Supplementary Materials for

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1 advances.sciencemag.org/cgi/content/full/4/4/eaaq1526/dc1 Supplementary Materials for Multi-watt, multi-octave, mid-infrared femtosecond source Marcus Seidel, Xiao Xiao, Syed A. Hussain, Gunnar Arisholm, Alexander Hartung, Kevin T. Zawilski, Peter G. Schunemann, Florian Habel, Michael Trubetskov, Vladimir Pervak, Oleg Pronin, Ferenc Krausz This PDF file includes: Published 20 April 2018, Sci. Adv. 4, eaaq1526 (2018) DOI: /sciadv.aaq1526 section S1. Seed generation in highly nonlinear all-normal dispersion fiber section S2. Beam distortions in the PPLN OPA section S3. Compression of the MIR pulses centered at 4.1 μm section S4. Supercontinuum generation section S5. LGS OPA fig. S1. OPA setup with FROG. fig. S2. All-normal dispersion fiber noise. fig. S3. Irradiance enhancement in the PPLN OPA. fig. S4. X-FROG measurements. fig. S5. Simulation of continuum generation in ZGP. fig. S6. Properties of the supercontinuum generated by cascaded quadratic nonlinearities in ZGP. fig. S7. Linear optical properties of LGS. fig. S8. LGS OPA simulations. fig. S9. Occurrence of LGS crystal damage at various input powers. References (42 62)

2 section S1. Seed generation in highly nonlinear all-normal dispersion fiber Continua generated in normally dispersive fibers typically exhibit high coherence due to the saturation of spectral broadening, and thus insensitivity to intensity noise of the input beam in contrast to anomalously dispersive fibers where modulation instabilities as well as sensitivity to phase noise lead to low pulse-to-pulse repeatability for high soliton orders (42). Large mode area fibers, like ESM12 used for the LGS seed generation, exhibit the (normal) dispersion of fused silica. They have therefore been used to precompress pulses prior supercontinuum generation in the NIR, for example. Initially, highly nonlinear, but also all-normal dispersive (ANDi) fibers were claimed to maintain full coherence even upon supercontinuum generation with 300 fs input pulses (43). The claim, however, originated from simulations which neglected the slight birefrigence of the non-polarization maintaining ANDi fiber (NL-1050-Neg-1, NKT Photonics). The resulting polarization instabilities led to an incoherent supercontinuum even for 230 fs input pulses (38). However, the polarization maintaining version of the ANDi fiber (NL-1050-Neg-PM, NKT Photonics), which was also used for seeding the PPLN OPA, improved the coherence of the output spectrum significantly - at least for a spectral extension up to 1300 nm as shown in ref. (38). For the presented experiments, a spectral extension to about 1400 nm was necessary to generate MIR around 4 µm (cf. Fig. 2 main text). Therefore, the stability of the fiber output was revised and noise measurements were recorded at the positions I and II that are indicated in fig. S1(A). Continuum generation in a non-polarization maintaining ANDi fiber (17 cm length) confirmed the results of ref. (38). This is indicated by the black solid line in fig. S2(A). It exhibits clearly stronger modulations than the continuum generated from the polarization maintaining fiber (red solid line). Using the NL-1050-Neg-PM consequently also led to a 25 % increase in MIR output power at 4.1 µm. To generate the broad continua shown in fig. S2(A), tight focusing to peak irradiances exceeding 2 TW/cm 2 at the fiber entrance surface was necessary. This resulted in degradation of the front facet after a few weeks of operation. However, after collapsing the air holes at the front facet, the highly nonlinear fibers did not have to be exchanged during the course of the experiments. The length of the collapse was about 50 µm. (A) (B) λ/2 (1) t TFP pump λ/2 (2) OC POL λ/2 (4) b. λ/2 (3) TFP seed ANDi fiber DM λ/2 (5) PPLN I reference II Si BS MIR Si Si Sa CaF 2 ZGP t D-shape FROG D-shape t Par LGS FCS fig. S1. OPA setup with FROG. (A) About W of the oscillator output (i.e. 2% of the total output) was used as a reference beam. In order to not saturate the fiber-coupled spectrometer (FCS), λ/2 (1) was adjusted. The optics in the box with the dashed blue outline show the pulse compression stage before supercontinuum generation. They were only placed after the compression of the OPA MIR output. The setup indicates positions I and II where the seed fluctuations prior and after amplification were measured. At position II, pump and MIR were blocked by a 1030 nm high reflective mirror coated on a silica substrate. (B) Detailed FROG setup. The D-shape mirror is moveable. It may split the wavefront of the reference beam which allowed to measure second harmonic FROG of the reference before conducting X-FROG measurements. In its shown position, the mirror reflects the full NIR beam while the MIR is transmitted to a piezo-actuated translation stage. Both beams are noncollinearly overlapped in a 110 µm thin LGS crystal. The resulting sum-frequency is focused with a spherical silver mirror into a multimode fiber coupled to a grating spectrometer. All reflective optics, including the parabolic mirror (Par), are silver mirrors. Apart from the nonlinear crystal, the FROG was not comprised of any transmissive optics which implies that it enabled measuring ultrashort pulses and that it could be utilized for characterizing spectra from the ultraviolet (by using a wide band gap nonlinear crystal) to the MIR.

3 fig. S2. All-normal dispersion fiber noise. (A) Spectra of non-polarization maintaining (black line) and polarization maintaining ANDi fibers (red and blue lines). The red spectrum was used for seeding the OPA. The spectrum is clearly less modulated than the spectrum of the non-polarization maintaining fiber, exhibiting better coherence. The blue spectrum shows a distinct spike between 1400 nm and 1450 nm which is not connected to the self-phase modulation broadened spectrum around the central wavelength. It is not predicted in simulations. (B) Stability of the fiber continuum emerging from a 20 cm long polarization maintaining ANDi fiber. It was measured with a thermal detector taking one data point every two seconds. (C) Stability of the MIR at 4.1 µm (red curve). The OPA was pumped with the full oscillator power. A minimal leakage not reflected by the thin-film polarizer ( 230mW) was recorded in parallel (gray curve). The power meter (Coherent LM-200XL) that otherwise measured the full oscillator power was used. At mw levels, it is very noisy itself, but clearly exhibits fluctuations with an about 10 min period. Similar fluctuations are also present in the seed power ((B), not measured in parallel) and the MIR power. The curves of (C) were measured with thermal detectors taking one data point every second. (D) - (F) Pulse-to-pulse fluctuations of the full seed spectrum (D), the amplified seed above (E) and below (F) the spectral noise threshold (both at full pump power). The traces span over a 10 µs time window corresponding to a train of 375 pulses. Data was taken with a GHz bandwidth InGaAs diode (responsive from 900 nm to 1700 nm) and sampled with a digital oscilloscope at a rate of s 1. The root mean square (RMS) value was calculated from the peak voltages marked with a red cross akin to the characterization in ref. (44). The power fluctuations of the polarization maintaining fiber output ( fig. S2(B), recorded at position I of Fig. S1(A)) and the 4.1 µm radiation at maximal pump power (fig. S2(C)) were measured. The fluctuations for both measurements are below 1 % RMS and seem to be mainly influenced by slow periodic drifts of the thin-disk oscillator. The pulse-to-pulse fluctuations of the fiber output measured with a fast InGaAs diode were below a 1 % RMS value as well ( fig. S2(D), also recorded at position I of fig. S1(A)). However, a spontaneous onset of strong pulse-to-pulse fluctuations was observed after amplification of the seed if 1.5 W of average power were incident on the polarization maintaining ANDi fiber (fig. S2(E), recorded at position II of fig. S1(A)). It is inferred, that despite the low relative intensity noise of the seed, it is prone to exhibit strong spectral noise. Crucially, the observed fluctuations did not continuously increase with input power but exhibited a threshold. Consequently, the OPA was operated below this threshold (fig. S2(F), also recorded at position II of fig. S1(A)) where pulse-to-pulse fluctuations of 1 % RMS were determined. This was realized by means of the half-wave plates (2) and (4) shown in fig. S1(A). The half-wave plate (2) was used in combination with a polarizing beam splitting cube for attenuating the input power at the fiber. The half-wave plate (4) was used for adjusting the light polarization with respect to the fiber s slow axis. A precise characterization of input polarization and power has not been performed. The optimization was done by monitoring the amplified pulse train with the InGaAs photodiode. The MIR power emerging from the OPA was not affected by this routine. 2/9

4 (A) (B) (C) (D) (E) (F) fig. S3. Irradiance enhancement in the PPLN OPA. (A) Simulated peak irradiances within the PPLN crystal for the seeded (red solid line) and the unseeded (blue solid line) OPA at 45 W pump power and 300 µm spot size. The seed leads to a considerable irradiance enhancement of more than a factor of two which is reached after about 2.2 mm of propagation. If the χ (2) nonlinearity is turned off, the solely n 2 induced self-focusing of the unseeded OPA becomes visible after about 4.5 mm of propagation, but is clearly less pronounced. The modulations of the peak irradiances result from interferences of the co-polarized beams. Although a damage threshold of about 50 GW/cm 2 was determined for the PPLN, the peak irradiance at the input facet was set to only 13 GW/cm 2 to account for the self-focusing effect. (B) Measured pump beam profile behind in the OPA in the presence of the seed and (C) without the presence of the seed. Both profiles were measured with a CCD camera. (D) Collimated MIR profile at 20 W pump power and (E) at full pump power. Both profiles were measured with a pyroelectric array detector. (F) Focused MIR beam lineouts at full pump power measured with a pyroelectric rotating slit scanner. The spot diameters are about 30 µm in x- and y-direction. A plano-convex silicon lens with a 25 mm focal length was used to focus the beam emerging from the OPA. The origin of the spontaneous fluctuation onset is unknown. It has not been reported in ref. (38). The paper also did not present the pronounced spike in the spectrum between 1400 nm and 1450 nm which is visible in blue spectrum of fig. S2(A). Neither the origin of this spectral feature, nor if there is a connection to the onset of strong fluctuations has yet been clarified. It was not investigated further since the primary interest within the scope of this paper was the stability of the MIR which was good after the described adjustments. section S2. Beam distortions in the PPLN OPA Recent studies on PPLN OPAs, utilizing pump pulses with hundreds of µj energies and sub-mhz repetition rates (40-80 W average power), have revealed strong pump beam distortions. These were attributed to high average power and photorefraction in ref. (45) and predominantly to high peak power in ref. (46). The latter distortions were qualitatively also apparent in the presented experiments, but were taken into account when choosing an appropriate spot size for efficient pumping. The simulation results shown in fig. S3(A) demonstrate in accordance with the observations in ref. (46) a strong peak irradiance enhancement in the presence of the weak seed (carries about 1 % of the input power). A typical self-focusing induced beam pattern (cf. e.g. ref. (47)) of the pump radiation was observed when the OPA was seeded at high pump powers (fig. S3(B)). If the temporal overlap of pump and seed was removed, the ring pattern almost completely vanished (fig. S3(C)), manifesting the instantaneous nature of the distortion. Since the conducted simulation did neither include thermal lensing, nor photorefraction, nor green induced infrared absorption, it is inferred that the parasitic effect originates from cascaded quadratic nonlinearities which were accounted for in the propagation code. Most importantly, the influence of the effect on the MIR beam is not nearly as strong as on the pump beam. Fig. S3(D) shows the MIR beam profile at 20 W of pump power, exhibiting a desirable Gaussian shape. At full pump power (fig. S3(E)), some of the MIR power is pushed into wings of the beam, but, as the line-outs show, most of the power is still concentrated in the central bell-shaped part. Notably, the beam could be focused well as fig. S3(F) displays. This was in particular crucial for the nonlinear spectral broadening and supercontinuum generation experiments which were performed with the MIR. section S3. Compression of the MIR pulses centered at 4.1 µ m The MIR pulses were characterized by X-FROG (cf. fig. S1). The MIR radiation was up-converted in a 110 µm thick LGS crystal. Pulse compression was achieved by adding material dispersion. A 5 mm thick Si window was used to compensate for the chirp of the beam splitter s CaF 2 substrate and the OPA. The pulses were compressed to about 140 fs which is close to 3/9

5 fig. S4. X-FROG measurements. (A) Measured and retrieved FROG traces of the OPA output after dispersion compensation. The grid size was 512 2, the residual FROG error 0.5 %. No marginal was enforced for the FROG retrieval. (B) Comparison between the retrieved FROG spectrum and the spectrum measured with an FTIR (Bristol 721). The blue shoulder is slightly more pronounced in the FROG retrieval. Otherwise, the agreement is very good. (C) The dispersion of 5 mm silicon compresses the MIR pulses close to their Fourier transform limit (FTL). Just a small pedestal is formed on the leading edge of the pulse. (D) Measured and retrieved FROG traces of the spectrally broadened MIR pulses after dispersion compensation. The grid size was 512 2, the residual FROG error 0.5 %. No marginal was enforced for the FROG retrieval. The traces show that the central part of the MIR spectrum is not ideally in phase with respect to the broadened parts. That is a typical phenomenon of single-stage bulk compression (cf. ref. (47)) (E) Comparison between the retrieved FROG spectrum and the spectrum measured with an FTIR (Lasnix L-FTS). The peak of the X-FROG spectrum is red-shifted and the CO 2 absorptions are more pronounced (due to longer propagation to the nonlinear crystal than to the FTIR detector). Otherwise, the agreement is also good. The Fourier transform limits are nearly identical. (F) Pure material dispersion also led to a good compression of the spectrally broadened pulses which are nearly Fourier limited as the comparison of the red and the black curve shows. the Fourier transform limit of the measured FTIR spectrum (fig. S4(C)). The X-FROG RMS error was 0.5 %. The spectra measured with X-FROG and a spectrometer are compared in fig. S4(B). When attempting to generate a supercontinuum with the 140 fs pulses after focusing with a f=25 mm Si lens into a 2 mm thick ZGP crystal, spectral broadening from about 3.5 µm to 5 µm at about -20 db of the maximum power spectral density and from 5 µm to 7 µm at about -30 db of the maximum power spectral density was observed. An additional pulse compression stage helped to increase the power spectral densities of the broadband MIR radiation clearly (cf. Fig. 5 main text). Bulk spectral broadening was utilized to reduce the pulse duration by a factor of two. Despite the moderate peak power of about 750 kw, highly nonlinear materials like silicon or GaAs led to spectral broadening. The broadest spectra could be reached with an entirely phase-mismatched 3 mm thick ZGP crystal (ASCUT Ltd & Co KG) and an 80 µm spot diameter. It is shown in fig. S4(E). The crystal had to be placed into the focus due to the short Rayleigh length of only about 1 mm. The phase of the uncompressed pulses was measured with the X-FROG and afterwards compressed by means of material dispersion. A 2 mm thick sapphire and a 5 mm thick CaF 2 plate were used for this purpose. The FROG traces are shown in fig. S4(D) and the retrieved, nearly Fourier transform limited pulse in fig. S4(F). No particular attention was paid to the beam profile emerging 4/9

6 from the broadening stage like in ref. (47). However, owing to the small broadening factor, the beam could be still focused well by a plano-convex silicon lens to a diameter of about 80 µm in order to trigger supercontinuum generation. section S4. Supercontinuum generation Rather established continuum generation schemes for wavelengths longer than 5 µm could not be transferred to the MIR sources presented here. For instance, chalcogenide fibers yielded spectral coverage from about µm (32,50). The fibers, however, performed clearly worse when pumped with MHz sources since small core diameters led to a low power damage threshold (51) and larger diameters only to moderate spectral broadening (52). On the contrary, both the ZGP crystal (30) and spectral broadening based on quadratic nonlinearities (34) are capable of high average power handling. Supercontinuum generation in bulk materials also does not require any sensitive coupling of the free beam transversal mode to a waveguide mode, and is thus straight forward to employ. On the other hand, the spectral homogeneity of the beam shows the typical features of bulk broadening (47). Cascaded quadratic nonlinearities allow suppressing these inhomogeneities (34), but this was not explicitly investigated in the experiments presented here. Another common approach to generate MIR supercontinua, namely filamentation (33), requires free carriers, i.e. absorption and subsequently heat dissipation. Moreover, the method has only been demonstrated with at least MW peak powers. In addition, filamentation leads, due to self-steeping, to a strong spectral blue shift. Beam collapse and filament formation can be avoided by means of cascaded quadratic nonlinearities since the tuning of the phase-mismatch between fundamental and second harmonic allows to obtain a negative (defocusing) effective cubic nonlinearity (53). Moreover, the self-steepening effect is controllable (54) which enabled more pronounced broadening towards longer wavelengths, and subsequently the overlap of the supercontinuum with the spectrum generated from the LGS OPA. In the context of spectral broadening beyond the multi-phonon absorption edge of oxide crystals, the usage of cascaded quadratic nonlinearities has mainly been discussed for strongly phase-mismatched (non-resonant) crystal orientations which require energetic pulses or waveguides (55,56). The publications showed that utilizing self-defocusing nonlinearities, i.e. effective negative nonlinear refractive indices n 2, led to broad, coherent continua with significant spectral extension towards longer wavelengths. Near-resonant quadratic nonlinearities can give rise to effective n 2 values which are orders of magnitude larger than pure Kerr nonlinearities. This is due to the deff 2 / k scaling where d eff is the effective χ (2) nonlinearity and k is the phase-mismatch per unit length of the incoming wave and its second harmonic (53). For ZGP, d eff = 71 pm/v for type I second harmonic generation of 4.1 µm results in an effective n 2 of about cm 2 /W at the tuning angle θ = 55. The Kerr effect of ZGP is estimated by n Kerr 2 = cm 2 /W (48), and thus significantly smaller. The huge nonlinearity has been very recently identified as the cause for broadband idler generation in a ZGP OPA pumped with mj pulses at 2.1 µm wavelength (57). Here, it is directly employed in supercontinuum generation around the central MIR wavelength of 4.1 µm. fig. S5. Simulation of continuum generation in ZGP. (A) Spectral evolution of the continuum (left: second harmonic, right: fundamental). Most of the spectral width is acquired within the first 1 mm of propagation. The spectrum covers the full transparency range of ZGP. (B) Simulated output spectrum with a -30 db width from 1.8 µm to 8.8 µm. It is qualitatively comparable to the experimental spectrum shown in Fig. 5 of the main text. The simulation included χ (2) - (d eff = 70.8 pm/v (27)) and χ (3) -nonlinearity (n 2 = cm 2 /W (48)), linear absorption and dispersion according to the crystal s Sellmeier equation (49). The tuning angle θ = 55 in the simulation corresponded to the cut angle of the birefrigent crystal that was used in the experiment. As input, the retrieved pulse after the first compression stage was used, carrying an energy of 53 nj. A Gaussian beam was launched on a spatial grid of points, each 7.5 µm 7.5 µm in size. Two frequency grids from 0 to 200 THz as well as from 100 THz to 300 THz were factored out. Each contained 512 points. Propagation to the detector was not included in the simulation. 5/9

7 fig. S6. Properties of the supercontinuum generated by cascaded quadratic nonlinearities in ZGP. (A) Simulated spectral widths for different input powers, the pulses of Fig. S4(F), a 2 mm thick ZGP crystal and a beam waist of 40 µm located at the entrance facet of the crystal. The increase in spectral width is practically linear for input powers larger than 600 mw. An exception occurs for the 30 db width. It exhibits a discontinuity at 1.5 W input power since the spectral side lobe, which is centered around 7.8 µm in Fig. S5(B), exceeds the -30 db threshold. (B) Simulated peak irradiances and pulse durations for 2 W input power. All other parameters are as in (A). The peak irradiance only moderately changes inside the 2 mm thick ZGP crystal. Due to negative effective n 2 and normal dispersion at the central wavelength, the pulses gently self-compress. The peak irradiance is calculated from the sum of the orthogonally polarized fundamental and frequency-doubled beams, whereas the pulse duration of the fundamental is shown. (C) Simulated RMS spectral widths and peak irradiances for varying crystal thicknesses. The beam waist is adjusted such that the free-space Rayleigh length is half of the crystal thickness. All other parameters are as in (B). Maximal spectral broadening is reached at a crystal length of 4 mm with a maximal peak irradiance of only about 15 GW/cm 2. (D) Measured far-field beam profile of the fundamental. No signs of filamentation are apparent. The profile is distorted by the degradation of the utilized thermopile camera, especially in the bottom-right corner. The second harmonic was filtered by an optical long pass with cut-on wavelength at 3.6 µm. (E) Simulated far-field profile for a perfect Gaussian input beam and simulation parameters like in (B). The wavelength averaged beam profile is excellent. (F) If the near-field beam is spectrally resolved at the center of the vertical axis (y = 0), inhomogeneities become apparent. They originate from spatio-temporal coupling of the effective χ (3) nonlinearities. (G) The normalized line-outs at 4 µm and 6 µm wavelength show that the longer wavelength is primarily generated in the beam center where the irradiance is maximal. The emergence of a supercontinuum was initially predicted by simulations whose results are shown in fig. S5. The simulations were also performed with the SISYFOS package in a very similar manner like those described in ref. (34). They included quadratic and cubic nonlinearities, but no plasma term which significantly contributes to filamentation continua (58). The simulated output spectrum (fig. S5(B)) agrees qualitatively well with the measured one presented in Fig. 5 of the main text. There are two main peaks. One at the central frequency at 4.1 µm and the other at its second harmonic. Moreover, the power spectral density exhibits a minimum between 2.5 µm and 2.75 µm. Most importantly, the spectrum broadens also significantly towards longer wavelengths which allows to close the spectral gap to the output of the LGS OPA. The simulations predict an even stronger extension into the long wavelength infrared: at the -30 db level to 8.8 µm and at the -50 db level (shown in fig. S5(A)) even over whole transparency range of ZGP (30). A reason for this discrepancy could be the unexpected nonlinear absorption of the crystal which amounted in about 20 % transmission loss when ZGP was moved into the focus. There are several reasons for this reduced transmission: Firstly, linear absorption sets in at wavelengths below 2 µm, overlapping with the spectral range of the broadband second harmonic (30). Secondly, the crystal was anti-reflection coated in the range from 2.04 µm µm and from 2.8 µm - 6 µm. The continuum, however, exceeded this range which caused additional reflection losses. Thirdly, the supercontinuum extended the spectrum 6/9

8 to regions of strong water vapor absorptions. Nevertheless, since most of the spectral power is concentrated around 4 µm, another mechanism must be present resulting in the high transmission losses. GaAs was tested as an alternative material for supercontinuum generation. In this case, a prominent blue shoulder was observed, indicating free carrier generation and consequent self-steepening. A nonlinear transmission loss of about 30 % was determined in this case. Since the laser peak power was on the order of the critical power of GaAs and the photon energy was only about 20 % of the semiconductor band gap, neither beam collapse nor significant multi-photon absorptions were expected. However, it is known that the carrier lifetime of GaAs is on the ns order which corresponds to the oscillator repetition rate and causes cumulative effects resulting in enhanced sample conductivity and hence absorption (59). The issue was solved by modifying the GaAs growth process and introducing additional material defects which led to carrier recombination times on the ps order (59). Similar cumulative effects are suspected to be present in ZGP. Removing those, for instance by also introducing a fast trap mechanism, would be beneficial for MHz rate supercontinuum generation with respect to a presumably extended spectral coverage of the long wavelength infrared and higher spectral stability of the continuum. Additional simulations have been conducted to study further details of the supercontinuum generation. Firstly, the dependence of the spectral width on the input power was investigated. fig. S6(A) demonstrates that the bandwidth rises linearly for input powers exceeding 600 mw. For lower powers, the slope is larger which is attributed to the negative effective nonlinear refractive index (34). This defocusing nonlinearity also prevents the beam from collapsing. This is shown in fig. S6(B) where the peak irradiance and the pulse duration is plotted over the 2 mm propagation length in the ZGP crystal. By contrast to propagation in self-focusing media (34,47), the peak irradiance hardly exceeds its value at the front facet. It is modulated due to the phase-mismatched conversion to the second harmonic. Moreover, a correlation to the pulse duration is apparent. The pulses gently self-compress inside the medium because of the the normal dispersion of ZGP at 4.1 µm. Only 2 mm thick crystals were available for our experiments. Somewhat longer crystals appear, however, to be more favorable for the given pulse parameters as fig. S6(C) demonstrates. The graph presents how spectral width and maximal peak irradiance inside the crystal depend on the crystal length. The simulations utilized the experimentally obtained pulses and the boundary condition that the crystal thicknesses are twice the free-space Rayleigh lengths of the launched Gaussian beams. The strongest spectral broadening is obtained for a 4 mm thick crystal, although the peak irradiance is clearly lower than for the used 2 mm thick one. The predicted output pulse duration of 46.5 fs for a 4 mm crystal is close to the minimum of 43.2 fs which was predicted for 3 mm thickness. An optimization for self-compression (55) or spectral homogeneity of the output beam (34) was beyond the scope of the presented work. In agreement with the predicted peak irradiances inside the 2 mm thick crystal, the measured beam profile (fig. S6(D)) does not exhibit signs of beam filamentation (58). It was somewhat distorted by astigmatism introduced by the sequence of infrared optics, in particular the collimating parabolic mirror. By contrast, the simulated far-field profile (fig. S6(E)) predicts an excellent output beam for a perfect Gaussian input. If the emerging beam is, however, spectrally resolved (shown in the near-field in fig. S6(F)), inhomogeneities become apparent. Those are typical for single-stage bulk spectral broadening where spatial and temporal nonlinearities are coupled (34,46). Essentially, the spectrum broadens stronger in the center of the beam where the irradiance is higher. The two line-outs in fig. S6(G) highlight this. The profile at the incoming wavelength of 4 µm is wider than that of the generated wavelength at 6 µm, resulting in stronger divergence of the longer wavelength. fig. S7. Linear optical properties of LGS. (A) Transmission measurements of a 1 mm (red solid line) and a 150 µm (blue solid line) thick LGS crystal. The thinner crystal exhibits fringes due to the etalon effect. These were used to determine the crystal thickness precisely. The black solid line shows the computed Fresnel losses for slow axis at the crystal cut angles θ = 48.3 and φ = 0. The line becomes dashed where no Sellmeier equations for LGS are specified. (B) Extracted linear absorption coefficient (α) of the 1 mm thick LGS. (C) Extracted linear absorption coefficient (α) of the 150 µm thick LGS. (D) Phase-matching curves based on the Sellmeier equations provided in ref. (29) for frequency down-conversion of 1030 nm pump light. For type I phase-matching θ is varied while for type II phase-matching φ is varied. 7/9

9 section S5. LGS OPA LGS was introduced as a crystal for nonlinear optics in 2003 (29) and is not nearly as established as LiNbO 3. To the best of the authors knowledge, the first LGS OPA pumped around 1 µm wavelength has been presented here. Therefore, the optical properties of the crystal are briefly reviewed: The transmission of the crystal in the MIR was determined by FTIR measurements (figs. S7(A)-(C)). The absorption coefficients agree well with those presented in ref. (29). The refractive indices and effective quadratic nonlinearities were extracted from ref. (29,60). The published data refers to room temperature measurements while the crystals were heated to about 60 C in the experiments. This could explain the blue-shift of the experimental spectra with respect to the simulated ones. The biaxial crystal LGS allows multiple phase-matching conditions. While type I phase-matching was used in ref. (13), yielding d eff 4.6 pm/v for the crystal angles θ = 48.3, φ = 0, type II phase-matched crystals were also investigated in the presented experiments owing to their higher figure of merit (d eff 6.0 pm/v for θ = 90, φ = 38.6 ) (60). The phase-matching curves in both cases are shown in fig. S7(D). The plots reveal turning points of the respective tuning angles, enabling very broad phase-matching bandwidths in their vicinities even for thick crystals. The wide transparency range and the favorable dispersion when pumped around 1 µm makes LGS unique among commercially available nonlinear crystals. The simulation results shown in figs. S8(A) and (B) predict that the crystal can generate broadband MIR radiation with Fourier transform limits corresponding to two to three optical cycles at hundreds of mw up to Watt level average powers for both types of phase-matching. This is in good agreement with the experimental results presented in the main text. The simulation results show that type I phase-matching leads larger bandwidths (turning point of phase-matching curve is blue-shifted, cf. fig. S7(D)) while type II phase-matching results in higher output power (due to the higher d eff ). fig. S8(C) shows a set of simulated MIR spectra which correspond roughly to the spectra shown in Fig. 4(B) of the main text. Except from the blue shift, the experimental curves reproduce the simulated ones well. In particular, the splitting of the spectral peaks is apparent in both graphs. It is a direct consequence of the phase-matching curves shown in fig. S7(D). The available crystal quality of LGS is inferior to that of PPLN from our experience. While the latter was not damaged a single time during the course of the experiments (i.e. for more than two years), multiple LGS crystals were destroyed at a huge range of peak irradiances as fig. S9 illustrates. The lowest encountered damage is only at 1 % of the specified irradiance threshold of ref. (13). Damage threshold measurements for LGS were also conducted with ns pulses at khz repetition rates (61). In this case the three tested crystals exhibited a very similar damage fluence (< 15% deviation). Anti-reflection coatings rather slightly increased the fluence where surface damage set in. An OPO containing an 8 mm thick was pumped six times below the damage threshold at a peak irradiance of about 550 MW/cm 2. Scaling this value with the square root of pulse duration law, yields 36 GW/cm 2 for 230 fs pulses and is in good agreement with the maximal peak irradiance of the experiments presented here. Other femtosecond source studies also pumped the crystal at least with 50 GW/cm 2 (60,62). Therefore, the described issue with the strongly varying damage threshold does apparently not stem from fundamental limitations of the crystal itself, but from its scarce availability at constantly high quality. While PPLN can be obtained from multiple suppliers and the most common poling periods can be delivered within a few weeks, the authors are only aware of one LGS supplier worldwide fig. S8. LGS OPA simulations. MIR power and Fourier transform limit (FTL) as a function of tuning angle for (A) a 7 mm long type II phase-matched LGS crystal and (B) an 8 mm long type I phase-matched LGS crystal. More efficient down-conversion is expected from type II phase-matching due to the higher figure of merit. Type I phase-matching predicts, however, a slightly lower Fourier transform limit near the tuning angle for maximal idler power and sub-2-cycle pulse bandwidth at clearly lower conversion efficiencies. (C) Simulated tuning curve for type I phase-matching. The tuning angles θ are chosen such that a direct comparison to the measured spectra presented in Fig. 4(B) of the main text is possible. Due to the phase-matching of two MIR wavelengths at the same tuning angle (cf. fig. S7(D)), the spectra exhibit two peaks for tuning angles smaller than θ = The spectra of the two perfectly phase-matched wavelengths overlap in the center at around 8.6 µm. A similar behavior is predicted for type II phase-matching at a red-shifted central frequency (cf. fig. S6(D)). A pump power of 28.8 W was set in both simulations. 8/9

10 fig. S9. Occurrence of LGS crystal damage at various input powers. The simulated curve that relates the pump power to the peak irradiance inside the crystal is shown as a black line with dots at the simulated points. The blue (red) stars show the pump powers at which the 7 mm to 8 mm long uncoated (coated) crystals were damaged. Anti-reflective coatings for NIR at the front facet and MIR at the rear facet were used. The pump power where damage occurred varies by a factor of two while the simulation predict that the peak irradiance where damage occurs varies even by a factor of six. (ASCUT Ltd & Co KG) at present and delivery usually takes several months. In conclusion, the LGS crystal has revealed outstanding properties for direct frequency down-conversion of 1 µm radiation to the deep MIR, resulting in the by-far highest power femtosecond laser source which has been presented at wavelengths longer than 5 µm. Yet, a further evolution towards higher reliability and better availability of the crystal would be desirable in order to establish it as a standard tool. 9/9