1 Introduction

In 1984, Matthews et al. [1] reported observations of amplified spontaneous emission on 3p–3s transition in Ne-like selenium ions at 206.3 and 209.6 Å. Since then, many experiments on the generation of extreme ultraviolet lasers have been conducted in which population inversion is achieved by collisional excitation of electrons from the ground states of closed-shell ions to upper levels [2, 3]. A promising scheme is the optical-field-ionization (OFI) collisional-excitation extreme-ultraviolet (EUV) laser, in which a gas target is optical-field ionized by a longitudinally incident laser pulse with appropriate laser intensity to form a nonequilibrium plasma channel [4]. The stripped electrons gain energy from the laser pulse via above-threshold-ionization (ATI) heating and collide with the ions to produce population inversion for the lasing levels of specific ion species.

The first collisionally excited OFI EUV laser was demonstrated by Lemoff et al. [5] with 5d–5p transition of Pd-like xenon at 41.8 nm. Saturated amplification of the same spectral line with an output of 5×109 photons per pulse and strong amplification for the 4d–4p transition of Ni-like krypton with (2–3)×109 photons per pulse were reported [6, 7]. Gas cells were adopted in the above experiments. Considering the flexibility of gas jets for target structure engineering, we demonstrated nearly saturated EUV lasing in xenon and krypton clustered gas jets with outputs of 2×1010 photons per pulse and about 1×109 photons per pulse, respectively [8, 9]. In OFI EUV lasers, longitudinal pumping is the preferred means to attain the requirements of high-intensity pumping and traveling-wave pumping. However, ionization-induced refraction effect limits the gain length to several millimeters for longitudinally pumped gas-target EUV lasers. To increase the length of gain region for the EUV lasing, a waveguide can be used to guide the laser pulse maintaining a small beam size over a long distance. Enhancement of the OFI EUV lasing at 41.8 nm in Xe8+ in a preformed plasma waveguide driven by capillary discharge was demonstrated, which showed that the lasing signal recorded with the waveguide was approximately 4 times larger than that achieved with the gas cell [10]. After that, Mocek et al. [11, 12] utilized a 15-mm-long, multimode, gas-filled capillary tube to enhance the output of EUV lasing at 41.8 nm by an order of magnitude with respect to that from a gas cell of the same length. Up to 1.5×1011 photons/pulse was produced by using a pump energy of 1 J. Recently, we demonstrated 400-fold enhancement of the OFI collisional-excitation EUV lasing of Ni-like krypton at 32.8 nm in a gas jet with an optically preformed plasma waveguide compared to that without the plasma waveguide, and the corresponding lasing photon number reaches 8×1010 per pulse  [13]. OFI EUV lasers in an optically preformed plasma waveguide for pure xenon, argon, and Kr/Ar mixture gases were also achieved subsequently, demonstrating the versatility of optically preformed plasma waveguide in providing a wide range of lasing configurations [14]. It is known that the EUV lasers with reduced beam divergences, shortened pulse durations, and enhanced spatial coherence can be achieved by seeding EUV amplifier with high-harmonic generation (HHG). HHG seeding with high gain was first achieved in OFI EUV lasers in a gas cell [15] and collisional-ionization EUV lasers in a solid target [16]. Recently, we demonstrated a strongly saturated EUV laser for 32.8-nm lasing with 1.1-mrad divergence angle and 1×1011 photons/pulse by integrating HHG seeding, optically preformed plasma waveguide, and optical-field-ionization pumping [17].

In this paper, we report the use of the 100-TW laser system to further increase the output photon number of the Ni-like krypton EUV laser at 32.8 nm via the OFI process in an optically preformed plasma waveguide. By using a 9-mm-long plasma waveguide of pure krypton gas fabricated with the axicon-ignitor-heater scheme [18], the 32.8-nm EUV lasing reached an average output of 1012 photons per pulse at a pump pulse energy of 1 J, more than one order of magnitude enhancement relative to the results based on the same scheme with the 10-TW laser system [13]. The large output photon number is comparable with that provided by a free-electron laser at the same wavelength [19]. In addition, far-field images of the 32.8-nm lasers were also recorded, showing that the far-field pattern of the EUV laser beams varies from a single peak profile at low pump energy to an annular profile at high pump energy due to over-ionization of krypton ions at the center of the plasma channel which limits further enhancement of lasing outputs. These phenomena observed in our experiments are similar to those found in EUV lasers employing capillary discharge pumping scheme through tuning the discharge pressure [20].

2 Experimental setup

The experiment was performed by using a Ti:sapphire laser system with 10-Hz pulse repetition rate at National Central University, Taiwan. The laser system was based on the chirp-pulse amplification technique and consisted of three beam lines. The first beam line generated laser pulses with a central wavelength of 810 nm, a minimum pulse duration of 30 fs, and a maximum peak power of 100 TW. The second beam line was of 810-nm central wavelength, 30-fs pulse duration, and 16-TW peak power. The third beam line was of 900-nm central wavelength, 35-fs pulse duration, and 6-TW peak power. Each laser beam can be further split into two beams with independent energy tuners, delay lines, and pulse compressors. The experimental layout is shown in Fig. 1. A 30-fs, 2-J pump pulse from the 100-TW beam line was used to prepare the lasing ionization stage through optical-field ionization and heating of the plasma electrons. It was focused with an off-axis parabolic mirror of 30-cm focal length onto a krypton gas jet. The focal spot size of the pump pulse was 10-µm diameter in full width at half maximum (FWHM) with 71% energy enclosed in a Gaussian-fit profile, corresponding to a vacuum peak intensity of 4×1019 W/cm2. A motorized quarter-wave plate in the pump beam path was used to vary the pump polarization. Two laser pulses from the 16-TW beam line, referred to as the ignitor and the heater pulses, were used to fabricate the plasma waveguide. The leading 35-fs, p-polarized ignitor pulse was 47 mJ in energy and was followed after 400-ps delay by the 210-ps s-polarized heater pulse with 208-mJ energy. After combined by a thin-film polarizer, the two pulses propagated collinearly and were then focused by an axicon of 30° base angle to a line focus of >2-cm length in FWHM. The line focus overlapped with the propagation path of the pump pulse in the gas jet. A hole of 5-mm diameter at the center of the axicon allows passage of the pump pulse. To increase the efficiency of plasma waveguide fabrication, a convex lens of 150-cm focal length with a hole of 2-cm diameter at the center was installed in front of the axicon to concentrate the laser energy in a length of approximately 1 cm, matching with that of the gas jet, and to optimize the uniformity of the longitudinal intensity distribution.

Fig. 1
figure 1

Experimental layout. OAP: off-axis parabolic mirror; TFP: thin-film polarizer; M: EUV mirror, CCD: charge-coupled device

Full size image

The krypton gas jet used for this experiment was produced from a supersonic slit nozzle and a pulsed valve. The nozzle had a slit outlet of 10 mm in length and produced a gas jet with 9-mm flat-top region and a sharp boundary of 300 µm at both edges along the slit direction. The primary diagnostics for EUV radiation was a flat-field grazing-incidence X-ray spectrometer consisting of a 1200 line/mm aperiodically ruled grating and a back-illuminated 16-bit X-ray charge-coupled device (CCD) camera. The spectrometer was used to measure the EUV spectrum and beam divergence of EUV lasing in the direction of pump-laser propagation. Two 0.25-µm-thick aluminum filters were used to block the transmitted pump laser pulse and attenuate EUV emission to avoid saturating the CCD camera. From the known grating reflectivity, filter transmittance, and CCD response, the approximate EUV photon number is determined. Mach–Zehnder interferometry with a probe pulse which was obtained from leakage of the pump pulse at a dielectric mirror and passed transversely through the gas jet was used to measure the plasma density distribution. A relayed imaging system consisting of a retractable wedge, a pair of lenses, an objective lens, a 40-nm bandpass filter centered at 810 nm, and a 16-bit CCD camera was used to measure the spatial profile of the pump pulse at the exit of the gas jet with an imaging resolution of 5.8 µm.

3 High-brightness EUV lasing at 32.8 nm in an optically preformed plasma waveguide

A plasma waveguide based on the axicon-ignitor-heater scheme was used to extend the length of gain region [18]. A short intense ignitor pulse ionized the neutral gas by multiphoton ionization to provide seed electrons. After a few hundred picoseconds, a long high-energy heater pulse heated up the plasma efficiently via inverse bremsstrahlung heating and further ionized the gas through collisional ionization. The resultant hot dense line-shaped plasma expanded outward, and thus the on-axis plasma electron density was greatly reduced while the plasma electron density at the encircling outer region was build up as a result of collisional ionization by the outgoing electrons and ions. After an adequate delay a cylindrically symmetric plasma with the electron density in the encircling outer region larger than the on-axis density was produced. Such a plasma channel can serve as a plasma waveguide to guide a laser pulse if the difference between the on-axis electron density and the electron density at the periphery is larger than \(\Delta n_{e}\approx1/{\pi r_{e} w^{2}_{0}}\), where r e and w 0 are the classical electron radius and the beam radius, respectively [21, 22]. A laser pulse coupled into the plasma waveguide can be guided, maintaining a small beam size over the entire channel. Under such a condition, diffraction and ionization-induced refraction of the guided laser pulse is counteracted by the focusing effect arising from parabolic distribution of plasma electron density in the plasma waveguide.

Figure 2 shows the number of photons for 32.8-nm Kr8+ lasing line with a pure-krypton plasma waveguide and the corresponding beam divergence angle as a function of pump pulse energy at a krypton density of 1.6×1019 cm−3. All of the data points in Fig. 2 represent the average of four laser shots with error bars representing the rms error. The uniform pure krypton plasma waveguide was produced by using a 47-mJ ignitor pulse followed by a 208-mJ heater pulse with a 400-ps temporal separation. The delay between the heater pulse and the circularly-polarized pump pulse was 2.5 ns. To achieve the optimal guiding (or coupling) condition of the pump pulse, the focal position of the pump pulse was set at 500 µm behind the entrance of the gas jet. The beam profile of the pump pulse at the exit of the plasma waveguide was measured by the relayed imaging system. The data indicate that the pump pulse was well guided over the entire length of the plasma waveguide with a guided beam size of ∼15 µm in FWHM at various pump energies. Typical relayed images and interferograms can be seen in our previous measurements [13, 14]. Based on the relaying imaging measurements, the efficiency of the krypton waveguide (beam energy at the exit of the waveguide divided by beam energy at the entrance of the waveguide) was estimated to be ∼20% for pump energy <300 mJ. When pump energy is higher than 300 mJ, the estimation of the waveguide efficiency becomes unreliable and underestimated because strong ionization blue shift [23] reduces the portion of the broadened spectrum received by the relay imaging system which consists of an 810±20 nm bandpass filter. The strong dependence of the 32.8-nm laser on pump pulse energy for energy smaller than 300 mJ is expected due to the higher Kr8+ ion fraction, wider lasing region, and longer gain length for higher pump intensity in the plasma waveguide. The declined rate of increase of lasing output at pump energies between 300 mJ and 600 mJ may be attributed to the saturated ion fraction (to unity), gain length (to the length of the plasma waveguide) and over-ionization at the center of lasing gain column. For pump energies larger than 600 mJ, the axial peak intensity in the waveguide channel is much higher than the ionization intensity threshold for producing Kr8+ ions (∼2×1016 W/cm2), resulting in significant over-ionization along the optical axis. The maximum lasing output of ∼1012 photons/pulse resulted from the balance between the axial gain depletion and the increasing peripheral gain volume. The increasing transverse dimension of the gain volume at higher pump energy is supported by the larger lasing source sizes derived from the far-field patterns of Kr lasers described in the next section. Figure 2 also shows the increase of beam divergence with increasing pump pulse energies, from approximately 3 mrad for pump energy at 100 mJ to around 12 mrad for pump energy at 1130 mJ. It is noted that the beam divergence increases dramatically at pump energy larger than 600 mJ due to transformations of the beam profile from a single dominant peak to an annular structure (see also the angular distributions derived from images recorded by the X-ray flat-field spectrometer as shown in Fig. 3(b)).

Fig. 2
figure 2

Number of photons for Ni-like krypton lasing at 32.8 nm and the corresponding beam divergence angle as a function of pump pulse energy at a krypton density of 1.6×1019 cm−3. The temporal separation between the 47-mJ ignitor pulse and 208-mJ heater pulse was 400 ps. The heater-pump delay was 2.5 ns

Full size image
Fig. 3
figure 3

(a) Far-field images of the 32.8-nm laser beam for increasing pump pulse energies. Each image adopts the same pseudocolor bar that scales with relative intensity. (b) Angular distributions of the 32.8-nm laser beam for the same increasing pump energies as in (a). Other parameters are the same as those in Fig. 2

Full size image

4 Far-field patterns of the 32.8-nm Kr8+ lasing

The spatial profile of the EUV laser was characterized by a far-field imaging system consisting of two 45°, Mo/B4C/Si EUV multilayer mirrors, two 0.25-µm-thick Al filters, and an X-ray CCD with a 1024×1024 array of 13-µm pixels at a distance of 65 cm downstream from the exit of the plasma waveguide. The EUV multilayer mirrors, served as spectral filters with relatively high reflectivities at 32.8 nm to prevent reflected light other than the 32.8 nm from being detected, were used to redirect the EUV beam to the X-ray CCD camera as shown in Fig. 1. In this study, the far-field patterns were recorded by accumulating 10 laser shots to obtain more uniform images with higher signal-to-noise ratios. Far-field images of the Kr laser at 32.8 nm for increasing pump energies are shown in Fig. 3(a). All experimental parameters were the same as those described in Sect. 3. At pump pulse energies lower than 300 mJ, the far-field intensity distribution of EUV laser beam shows a narrow circular peak. As the pump pulse energy increases, the beam size defined in FWHM becomes increasingly larger, and so does the corresponding beam divergence angle. Meanwhile, the far-field beam profile gradually evolves from a single dominant peak into an annular pattern starting from the vicinity of the central axis. The ring structure in the annular beam gradually moves outward to form a wider and deeper intensity valley. Figure 3(b) shows the angular profiles of the 32.8-nm EUV laser at various pump energies. The output photon number and beam divergence measured by both the flat-field spectrometer and the far-field imaging system are found to be in good agreement. It is interesting to note that the size of speckles observed in the far-field pattern decreased when the pump energy was gradually increased. This implies that Kr EUV lasers had a larger source size under higher energy pumping. The mean small speckle sizes of Kr lasers at various pump energies were measured to be 1.06 mm at 200 mJ, 0.59 mm at 300 mJ, 0.52 mm at 700 mJ, and 0.38 mm at 1130 mJ, which correspond to source sizes of 20 µm, 36 µm, 41 µm, and 56 µm, respectively. The retrieved source sizes are well comparable with the guided beam size and the transverse dimension of the plasma waveguide. The increasing source size at higher pump energy also agrees with the wider gain regions suggested in the previous section.

The formation of the annular EUV laser beam previously observed in capillary discharge plasma channels was due to relatively strong refraction caused by radial electron density gradients inside the plasma column [20]. In our experiment, pump pulse intensity >2×1017 W/cm2 (∼the ionization threshold of Kr9+) was observed at the exit of the plasma waveguide for pump pulse energy higher than 300 mJ. Under such experimental condition, the intensity in the pump pulse wings, which is originally lower than the ionization threshold for Kr8+, begins to exceed the threshold and thus results in a wider gain region when the pump energy is gradually increased. However, the increase of the pump energy results in higher peak intensity which may exceed the ionization threshold of Kr9+ and generate an overionization region to reduce the gain volume. Over-ionization took place from the central region outwardly in the channel and may reduce the density barrier of the plasma waveguide by increasing the electron density in the central region. Nonetheless, the transverse intensity distribution of the guided pump pulse also further ionized the outer region of the waveguide to increase the electron density barrier which maintained the guiding condition. The interferometry and relayed imaging system showed that the guiding of the pump pulse in the channel was sufficiently good and the waveguide structure was also sustained even at high pump energy. The propagation of the amplified EUV laser beam is thus guided by the gain volume which had a depressed gain column in the vicinity of the optical axis to produce an annular EUV laser beam.

5 Summary

In conclusion, high-brightness OFI collisional-excitation EUV lasing of Ni-like krypton at 32.8 nm pumped by the 100-TW laser system is demonstrated. An average output of 1012 photons per pulse for 32.8-nm laser at a pump energy of 1 J is achieved with an optically preformed plasma waveguide fabricated by using the axicon-ignitor-heater scheme. The far-field patten of the laser changes with increasing pump energies from a single peak to an annular profile due to over-ionization of krypton ions at the center of the plasma channel. Running at a 10-Hz repetition rate, the EUV laser is capable of supporting applications that require high repetition rate. Its large photon number per pulse is also an advantage for coherent flash imaging.