1. Introduction

The first collisionally pumped X-ray laser (XRL) was demonstrated by [2], using a pumping laser energy near 5 kJ. Since then, the required pumping energy was significantly reduced by orders of magnitude, thanks to optimized pumping schemes backed by strong theoretical support. An important step was the use of pre-pulse pumping [3] and [4] helping to establish low plasma gradients by introducing an expansion phase between the pulses. This was improved further by the use of a short (CPA) pulse to heat the plasma, clearly separating the plasma production, provided by a nanosecond pulse, from the heating phase needed for the inversion [5] and [6], a scheme known as transient collisional excitation. Traveling wave pumping was used to match the position of the short-lived gain with the transit of the generated XRL pulse, which was further refined by introducing longer delays between the pre-pulse and the main pulse [7]. Though oblique incidence pumping dates back to [8], experiments using a non-normal incidence pumping scheme optimized for efficient traveling wave excitation were published by [9], [10], [11] and [12]. Recently, the use of grazing incidence pumping (GRIP) optimizes the deposition of the main pulse energy in the anticipated region of gain by bringing the main pulse onto the target under near-grazing incidence, thus decreasing the required pumping energy [13] and [14]. With an optimized incidence angle, and making full use of the GRIP energy deposition characteristics, gain at wavelengths as low as 10 nm was observed with pump energies around 1 J [15], [16] and [17], allowing for XRL operation at repetition rates of up to 10 Hz. To extend the field of application of XRL, the demonstration of a high energy XRL in the water window is highly desirable. This requires a much higher pumping energy, which is in the current layout of the GRIP scheme experimentally demanding, because of the complications and costs to propagate and focus two independent beamlines with large diameters.

In this paper, we report on an improvement to the pumping geometries proposed by [1] and [18]. We investigated the XRL operation under optimized pumping parameters. The pre-pulse is created in the front end of the laser system and then, collinearly to the main pulse, propagated through the amplifiers and the compressor, which radically reduces the complication of the beam delivery while working with a comparable pumping efficiency. It yields a simplification of the XRL pumping scheme which is especially appealing to large aperture systems. On the one hand, this simplifies greatly the alignment of the XRL set-up since only one beamline is used; but on the other hand one loses the ability to control independently the focus parameters and angle of incidence of each beam. We have found experimentally that lasing of Ni-like palladium is reached at a low pumping energy threshold without the tedious alignment required for the two beamline geometry thus confirming that the advantages of this pumping scheme overcome the inability to control the parameters of each beam separately.

2. Experiment

In the front-end of the driving CPA laser system the double pumping pulse is generated in a standard Mach-Zehnder type set-up. The stretched pulse is distributed into the two arms with an adjustable ratio via the combination of a wave plate and a polarizing beam splitter. One of the arms incorporates a delay line adjustable between 0 and 3 nanoseconds delay. The two pulses are then amplified through the chain of the CPA system which includes two regenerative Ti:Sapphire amplifiers and two Nd:Glass laser heads. After re-compression, the two short pulses are then sent to the experiment chamber. It should be noted that in this configuration - in contrast to the more elaborate scheme of [19], but similar to [1] the two pulses have the same duration, which can be adjusted between around 0.3 and 50 picoseconds by tuning the grating-to-grating distance of the stretcher or the compressor.

 

Fig. 1. The experimental setup on the left is showing the beamline of the focussing system for the pump laser and the X-ray laser diagnostics. The insert to the right shows the schematic view of the non-normal incidence pumping scheme.

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In this experiment we investigated a nickel-like palladium 4d ¹ S ₀-4p ¹ P ₁ transient soft X-ray laser at 14.7nm by using a two-dimensional high-spatial-resolution diagnostics recording the XRL far-field. The experimental set-up in the target chamber is depicted in Fig. 1: We used the focusing system of [20] which produces a line focus with an intrinsic traveling wave speed of 1.2 c. The beam from the compressor is deflected by a flat mirror onto a spherical mirror with a focal length of 600mm which is positioned off the normal incidence. The line focus on the Pd slab target was 5.5mm×50µm FWHM. Both pulses hit the target at the same grazing incidence angle Φ of 29 degrees, a value determined to be the optimal GRIP configuration in the classical scheme for the operating pump laser as shown in Fig. 2. For our wavelength of 1053nm the electron density at which the energy is absorbed amounts to n_e,abs ≈2.3×10²⁰ cm ^-3, following n_e=n_c·sin²Φ with the critical density n_c.

The insert in Fig. 1 shows the effect of the geometry for the absorption of the two pulses on the target. The pre-pulse is - except for a possible weak pre-plasma, produced by the <10^-3 pedestal - hitting directly onto the target, creating an expanding plume of plasma, in which the second pulse is refracted. In view of the formation of the pre-plasma, the fact that the pre-pulse has the same short time duration as the main pulse certainly introduces some difference to the typical scheme. This might possibly cause a slight deterioration of the efficiency. However, it was assumed that thermalization should be reached before the main pulse is impinging onto the plasma. The dramatic influence of choosing the correct GRIP angle is demonstrated in Fig. 2, where data obtained at our apparatus in the standard pumping geometry are given, together with a spectrum of the XRL emission. For the new geometry the optimal angle determined in the standard GRIP scheme was used. Laser operation was achieved using a pulse separation of 1 ns, seemingly benefitting from the perfect overlap of both pulses due to the same optical path, which allows an optimized pumping of the gain region.

In the experiment the intensity ratio between the two pulses was fixed to 1:4 and the level of other pre-pulses created in the chain by ASE and other effects was below 1:1000. The resulting irradiances on the target were ~3.5×10¹² W/cm ² for the pre-pulse and ~1.5×10¹³ W/cm ² for the main pulse respectively. The quality and orientation of the line focus were checked with a microscope imaging its shape on a glass diffuser at the final target position. The XRL diagnostics consisted of a 2-D XUV far-field camera. The image was detected on a 16-bit back-thinned XUV charge-coupled CCD camera after a deflection by a flat multi-layer mirror optimized for 14.7 nm, and a total propagation path of 30 cm. The resolution was limited by the 26µm pixel size. Zirconium filters were used to adjust the signal level. In the experiments using the standard pump geometry, the lasing output was also identified by a flat-field spectrometer. The clear signal as shown in the insert of Fig. 2 gives proof, that the recorded far-field images (Fig. 3) represent the Pd-XRL emission.

 

Fig. 2. XRL intensity as a function of the pump pulse incidence angle in the standard GRIP scheme at 27, 29 and 38.5 degrees, compared with results of the double-pulse scheme at 29 degrees (blue stars). The insert shows a spectrum of the Pd-XRL at 14.7 nm produced in the standard scheme.

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Fig. 3. On the left: The XRL far-field image pumped by the double-pulse scheme with 500 mJ with a vertical and horizontal divergence of ~9 mrad and ~4.5 mrad respectively. On the right: The XRL far-field image pumped in the standard scheme with 700 mJ showing a divergence of ~4.5 mrad.

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3. Results

The XRL output is measured by integration of the plasma background corrected counts on the XUV CCD. The XRL intensity was recorded for pumping energies of 600 ±10% mJ. To obtain comparable results the output intensities are normalized to 600mJ pump energy and used to investigate the influence of pulse delay and pulse duration. The dependence of the XRL output energy on the pulse separation is shown in Fig. 4(a). A maximum of the XRL output is identified around 1 ns of delay. The width of the distribution is in the order of 0.4 ns. This indicates that the influence of the timing is similarly or even slightly less critical than reported for the standard pulse scheme [21].

 

Fig. 4. On the left: Dependence of the XRL intensity on the time delay of the pumping pulses with a pulse duration of 11 ps. On the right: Dependence of the XRL intensity on the time duration of the pumping pulses with a pulse delay of 1 ns.

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Figure 4(b) shows the result for different pulse durations. This variation affected both pulses equally, since only the compressor settings were changed. The pulse duration was changed between 6 ps and 28 ps. A wide maximum is observed around 16 ps, indeed a factor of 4 to 5 longer than the typical value for optimized pumping in the standard scheme [22], [16] even longer than used in [1] and [18]. This effect could be related to a longer interaction time necessary to enable suitable pre-plasma conditions. In the scheme with two equally short pulses, the duration of the pre-pulse might be problematic in terms of the production of a homogenous plasma plume. This could be the reason for the untypically long optimal pulse duration. With the optimal timing and delay, lasing was achieved at pump pulse energies below 500 mJ, which is a reduction by 25% compared to the threshold of 680mJ we obtained under optimized conditions in the standard geometry. In Fig. 2 the output energies at the optimum incidence angle of 29 degrees demonstrate a similar pumping efficiency for both configurations. A further improvement of the pumping efficiency might be achieved by using an additional module in one of the arms of the Mach-Zehnder set-up to adjust the pulse duration separately, as reported by [19]. With this modification of the double-pulse generation one expects to reach even better performance at still undemanding operating conditions.

4. Conclusion

In conclusion, the improved double-pulse non-normal incidence pumping geometry for transient collisionally excited soft X-ray lasers provides a simple and efficient way to produce XRL output at close to 100eV photon energy. Creating two pulses of equal duration can be well achieved in a standard Mach-Zehnder geometry. Using the traveling wave focusing geometry from [20] the adjustment of the pump optics is straightforward and stable. In comparison to earlier work using similar double-pulse schemes the pumping energy for a reliable operation of a Pd-XRL is strongly reduced from above 1 J ([1]) to less than 500 mJ. The drastic improvement is attributed mainly to the optimized GRIP angle, pulse separation, and duration. The highest intensity registered on the CCD camera corresponds to ~0.3µJ of XRL energy at 700mJ total pump energy. This is comparable with the best reported values e.g. in [22]. This opens the way for the improvement of XRL in high repetition-rate facilities like LASERIX [23] or at even higher repetition rates, as envisioned by [24]. The possibility for efficient operation at pulse durations above 20 ps can be used for a further reduction of pump laser requirements for applications [25]. The simplified geometry will also ease the application of higher pumping pulse energies, which is still necessary for reaching shorter XRL wavelengths [26].