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1 Non-collinear generation of angularly isolated circularly polarized high harmonics Daniel D. Hickstein 1, Franklin J. Dollar 1, Patrik Grychtol 1, Jennifer L. Ellis 1, Ronny Knut 1, Carlos Hernández- García 1,2, Dmitriy Zusin 1, Christian Gentry 1, Justin M. Shaw 3, Tingting Fan 1, Kevin M. Dorney 1, Andreas Becker 1, Agnieszka Jaroń- Becker 1, Henry C. Kapteyn 1, Margaret M. Murnane 1, and Charles G. Durfee 1,4 1 JILA Department of Physics, University of Colorado and NIST, Boulder, Colorado 80309, USA 2 Grupo de Investigación en Óptica Extrema, Universidad de Salamanca, E Salamanca, Spain 3 Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA 4 Department of Physics, Colorado School of Mines, Golden, CO 80401, USA Section 1. Comparison of two- pulse HHG methods Figure S1 Comparison of two- pulse high harmonic generation (HHG) methods. a, Noncollinear HHG with linearly polarized pulses 1 3 produces a fan of harmonics, all linearly polarized. b, Newly developed noncollinear circularly polarized HHG (NCP- HHG) produces circularly polarized, angularly separated harmonics. c, NCP- HHG with different frequency driving lasers also produces angularly separated circularly polarized harmonics, but with the left and right circularly polarized beams at different harmonic orders. d, Two- color- collinear HHG 4,5 produces circularly polarized harmonics that co- propagate with the fundamental, requiring a filter to block the driving laser beams. In the manuscript, we present a new method for high harmonic generation (HHG), namely noncollinear circularly polarized high harmonic generation (NCP- HHG), which uses two counter- rotating circularly NATURE PHOTONICS 1

2 polarized laser beams to generate circularly polarized high harmonics. Fig. S1 presents a comparison of the NCP- HHG method with related methods of HHG, demonstrating how it fits into the larger landscape of two- pulse driven HHG. Several previous studies 1 3 have investigated noncollinear harmonic generation with linearly polarized beams (Fig. S1a). Since the beams are linearly polarized, many mixing options are possible and each harmonic can be emitted at many angles. In contrast, the NCP- HHG method (Figs. S1b,c) introduces an additional selection rule, which restricts the output to just two beams for each harmonic order, allowing the harmonics to be angularly separated without a spectrometer. Additionally, circularly polarized harmonic beams are produced with opposite helicities, allowing for the implementation of spectroscopy techniques such as magnetic circular dichroism (MCD) or photoelectron circular dichroism. In contrast to the NCP- HHG method, previously established methods of collinear circularly polarized HHG 4,5 produce a single beam of EUV light that contains both left and right circularly polarized harmonics at different frequencies (Fig. S1d). The NCP- HHG method is distinct from the previous HHG schemes of attosecond lighthouse 6,7 (AL) or noncollinear optical gating 3,8 (NOG). AL and NOG produce angularly separated HHG beams that consist of isolated attosecond pulses that are linearly polarized. In contrast, the NCP- HHG method produces angularly separated HHG beams that consist of circularly polarized light of the opposite helicity. Under some conditions, the NCP- HHG technique may additionally separate the beams by the harmonic order. The AL and NOG methods provide a gating mechanism, whereby isolated attosecond pulses can be obtained from several- cycle driving laser pulses that would otherwise produce a pulse train. In contrast, NCP- HHG offers no such gating mechanism. But, if the NCP- HHG process is driven with very short duration pulses, the NCP- HHG method is predicted to be capable of producing the first circularly polarized isolated attosecond pulses (Fig. 6d). Section 2. Spatially separated harmonics using NCP- HHG with UV driving lasers The NCP- HHG method is capable of producing angularly separated harmonics across a wide range of driving laser wavelengths. However, the lower phase- matching pressures and larger separation angles of UV- driven NCP- HHG mean that full angular separation of the harmonics is easiest to experimentally achieve using driving lasers in the UV spectral region. Using two 267 nm driving laser beams in argon gas, we demonstrate that NCP- HHG generates four separate beams (Fig. S2b), corresponding to the left and right circularly polarized harmonics at 14.0 ev and 23.4 ev (3 rd and 5 th harmonic of 267 nm, which correspond to the 9 th and 15 th harmonic of the 800 nm fundamental). By using an Al filter, we block the 3 rd harmonic and transmit only the 5 th harmonic (Fig. 2a), confirming these spectral assignments. To our knowledge, this is the first demonstration of a HHG process that naturally separates different harmonic orders. With sufficient pressure, angularly separated harmonics can be produced using longer wavelength driving lasers, allowing for spectroscopy experiments without the need for a spectrometer (Fig. 6b). Due to favorable conversion efficiency scaling of HHG at shorter wavelength driving lasers 9, very little pulse energy is required for NCP- HHG using 267 nm driving lasers. For example, the bright harmonics shown in Fig. S2 were generated using only 15 μj in each beam. Furthermore, the relative intensity of 2 NATURE PHOTONICS

3 SUPPLEMENTARY INFORMATION the various harmonic orders can be tuned through the overall intensity of the driving laser. In this case, we generated much more 3 rd harmonic than 5 th harmonic, so that the harmonics would appear comparable on the CCD camera after passing through the Sn filter, which is more transmissive for the 5 th harmonic. However, the relative intensity of the 3 rd and 5 th harmonic beams can be easily adjusted by changing the overall intensity of the driving lasers, with higher intensities of the driving laser providing a higher ratio of 5 th to 3 rd harmonic. Figure S2. Angularly separated harmonics using NCP- HHG driven by UV (267 nm) beams. a, When a 200 nm Al filter is placed between the HHG region and the camera, only two beams are seen, which correspond to the left and right circularly polarized beams of the 5 th harmonic of 267 nm (15 th harmonic of the fundamental) at 23.4 ev. b, When a tin (Sn) filter is used, the 3 rd harmonic (9 th harmonic of the fundamental, 14.0 ev) is also transmitted. The 3 rd harmonic is angularly separated from the 5 th harmonic and 4 distinct beams are seen at the camera. The Sn filter is only ~0.1% transmissive at 14.0 ev and ~10% transmissive at 23.4 ev, meaning that, despite the appearance of equal intensities, the 14 ev harmonic is actually much brighter before the Sn filter. We note that the unequal intensities of the left and right circularly polarized light is likely due to imperfect mode of the driving beams and not inherent to the NCP- HHG process. Section 3. Noncollinear circularly polarized HHG at 400 nm In addition to the noncollinear circularly polarized HHG experiments at 800 and 267 nm, we also generated circularly polarized high harmonics with the noncollinear mixing of two 400 nm lasers with counter- rotating circular polarization (Figs. S3 and S4). As expected, the photon energies produced with 400 nm lasers were lower than for 800 nm, but the photon flux is high, reaching 2x10 8 photons per pulse (see Supplementary Information Section 5). When argon was used as the HHG medium (Figs. S3a,b), a single harmonic (22 ev) was observed (lower energy harmonics are blocked by the 200 nm Al filter). The isolation of a single harmonic makes this source attractive for applications such as coherent diffractive imaging and photoelectron spectroscopy that require a bright monochromatic light source. When neon is used as the generation medium (Fig. S3c,d), additional harmonics are observed at higher photon NATURE PHOTONICS 3

4 energies, mirroring the behavior of single- beam HHG. The large energy separation between these harmonics may prove useful for multicolor nanoscale imaging techniques 10. Figure S3. NCP- HHG with two 400 nm beams. a and b, Mixing of nm light in argon produces a single harmonic at 22 ev (lower harmonics are blocked by an aluminum filter), which is ideally suited for applications that require a high- flux monochromatic source, such as photoelectron spectroscopy or nanoscale imaging. c and d, The higher ionization potential of neon allows additional well- separated (6 ev) harmonics to be produced, providing a convenient source for multi- wavelength imaging techniques 10. Figure S4 demonstrates how the spatial profile of the circularly polarized HHG beams can be controlled by adjusting the crossing angle of the driving lasers; a higher crossing angle can dramatically increase the separation of the HHG beams (Fig. S4b). Switching to linear polarization produces additional EUV beams (Fig. S4c), as predicted by the photon and wave models presented in Fig. 3 of the manuscript. Importantly, Fig. S4d demonstrates how the spatial separation of the EUV beams from the fundamental can be utilized to deliver high- fluence harmonics directly to a μμm- scale sample without additional optics or filters and without damage to the sample. In single- beam HHG, the intense fundamental light co- propagates with the EUV light, necessitating that optically dense filters must be inserted into the diverging EUV beam before the sample can be illuminated with the EUV light alone. In practice, the fragility of the filters under illumination by the diving laser beams means that the filters (and therefore the sample) sample must be located several 10s of cm from the HHG medium. The divergence of the EUV beam means that additional focusing optics must be included in the EUV beam path if a high EUV fluence is required. In the case of noncollinear HHG, the generated EUV light does not co- propagate with the driving laser beams and samples can be inserted immediately after the harmonic generation region. This allows the sample to experience unusually high EUV fluence without damage from the driving laser beams. We demonstrate this unique experimental geometry by inserting a single human hair into the EUV beam only 1 cm from the interaction region (Fig. S4d). The hair completely blocks one of the circularly polarized EUV beams and is not damaged, demonstrating that the EUV pulse is confined to a region smaller than 100 μμm and that the driving laser beams are well separated. This demonstrates how the 4 NATURE PHOTONICS

5 SUPPLEMENTARY INFORMATION NCP- HHG method makes it straightforward to utilize EUV pulses with high intensities. For example, if we assume a EUV flux of 0.4 nj/pulse (see Supplementary Information, Section 5), a beam diameter of 50 μμm at the sample, and a pulse- duration of 20 fs, then the EUV intensity is ~1 GW/cm 2. Figure S4. Beam profiles of EUV emission from NCP- HHG driven by nm lasers. a, NCP- HHG with 25 mrad crossing half- angle produces two EUV beams, with a divergence ~1/7th of the original crossing angle, since the primary harmonic order is the 7th (~22eV). b, When the fundamental crossing angle is increased to 50 mrad, the angle between the EUV beams increases. c, Linearly polarized 400 nm lasers with the same crossing angle (25 mrad) produce HHG beams at the same angle, but additional beams appear at higher angles due to the relaxed selection rules. d, Even with a small crossing angle (~30 mrad), it is still possible to place a fragile sample (in this case a single human hair) extremely close (1 cm) to the interaction region without damage from the laser beams. Here the hair almost completely blocks one of the beams, demonstrating that the full HHG flux is still confined to a size of <0.1 mm. Moreover, the diffraction peaks on the lower left of the image demonstrate the spatial coherence of the source. The small satellite peak to the left of the main peaks in Fig. S4a is due to slight ellipticity of the driving lasers. Since the production of circularly polarized high- harmonics is very sensitive to the polarization of the fundamental beams, even a small (~2 degree) rotation of the quarter- waveplates is enough to cause additional satellite peaks to appear outside of the two primary peaks. While the main peaks correspond to a nearly equal mixing of photons by both beams (nn! = nn! ± 1), the satellite peaks correspond to an unbalanced absorption (nn! = nn! ± 3, 5, etc.) and are forbidden by selection rules if both beams are perfectly circularly polarized. Indeed, the complete suppression of the satellite peaks provides a convenient real- time diagnostic with which to optimize the polarization, power, position, and focal spot size of each beam in order to maximize the circularity of the emitted HHG light. This method can be applied even when the harmonics are not spectrally dispersed or when only one harmonic is generated. Section 4. Theory of noncollinear HHG at different driving frequencies The noncollinear mixing of different frequencies (Fig. 4 of the manuscript) can be explained using similar conservation of momentum arguments as when mixing at the same frequency. For the mixing of n 1 photons of the fundamental with n 2 of the second harmonic, the effective harmonic order relative to the fundamental is q = n 1 +2n 2, and conservation of spin angular momentum requires n 1 - n 2 =1. This restricts the allowed mixing orders: NATURE PHOTONICS 5

6 for n 2 = n 1 +1, q = 3n 1 +2 ; for n 2 = n 1-1, q = 3n 1-2 ; and n 2 = n 1 is forbidden. The relationship between the harmonic signal angle θθ! and the input angle θθ! relative to the bisecting line is somewhat more complicated than we found earlier in the degenerate mixing case: tan θθ! =!!!!!! tan θθ!!. For nn! = nn! ± 1, tan θθ! =!±! tan θθ!!!. Taking the limit of high harmonic order, we see that the harmonics are again divided into left and right circularly polarized directions, centered on an angle tan θθ! /3, which is displaced away from the bisecting line toward the direction of the second harmonic beam. The same principles of conservation of spin angular momentum and linear momentum can be used to find the output angles for any mixing frequencies. The wave mixing picture can be extended to the ωω + 2ωω case as well: when the relative ωω/2ωω phase varies, the orientation of the bursts of linearly polarized attosecond pulses rotates in a manner similar to the rotation of the linear polarization shown in Fig. 3d. The result is a rotating polarization grating that behaves identically to the ωω + ωω case, producing two beams of opposite- helicity circularly polarized light. Section 5. Calibration of EUV photon flux The EUV photon flux was calculated from the response of the CCD detector, which is characterized, but not precisely calibrated. Thus, while the resulting estimate of the photon flux is a valid order- of- magnitude estimate, it should not be regarded as a precise measurement of the exact photon flux. We calculate the EUV flux for the NCP- HHG using nm in argon gas, because under these conditions monochromatic light (22 ev) is generated and this allows for the calibration to be performed without the spectrometer in place, thereby reducing the uncertainty of the estimation. For the NCP- HHG at 400 nm presented in Fig. S3a, the integrated counts for each beam was ! for the 0.1 second camera exposure, giving a total of ! counts per pulse for both beams, considering the 1 khz repetition rate of the laser. The camera (see Methods Section) was operated with a 2.5 MHz readout rate and a pre- amplifier gain of 2x, which corresponds to 5.4 electrons per count per the camera specifications. At 20 ev, the CCD used has a quantum efficiency of approximately 20%, and 6 electrons are excited per 20 ev photon absorbed. Thus, we calculate that there are ~4 10! photons per pulse incident on the CCD. A 200 nm aluminum filter (Luxel) was used to block scattered visible light from reaching the CCD. While the theoretical transmission of 200 nanometers of aluminum is better than 60% (CXRO database), oxide layers on the surface reduce the actual transmission of the filter, and we measured the filter to be only 20% transmissive. Thus, the generated EUV output of the HHG process is ~2 10! photons per pulse, which is 0.7 nj/pulse. Given that ~200 uj of 400 nm energy was used, this represents a conversion efficiency of !!, which is comparable to single- beam HHG NATURE PHOTONICS

7 SUPPLEMENTARY INFORMATION In many applications, the NCP- HHG method actually represents a dramatic increase in usable photon flux due to the fact that it separates the EUV light from the pump beams. In collinear or single- beam HHG, numerous filters are often required to attenuate the pump beams and this can reduce the photon flux by orders of magnitude. Additionally, such filters are extremely fragile and can be damaged by the pump beam. In the noncollinear geometry, we were able to employ just a single filter, and, since the filter blocks only the scattered light from the argon plasma and is not exposed to the direct pump beam, the filter was never damaged by the pump beams. Section 6. EUV magnetic circular dichroism (MCD) measurements To demonstrate the applicability of the NCP- HHG source to study magnetic materials, we performed a magnetic circular dichroism (MCD) measurement on thin film of iron. To confirm that our iron sample could be fully saturated with the magnetic fields accessible to our apparatus, we measured both the maximum field strength of our electromagnet (+/- 15 mt) with a Hall probe and the magnetization of the sample as a function of the magnetic field by using an alternating gradient magnetometer (Fig. S5). We also calculated and extrapolated the MCD asymmetry for the 20 nm thick iron sample that is at 45 incident on the EUV beam based on the magneto- optical constants obtained at a synchrotron 12 (Fig. S6). To demonstrate that the flux and stability of the generated harmonics are high enough for fast and reliable MCD measurements, we show in Fig. S7 data obtained using a 2 min total acquisition time. Figure S5. Alternating gradient magnetometry measurements of the 20 nm iron sample. This measurement confirms that the experimentally employed magnetic field of 15 mt is larger than the coercive field μμ! H C +/- 10 mt of the sample and therefore high enough to magnetically saturate the sample for the MCD measurement. NATURE PHOTONICS 7

8 Figure S6. Predicted MCD contrast for a 20 nm iron sample at 45. In this study we probed the iron sample in the range of 29 ev to 39 ev, which is not explicitly covered by the available data and this graph. However, the MCD asymmetry is approximately 3.5% at 45 ev, and slowly decreasing. Thus, the MCD asymmetry of approximately 1.5% seen experimentally at 33 ev is consistent with an extrapolation of this synchrotron- derived data NATURE PHOTONICS

9 SUPPLEMENTARY INFORMATION Figure S7. Rapid collection of an EUV MCD measurement. This figure is identical to the MCD measurement presented in Fig. 5 of the manuscript, except that it was calculated using only six 10- second exposures for each field direction, for a total acquisition time of 2 minutes. While the data quality is lower than the 30- minute exposure, the magneto- optical contrast is still clearly visible. This demonstrates the practicality of rapidly collecting MCD spectra at many time delays in order to study ultrafast dynamics of magnetic materials. References 1. Bertrand, J. B. et al. Ultrahigh- Order Wave Mixing in Noncollinear High Harmonic Generation. Phys. Rev. Lett. 106, (2011). 2. Heyl, C. M. et al. Macroscopic Effects in Noncollinear High- Order Harmonic Generation. Phys. Rev. Lett. 112, (2014). 3. Heyl, C. M. et al. Noncollinear optical gating. N. J. Phys 16, (2014). 4. Fleischer, A., Kfir, O., Diskin, T., Sidorenko, P. & Cohen, O. Spin angular momentum and tunable polarization in high- harmonic generation. Nat. Photon. 8, (2014). 5. Kfir, O. et al. Generation of bright circularly- polarized extreme ultraviolet high harmonics for magnetic circular dichroism spectroscopy. Nat. Photon. 9, (2015). 6. Vincenti, H. & Quéré, F. Attosecond lighthouses: How to use spatiotemporally coupled light fields to generate isolated attosecond pulses. Phys. Rev. Lett. 108, 1 5 (2012). NATURE PHOTONICS 9

10 7. Quéré, F. et al. Applications of ultrafast wavefront rotation in highly nonlinear optics. J. Phys. B 47, (2014). 8. Louisy, M. et al. Gating attosecond pulses in a noncollinear geometry. Optica 2, (2015). 9. Popmintchev, T., Chen, M.- C., Arpin, P., Murnane, M. M. & Kapteyn, H. C. The attosecond nonlinear optics of bright coherent X- ray generation. Nat. Phot. 4, (2010). 10. Witte, S., Tenner, V. T., Noom, D. W. & Eikema, K. S. Lensless diffractive imaging with ultra- broadband table- top sources: from infrared to extreme- ultraviolet wavelengths. Nat. LSA 3, e163 (2014). 11. Rothhardt, J. et al. Absorption- limited and phase- matched high harmonic generation in the tight focusing regime. N. J. Phys. 16, (2014). 12. Valencia, S. et al. Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni. N. J. Phys. 8, 254 (2006). 10 NATURE PHOTONICS