1. Introduction

State-of-the-art high-power laser systems can produce ultra-short light pulses with peak powers P₀ in excess of 1 PW [1, 2]. When such pulses are focussed to an area of only a few μm², they reach peak intensities I₀ in excess of 1020 W/cm² [2, 3]. During the interaction of such high-intensity pulses with a target, quasi-static electric fields with amplitudes of up to 10¹² V/m can be generated. Such fields have potential applications for the acceleration of charged particles, e.g. electrons [4] or protons [5] and heavier ions [5]. For many of these applications, diode-pumped high-power laser systems using Yb³⁺–doped laser materials (e.g. glass or CaF₂) are a promising alternative to conventional Ti:Sapphire or flash-lamp pumped Nd:glass systems. Diode-pumped systems have the potential to deliver high-energy pulses (4...100J) at a high repetition rate (∼ 0.1...1Hz) with moderate pulse durations (∼ 130fs).

For a comprehensive description of the physics dominating the various interaction scenarios, a precise characterization of the laser pulse parameters and the target conditions at the beginning of the high-intensity interaction is required. In addition to the wavelength, energy, duration, and peak intensity of the laser pulse, the temporal evolution of the pulse contrast is a crucial parameter. The contrast can be defined as the ratio between the power P(t) at times before (t < 0) or after (t > 0) the arrival of the main pulse and the main pulse peak power P₀, i.e. η(t) = P(t)/P₀. Both amplified spontaneous emission (ASE) of laser radiation within the laser amplifier chain and short prepulses (mainly replicas of the main pulse caused by, for example, parasitic reflections [6, 7]) are factors which can reduce the pulse contrast. A low pulse contrast means that the target will be significantly modified before the arrival of the main pulse due to pre-ionization, plasma expansion and heating which are all dependent on the intensity, duration and relative timing of any prepulses or ASE. For example, during interactions with μm-thin foils, target pre-ionization due to strong prepulses or an intense ASE-pedestal can render the acceleration of electrons or ions ineffective. Hence, a complete characterization and improvement of the pulse contrast are key issues for the optimization of high-power laser systems for laser-matter experiments.

However, state-of-the-art measurement techniques for the pulse contrast are limited with respect to the covered time window and the achievable dynamic range. On the one hand, multi-shot 3^rd-order cross-correlators (e.g. Sequoia, Amplitude Technology) can cover a time window of 650 ps and a dynamic range of 10 orders of magnitude [8]. By introducing two additional delay lines into such a cross-correlator, the time window can be extended. Here, a number of different measurement sets need to be taken and carefully combined afterwards, leading to a contrast trace covering a total time window of up to 6ns before and 2ns after the main pulse [9]. However, such measurements are very time-consuming, especially for low repetition rate systems. On the other hand, single-shot contrast measurements [10, 11] have been demonstrated covering a dynamic range of 7 orders of magnitude and a time window of up to 200ps in a single shot.

Furthermore, these techniques usually measure the relative contrast in the near-field of the laser pulse by taking an unfocussed beam for the measurement. However, in intense laser interactions one is interested in the pulse contrast in the far-field (i.e. in the focussed beam), therefore this method only strictly provides information on the power contrast temporal shape. The absolute contrast measurement is only valid when the prepulses and ASE have the same focusability as the main pulse which is not necessarily the case in particular for power amplifiers with a non-imaging architecture, which are often used for the amplification of laser pulses to high energy levels.

In this paper, we present a complete temporal characterization of the on-target intensity evolution of the ASE from the individual amplifiers of the fully diode-pumped Yb:glass laser system Polaris. The combined measurements, using multiple detectors, cover a time window spanning several milliseconds around the main pulse. Since only the ASE contribution is to be detected, the entrance of each amplifier has to be blocked. However, this can significantly change the saturation conditions, and thus the gain per pass of the measured ASE. Therefore, it must be ensured that both the measured and subsequent amplifiers are not operated in saturation, which is shown for the first amplifier in section 2. Furthermore, we measured the lateral distribution of the ASE from the different amplifiers in the focal plane of the main pulse. This allows us to deduce the ASE intensity evolution with a dynamic range of more than 16 orders of magnitude. Since our results also reveal which amplifier has the largest absolute contribution to the ASE on different time scales it is now feasible to further reduce the ASE level by optimizing the respective amplifier for applications with specific contrast requirements.

The Polaris laser system is operated both by the Helmholtz-Institute Jena and by the Institute of Optics and Quantum Electronics in Jena, Germany. A schematic of its architecture is shown in Fig. 1. An 85 fs seed pulse – picked from the oscillator pulse train and preamplified by the first regenerative amplifier A1 – is stretched to a pulse duration of τ_stretch = 2.5ns in a grating stretcher. The second regenerative amplifier A2 and the following three multipass amplifiers, A2.5, A3 and A4, increase the pulse energy to currently E_max = 6.5J [9]. In the amplifiers, Yb:glass is used as the active medium. In each amplifier, ASE can be generated over the full duration of the optical pump pulse. In Polaris, the amplifiers are pumped by 940 nm light emitted by high-power laser diodes over a duration of 2.7 ms [12]. Finally, the stretched and amplified pulses are recompressed by a grating compressor down to a pulse duration of τ_comp = 164fs [9].

 

Fig. 1 Schematic layout of the Polaris laser system. An oscillator and a first amplifier are followed by a grating stretcher, four ns-amplifiers and a grating compressor. The pulses are finally focused by a parabolic mirror onto the target.

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2. Gain characterization of the first regenerative amplifier A1

Since the saturation fluence of the Yb:glass of 44J/cm² [13] is much higher than the laser induced damage threshold of 3J/cm² [12], the amplifiers of the Polaris system cannot be operated in saturation. This enables for the independent characterization of the ASE generated by each individual amplifier without the seed pulse from the oscillator. To demonstrate this, the small signal gain of the first amplifier A1 was measured for the ASE and the main pulse. Here, the pulses to be amplified were detected by a photo diode behind a resonator mirror with a transmission of ≈ 3%. To be able to measure the full 5 orders of magnitude of the total gain, the pulses leaking out of the cavity were focussed onto the photo diode and attenuated by several ND filters calibrated for the laser wavelength. The diode (Thorlabs DET210) had a rise time of t_rise = 1ns and was used in conjunction with an oscilloscope (Tektronix TDS3054C) with a rise time of t_rise = 0.7ns. The combination of both elements allowed measurements with a temporal resolution of τ_s1 = 1ns. This was sufficient to measure the evolution of the pulse energy after each round-trip in the cavity as indicated by the black line in Fig. 2. Note that the duration of the amplified laser pulse in the cavity was τ₀ = 85fs during the first round-trip. During the repeated propagation through optical elements in the A1-cavity the pulse is stretched due to group-velocity dispersion to τ₃₉ ≈ 1ps at the last pass. These pulse durations could not be resolved by our measurements, however, since the photo diode accumulates the signal over the time interval determined by its temporal resolution (which is shorter than the round-trip time of 13.25ns), the relative energy amplification of the pulse circulating in A1 is measured correctly by the diode. This photo diode measurement was calibrated with an absolute energy measurement (Coherent J8LP) which recorded an output energy of E_out = 100μJ for amplifier A1 after 39 round-trips. Note that deviations from the fitted single pass gain, noticeable during the first round-trips, are due to a slight mismatch between the spatial mode of the seed pulse and the cavity. The resulting single pass gain of g_A1 = 1.3434, shown by the black circles in Fig. 2, remains constant over the whole number of round-trips. This confirms that the amplifier is not saturated suggesting that the expected gain for smaller signals such as the ASE should be similar. The temporal resolution of our measurement was sufficient to monitor the evolution of the ASE level which can be assumed to be constant during the round-trip of 13.25 ns in A1. For the ASE characterization, the seed pulse was blocked. Thus, only the spontaneously emitted laser radiation was amplified, which was characterized with the same method as described above. However, due to the low intensity of the ASE during the first round-trips, it was only possible to detect a signal after the 20^th round-trip. The evolution of the ASE is shown by the red line in Fig. 2. From this measurement, we could determine the single pass gain for the ASE to have exactly the same value as the single pass gain for the amplified laser pulse, indicated by the red circles in Fig. 2. For a correct calibration within the energy range of the detector, the numbers of round trips were increased to 63 leading to an ASE energy of E_A1,n=63 = 10μJ. Since the subsequent amplifiers A2 – A4 all provide a single-pass gain which is also constant during the amplification of the laser pulses, the ASE generated by all individual Polaris amplifiers could be characterized independently from the seed pulse.

 

Fig. 2 Amplification characterization of the first regenerative amplifier A1: photo diode measurement of the circulating pulse referenced to the output energy (black line); energy calibrated photo diode measurement of the ASE while the seed was blocked at the entrance (red line); corresponding ideal amplification of the respective measurement with the averaged small signal gain (black and red circles).

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3. Fully amplified ASE of the individual Polaris amplifiers

The temporal characteristics of the ASE of both regenerative amplifiers and of the subsequent multipass amplifiers A2.5, A3, and A4 were measured after recompression. For the measurement of the ASE of a particular amplifier, all subsequent amplifiers were operating with their usual parameters while the entrance of this particular amplifier was blocked. Hence, each measurement takes into account the ASE of all subsequent amplifiers which can be assumed to be small compared to the amplifier to be characterized as shown by the following measurements. An influence of the oscillator on the total ASE level could not be detected. For the individual measurements, a photo diode (EOT-3000) with a rise time of t_rise = 175ps, the oscilloscope from section 2 and calibrated neutral density filters were used. Thus, the temporal resolution of the setup was τ_s2 = 0.7ns. However, the main pulse duration after compression τ_p is still much shorter than τ_s2. Thus, for absolutely calibrating the measured prepulse intensity with respect to the main pulse, the attenuation coefficient introduced by the filters as well as a temporal correction factor F = τ_s2/τ_p [6] needed to be considered. For a pulse duration of τ_p = 200fs, as measured during the characterization, F = 3500. For specifying t₀ = 0 when the main pulse arrives, the oscilloscope was triggered externally with a jitter of less than 250ps [14]. Hence, the temporal evolution of the ASE could be accurately measured relative to the main pulse as shown in Fig. 3.

 

Fig. 3 Combined log-log plot of the ASE for times t ≤ t₀ (a) and times t ≥ t₀ (b) regarding the different Polaris amplifiers. The insets show the respective spatial distribution which was measured in the focal plane of the main pulse. The ASE measurements were carried out with a photo diode/oscilloscope combination while the main pulse was measured with a 3^rd-order cross-correlator.

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Fig. 3 shows a combination of two log-log plots (a) for times −10ms ≤ t ≤ −10fs and (b) for times 10fs ≤ t ≤ 10ms. The axis of symmetry, represented by the vertical dashed black line, indicates the time t₀, which was used as the absolute time reference during the measurement.

The temporal evolution of the main pulse was measured with a 3^rd-order cross-correlator from −450ps ≤ t ≤ 200ps with time steps of 15fs for ±600fs around t₀ and with time steps of 150fs elsewhere. With the cross-correlator, the total ASE level with seeded amplifiers was determined to be 3.6×10⁻⁹ for t < −30ps, which is consistent with the relative peak power of the A1-ASE of 2.8 × 10⁻⁹, measured with the calibrated photo diode and the blocked entrance of the amplifier A1. Here, the temporal resolution of the photo diode/oscilloscope limits the measured temporal range to |t| ≥ τ_s2. The characteristic of the A1-ASE was interpolated between −τ_s2 ≤ t ≤ τ_s2, as represented by the dashed line. The full-width-at-half-maximum (FWHM) pulse duration of the main pulse during this measurement was τ_p = 200fs and the total energy after the compressor was E_total = 2.8J. Note that the compressor efficiency of η_comp = 63% has already been taken into account. The duration (FWHM) of the A1-ASE, corresponding to the full amplified ASE (A1 seed blocked), was measured to be τ_A1–ASE = 12ns which is slightly shorter than the round-trip time of 13.25ns. Since the pulses to be amplified, and thus the ASE, circulate in a closed cavity and are coupled out after the final number of round-trips, the temporal ASE characteristics are determined by the cavity length (i.e. the round-trip time) and the rising edge of the Pockels cell (PC). The difference of the measured duration and the round-trip time can be explained by several additional PCs installed for a further enhancement of the pulse contrast by suppressing short prepulses. For this purpose, a double PC-polarizer cascade was implemented after the second regenerative amplifier A2, which ensures a relative contrast improvement of ≈ 10⁻⁷ within the rise time of the PCs [6]. Note that these PCs not only suppress prepulses but also the fraction of the ASE leaking out of the cavity during the round-trips the main pulse experiences [6] which leads to the steep slope of the A1-and A2-ASE. Furthermore the energy of the A1-ASE after the compressor was measured to E_A1 = 140μJ. The relative peak power of the A2-ASE was measured to 4.8 × 10⁻¹³ with a duration (FWHM) of τ_A2–ASE = 12.5ns. Here, the energy could not be measured with an energy detector since the integrated energy of the fluorescence from the subsequent multipass amplifiers was higher. However, integrating the calibrated diode measurement leads to an estimated energy of E_A2 = 30nJ.

In contrast to the regenerative amplifiers, multipass amplifiers do not form a resonator. Hence, the ASE duration is not determined by the cavity length and the rising edge of the PC, but by the temporal shape of the pump radiation with a duration of τ_pump = 2.7ms and the fluorescence life time τ_f = 1.4ms of the amplifying medium [12]. Furthermore, the spatial characteristics are determined by the solid angle Ω of the spontaneously emitted radiation, which differ from pass to pass. Assuming that Ω is defined by the last limiting aperture, which is, in most cases, the first lens of the next magnification telescope, and the distance to the amplifying medium, the main fraction of the ASE comes from the spontaneously emitted radiation in the direction of the last pass of the last amplifier. Hence, it is reasonable to characterize the multipass amplifiers as one as was confirmed by the measurement. For the photo diode measurement, shown in Fig. 3, the input impedance of the oscilloscope was set from 50Ω to 1MΩ which increases the sensitivity by a factor of 2 × 10⁴, while the temporal resolution decreases to τ_s3 = 2μs. In Fig. 3 the times −τ_s3 ≤ t ≤ τ_s3 are again interpolated and represented by a dashed line. The relative peak power was measured to be 4.6 × 10⁻¹⁶, the energy was E_mp = 6.5μJ and the duration (FWHM) was τ_mp = 2.3ms.

In addition to the temporal characterization of the ASE power in the Polaris system, the spatial characteristics were measured in the focal plane of the main pulse, as shown in Fig. 3. For this purpose, the ASE was imaged onto a high-dynamic CCD with the same setup that is used to characterize the focal spot of the main pulse [9]. The intensity distributions in the far field of the main pulse and the different ASE contributions were first characterized by the FWHM focal spot area. Secondly, the q-factor representing the fraction of the total pulse energy contained within this area was determined. For the A1-ASE, an area of A_A1–ASE = 8.7μm² and a q-factor of q = 0.24 were measured, which is comparable to the main pulse focus which had A_p = 9.8μm² and q = 0.28. The measured differences are on the order of the pulse-to-pulse fluctuations. Due to the minimal exposure time of the camera of several μs, the spatial characteristic of the A2-ASE could not be distinguished from the ASE of the main amplifiers. However, due to the distinct divergence and spatial mode, defined by the A2-cavity, the area is assumed to have the same value as for A1 in the following calculations. The spatial characteristics of the ASE from the multipass amplifiers, however, differ significantly due to the absence of a cavity. Here the area in the plane of the main pulse focal spot was measured to A_mp = 85μm² with q = 0.28. These results are summarized in table 1 including the calculated average intensity within the spatial FWHM, which can be calculated by Ī = q · E/(τ · A). Furthermore, the average fluence for the ASE from A1 and A2 was calculated using F̄ = q · E/A.

Table 1. Summary of the measured parameters relative peak intensity I/I₀, energy E, duration τ, spot area A and q-factor of the several Polaris amplifiers as well as the average intensity Ī and fluence F̄ calculated from the measurement. The ASE parameters were carried out with the seed blocked before the amplifier to be characterized while all subsequent amplifiers were operating with their usual parameters.

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From Fig. 3 it is obvious, that the main fraction of ASE that will affect a laser-plasma interaction, is generated within the first regenerative amplifier A1. Bogeaerts et al. [15, 16], have developed a theoretical model describing the effect of laser pulses irradiating a Cu-foil at intensities of I ≈ 10⁹ ...10¹¹ W/cm² over durations of τ ≈ 5...10ns at a wavelength of λ = 1064nm. It was found that a minimum intensity of I ≈ 2×10⁹ W/cm² is necessary to melt a Cu-target, which leads to a threshold of F ≈ 10J/cm². This threshold was also confirmed experimentally by several groups [17, 18]. Furthermore, it was found that other metals provide a comparable threshold [19]. These values are comparable to the contribution from the A1-ASE, while the ASE-contribution from the other amplifiers alone would not be sufficient to affect a metal target. Hence, for our laser parameters an ASE-improvement of at least 3 orders of magnitude is necessary to prevent the formation of a preplasma in laser-plasma experiments when using thin Cu-foils as a target. This may be achieved in the future using the principle of cross polarized wave generation (XPW) [20, 21] or optical parametric amplification (OPA) [22, 23] which have been shown to improve the ASE contrast by up to 4 orders of magnitude. Applying such contrast-cleaning techniques after the amplifier responsible for the largest ASE contribution (i.e. after A1 for Polaris), one can significantly reduce unwanted pre-modification of the target during high-intensity laser interactions.

The measured ASE level of the multipass amplifiers was sufficiently low that it would not be expected to have any significant impact on the laser-plasma interaction. However, by implementing a PC with a rise time in the ns-range, the duration, and thus the fluence, of this fraction of the ASE can be further reduced.

4. Conclusion

In conclusion, we presented the first complete temporal and spatial characterization of the ASE from a high-power diode-pumped laser system. The independently measured ASE contributions from the individual amplifiers were characterized in terms of their temporal shape, their spot size in the focal plane of the main pulse, and their energy content. Our measurements spanned a time window of several ms around the main pulse and covered an intensity range of 16 orders of magnitude. This represents - to our knowledge - the longest time interval and the highest dynamic range for a combined spatio-temporal ASE characterization. With our technique it was possible to identify the main source of ASE which is likely to affect laser-plasma experiments through the formation of a preplasma. In the future, an improvement of this main ASE contribution by at least 3 orders of magnitude should be possible, e.g. by implementing an XPW or OPA pulse-cleaning concept in combination with a double CPA-system [24]. This is likely to be sufficient to significantly suppress the formation of a preplasma in experiments using thin metal foils.