1 Introduction

Thanks to the inventions of chirped pulse amplification (CPA) and optical parametric chirped pulse amplification (OPCPA) techniques [1, 2], the laser peak power and focused peak intensity have been rapidly developed. Plenty of PW and 10PW level lasers have been built up over the world, and the focused peak intensity has reached 1022 W/cm2 and even 1023 W/cm2 [3,4,5,6,7,8,9,10]. Such ultra-intense lasers can provide unprecedented condition and bring significant breakthrough of a wide range of strong field physical researches. For example, high energy particles acceleration, the fast ignition of inertial confinement fusion, high-order harmonic and γ-ray generation, and vacuum quantum electrodynamics (QED) [11,12,13,14]. In such laser–matter interactions, the laser intensity at target is a key parameter governing the physical process of strong field phenomena, e.g. linear, weakly nonlinear, strongly nonlinear, relativistic, and even QED regimes. To obtain higher laser intensity and hence further extend the basic knowledge in physical field, great effort has been devoted to enhancing the laser energy, shortening the pulse duration and decreasing the focal spot size. Nevertheless, there are seldom attentions attracted to accurately positioning the focal spots of driving lasers, which can be quite important for the practical laser intensity available at target, especially for the focusing systems with small F number. Only when the target is placed rightly at the focal spot of driving laser, the maximal laser intensity can be utilized for laser–matter interactions.

The common methods for the focal spot positioning of high peak power driving lasers can be classified into three categories. Firstly, the laser is only pre-amplified while without running the power amplifiers. However, due to the thermal lens effect in amplifiers [15, 16], the divergence of the laser beams with and without full-energy amplification can be quite different, and hence the measured results will suffer great error. Secondly, all the amplifiers are running but the time delay between seed pulse and pump pulse is enlarged to avoid amplification. In this case, though the influence of thermal lens is considered, the transvers amplified spontaneous emission under high pumping intensity can also degrade the beam quality [17], and thus affect the spatial profile and position of focal spot. Thirdly, the laser is full-energy amplified and some extra energy attenuation modules (EAM) are introduced. Compare with above two methods, this is a more accurate focal spot positioning method for high peak power lasers. In a word, the key point of focal spot positioning is to realize sufficient energy attenuation while without changing laser-focusing characteristic.

There are two main types of EAM, one is based on the partial reflection mirrors [8, 9, 18, 19], and the other is relied on the polarizing plates and wave plate [20,21,22]. For the first kind of EAM: (i) high-quality partial reflection mirrors are necessary to avoid the beam quality degradation, while the number and aperture of partial reflection mirrors are increasing with the increase of laser energy; (ii) the resulting attenuation of laser energy is discontinuous; (iii) an extra pointing monitoring module is needed to guarantee the calibration of laser beam with and without this EAM. For the second kind of EAM: (i) though continuous attenuation of laser energy can be realized, the level of attenuation is limited by the extinction ratio of polarizing plates; (ii) large-aperture, broadband polarizing plates and wave plates are usually large-cost and difficult to manufacture. As these existing EAMs have some problems more or less in actual application, it should be of great significance to explore an effective, simple and low-cost focal spot positioning method for high peak power lasers.

In this work, a novel method based on the porous mask is firstly proposed and demonstrated for the direct focal spot positioning of high peak power lasers. Without using any complicated setups, this method can sufficiently weaken laser energy while unchanging laser-focusing characteristic, by introducing a specially designed porous mask before the laser compressor. And different levels of energy attenuation can be easily realized just by optimizing the mask. The experimental results show that this method can directly positioning the focal spots of high peak power femtosecond lasers up to hundreds-TW level. Moreover, this method has great potential to be used in higher peak power lasers, and can facilitate the experimental investigations of strong field laser–matter interactions. The organization of this paper is as follows. In Sect. 2, the positioning method and theoretical analysis are briefly illustrated. In Sect. 3, the experimental setup is described. In Sect. 4, proof-of-principle experiments are carried out. Lastly, the conclusion is presented.

2 Positioning method and theoretical analysis

A simple schematic of the focal spot positioning method for high peak power lasers is illustrated in Fig. 1, in which there is no complex setups for laser energy attenuation. The amplified laser firstly passes through a mask, equipped with several identical small circular holes. The leaked small-aperture laser beams are temporally compressed in a grating compressor and then focused by an off-axis parabolic (OAP) mirror. Lastly, the focal spot position of amplified laser is directly detected by a CCD. In this method, the porous mask is used to achieve sufficient energy attenuation of amplified laser while without changing its focusing characteristic, which is the key issue to realize the direct positioning of the focal spots of high peak power lasers. After passing through the porous mask, most of laser energy is blocked off, while the focal plane of this focusing system can be analyzed based on the Fraunhofer diffraction theorem [23, 24].

Fig.1
figure 1

Direct positioning method for the focal spots of high peak power lasers

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The schematic of single circular hole Fraunhofer diffraction is also shown as the inset of Fig. 1, and the viewing screen is placed at the focal plane of lens L. After passing through the single circular hole, the laser beam will propagate with an angle θ due to the diffraction effect, and then focused on the position P on the viewing screen. The intensity of position P can be calculated by Eq. 1. Here, D is the diameter of the circular hole, λ is the wavelength of laser, f is the focal length of lens L, (x, y) is the rectangular coordinate of P on the viewing screen while the original position (0, 0) is the focal spot position of lens L on its optical axis, and J1 is the first order Bessel function. Based on Eqs. 1 and 2, we can find that the center of diffraction pattern, i.e. the maximal intensity of P, is just at the original position (0, 0). In other words, the diffraction pattern is always symmetrical along the optical axis of lens L, while the position with maximal intensity is just at the focal spot of lens L on its optical axis. In turn, the focal spot can also be directly positioned by scanning the optical axis with a CCD, at where the laser intensity is maximum.

$$I\left(P\right)\propto {\pi }^{2}{\left(\frac{D}{4}\right)}^{4}{\left[2\frac{{J}_{1}\left(u\right)}{u}\right]}^{2},$$
(1)
$$u=\frac{\pi D\mathrm{sin}\theta }{\lambda }\approx \frac{\pi D\sqrt{{x}^{2}+{y}^{2}}}{\lambda f}.$$
(2)

We also find that the position of the center of diffraction pattern has nothing to do with the position of the single circular hole. Hence, the Fraunhofer diffraction pattern of randomly distributed circular holes (i.e. porous mask) has the same geometry characteristics with that of a single circular hole featuring the same radius. The former is a superposition of the diffraction pattern of each circular hole, and the position of its center with maximal intensity is coincident with the focal spot of the laser. Hence, the focal spot positioning of lasers can be realized by measuring the center of the diffraction pattern caused by porous mask as well. In addition, the energy of lasers can also be sufficiently attenuated by the porous mask. As a result, the focal spots of high peak power lasers are promising to be directly positioned by this method based on the porous mask.

Several points should be noted in this method. Firstly, the circular holes on mask should be designed with identical diameter to achieve the same diffraction angle. Because different circular holes can cause different diffraction direction, and hence affect the focusing of OAP mirrors. Secondly, the diameter of the circular holes on mask should be designed as small as possible but simultaneously much larger than the wavelength of laser. One is to obtain sufficient energy attenuation of high peak power laser, and the other is to avoid the influence on pulse compression caused by strong diffraction. Thirdly, the mask should be introduced before the laser compressor. As the laser duration is usually in nanosecond level before compression, and thus can avoid the occurrence of nonlinear effect and the optical damage of mask. Lastly, the material of mask should be carefully selected to avoid the strong absorption, reflection and sputtering of high peak power lasers. Besides, to avoid the reflection induced optical damage, the masks should be processed into an unsmooth surface.

3 Experimental setup

To demonstrate the validity and feasibility of this method, proof-of-principle experiments are carried out based on the SULF-1PW laser facility [9]. This laser is consisted of a KHz CPA front-end, a cascaded cross-polarized wave generation and femtosecond OPA filter, an Öffner stretcher, a regenerative amplifier, a multi-pass amplifier, two power amplifiers, a final amplifier, and a grating compressor. Figure 2 shows the layout of this PW laser and the experimental setup. The laser pulses can be amplified to ~ 8 J in two power amplifiers at 1 Hz repetition rate, and amplified to ~ 50 J in the final amplifier at 0.1 Hz repetition rate. After amplification, the laser beam is then up-collimated from 65 to 215 mm by the final telescope, to avoid the optical damage of gratings in compressor. This telescope is composed of achromatic lenses, to prevent the chromatic caused pulse front distortion [25, 26]. Following, the laser pulses are compressed to ~ 30 fs in the grating compressor. Lastly, a deformable mirror (DM) is used to correct the wavefront aberration of output laser pulses and improve the focusing quality.

Fig. 2
figure 2

Layout of the SULF-1PW laser facility and the experimental setup

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Besides, to realize the alignment of OAP mirror and the measurement of laser parameters under a reasonable energy level, an EAM with four partial reflection mirrors is inserted after the final amplifier. The surface flatness of the mirrors in EAM are all less than λ/30 (rms), measured by a Zygo interferometer. In this case, the influence on wavefront aberration induced by EAM can be neglected. A beam pointing (near- and far-field) monitoring module with two CCDs is also introduced after the EAM to ensure the alignment of laser beam with and without EAM.

Though laser energy can be greatly attenuated by this EAM, it is still too high for the direct focal spot positioning of such PW laser. Hence, a porous mask is introduced before the grating compressor, in which way the laser energy can be sufficiently weakened while without changing the focusing characteristic. As a result, the focal spots of high peak power driving lasers can be directly positioned. In this work, proof-of-principle experiments are carried out in two modes: 100 TW/1 Hz and 350 TW/0.1 Hz, and the laser is focused by an F/26.5 OAP mirror. This focusing system is prepared for the laser wakefield electron acceleration experiments aiming at 5–10 GeV electrons.

Here, the porous masks are manufactured of white ceramic, and the diameter of its circular holes is designed on 100 μm scale, which is 125 times the laser central wavelength (0.8 μm). In this case, the diffraction is not strong and the most of laser energy will propagate along with their original direction. Moreover, three kinds of masks equipped with different spatial distribution of the circular holes are used and tested, as shown in Fig. 3. The dotted circle on masks is the full beam size of incident laser. It is worth noting that, different level of laser energy attenuation can be easily realized by optimizing the diameter and amount of the circular holes on mask.

Fig. 3
figure 3

Schematic diagrams of the three different kinds of masks

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4 Experimental results

4.1 Focal spot positioning of 100 TW/1 Hz laser

The focal spot positioning of high peak power laser is firstly performed in 100 TW/1 Hz mode, in which the laser is amplified to ~ 6 J in two power amplifiers while without running the final amplifier.

To demonstrate the validity and feasibility of this method, the focal spot of this 100 TW/1 Hz laser is measured first using above EAM with proper energy attenuation. The CCD is placed on a high-precision linear translation stage, to precisely positioning the focal spots. The measured result is shown as Fig. 4a, with a diameter of ~ 29 μm at FWHM and the energy inside this diameter is ~ 39%. For the sake of simplicity, the position of CCD is set as 0 in this case, and the positions in following experiments will be represented in terms of its relative value. Besides, the focal depth of this focusing system is measured to be about 4 mm.

Fig. 4
figure 4

The experimental results of laser in 100TW/1 Hz mode: a the focal spot measured using EAM, b–d the measured results based on the porous mask 1–3, respectively

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Then, the focal spot of 100 TW/1 Hz laser is directly positioned by introducing a porous mask before laser compressor, while without using the EAM. The sufficient laser energy attenuation is realized by optimizing the amount of the circular holes on mask. The measured results based on the mask 1–3 are shown as Fig. 4b–d, respectively. Obviously, some diffraction rings appear around the bright spots after introducing the porous masks, while the bright spots are the centers of the diffraction patterns induced by above three porous masks. The positions of CCD in above experiments are − 0.07 mm, − 0.04 mm, − 0.03 mm respectively, and the negative (or positive) sign shows that the CCD is closer (or farther) to the OAP mirror. Though these measured results have different profile and intensity, the difference between the positions of their CCD is tiny. Thus, we can find that the measured focal spot positions based on this method have nothing to do with the amount and distribution of the circular holes on masks. In turn, these results also can demonstrate to some extent that the spatial intensity distribution of amplified lasers has no obvious influence on the focal spot positioning by this method. Moreover, these focal spot positions are also in good agreement with that measured based on EAM, and the differences between them are less than 2%, 1% and 1% of the focal depth (~ 4 mm), respectively. This agreement also efficiently demonstrates the validity and feasibility of this focal spot positioning method for high peak power lasers.

4.2 Focal spot positioning of 350TW/0.1 Hz laser

To further demonstrate the validity and feasibility of this method, the focal spot position of 350TW laser is also measured based on traditional EAM and porous masks, at the repetition rate of 0.1 Hz. The laser is amplified to ~ 6 J in two power amplifiers, and then amplified to ~ 17 J in the final amplifier. The driving voltage of DM is the same as that in 100 TW/1 Hz mode.

In the traditional measurement method, a partial reflection mirror in above EAM is replaced by another with lower reflection. The measured focal spot is shown in Fig. 5a. Compared with above 100 TW/1 Hz laser, there is no obvious change of the focusing quality, and the focal spot is a little closer to the OAP mirror, with a position of − 0.23 mm. This is resulted from the thermal effect in final amplifier, while the influence is little due to its low repetition rate.

Fig. 5
figure 5

The experimental results of laser in 350TW/0.1 Hz mode: a the focal spot measured using EAM, b–d the measured results based on the porous mask 1–3, respectively

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As the next step, the focal spot position of 350 TW/0.1 Hz laser is also detected based on the porous masks. To further weaken laser energy, the amounts of the circular holes on above three masks are all decreased. The experimental results are shown as Fig. 5b–d, with the position of − 0.28 mm, − 0.26 mm and − 0.21 mm, respectively. These results are also fitting with the focal spot position (− 0.23 mm) measured by EAM above, and the differences between them are − 0.05 mm, − 0.03 mm and 0.02 mm, respectively. In other words, the measurement errors between EAM and the masks are all less than 1.3% of the focal depth, which once again demonstrate the feasibility and validity of the focal spot positioning method for high peak power lasers based on the porous mask. In addition, the further energy attenuation can also be achieved by appropriately reducing the diameter of the circular holes on masks.

In all, this new focal spot positioning method for high peak power lasers has been efficiently demonstrated based on the proof-of-principle experiments above. Moreover, this is the first time to realize the direct positioning of the focal spots of hundreds-TW lasers, under the case of full-energy amplification while without EAM. Moreover, we believe this method is also applicable for higher peak power lasers.

5 Conclusion

In conclusion, we firstly proposed and demonstrated a novel focal spot positioning method for high peak power lasers. In this method, the amplified laser can be sufficiently attenuated without changing focusing characteristic by the porous mask before laser compressor, and then the focal spot positioning of lasers is directly realized. Moreover, this method is simpler, more flexible and lower-cost with respect to conventional methods. The experimental results indicate that the direct focal spot positioning can be realized in femtosecond lasers with the peak power of hundreds-TW by the use of this method. And we also believe that this method is promising to be applied in higher peak power lasers, and can facilitate the experimental investigations of strong field laser–matter interactions.