Abstract
We report recent experimental progress in the characterization of the temporal coherence and related spectral linewidth of plasma-based soft X-ray lasers (SXRL). New measurements were carried out with two types of SXRLs pumped in the quasi-steady state (QSS) regime, in a capillary-discharge plasma and in a laser-produced plasma. We describe the main results obtained from both experiments and compare them to dedicated numerical simulations. We discuss the results in the context of the possibility to achieve XUV lasers with pulse duration below 1 picosecond.
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1 Introduction
The progress of collisional soft X-ray lasers (SXRL), generated by quasi-steady state [1] or transient pumping in solid target plasmas [2], optical-field-ionization in gaseous targets [3], and capillary discharges [4], have opened the way to compact devices and new prospects for various applications. This requires a detailed characterization of their output parameters, like the energy per pulse, duration etc. The spectral linewidth Δλ, or the coherence time τ c are also very important parameters, since they determine the shortest pulse duration (Fourier-transform limit τ FL) that can be achieved (in a linear amplification regime), through the relation: \(\tau_{\mathrm{FL}} = \alpha\frac{\lambda^{2}}{\Delta \lambda} = \beta\tau_{\mathrm{c}}\), where α and β are numerical factors depending on the particular shape of the line profile. The spectral width of the SXRL line results from the complex combination of several processes, namely the contribution of homogeneous (natural and collisional) and inhomogeneous (Doppler) broadenings of the intrinsic profile, followed by gain narrowing with amplification of the line along the plasma length [5]. When inhomogeneous broadening is the dominant cause of broadening the line can be rebroadened when the laser reaches saturation [6].
The purpose of our work is to characterize experimentally the spectral behavior of existing collisional excitation SXRLs, and to evaluate their potential to support the amplification of pulses with duration below 1 ps. Over the recent years, our previous studies were devoted to short pulse (femtosecond to picosecond) pumped systems, in which the duration of the SXRL pulse is of the same order of magnitude as the coherence time. At LOA-Palaiseau (France), a coherence time of ∼5 ps was measured in a Ni-like Kr laser generated at 32.8 nm from an optical-field ionized plasma [7]. At Colorado State University (USA), a shorter coherence time of ∼1 ps was measured in a Ni-like Mo laser (λ=18.9 nm) pumped in the transient regime with a grazing incidence irradiation geometry [8]. Here in the present paper, we present new measurements that were carried out with two types of neon-like SXRLs, pumped in the quasi-steady state (QSS), long pulse (100 ps to nanosecond) regime: the capillary-discharge argon laser generated at CSU (USA) [9, 10], and the Ne-like Zn laser generated at PALS (Czech Republic) [1]. These sources differ from the previous ones by several aspects, among which a higher ionic temperature leading to a larger contribution of Doppler broadening of the laser lines.
We used a variable path-difference, wavefront-division interferometer, which was specifically designed to measure the temporal coherence of the source. This interferometer, described in [11], is composed of two dihedrons, tilted towards each other with a small angle. The incoming beam is separated into two beamlets that slightly converge towards each other after reflection on the dihedrons. In their overlapping region, interference fringes can be recorded using a XUV CCD camera. One of the dihedrons can be accurately translated vertically in order to introduce a path difference between the interfering beams. By following the evolution of the fringe visibility as a function of the delay with successive shots performed in identical conditions, it is possible to measure the coherence time of the pulse, and to infer the spectral width of the line through a Fourier transform.
2 Capillary-Discharge Ne-Like Ar Laser
Capillary discharge XUV lasers are the highest average power tabletop source of coherent soft-x-ray radiation [9, 12] up to date. The capillary discharge Ne-like Ar laser operating at λ=46.9 nm (3p-3s J=0–1 line), was first demonstrated in 1994 [4] and has been widely characterized [13–17]. However, the spectral linewidth and the temporal coherence, which are important parameters in applications such as interferometry [18] and large area nanopatterning [19], remained to be measured. Capillary discharge plasmas are characterized by a low electron density (Ne∼2×1018 cm−3) and a relatively high ionic temperature (kTi∼100 eV). The Doppler effect is thus expected to be the dominant cause of broadening of the laser line. The Ne-like Ar laser is thus an appropriate system to study the possible existence of saturation rebroadening predicted in highly inhomogeneous line profiles [20]. This is achieved by measuring the linewidth evolution with the plasma column length.
The experiment was performed at CSU (USA). The experimental setup and the results obtained are presented in more detail in [10] as well as in a companion paper (see [21]). Figure 1(a) shows an example of the measured variation of the fringe visibility with the path difference. The coherence time is defined as the delay at which the visibility is decreased by 1/e of its maximum. We find that the experimental data fit very well to a Gaussian curve. The corresponding spectral profile, inferred by a Fourier transform of the visibility curve, is also Gaussian. The linewidth is defined as the FWHM of the spectral profile.
The measured variation of the spectral bandwidth as a function of the plasma length is shown in Fig. 1(b). One can see that the bandwidth decreases slowly, while no rebroadening of the line is apparent for the longest lengths, although the laser is operated at saturation. The experimental data are compared to the predictions of numerical simulations, performed at CSU, that compute the line propagation along the amplifier axis taking into account gain saturation and refraction losses. One can see that these calculations predict a weak rebroadening of the line beyond L∼24 cm. However this effect is small compared to our experimental error bars. For the longest plasma length, the typical coherence time τ c is 2.3 ps, corresponding to a Fourier limit pulse duration τ FL of 1.9 ps, which are both much shorter than the duration of the SXRL pulse (1.2–1.8 ns).
3 Laser-Based Ne-Like Zn Laser
More recently we carried out a temporal coherence measurement of the Ne-like Zn laser, emitting at 21.2 nm (3p-3s J=0–1 line, as above). This SXRL is generated at the PALS (Prague, Czech Republic) laser facility and was used for several applications [22]. The lasing plasma is pumped by a succession of a low-energy prepulse and high-energy main pulse, both ∼300 ps in duration, delivered by an iodine pump laser (λ=1.315 μm). After double-pass amplification in a 3-cm zinc plasma column, the 21.2 nm pulse reaches saturation with a typical energy of ∼1 mJ per pulse or more [1].
Although lasing is obtained on the same Ne-like 3p-3s transition as for the capillary discharge laser discussed above, the plasma conditions in the gain zone are markedly different. Here the electron density is typically ×100 times higher (Ne∼2–5×1020 cm−3), while the ionic temperature is only twice as high (kTi∼150–200 eV). As a result, in Ne-like Zn, both collisional and Doppler broadenings contribute at the same level, as will be shown below.
The interferometer was implemented along the 21.2 nm beam path, at a distance of ∼5.5 meters from the source. Figure 2 shows a typical example of a single-shot interferogram, when the path-difference between the interfering beams was close to zero. The size of the overlapping region, where fringes are apparent, is ∼650 μm. This is slightly larger than the spatial coherence of the beam at the interferometer position, so that the fringe visibility is relatively low, of the order of 30 %. The distance from the source was increased by ∼1.5 m in a second series of measurements, but the fringe visibility was not significantly improved. Another difficulty was the limited number of shots available in a data set, due to the low repetition rate of the laser (2 shots per hour). Two series of data, where the path difference was varied from −300 μm to +300 μm, were obtained for the two different distances from the source mentioned above. They led to slightly different, although consistent values for the coherence time of the 21.2 nm laser, namely τ c=1 ps and 0.7 ps for the 5.5 m and 7 m distance respectively. The corresponding spectral linewidth are 11.3 mÅ and 7.7 mÅ respectively.
The measured Δλ values were compared to the predictions of numerical simulations, using the PPP lineshape code [23] to calculate the intrinsic broadening, and a 1D-radiative transfer code [24] that computes the amplified profile, taking into account saturation. The plasma conditions in the gain zone are not known precisely, but estimated as Ne∼2–5×1020 cm−3, kTe=200–300 eV; kTi=150–200 eV. A small-signal gain coefficient of 7 cm−1 was considered. We find that within this parameter range, the amplified linewidth of the 21.2 nm laser varies between 7.4 and 10.6 mÅ, in good agreement with our measurements. The contribution of the collisional broadening to the intrinsic line profile ranges from 11 to 24 mÅ, whereas the Doppler one is of the order of 25 mÅ.
Finally the measured τ c values were used to estimate the corresponding Fourier-transform limit τ FL, which is the shortest duration that could be reached if the 21.2 nm was fully temporally coherent. From the definition recalled in Sect. 1, and considering a Gaussian shape, we find that τ FL is below 1 ps for both measurements, namely 0.6 and 0.7 ps. This is the shortest value ever measured for a plasma-based SXRL and this confirms the high potential of the Zn quasi-steady state laser for the generation of femtosecond amplified pulses, through seeding with high-harmonic radiation.
4 Conclusion
We have measured the temporal coherence and spectral width of two Ne-like soft X-ray lasers pumped in the quasi-steady state regime with two distinct techniques, leading to different plasma conditions and spectral characteristics.
The Ne-like Ar, capillary-discharge pumped laser exhibits a spectral width that decreases slowly as the plasma length increases, as a result of gain narrowing. The small saturation rebroadening, predicted by numerical simulations, was not observed and could be beyond our experimental accuracy. The measured coherence time is ∼2 ps, much shorter than the pulse duration of 1.2–1.8 ns. For the laser-pumped Ne-like Zn laser, the measured coherence time is shorter (0.7–1 ps), leading for the first time to a Fourier-transform limit duration that lies below 1 ps.
In both cases, the inferred values for the spectral width of the laser line are in good quantitative agreement with the predictions of numerical simulations. Finally since the measured coherence times are in both cases much smaller than the duration of the SXRL pulse, picosecond (or potentially sub picosecond) durations could be reached through seeding with femtosecond high-order harmonic radiation.
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Meng, L. et al. (2014). Temporal Coherence and Spectral Linewidth of Neon-Like XUV Lasers Pumped in the Quasi-steady State Regime. In: Sebban, S., Gautier, J., Ros, D., Zeitoun, P. (eds) X-Ray Lasers 2012. Springer Proceedings in Physics, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-319-00696-3_28
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