1 Introduction

Capillary discharge has been used as the exciting schemes to develop the small-scale, high-efficiency and low-cost soft X-ray and EUV laser sources, which could be potentially utilized in numerous fields of science and technology such as holography, interferometers, microscopy and other applications. In 1994, J. J. Rocca et al. reported the first demonstration of large soft X-ray amplification in the plasma of a capillary discharge [1]. A population inversion between 2p 5 3p 1 S 0 and 2p 5 3s 1 P 1 (J = 0-1) in the Ne-like Ar ions was produced by the electron collisional excitation, and the gain coefficient at 46.9 nm (A line) was measured as 0.6 cm−1. A saturated Ne-like Ar soft X-ray laser at 46.9 nm pumped by capillary discharge has produced millijoule-level laser pulses at a repetition rate of 4 Hz [2] and has led to many applications such as the diagnostics of dense plasma [3], lithography [4], nanoimaging [5], nanomachining [6] and material ablation [7].

Other groups also had developed 46.9 nm laser pumped by capillary discharge [8–16]. Some groups studied the 46.9 nm laser with a low current, which is benefit to reduce the size and enhance the repetitive frequency of the laser. G. Niimi et al. firstly reported the observation of 46.9 nm laser output at a low discharge current of 9 kA [8]. G. Tomassetti et al. reported that 46.9 nm laser was realized with low amplitude 17–20 kA current pulses at pulse repetition rate up to 0.1 Hz [9]. The saturated laser at 46.9 nm was achieved by C. A. Tan et al. using the main current as low as 16 kA [13]. However, the other Ne-like Ar lasers were not observed by these groups.

Except for J = 0-1 transition at 46.9 nm, EUV lasers can also be expected on some other 3p–3s transitions of Ne-like Ar in principle. The populations and gain coefficients of the 3p–3s transitions in Ne-like Ar were investigated by D. E. Kim et al. in theory [17]. It was found that large gains on the 3p 1 S 0–3s 1 P 1 (J = 0-1), 3p 3 P 2–3s 1 P 1 (J = 2-1) and 3p 3 D 2–3s 3 P 1 (J = 2-1) transitions were formed for the electron density between 1018 and 1019 cm−3. Due to the observation of intense laser on 3p 1 S 0–3s 1 P 1 (J = 0-1) transition at 46.9 nm (A line), the two other lasers on 3p 3 P 2–3s 1 P 1 (J = 2-1) transition at 69.8 nm (C line) and 3p 3 D 2–3s 3 P 1 (J = 2-1) transition at 72.6 nm (E line) were hopefully realized in the plasma of capillary discharge. In experiment, the superlinear increase in intensity at 69.8 nm had been observed with capillary discharge scheme [18, 19]. A. Hildebrand et al. reported that the gain coefficients at 69.8 nm are between 0.17 and 0.25 cm−1 [19]. The intensity of 69.8 nm line was lower than that of Ar VIII resonant line [18, 19], which indicated the absence of strong amplification. At the same time, the other J = 2-1 line at 72.6 nm had not been observed in capillary discharge produced plasma.

In 1996, the soft X-ray laser of J = 0-1 line at 46.9 nm was observed in an elongated plasma column produced by laser irradiation of a gas puff target [20]. In addition, the laser at 46.9 nm was realized with a traveling-wave excitation scheme [21] and an optical field ionization scheme [22]. However, the two J = 2-1 lines at 69.8 nm and 72.6 nm were not observed in these laser produced plasmas.

In 2011, our group firstly demonstrated Ne-like Ar EUV laser at 69.8 nm (C line) and relatively weak laser at 72.6 nm (E line) [23]. In the initial experiments, a gain coefficient of 0.34 cm−1 and gain–length product of 11 were obtained at 69.8 nm in 35-cm-long plasma column generated by capillary discharge. Herein, we report the temporal and spatial characteristics of the 46.9 and 69.8 nm lasers, the enhancement of gain coefficient up to 0.41 cm−1 at 69.8 nm, the gain coefficient of 0.22 cm−1 at 72.6 nm and the saturated laser at 46.9 nm, conditioning the main current as low as 12 kA.

2 Experimental setup

The capillary discharge setup used to conduct the experiments was described in the previous publications [23, 24]. The main pulse generator consists of a 7 nF Blumlein line filled with de-ionized water. The Blumlein line is pulse charged by a ten-stage Marx generator and discharge through the capillary by a self-breakdown main switch pressurized with N2 gas. The experiments were conducted at low main current. To decrease the amplitude of main current, we decreased the charging voltage of the capacitors and increased the conducting inductance of the main switch. Before the main current pulse, the capillary filled with Ar is predischarged by a current of ~20 A, which is provided by a predischarge generator.

A 2-cm-long molybdenum rod electrode was inserted into the capillary which is made of Al2O3 and has an inner diameter of 3.0 mm and a length of 35 cm. The ground electrode has a hole with a diameter of 3 mm. The axial soft X-ray and EUV light emanating from the hollowed ground electrode was measured with a VUV monochromator, a space-resolving flat-field EUV spectrograph or a grazing-incidence EUV spectrograph. A VUV monochromator (Acton VSN-515) was used to disperse the multi-wavelength laser. Then the temporal evolutions of different wavelength laser pulses were measured by a vacuum X-ray diode (XRD) behind the exit slit of the monochromator. The photocathode of XRD was coated with a gold layer. A negative bias voltage of −600 V was applied to the photocathode. A wire mesh with fine grids was used as anode. A space-resolving flat-field EUV spectrograph combined with an EUV CCD (Andor Newton DO920P-BN) was used to measure the intensity distribution of the multi-wavelength laser. A 1 m grazing-incidence spectrograph (McPherson 248/310G) was used to measure the time-integrated axial emission spectra. According to the time-integrated spectra, the influences of initial pressure and plasma length on intensity of multi-wavelength laser were observed.

3 Experimental results and discussion

The multi-wavelength Ne-like Ar laser of 3p–3s transitions (A line, C line and E line) was pumped by capillary discharge synchronously. The typical waveform of the main current is similar to the one reported in Ref. [23]. The amplitude of the main current is 12 kA, and the 10–90 % rise time is 40 ns. These are indicative of an average dI/dt of 2.4 × 1011 A/s. According to the experimental results about the spectrum in Ref. [23], the multi-wavelength laser pulse should include three laser lines at 46.9, 69.8 and 72.6 nm. In order to, respectively, observe temporal characteristics of the three Ne-like Ar lasers, a VUV monochromator combined with an XRD was used to measure the laser pulse. Figure 1 shows the temporal evolutions of the 46.9 and 69.8 nm laser pulses at the initial pressure of 19 Pa. Because of too weak intensity, the 72.6 nm laser pulse cannot be detected by XRD. The 46.9 and 69.8 nm lasers occur at ~35 ns almost simultaneously. The full width at half maximum (FWHM) for 46.9 nm laser pulse is about 1.3 ns, which is little larger than the FWHM of 1.2 ns for 69.8 nm laser pulse. Therefore, the 46.9 and 69.8 nm lasers were generated with the same plasma parameters. However, the intensity of 46.9 nm laser is about 24 times larger than that of 69.8 nm laser. It means that the gain coefficient of 46.9 nm laser is larger than that of 69.8 nm laser at the initial pressure of 19 Pa.

Fig. 1
figure 1

Laser pulse waveforms at 46.9 nm (solid line) and 69.8 nm (dashed line) measured by XRD, corresponding to initial Ar pressure of 19 Pa, capillary length of 35 mm and capillary inner diameter of 3.0 mm

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In order to measure the spatial characteristics of 46.9 and 69.8 nm lasers, a space-resolving flat-field EUV spectrograph combined with an EUV CCD allowed for the acquisition of space-resolving spectra. The space-resolving flat-field EUV spectrograph mainly consists of a toroidal mirror, a varied line-spacing concave grating and an EUV CCD [25]. The distance between the toroidal mirror in the EUV spectrograph and the exit of the capillary was 1047 mm. For the EUV spectrograph, the distance between light source and toroidal mirror should be 747 mm. Therefore, the CCD recorded the intensity distribution of the laser beam which is at a distance of 300 mm from the exit of the capillary. Figure 2a, b illustrates the typical space-resolving spectra at 46–51 and 66–71 nm corresponding to initial pressure of 16 Pa. The A line of 46.9 nm and C line of 69.8 nm completely dominated the spectra, which provides clear evidence of large amplification of A line and C line. Figure 2c, d shows the intensity distributions of 46.9 and 69.8 nm lasers, which were recorded along the direction of the spectrometer slit and correspond to Fig. 2a, b, respectively. The full width at half maximum (FWHM) beam divergence for 46.9 nm laser is about 0.5 mrad, which is little larger than that of approximately 0.4 mrad for 69.8 nm laser. In both cases, the beam divergences are smaller than 1 mrad. The intensity distribution of 46.9 nm laser has two central peaks, which result in a larger central divergence than that of 69.8 nm laser which has a signal central peak. The 72.6 nm laser is still too weak to be detected.

Fig. 2
figure 2

Typical space-resolving spectra of a 46.9 nm laser and b 69.8 nm laser at the initial pressure of 16 Pa, and the intensity distributions of c 46.9 nm laser and d 69.8 nm laser corresponding to a and b, respectively

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A grazing-incidence spectrograph was used to measure the time-integrated spectra between 45 nm and 90 nm. The typical spectrum is shown in Fig. 4 of Ref. [23]. The spectra were used to analyze the effects of initial pressure and plasma length on intensity of multi-wavelength laser.

Because the effects of pressure on 46.9, 69.8 and 72.6 nm lasers are different, we measured the variations in the intensities of A line, C line and E line versus initial pressure as shown in Fig. 3. Figure 3 shows that the A line was observed in the range of 13–24 Pa, and the largest emission appears at about 19 Pa. However, the pressure ranges for C line and E line are 12–20 and 14–20 Pa, respectively, which are narrower than that for A line. In addition, the optimum pressures for 69.8 and 72.6 nm laser are all about 16 Pa, which are lower than that for 46.9 nm laser. In the same discharge condition, the low initial pressure corresponds to low electron density. Therefore, in comparison with 46.9 nm laser, the low electron density is suitable for the 69.8 and 72.6 nm lasers. This analysis is in good agreement with the theoretical results reported in Ref. [17].

Fig. 3
figure 3

Variations in 46.9, 69.8 and 72.6 nm laser intensity as functions of initial pressure

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The gain coefficient was measured to obtain quantitative evidence for amplification and the increase in the intensity. The amplitude and rise time of the current pulse were maintained approximately constant for different plasma lengths at 12 kA and 40 ns. This was realized by keeping the same inductance of the discharge circuit in the gain measurements. The gain coefficients of the 46.9, 69.8 and 72.6 nm lasers were measured at the optimum pressures. Because the intensity of 46.9 nm laser at 19 Pa is much larger than those of 69.8 and 72.6 nm lasers at 16 Pa, the slit width of the grazing-incidence spectrograph was decreased to avoid saturating the EUV CCD, when the 46.9 nm laser was measured. Figure 4 shows a plot of the integrated intensity of 46.9 nm laser as a function of plasma length at the pressure of 19 Pa. The intensity increases exponentially up to 23 cm. A fit of the data for lengths <23 cm with the Linford formula yields a gain coefficient of 0.58 cm−1. The gain saturation was observed at the plasma length of 23 cm corresponding to a gain–length product GL = 13.3. To our knowledge, we have realized the saturated 46.9 nm laser at the lowest current. Above 23 cm, the intensity starts to have the linear behavior. The intensity at the plasma length of 33 cm is nearly four times higher than that at the saturation length.

Fig. 4
figure 4

Integrated intensity of A line at 46.9 nm versus plasma length at the optimum pressure. The corresponding gain coefficient for lengths <23 cm determined by the Linford formula is 0.58 cm−1

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With the similar discharge conditions, the gain coefficients of the 69.8 and 72.6 nm lasers were measured at the pressure of 16 Pa. Figures 5 and 6 show the plots of the intensity of the 69.8 and 72.6 nm lasers as a function of plasma length. Fitting the data with the Linford formula result in a gain coefficient of 0.41 cm−1 corresponding to a gain–length product GL = 13.5, and a gain coefficient of 0.22 cm−1 corresponding to a gain–length product GL = 7.3. The gain coefficient of 68.9 nm laser was measured at the pressure of 16 Pa, which is higher than that obtained at the pressure of 12.5 Pa reported in 2011 [23]. Figure 3 shows that the intensity of C line at 16 Pa is about five times larger than that at 12.5 Pa. The increase in intensity means the increase in gain coefficient. The higher initial pressure results in a higher plasma density and consequently a higher collisional excitation rate, which is helpful to enhance the gain coefficient from 0.34 [23] to 0.41 cm−1. In addition, compared the gain–length product of 69.8 nm laser with that of 46.9 nm laser at the saturation length, the 69.8 nm laser should be near gain saturation. In order to obtain the saturated 69.8 nm laser, the gain coefficient or the length of the capillary should be increased to enhance the gain–length product in the near future experiments.

Fig. 5
figure 5

Integrated intensity of C line at 69.8 nm versus plasma length at the optimum pressure of 16 Pa. A fit to the Linford formula results in gain coefficient of 0.41 cm−1, corresponding to gain–length product of 13.5

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Fig. 6
figure 6

Integrated intensity of E line at 72.6 nm versus plasma length at the optimum pressure of 16 Pa. A fit to the Linford formula results in gain coefficient of 0.22 cm−1, corresponding to gain–length product of 7.3

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According to the theoretical results of Ref. [17], 3p 3 P 2–3s 1 P 1 (J = 2-1) transition (C line) and 3p 3 D 2–3s 3 P 1 (J = 2-1) transition (E line) have stimulated emission cross sections 4.6 times and 3.1 times larger than 3p 1 S 0–3s 1 P 1 (J = 0-1) transition (A line). In our experiment, the gain coefficient of 0.58 cm−1 at 46.9 nm is 1.4 times larger than that of 0.41 cm−1 at 69.8 nm and 2.6 times larger than that of 0.22 cm−1 at 72.6 nm. This means that the population inversion between the levels 3p 1 S 0 and 3s 1 P 1 is about 6 times larger than that between levels 3p 3 P 2 and 3s 1 P 1, and about eight times larger than that between levels 3p 3 D 2 and 3s 3 P 1. In comparison with 69.8 and 72.6 nm lasers, the high intensity and gain coefficient of 46.9 nm laser at 19 Pa result from the large population inversion.

4 Conclusion

By changing the initial pressure, we have achieved a saturated laser on 3p 1 S 0–3s 1 P 1 (J = 0-1) transition at 46.9 nm (A line) and a near-saturated laser on 3p 3 P 2–3s 1 P 1 (J = 2-1) transition at 69.8 nm (C line) and a weak laser on 3p 3 D 2–3s 3 P 1 (J = 2-1) transition at 72.6 nm (E line) in a capillary discharge plasma. The multi-wavelength laser was excited at the low current of 12 kA. The 46.9 and 69.8 nm lasers occur at almost the same time with similar pulse duration of about 1.2–1.3 ns. The experimental results about intensity distributions show that the FWHM divergences of the two lasers are smaller than 1 mrad.

The intensity of the A line, C line and E line as a function of the initial pressure was measured, and the optimum initial pressures of A line, C line and E line were found at 19, 16 and 16 Pa. The higher optimum pressure for the A line laser was helpful to enhance its intensity. At the optimum pressures, the gain coefficients of A line, C line and E line lasers were measured in the same discharge current. A gain coefficient of 0.58 cm−1 was obtained for A line laser, and the gain saturation was observed at a gain–length product of about 13.3. Meanwhile a gain coefficient of 0.41 cm−1 and gain–length product of 13.5 was obtained for the C line laser, which was obviously higher than the experimental result at 2011 [23]. In addition, the gain coefficient of 0.22 cm−1 was obtained for the E line laser. The above results are expected to lead to the development of very compact and multi-wavelength laser that can be widely utilized in applications.