Ultrafast laser technology has experienced immense progress within recent years. Ultrashort, high-peak-power lasers are used in a vast range of applications, including attosecond science and high-harmonic generation [1–4], laser-plasma acceleration [5,6], or high-field science including laser-based nuclear fusion [7]. However, developing a laser source that is simultaneously average and peak power scalable remains a major challenge.

The invention of mode-locked solid-state laser technology, in particular titanium-doped sapphire (Ti:Sa) lasers in combination with chirped-pulse amplification (CPA), enabled ultrashort, few-cycle pulses with unprecedented pulse energy [8–10]. Nowadays, peak powers exceeding the terawatt regime are routinely employed [9]. While excelling in peak power performance, Ti:Sa amplifiers are commonly constrained in average power to a few tens of watts, which can be attributed to their large quantum defect [11]. As an alternative to laser amplification in active gain media, optical parametric processes can be employed. In particular optical parametric chirped-pulse amplifiers (OPCPAs) offer broad bandwidths supporting few-cycle pulses and simultaneously high average powers [10,12]. However, OPCPA systems suffer from low pump-to-signal efficiencies typically around 10%–20% for pulses in the range of 10s of femtoseconds (fs) [13]. Ultrafast ytterbium (Yb)-based laser architectures on the other hand provide excellent average power scalability exceeding 10 kW [14], but pulse durations limited to 100s of femtoseconds up to about 1 picosecond (ps). Combining Yb lasers with efficient post-compression methods supporting large (>10) compression factors and high pulse energies can offer an excellent solution to the power scaling challenge.

In recent years, a number of post-compression techniques have been developed, mostly relying on self-phase modulation (SPM) as the nonlinear process for spectral broadening [15]. In particular, gas-based technologies provide excellent tools for post-compression of high-power lasers. Example systems rely on gas-filled hollow-core fibers (HCF) [16–18], cascaded focus and compression (CASCADE) [19], white-light filaments [20], as well as Herriott-type multi-pass cells (MPCs) [15,21–23]. In HCFs, post-compression of 70 mJ 220 fs pulses down to 30 fs has been demonstrated in a 3 m long fiber [24]. Post-compression of very high pulse energies in the multiple Joule range has been achieved via thin-film spectral broadening techniques. However, typical compression factors lie in the range of only two to five [25,26]. Similar to HCFs, MPCs enable large compression factors reaching 10–20 or more while supporting a wide range of pulse energies. In addition, MPCs support high average powers [27] and outperform HCFs in system footprint especially for large compression factors [15]. The maximum attainable energy acceptance in a standard, two-mirror MPC is directly proportional to its size [15,28]. A record of 200 mJ has been achieved in a 10 m long MPC setup [29]. Further energy up-scaling leads to MPC sizes that are impractical for standard laboratory settings. The development of a highly efficient post-compression method supporting large compression factors and high pulse energies thus remains a key challenge.

We here introduce a new MPC type, the compact MPC (CMPC), which possesses a weakly focused fundamental mode as well as a linear beam pattern on the focusing mirrors. This geometry allows us to fold the beams inside the MPC using two additional planar mirrors, thus introducing a new energy scaling parameter, the folding ratio Γ. The CMPC in principle allows for an arbitrary amount of folding and thus, very compact setup sizes while sharing key properties of standard MPCs such as high average power support, excellent beam quality, and efficiency. We experimentally demonstrate spectral broadening of 1030 nm, 8 mJ, 1 ps pulses in a CMPC in atmospheric air using a setup with an effective length of around 45 cm. We keep the maximum mirror fluence at a moderate level of around 170mJ/cm2 and demonstrate compressibility of 1 ps input pulses down to 51 fs with an MPC throughput reaching 89% while maintaining excellent spatio-temporal pulse characteristics.

Most MPCs demonstrated for post-compression to date rely on two identical concave mirrors, resembling the most basic optical cavity arrangement. However, more complex designs employing a convex mirror and a concave mirror [30,31] or even multiple additional mirrors can provide advantageous mode-forming capabilities. MPCs with more than two mirrors have been proposed in previous works focusing on energy scaling of MPCs [31,32]. Other energy scaling methods that do not rely on modifications on the MPC geometry include divided pulse nonlinear post-compression [33,34], or using higher-order Laguerre beams to decrease the fluence on the mirrors [35]. These techniques can be combined with geometrical scaling methods. With the CMPC we demonstrate a new geometrical approach. The concept of the CMPC is based on a weakly focused beam and folding of the beam path via multiple reflections on two additional, planar mirrors in each pass through the cell, as shown in Fig. 1. This provides an additional tuning parameter, namely, the folding ratio Γ, which reduces the length of the CMPC by Leff≈L/Γ. Figures 1(A) and 1(B) depict the principle of beam folding and the effective size reduction of the cell together with the configuration regimes for standard MPCs and the CMPC. In Fig. 1(B) the original beam path is divided into three parts and then folded such that the setup length reduces by approximately a factor of three and thus Γ=3.

In general, the geometry of a symmetric Herriott-type MPC—including a CMPC—is fully determined by three of the following four parameters: radius-of-curvature (ROC) of the mirrors R, the propagation length between the two focusing mirrors L, the number of round-trips N, and the configuration parameter k. These parameters are related by [15] LR=1−cos(πkN).(1)Typically, k is chosen to be integer and prime to the number of round-trips N, in order to ensure the re-entrant condition of the MPC. Moreover, the parameter k determines the angular advance of the beam on the MPC mirror, which is equivalent to the Gouy phase per pass ϕG(1)=πk/N [15]. The amount of Gouy phase per pass determines the caustic of the beam in the MPC. For a standard MPC, ϕG(1) approaches π, which leads to a large mode size wm on the mirrors and a small waist w0 in the focus. In the CMPC, the beam propagates within the Rayleigh-range, where the accumulated Gouy phase per pass is ϕG(1)<π/2. This is the case when L/R<1, where the beam radius at the mirror wm is comparable to the beam radius at focus w0. The peak fluence of the beam follows a similar behavior, with F0/Fm<2 for L/R<1 [Fig. 1(C)]. This weak focusing geometry with small fluence variations enables the placement of additional optical components within the beam path of the CMPC and thus folding of the beam. In addition, a weakly focused mode eliminates pulse energy limitations arising due to ionization in standard gas-filled MPCs. Figure 2 illustrates the CMPC scheme. In Fig. 2(A) the setup schematic of a standard MPC with linear pattern alignment is shown. Here, the strongly focused beams propagate directly between the two focusing mirrors FM1 and FM2, without any optical components in-between. In the CMPC [Fig. 2(B)], two additional planar mirrors PM1 and PM2 are placed behind FM1 and FM2. As seen in Fig. 2(B-ii), the beam propagates from FM1 to PM2 and PM1, where it is folded multiple times before reaching FM2. Here, the depicted folding ratio is Γ=9. The total path length between FM1 and FM2 is the length determined by Eq. (1). However, the effective length is now reduced by Leff≈L/Γ, which under the correct choice of R and Γ can become significantly shorter than that of a standard MPC with similar pulse energy acceptance.

The pulse energy acceptance of a gas-filled MPC can be estimated considering the mirror fluence and the focus intensity. The beam waist radius in the focus and on the mirrors in an MPC can be calculated using the equations w02=(Rλ/2π)sin(π/kN) and wm2=(Rλ/π)tan(πk/2N), respectively, where λ is the wavelength of the laser [32]. The parameters L/R can be directly mapped to k/N according to Eq. (1). Assuming a laser with Gaussian pulses and pulse energy E, the maximum peak fluence in the focus F0=2E/πw02, as well as the peak fluence on the mirror Fm=2E/πwm2 can be calculated [32]. For a standard MPC consisting of two identical focusing mirrors, the fluence on these mirrors should not exceed the threshold fluence Fth, yielding a maximum pulse energy of EMPC≤RλFth2tan(πk/2N).(2)For simplicity, the second energy limitation that can arise at high focus intensity due to ionization is omitted in this discussion as it has little or no relevance for the CMPC. In a CMPC, where beam folding is achieved by additional mirrors (Fig. 2) the beam can be reflected at almost any point between the focusing mirrors including the focus. Therefore, the condition for avoiding damage needs to be F0≤Fth and thus ECMPC≤RλFth4sin(πk/N).(3)In addition, replacing R with L using Eq. (1) and writing L in terms of Leff≈L/Γ, we obtain ECMPC≤λFthΓLeff4tan(πk/2N).(4)

Equations (2)–(4) illustrate the energy scaling possibilities of MPCs. For standard MPCs [Eq. (2)], the energy scaling options are restricted to maximizing the ratio k/N→1, increasing the ROC of the mirrors R (which increases L proportionally at constant k/N), or increasing the threshold fluence Fth. In the case of CMPCs, energy scaling can be achieved differently. Since k/N is generally smaller, the energy acceptance for the same set of parameters R and Fth is typically reduced according to Eq. (3). Thus, the first step of scaling is achieved by adjusting R in Eq. (3) such that ECMPC=EMPC. This typically increases L, i.e., LCMPC>LMPC. The second step is to fold the beam by the factor Γ and decrease the length of the system by exploiting Leff=L/Γ.

To illustrate the discussion with an example, we use a typical set of parameters for a standard MPC with R=1m and a λ=1030nm, 1 ps level laser. The threshold fluence for quarter-wave-stack high-reflectance dielectric coatings can, e.g., be set to Fth=0.17J/cm2 (corresponding to the linear fluence in our experiment), leaving headroom to damage. With N=15 round-trips and k=14, we arrive at EMPC≤8.3mJ and a length of close to 2 m. To match the pulse energy acceptance of the CMPC to the MPC, we first set k=4, and increase the ROC to R=25m and the length to L=8.27m. Now folding the beam Γ=25 times, we arrive at ECMPC≤8.1mJ with an effective length of Leff=33cm. A second example is illustrated in Fig. 3. Here we refer to the works reported by Pfaff et al., where 200 mJ pulses have been compressed in a 10 m long MPC, with a fluence on the mirrors of approximately 0.5J/cm2 [29]. Figure 3 shows that the energy acceptance increases with larger folding ratio and effective system length. At 10 m length, a folding ratio of Γ=25 supports an energy of 700 mJ and at Γ=49, the accepted energy exceeds 1 J. At these parameters, the CMPC with 1 J energy acceptance and Γ=49 would require an ROC of R>1km with a focusing mirror diameter of 60 cm and a planar mirror size of 60cm×68cm [see Eqs. (A3)–(A5) in Appendix A]. In particular the large ROCs can become a limiting factor, as discussed in Section 4. Conversely, for a pulse energy of 200 mJ, the CMPC size can be scaled down to about 3 m or 1.5 m considering Γ=25 and Γ=49, respectively. As visible in Fig. 3, for Γ=1, the fully “unfolded” CMPC is generally longer than the standard MPC considering an identical threshold fluence for both cases. This is due to the fact that the CMPC operates in the L/R<1 regime while the MPC operates at L/R≈2.

A second limitation in MPCs, which we omitted in the above discussion, typically arises due to the peak intensity of the laser exceeding the ionization threshold of the gas in the MPC [15]. Due to the loose focusing geometry of the CMPC however, this problem is fully avoided here, as the limitation due to the LIDT of the coating typically sets in much earlier. For example, in the above discussed system with k/N=4/15 and R=25m, ionization of a gas with an ionization threshold of Ith=1×1013W/cm2 would set in at 478 mJ for 1 ps pulses [32].

Our experimental setup displayed in Fig. 4 uses a commercial innoslab Yb laser system (AMPHOS GmbH), delivering 1030 nm 1 ps pulses at a repetition rate of 1 kHz with a pulse energy of >8mJ. After suitable mode-matching, the beam is sent onto the pick-off mirror POM1 and into the CMPC [Fig. 4(B)]. The CMPC consists of two concave 4 inch mirrors with R=25m and two planar folding mirrors with size 10cm×10cm. The configuration is set to N=11 round-trips and k=3, which corresponds, according to Eq. (1), to an unfolded MPC length of L=8.63m. Following in-coupling at the pick-off mirror POM1, the beam is sent onto the planar folding mirror PM2 and is subsequently reflected by PM1, with both mirrors being aligned in a V-shaped configuration and separated by about 34 cm. The beam continues its path as described in Fig. 2, forming the typical CMPC pattern. A folding ratio of Γ=25 results in an effective CMPC length of Leff=34.5cm. However, due to spatial constraints, the two focusing mirrors FM1 and FM2 are placed a few centimeters behind PM1 and PM2, making the total CMPC length slightly larger, resulting in around 45 cm [see Fig. 4(B)]. After propagating N=11 round-trips (22 passes), the beam returns on PM1 and is coupled out with a different angle in the vertical direction. The total number of mirror reflections amounts to 2NΓ=550 and the total propagation length is roughly 190 m. We use ambient air at atmospheric pressure (1006 mbar) as the nonlinear medium for spectral broadening. Nevertheless, a chamber or housing is necessary to avoid beam fluctuations due to turbulences in air.

After out-coupling, the spectrally broadened beam is separated from the input beam with another pick-off mirror POM2 [Fig. 4(A)]. Here, we measure an output power of around 7.1 W and thus a total transmission of roughly 89%. This corresponds to a reflectance of the mirrors of at least 99.98% per reflection, disregarding clipping losses. Subsequently, a wedge is used for beam sampling, reflecting around 8%, corresponding to roughly 570 mW. The transmission of the wedge is sent onto a power meter. The wedge-reflected pulse is compressed using a chirped-mirror compressor with 26 reflections corresponding to about −5200fs2 of compensated second-order dispersion.

We analyze the compressed pulses using frequency-resolved optical gating (FROG) and measure the spectrum. In addition, the beam quality parameter M2 is analyzed using the same wedge reflection. We furthermore record input and output near-field pointing using the input/output mirror (Min) transmission of both input and output beams. For direct comparison of input and output, both cameras are placed in the exact same distance d=42cm from a common reference point z0, located at the vacuum chamber input window. The spectrum and FROG results are shown in Fig. 5. The input pulse has a pulse duration of about 1.1 ps with a Fourier-transform-limit (FTL) of about 1 ps. After spectral broadening in the CMPC, the output pulse FTL reaches 50 fs. Following compression, we reach 51 fs [Fig. 5(A)]. We simulate the spectral broadening process using the measured input pulse [Fig. 5(A)]. The simulations are conducted using our in-house developed (2 + 1)D radially symmetric simulation code based on Hankel-transforms in the spatial dimension, which is described in Appendix A [Eqs. (A1) and (A2)]. The simulated output pulse agrees very well with the measured output pulse, exhibiting similar temporal characteristics after compression. In both measurement and simulation, we observe a temporal pedestal likely stemming from uncompressed spectral components in the longer wavelength range. On the trailing edge, a post-pulse appears at around 800 fs, which we attribute to a pulse-breakup caused by the delayed response of the Raman-Kerr contribution in air. The measured and simulated spectra [Fig. 5(B)] also show similar characteristics as well as similar broadening, except for the strength of the side lobes compared to the background close to 1030 nm.

The molecular nature of air results in a broadened spectrum that qualitatively deviates from a typical “SPM-like” spectrum, obtained from atomic gases. We therefore conduct spectral broadening measurements in Krypton as well, in order to demonstrate typical SPM broadening and compare it with the simulations. Due to technical constraints originating from mechanical instabilities of the vacuum chamber, the chamber could only be operated at 1 bar pressure. We measure the spectral broadening with 6.5 mJ pulse energy and the results are shown in Fig. 6, where we reach an FTL of approximately 120 fs.

The beam path inside the CMPC involves 550 reflections and a long propagation path of about 190 m. The beam is particularly sensitive to displacements of the folding mirrors PM1 and PM2 (Fig. 4), where most of the reflections take place. Thus, it is important to characterize the stability of the beam. Figures 7(A) and 7(B) show the measured beam position stability for both input and output beams. We conduct the measurements separately within a few minutes. The measurements show only a very slight increase in the RMS beam position deviation of approximately 5% in the output, compared to the input. This demonstrates the spatial stability owing to the input-to-output imaging property of the CMPC, also known from standard MPCs. In addition, we measure the spectral stability of the system over 5 min [Fig. 7(C)]. We measure RMS fluctuations of the FTL of 0.33 fs, with a mean value of 50.9 fs, resulting in a relative RMS deviation of 0.65%, indicating that the spectral broadening is stable.

We further measure the beam quality parameter M2 of the input beam after the mode-matching telescope and the output beam. We observe a beam quality degradation from M2=1.36 at the input to 1.76 at the output at full power. As this observation may indicate spatio-temporal coupling (STC) effects, we decided to further investigate the spatio-spectral pulse characteristics using spatially resolved Fourier-transform spectrometry [36]. The STC measurements provide information about the spatially dependent spectral homogeneity of the pulse V(x,y), which we calculate via the spectral overlap integral as defined in Eqs. (A6) and (A7) in Appendix A. An average spectral overlap Vavg is then computed by weighting the V(x,y) with the fluence F(x,y) obtained from the same dataset and averaging over an area defined by the measured 1/e2 diameter of the beam. In air (Fig. 12, Appendix A), we measure Vavg=90.6% at full power, confirming a slight degradation of the spatio-spectral homogeneity compared to the input beam, which exhibits an almost perfect homogeneity of Vavg≈99%. We further investigate more generally how the spatio-spectral homogeneity behaves in atomic gases as a function of the input peak power P of the pulse, compared to the critical power Pc of the gas. The measurement is performed using Krypton as the nonlinear medium at 1 bar pressure and the same CMPC configuration is used as described in the beginning of this section. We carry out STC measurements at four different pulse energies and thus four different values for P/Pc and measure an STC trace for each point. Figure 8 summarizes the STC measurement results. From the first measurement point [Fig. 8(A)] at P/Pc≈0.4 to the third at P/Pc≈0.6, we observe a linear decline from 98.3% to 90.5%. The fourth point at P/Pc≈0.65 exhibits a stronger deterioration. We compare our results with simulations considering again the measured input pulse as input for the simulation. Here we observe an onset of homogeneity reduction [Fig. 8(A)] at approximately P/Pc=0.55 and an overall weaker deterioration compared to the measurements. However, the simulations reproduce the measured behavior qualitatively including the onset of homogeneity degradation at around P/Pc≈0.6 well. At P/Pc≈0.8, the simulations predict a beam collapse causing a sharp decline of Vavg. The faster degradation of the spatio-spectral homogeneity in the experimental data might be related to imperfect input beam characteristics in the experiment and/or possible spatial phase distortions arising due to many beam reflections on the CMPC mirrors.

For an example point at P/Pc≈0.6, the spatio-spectral distribution obtained via an STC scan is shown in Fig. 8(B). We compare the results with a spectrally broadened pulse from a standard gas-filled MPC with N=17, k=16, and R=1m at similar spectral broadening characteristics. The corresponding spatio-spectral distribution is shown in Fig. 8(C). Both measurements indicate rather homogeneous spatio-spectral characteristics and thus a similar spectral broadening performance for both MPC types, with Vavg=96.4% for the standard MPC and a slightly reduced Vavg=90.5% for the CMPC. We can further compare our measured Vavg values to another non-standard MPC, where a convex-concave MPC arrangement was used for spectral broadening. In Ref. [31], a value of Vavg=98% was achieved, albeit with a lower spectral broadening factor corresponding to compression from 260 fs to 50 fs (spectral broadening factor of approximately five) and in a solid medium. Another experiment using a convex-concave MPC and a solid medium yielded Vavg=90% [30], with a spectrum that supports 133 fs, starting from 670 fs. In the latter example, the bandwidth of the broadened spectrum is roughly similar to our measurements in air, where we measure Vavg=90.6%.

The CMPC enables post-compression for high pulse energies at compact setup length, tunable via the folding ratio Γ [Eq. (3)] while exhibiting excellent characteristics known from conventional MPCs. These include support for large compression factors, excellent beam quality and pointing properties, as well as high transmission efficiency. In principle, Γ can be increased to arbitrarily large values, enabling very compact systems. There are, however, practical limitations. The mirror size, in particular the length (corresponding to the x-dimension in Fig. 2), sets a limit on Γ [a mirror dimension estimate is provided in Eqs. (A3)–(A5) in Appendix A]. Increasing Γ also gives rise to a larger amount of total reflections. This can lead to a decreased throughput and lower efficiency of the system. The large number of reflections in a CMPC further restricts the mirror coatings to low GDD and at the same time high reflectivity. Typical coatings fulfilling these properties are quarter-wave-stack coatings with bandwidths supporting pulse durations of around 30 fs at 1030 nm. Consequently, post-compression to few-cycles cannot be achieved using the CMPC scheme. In our experiment we measure a throughput of 89% at 550 reflections corresponding to an average mirror reflectivity of >99.98%. Moreover, a large number of reflections can cause wavefront distortions, which we minimize by using mirrors with a high surface flatness of λ/20. Another factor that can restrict energy scalability is the radius-of-curvature of the mirror substrate. While mirrors with an ROC of 2 km can be manufactured [37], large ROCs can become more strongly affected by mirror distortions, such as mechanical stress or thermal effects, which could potentially limit the average power acceptance of the CMPC.

As discussed in Section 2 the CMPC scheme requires a regime where the beam inside the cell is loosely focused in order to enable beam folding on additional mirrors. This in turn fundamentally limits the amount of nonlinear phase ϕNL(1) that can be accumulated per pass to smaller values compared to a strongly focused geometry. In gas-filled MPCs, the accumulated Gouy phase per pass ϕNL(1) sets a theoretical limit on the nonlinear phase ϕNL(1)≤ϕG(1) [15], which is directly related to the MPC geometry via ϕG(1)=πk/N. In standard MPCs with k/N→1 this limit approaches ϕNL(1)=π, whereas in the CMPC typically k/N is lower. In our experiment, the configuration is set to N=11 and k=3 and thus ϕNL(1)≤0.27π. Getting close to this limit, the peak power approaches the critical power of the medium Pc and spatio-temporal couplings can become more pronounced leading to a sudden degradation of the spatio-spectral homogeneity. However, this effect is not necessarily a limiting factor for spectral broadening in a CMPC. The generally smaller ϕNL(1) in a CMPC can be compensated by simply employing more passes through the cell, while keeping the ratio k/N approximately constant. For both MPC types, operation at P<Pc ensures that excellent spatio-spectral and thus spatio-temporal pulse characteristics can be reached.

In our proof-of-principle experiment we demonstrate post-compression of 8 mJ pulses in a compact setup. However, we can further scale up the energy by increasing the mirror sizes as well as the radius-of-curvature R of the mirrors. As an outlook for high-energy CMPC operation, we simulate the post-compression of 200 mJ, 1 ps pulses at 1030 nm central wavelength in a CMPC using 50 mbar of argon as the nonlinear medium. We show that post-compression down to 80 fs can be achieved, with a transmission of almost 80%. Figure 9 summarizes the simulation results for this scenario, indicating excellent post-compression performance. Here, we assume a mirror reflectivity of 99.98% and consider the influence of the mirror on the spectral phase of the pulse. We include the effects of all reflections on the mirrors in the simulations, which amount to 2NΓ=1170. Using focusing mirrors with R=300m and folding mirrors of 35cm×35cm, a folding ratio of Γ=39 is achievable, assuming a clear aperture of five times the beam radius wm (see Appendix A Section A.2). In this case an effective length of the setup of 2.5 m can be reached. The calculated fluence on the mirrors is kept at roughly of 0.5J/cm2, including nonlinear self-focusing effects and nonlinear mode-matching taking into account Kerr lensing in the cell [38]. The peak power is kept at P/Pc<0.6, where we still measure Vavg>90% [Fig. 8(A)], in order to avoid strong spatio-spectral inhomogeneities and prospectively still achieve a good beam quality.

In conclusion, we introduce a novel multi-pass cell scheme enabling post-compression of high-energy laser pulses in a compact setup. The CMPC enables tuning and down-scaling of the setup size via beam folding using additional planar mirrors, using weakly focused cell modes. Instead of increasing the length of the setup, the folding ratio Γ acts as the energy scaling parameter. We demonstrate post-compression in air from 1.1 ps down to 51 fs in a CMPC with an effective length of 45 cm and a folding ratio Γ=25, while keeping the fluence comparable to a standard MPC supporting the same pulse energy but requiring around 2 m cell length. Further up-scaling options promise post-compression of pulses with an energy of 100 mJ and beyond in a table-top setup.

Acknowledgment. We acknowledge Deutsches Elektronen-Synchrotron DESY (Hamburg, Germany), the Helmholtz Institute Jena (Jena, Germany), and members of the Helmholtz Association HGF for support and/or the provision of experimental facilities.