another laser, leads to high-energy and high-beam quality of large diameter. Under these conditions, a gain medium pumped by a Gaussian beam can produce a large Gaussian beam from geometrically unstable cavities.

Fig. 1

Scheme of the pulsed slave cavity with the pumping beam @ 532 nm and the injection seeding CW beam. The prisms allow coarse wavelength selection and longitudinal pumping. The output coupling is achieved by reflection.The BK7 rectangular parallelepiped mirror is mounted on a piezoelectric transducer. Its azimuthal rotation allows easy tuning of the wavelength

The length of the ring cavity is 0.45 m. One of the mirrors, a BK7 rectangular parallelepiped ($12\,\hbox {mm} \times 18.25 \,\hbox {mm}$, thickness 6 mm), is actually a prism mounted on a piezoelectric translator (PSt 150/20/18 from Piezomechanik) so that the cavity mode can be matched to the seed-beam frequency. The intra-cavity beam is incident at Brewster’s angle on the lateral faces and in total internal reflection on the back face. This prism is equivalent to a quasi-achromatic mirror and has a high damage threshold. Two high reflectivity plane mirrors, $\hbox {R}_{Max}$ mirrors were used depending on the spectral range. Mirror M1 (resp. M2) from CVI (resp. Layertec) was coated for a wavelength range of 690–900 nm (resp. 900–1000 nm), at $0^{\circ }$ angle of incidence. The reflectivity range was a little shifted because a slightly different angle of $10^{\circ }$ was used in the cavity. The output coupling is produced by reflection off a partially reflecting thick plate (diameter 12.7 mm, thickness 15 mm). One face is anti-reflection coated in the range 700–1000 nm and the other face is coated [29, 30] to optimize the output coupling reflection with respect to the gain. This reflection coefficient was also measured as shown in Fig. 2a. Such a broadband wavelength-dependent coupling variation is easier to achieve in reflection than in transmission. Obtaining a 10–50% reflection coefficient starting from the nearly achromatic 4% reflection coefficient of a bare air-glass surface appears more natural than reducing the 96% transmission of a mirror down to 10 to 50% selectively in a wide spectral area. For a round-trip loss of 10% and considering the dependence of emission cross-section on wavelength given by [31], the normalized population inversion density at the threshold, $\hbox {n}_t$, is about 0.016 and rather constant, with a variation of $\pm 12.5\%$ for the whole spectral range (cf. Fig 2b). This spectral range, after two frequency doubling stages, allows access to typical transitions for important species present in plasmas (cf. Fig 2a).

Fig. 2

Measured reflectivity of the coupling mirror and population inversion density at threshold. a Characterization of the output coupling, produced by reflection on a thick plate. Its broadband reflectivity allows us to operate the laser over the whole tuning range without changing the coupler and to reach transitions of interest for TALIF experiments. These transitions are reached after two frequency doubling stages; the fundamental wavelengths are indicated by an arrow for different atomic elements. b The normalized population inversion density at threshold is almost constant, because the variation of the reflectivity compensates the gain dependence of the Ti:Sapphire crystal as a function of the wavelength

Coarse wavelength selection is provided by two BK7 Brewster dispersion prisms with an apex angle of $67^{\circ }$ and an incidence angle close to Brewster’s angle. Wavelength tuning is obtained by adjusting the azimuthal angle of the BK7 parallelepiped mirror. The free-laser spectral linewidth was narrowed to $\approx 1 \hbox { nm }$ and the laser wavelength tunable from 700 to 1000 nm. The pump beam is a commercial flashlamp-pumped frequency-doubled Nd:YAG laser (CRF200 Quantel), providing up to 130 mJ, 10-ns, linearly polarized green pulses. This stable resonator produces a smooth beam profile with low energy fluctuations (< 2.5 $\%$). The shot-to-shot energy stability is important to reduce fluctuations of the gain-switched laser. Indeed, the buildup time (temporal jitter) of the $\hbox {Ti:Al}_2\hbox {O}_3$ system and the energy variations mainly originate from the pump energy fluctuations [32]. The pumping energy is adjusted with a $\lambda /2$ plate and a polarizing beam splitter (PBS). A telescope reduces the 532-nm pump beam to a 2.5-mm-diameter roughly Gaussian spot in the crystal after being dispersed by the 2 prisms. Under these conditions, the maximum pump fluency, of about $4\,\hbox { J/cm }^2$, stays below the damage threshold of the $\hbox {Ti:Al}_2\hbox {O}_3$ crystal (8–10 $\hbox {J/cm}^2$).

2.2 Overview of the system

Fig. 3

Overview of the laser system. The gain-switched Ti:sapphire cavity is pumped by a frequency-doubled Nd:YAG pulsed laser (CFR 200 from Quantel), having a repetition rate of 20 Hz and emitting 12 ns long pulses. We set the energy using a half-wave plate before the polarization separation cube. Two lenses are used to enter the crystal with a pump beam of diameter 2.5 mm. The ring resonator length is regulated through the PZT-mounted Brewster prism. The latter permits locking of the cavity using an homemade electronic box. This injection seeding is here made by a CW Ti:Sapphire (MBR from Coherent) pumped by a green pump laser (Verdi from Coherent). Two optical isolators (OI) prevent feedback of the pulsed light. The high-resolution lambda meter is not represented. The blue light is obtained by two BBO crystals and the produced radiations are separated by a Pellin–Broca prism

An overview of the system is presented in Fig. 3. The CW seed beam is provided by a commercial Ti:sapphire laser (MBR 200 from Coherent) pumped by a 10 W green laser (Verdi from Coherent). A small percent of the laser beam is reflected by a broadband plate beam splitter (96/4) and sent to a high-resolution lambda meter (WS-8 from High Finesse) to measure the IR wavelength. We used a 1-m focal lens at the output of the laser to adapt the size of the beam to the slave cavity. Two 30 dB optical isolators set before the pulsed slave laser prevent feedback to the CW laser to maintain stable single-mode operation and to avoid optical damage.

Fig. 4

a Fringes in the slave cavity produced by the forward interfering light of the seeding CW laser: they appear while sweeping the piezo of the BK7 rectangular parallelepiped, hence, the cavity length. As the coupling is achieved by reflection, the fringes correspond to the fraction of the incident intensity reflected by the cavity. Their processing by our electronics allows servoing the resonator. b Temporal behavior of the pulsed laser at E$_\mathrm{{p}}$ = 85 mJ recorded by a photodiode. First the pump and second the gain-switched pulse of the slave Ti:sapphire cavity. We verify that the injection seeding reduces the pulse building time and doubles the energy of the pulse in the forward direction

At the output of the pulsed cavity, a part of the beam is detected by a photodiode (UDT450 HS) and two frequency doubling crystals allow the production of blue light. The crystals are set as close as possible to the cavity exit to optimize the non-linear conversion without using an optical lens. In the case of two-photon excitation of oxygen (around 225 nm), the first crystal is a $5 \times 5 \times 10 \hbox { mm }$ AR-coated BBO crystal ($\theta = 25.6^{\circ }, \phi = 0^{\circ }$). The second one is a $4 \times 4 \times 10 \hbox { mm }$ AR-coated BBO crystal ($\theta = 63.3^{\circ }, \phi = 90^{\circ }$). For 10 mJ of IR light at 900 nm, we produce about 2.5 mJ at 450 nm and 1 mJ at 225 nm. To measure the wavelength emitted by the unseeded cavity and compare it to that of the continuous laser, a grating spectrometer is used with a fiber (AvaSpec-2048 from Avantes) that detects both the fluorescence of the crystal and the laser light, more intense and scattered by the optical components. To ensure injection seeding, the cavity is tuned so that the emission gain band is at the same frequency as the one of the CW laser. We also used a laser diode (DL100 from Toptica) with a power of about 100 mW for injection. A few mW is enough for the seeding [29, 33], provided that the beam is of good spatial quality. To obtain a $\hbox {TEM}_{00}$ mode, we used two cylindrical lenses to make it symmetrical and two other lenses and a 100 $\upmu \hbox {m}$ pinhole for spatial filtering.

2.3 Injection seeding and stabilization scheme

Fig. 5

Electronic diagrams. a Sweep mode: an adjustable sawtooth signal is generated. b Off pulse servoing mode: a correction loop (PI) is applied when the laser is off. The offset setting for the signal input makes it possible to lock the laser on the steepest part of the interference fringes. c During laser pulse, the corrective loop is disabled. During this time (from 0.1 to 3 ms), we can apply a compensation voltage to correct the frequency pulling of cavity modes. We can also reset the integrator voltage if the signal reaches a threshold, for scans of large amplitude

For stable single-mode emission, the cavity has to be kept in resonance with the frequency of the injected beam. It is necessary to lock the pulsed cavity length to a multiple of the seed laser wavelength. Seeded operation may be evidenced by: (1) the reduction of the buildup time of the pulse, (2) the line narrowing of the spectrum recorded by the spectrometer, (3) forced unidirectional beam propagation. As a matter of fact, in the unseeded case, the beam propagates in both directions, backwards and forwards. In presence of the seed beam, the forward-wave output increases to twice the unseeded value. An example of the time evolution of the pulse is shown in Fig. 4b, for the free or injected laser, for a pump energy of about 85 mJ. The reduction of the buildup time and the increase of the energy in the forward direction are clearly visible. To drive the cavity, we developed in-house electronics (see Fig. 5) using a high-density programmable digital component, of type FPGA Xilinx Spartan 6, coupled to a Microchip PIC18 microcontroller and a USB interface. All digital electronics are integrated into the FPGA and developed in VHDL logical synthesis language. The FPGA’s unlimited reconfiguration flexibility made it very easy to upgrade the prototype during the development phase. In addition, all digital functions can be controlled remotely via a USB interface and a LabVIEW HMI interface for PC computers. Furthermore, the box is perfectly autonomous and all parameters can be easily modified by the user thanks to a display on the front panel.

Table 1 Parameters of Ti:Al$_2$O$_3$ pulsed laser, example @ 903 nm

Fig. 6

Laser energy characteristics. a Measurement of the laser energy (without seeding) for two possible mirrors in the cavity at a pump energy of 120 mJ and 127 mJ. We have to interchange them for long or short wave operation. b Energy laser (with seeding) variation at 903 nm as a function of pumping energy. The lasing threshold is 50 mJ and the efficiency slope is about 25$\%$

The servo electronics for the injected laser performs two distinct functions. The first function is the “sweep” mode of the laser (cf. Fig. 5a). The functional electronics in this mode are almost completely digital. A sawtooth signal with adjustable ramps, up and down, is generated. The user can adjust the signal period between 20 and 200 ms (50–5 Hz) and the amplitude from 0 to ±5 V. This signal is sent to the HV amplifier (LE 150/100/EBW from Piezomechanik) of the piezoelectric translator. The second function is the “Servo” mode itself. The operation is based on the “side-lock” technique, where the error signal results from CW laser interferences in the cavity (cf. Fig. 4a). In this mode, the functional electronics are analogic for the integrator/gain proportional part and digital for the control of four functions, specifically developed and detailed as follows:

• Temporal sequence: the electronic box is synchronized with the laser shots thanks to an external synchronization signal (Q-Switch trigger from the pump laser): a time gate, adjustable from 0.1 to 3 ms, is generated. The error signal detected by the photodiode is sent to the analog integrator only if the laser gate is at its low value (cf. Fig. 5b). This allows inhibiting the electronics when the pump pulse is applied, to avoid any large intensity spike. The inhibition time of the correction signal is short enough to make cavity drifts negligible. The integration time constant of the corrective loop can be selected manually from five step values. We have also the possibility to reverse the signal phase by 180$^{\circ }$.

• Offset on input signal: the input laser signal, from a photodiode, is compensated by a DC offset voltage adjustable between ±1 and ±5 V. This allows the laser frequency to be controlled on the steepest part of the interference fringe. To take into account the power variation of the CW laser during the scanning, we normalize the interference signal with a part of the beam taken upstream by another photodiode. The difference to a setpoint generates the error signal.

• Compensation: during the inhibition time when the laser gate is at its high value (cf. Fig. 5c), we added the possibility to apply a compensation DC voltage, adjustable between $-3.3$ and $+3.3$ V to the correction signal. The compensation makes it possible to stand on the slope of an interference fringe (where the response dynamics of the error signal is the most important) when servo-locking is active, and to fix the length of the cavity at the resonance position during the laser pulse. Moreover, this compensates for possible frequency pulling of cavity modes [34]. To adjust the compensation value, we minimize the buildup time of the pulse, so as to ensure a minimum frequency pull [2].

• Reset for scanning: finally, for scans of large amplitudes (greater than the possibilities of the HV amplifier), the user can choose whether or not to force the integrator to reset if the signal reaches, in absolute value, a threshold that is adjustable from 5 to 100$\%$ of the maximum excursion ($-5$ or $+5$ V before HV amplification). This allowed us to perform scans limited only by the CW scanning range and the free-laser spectral linewidth.

3 Results

3.1 Threshold and efficiency

Fig. 7

Laser spectral characteristics. a Output as a function of the wavelength of the Ti:sapphire laser tuned around 903 nm recorded with a low-resolution spectrometer. The apparent blue shift of the position of the fluorescence maximum (around 790 nm for the Ti:Al₂O₃ crystal) is due to the strong decrease of the sensitivity of the detector from the blue to the red. b Tuning bandwidth: the slave cavity being aligned for a given wavelength, we sweep the injection seeding laser and lock the slave cavity. The variation of the forward energy corresponds to the tuning bandwidth of the laser: $15.5\,\hbox {cm}^{-1}$ FWHM, achieved thanks to the pair of prisms. Note that at maximum, we have doubled the energy in the forward direction from 5.7 to 11.4 mJ

The cavity is adjusted by aligning the injection laser and observing interference fringes with the output photodiode during the scan of the cavity length. Then, we simply adjust the size of the pump laser size using a camera. This camera also allowed us to monitor the size of the laser modes which is elliptic due to the high incidence angle of the $\hbox {Ti:Al}_2\hbox {O}_3$ crystal. We typically have an IR beam size at the output of the cavity of $w_x=670\,\,\upmu \hbox {m}$ and $w_y=600\,\,\upmu \hbox {m}$. This value is compatible with expressions given in the literature (relations 8 and 9 from [28]), which give a value of $690\,\,\upmu \hbox {m}$ due to gain guiding in a solid-state laser. The measured threshold is also compatible (but a bit higher) when compared with the value calculated from Moulton’s work [35] in the case of longitudinal pumping and a ring cavity (see table 1 for notations):

$$\begin{aligned} E_\mathrm{P(Th)}=\frac{\pi h c n w_\mathrm{{L}}^2 (\beta -\log R)((\frac{w_\mathrm{{P}}}{w_\mathrm{{L}}})^2+1)}{2\sigma \lambda _\mathrm{{P}}[1-\exp (-\alpha l)]} \end{aligned}$$

(1)

For numerical applications, the parameters of the laser are summarized in Table 1 with some values which are specified for the wavelength of 903 nm. The round-trip loss $\beta$ is estimated at $10\%$ if we suppose an intensity loss of about $1\%$ by optical interface. For the 700–940 nm range, the analytical formula (1) gives a threshold of about 58 mJ, with a variation of $+/-$ 15 mJ depending on the spectral range.

The energy variation of the pulsed seeded laser at 903 nm as a function of the pump energy is given by Fig. 6b. As explained by [31], we observe also a non-linear shifting of the threshold, which is predicted to be more important in cavities with long optical decay times. We have measured the energy dependence of the unseeded pulsed laser as a function of the wavelength (cf. Fig. 6a). Although we could not measure the reflectivity of the coupler beyond 950 nm, we can still produce 2.5 mJ at 980 nm. The laser efficiency is about 25–35$\%$ over a large spectral range, from 710 nm to 940 nm. This experimental laser efficiency as a function of the wavelength can also be compared to an analytical model. The laser energy, above the threshold, can be expressed by [36]:

$$\begin{aligned} E_{\mathrm{{Laser}}}= & {} \eta \times [E_\mathrm{{P}}-E_\mathrm{{P(Th)}}] \end{aligned}$$

(2)

$$\begin{aligned} \eta= & {} \eta _S \times \eta _C \times \eta _a \times \eta _B \times \eta _f \times \eta _{EE} \end{aligned}$$

(3)

where $\eta _\mathrm{{S}}$ is the $\lambda _\mathrm{{P}}/\lambda _\mathrm{{L}}$ Stokes factor; $\eta _\mathrm{{C}}$ is the $\hbox {R}/(\beta -\log \hbox {R})$ coupling efficiency, depending on the wavelength; $\eta _\mathrm{{a}}$ is the $1-\exp (-\alpha \hbox {l})$ pump absorption in the crystal; $\eta _\mathrm{{B}}$ is the $2 w _\mathrm{{L}}^2/({w}_\mathrm{{P}}^2+{w}_\mathrm{{L}}^2)$ geometric factor taking into account the overlap between the beams; $\eta _\mathrm{{f}}$ is the transient factor, close to unity in our case when the pump duration is very short compared to the fluorescence lifetime; $\eta _\mathrm{{{EE}}}$ is the extraction efficiency. We calculated this last value using Degnan’s analytical formulas, assuming optimal coupling [37]. Over our spectral range, this coefficient is rather constant—of about $80\%$—and the total efficiency calculated as the function of the wavelength, taking into account the variation of the coupling, is comparable to the experimental ones, around 15–32.5 $\%$.

Fig. 8

Laser spatial characteristics. a One of the beam images obtained using an Ophir camera. b Plotting and fitting the beam diameter versus the translation along the beam propagation allowed us to deduce the ${M}^{2}$ factor. These measurements were conducted longitudinally around a waist imaged by a lens of 250 mm focal length. The fits follow accurately $w(z)=w_0 \sqrt{(1+(M^2 z/z_R )^2 )}$

3.2 Single-mode operation and tuning bandwidth

Thanks to the presence of prisms, the free-laser spectral linewidth of the emission, containing different modes of the cavity, is reduced and the position of the maximum can be tuned. The spectrometer has a limited resolution (of the order of 1 nm), but it allows to make a rough adjustment of the wavelength and to tune it with the azimuthal adjustment of the parallelepiped mirror. An example of a recorded emission around 903 nm, is shown in Fig. 7a. The shape of the gain bandwidth depends on the spectral dependence of the laser medium gain and how the two prisms geometrically shift the beam path in the cavity. Experimentally, it is interesting to determine the tuning range without having to realign the cavity. For this measurement, we change the wavelength of the seeding CW laser without changing the azimuthal setting of the cavity, and we record the energy emitted in the forward direction. When the wavelength is beyond the gain bandwidth, even when the cavity is locked, we obtain an emission in both directions, just as without seeding. When the wavelength of the CW laser coincides with the maximum gain of the laser, the energy is concentrated in the forward direction, which results in an amplification by a factor of 2, and the setting is optimal. The variation of the forward direction energy around 903 nm is plotted in Fig. 7b. The FWHM of tuning bandwidth is about $15.5 \hbox { cm }^{-1}$ and we can achieve a scan of about $6 \hbox { cm }^{-1}$ with a constant energy. It is possible to deduce from this tuning bandwidth the variation of the free-laser spectral linewidth, by modeling the spectral selectivity of the two prisms and the laser dynamic of the different modes of the cavity, but this work is beyond the scope of this paper.

3.3 Spatial characterization

The spatial IR beam profile was measured with a CCD camera (from Ophir). The spatial shape of the unseeded beam is reported in Fig. 8a and exhibits a profile close to a Gaussian shape. In single-mode operation, with seeding, interference fringes appear due to the filter mounted on the camera. The laser beam is also characterized with a ${M}^{2}$ measurement (cf. Fig. 8b). We use a 250 mm focal length and record the beam diameter as a function of the distance. We find ${M}^{2}$ values of about 1.15 in both configurations, seeded and unseeded. We measured also the profile of the beam after the 2-stage frequency doubling and found that the shape was always a little asymmetric in each axes but close to a Gaussian.

3.4 Two-photon excitation O I

Fig. 9

TALIF setup. a Two-photon excitation scheme and radiative decay of atomic oxygen. b The DC discharge reactor and excitation laser. Fluorescence is detected by a photomultiplier tube (PMT), a boxcar integrator and recorded by a PC computer to measure the TALIF signal. For measurements without Doppler broadening, we use a mirror at the end of the plasma to double pass

The characterization of the spectral purity of the single-mode emission can be analyzed by measuring the efficiency of resonance absorption [5, 6], by analyzing the profile of an atomic or molecular line [15] or as previously performed by optical heterodyne measurement [7, 38]. Here, we analyze the profile of the TALIF signal obtained from oxygen with a pulsed single-mode excitation. The relevant electronic states are shown in Fig. 9a. The ground is the $2p^4~^3P_2$ level and the levels reached by two-photon absorption (around 225.6 nm) are the $3p~^3P_{1,2,0}$. The atom relaxes back down to the $^3S_1$ level. This emission at 844.6 nm is the TALIF recorded signal. We have already implemented this TALIF scheme for temperature [39] and pressure [40] measurements in an $\hbox {O}_2$ plasma, and for spectroscopic measurements on O I [41], but without taking into account the spectral width linked to the finite duration of the excitation. In addition, we determine here the two characteristic phenomenological damping terms of the response of an atomic system to the electric field of a pulsed laser: the time ${T}_1$ which describes the collisional population transfer and the time ${T}_2$ which characterizes the dephasing of the coherences [42].

The simplified setup is shown in Fig. 9b. A DC (typically 10-40 mA) glow plasma was ignited in a 2 cm inner diameter discharge tube. The anode and hollow cathode are installed in side tubes perpendicular to the main tube, 60 cm apart, allowing the laser beam to pass (via fused silica windows) along the tube axis. Oxygen was supplied from a cylinder with a gas flow of about 3 sccm. The pressure was measured with a Pfeiffer gauge upstream from the reactor and adjusted over the range 50–500 Pa. The laser beam passes through the discharge tube with a diameter of about 1mm. Fluorescence at 844.6 nm emitted perpendicular to the laser beam is collected by a lens with a focal length of 25 mm, imaged onto a horizontal slit, passed through an interference filter (840 nm centre wavelength, 13 nm FWHM) to reduce the plasma emission, and detected with a red-enhanced photomultiplier (Hamamatsu R3896). The fluorescence signal is recorded with a Labview™ program. At the exit of the tube, a mirror reflects the beam along its original path and the two-photon excitation by a pair of counter-propagating beams provides an opportunity for Doppler-free spectroscopy [43]. In this case, all velocity classes of the illuminated gaseous sample contribute to the signal at the same frequency.

The density-matrix equations describe the coupling between the atom and the optical field. The diagonal elements of this matrix are the populations of the atoms, with a damping term ${T}_1$ for the excited state. The off-diagonal elements are the coherences generated between the states, with a damping term ${T}_2$. The excited-state decay (${T}_1$) depends on the quenching rate Q and spontaneous emission by the Einstein coefficient A: $T_1 = (A+Q)^{-1}$. We can determine the lifetime of the O atoms in the excited state ($2p^{3}3p ^{3}~^3 {P}_2$) from the evolution of the TALIF fluorescence signal as a function of time (such as shown in Fig. 10a). After the end of the laser pulse, the signal follows an exponential decay. In this experiment, the pressure was 40 Pa and the current 40 mA. The corresponding atomic temperature, otherwise determined by single beam experiment, was 370 K. The experimental decay time is about $36\times 10^6 \hbox {s}^{-1}$, which is compatible with the values previously determined [20, 26] for the radiative lifetime (34.7 ns) and the quenching coefficient k ($9.4 \times 10^{-10} \,\hbox {cm}^3\,\hbox {s}^{-1}$). If we suppose the molecular and atomic temperatures equal, with our parameters and the coefficient given by the literature, the decay rate is $37\times 10^6 \hbox {s}^{-1}$. The relaxation time of the coherences, ${T}_2$, depends on ${T}_1$ and the collisional dephasing rate $\gamma _c$ as: $1/T_2 = \varGamma = 1/(2T_1)+\gamma _c$. In Doppler-free spectroscopy experiments, this parameter determines the atomic response function reflecting homogeneous Lorentzian broadening of the upper state. But with pulsed emission, we must also take into account the finite duration of the interaction to describe the absorption line shape. For that, we adapt a model developed in [44] where a formalism was established to calculate the line shapes in two-photon absorption with a finite transit time of the atoms through the laser beam. In our case, the speed of the atoms is related to the plasma temperature. In our experiment, we measured temperatures from 350 to 550 K. Thus, the maximum velocity of oxygen atoms is about $750~\hbox {ms}^{-1}$ and the transit time in the beam is of the order of $\upmu \hbox {s}$, much longer than the pulse duration. So we replace the transit time in the relationship (43) of [44] by the pulse duration. The line shape is the convolution between a Lorentzian profile and a Gaussian one, i.e., a Voigt profile:

$$\begin{aligned} P(\delta =2 \omega _{\mathrm{{L}}}- \omega _\mathrm{{{eg}}})=\int _{-\infty }^{\infty } \frac{\varGamma }{\omega ^2+\frac{\varGamma ^2}{4}}\exp ^{ -\frac{(\delta -\omega )^2}{4 \varDelta ^2 }}\mathrm{{d}}\omega \end{aligned}$$

(4)

where $\omega _\mathrm{{{eg}}}$ is the difference energy between the ground and excited states and $\omega _\mathrm{{{L}}}$ is the laser frequency. $\varDelta$ is linked to the pulse duration $\tau$, measured at $1/e^2$, given by $\varDelta \times \tau =1$.

Figure 10b shows a Doppler-free spectrum centered around the resonance from $2p^4~^3P_2$ to $2p^{3}3p~^3 {P}_2$. For modeling, we measured the pulse duration at 225 nm. The length of the pulse is about 9.1 ns which gives a value of $\varDelta =110\times 10^6\,\hbox { rad.s }^{-1}$. For a pressure of 67 Pa, the decay rate is $1/T_1=42.9\times 10^6\,\hbox {s}^{-1}$ [20]. The experimental line shape is well-reproduced with a collisional dephasing rate $\gamma _c\approx 685\times 10^6 \hbox {s}^{-1}$, i.e., that the decay time of the coherence is about 16 times shorter than the decay time of the population because of electronic, atomic and molecular collisions in the plasma. Despite this large spectral width due to collisions, the resulting spectrum, with a width of about 150 MHz, would be very different with multimode emission, with the modes of the pulse cavity separated by about 660 MHz. We can see also in Fig. 10b a slight difference between the data and the modeling in the blue part of the spectra. This effect can be linked to a frequency drift during the pulse because the time-dependent gain in the laser crystal gives rise to phase excursions and modifications of the emitted frequency [7]. It can also be attributed to the choice for modeling the temporal profile of the laser pulse. We used a Gaussian interpolation but the temporal pulse is rather asymmetric, with a small difference between the rise and the decay time.

Fig. 10

a Time-resolved O ($2p^{3}3p ~^3 {P}_2$) TALIF signal in $\hbox {O}_2$ with a pressure of 40 Pa and a current of 40 mA. b TALIF response to ground state-to-$2p^{3}3p ~^{3} {P}_{2}$ two-photon resonance line of oxygen and Voigt modeling. The points are taken in the following experimental conditions (without Doppler broadening): 67 Pa and 40 mA. The signal is plotted as a function of the detuning from the two-photon pulsation $2 \omega _{L}$ to the resonance $\omega _{eg}$ (its wavenumber is $88631.133 \hbox { cm }^{-1}$). We used a Voigt profile to model the TALIF signal taking into account the broadening due to the finite duration of the pulse

4 Conclusion

We have described an injection-seeded Ti:sapphire laser that produces single-mode nanosecond pulses of about 10 mJ over a wide spectral range. This is a ring cavity containing two prisms, which allows longitudinal pumping and coarse wavelength selection, facilitating injection far from the gain maximum. We measured a tuning bandwidth of the order of $15.5 \hbox { cm }^{-1}$ and which allows having, after injection, an approximately constant energy over $6 \hbox { cm }^{-1}$. We have also developed a robust electronic servo system that allows single-mode emission for hours of operation, even when scanning the laser frequency continuously over several $\hbox {cm}^{-1}$. In the future, we would also consider introducing other frequency-selective elements in the pulsed cavity, such as a VBG (Volume Bragg Grating) that has already been used in continuous operation with a Ti:sapphire crystal [45]. This element, which can operate in reflection, will provide a constant gain bandwidth over a wider spectral range. The laser system presented here can be used for optical diagnostics in plasmas performed by the TALIF (two-photon absorption laser-induced fluorescence) method after using two successive frequency doubling stages. We have presented an example of a two-photon Doppler-free spectrum obtained from oxygen with the single-mode seeded laser, where the observed transition linewidth is limited by the finite duration of the pulse and the collisional dephasing rate. We plan to use this laser system in a low-pressure inductively coupled plasma operating with chlorine atoms [46].