Coherent manipulation of extreme-ultraviolet Bessel vortex beam from solids by active wavefront shaping of driving fundamental beam

doi:10.21203/rs.3.rs-2598867/v1

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Coherent manipulation of extreme-ultraviolet Bessel vortex beam from solids by active wavefront shaping of driving fundamental beam

https://doi.org/10.21203/rs.3.rs-2598867/v1

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published 19 Sep, 2023

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High-harmonic generation (HHG) of extreme ultraviolet (EUV) radiation enables ultrafast spectroscopy and nanoscale coherent imaging with timing resolutions down to the attosecond regime. However, beam manipulations such as steering and focusing remain a major challenge for handy implementation of such applications towards the achievement of a wavelength-scale spatial resolution. Here, we present a solid-based non-collinear HHG scheme mediating the propagation control and helical wavefront generation commanded via a spatial light modulator. The phase-matching-insensitive nature of the solid-HHG leads to the coherent multi-fold conversion of wavefronts enabling active control of the EUV harmonic beam propagation. Further, EUV harmonics generated by double-annular beams were converted to the Bessel vortex beam, for the first time, narrowing the beam diameter to 3.4 wavelengths with a long millimetre-level depth-of-focus without extra EUV-dedicated optical components. Our results will suggest a solid-HHG as a powerful tool for high photon-energy applications with a nanoscale spatial resolution.

Physical sciences/Optics and photonics/Optical physics/High-harmonic generation

Physical sciences/Optics and photonics/Lasers, LEDs and light sources/Ultrafast lasers

High-harmonic generation (HHG) enables frequency multiplication by nonlinear photon-electron interaction as demonstrated by irradiating intense laser pulses on not just noble gases^1-3 but bare solids^4,5, engineered solid surfaces^6,7, and liquid curtains⁸. The optical frequency up-conversion by means of HHG has been exercised for diverse applications, with particular attention being paid to achieve extreme ultraviolet (EUV) radiation in the form of coherent ultrashort pulses for the sake of ultrafast observation of physical phenomena via pump-probe spectroscopy⁹ or lens-less coherent diffraction imaging^10-12, even with angle-resolved photoemission spectroscopy¹³.

For more efficient implementation of ultrafast imaging and/or spectroscopic observation, generated EUV radiation should be well delivered and focused onto targeted samples with strict control of the spatiotemporal coherence with respect to the driving laser pulse. However, EUV light is relatively not easy to handle by traditional refractive optics because of its short wavelengths and, more severely, its attribute of being strongly absorbed in most optical materials. Hence, EUV beam delivery and focusing is routinely made using reflective optics, by devising non-spherical mirrors with either a large incidence angle or multi-layered film coating. Such elaborate reflective optics are operative just for a given design specification despite high fabrication complexity and cost. Several schemes have subsequently been proposed for the sake of flexible EUV beam manipulation; adaptive optics-based wavefront correction for hard X-ray focusing¹⁴, refractive optics engineered using a gas jet¹⁵, and EUV focusing by spatial chirping of the driving laser field¹⁶. Other upfront approaches entailed diffractive Fresnel zone plates as demonstrated for ptychographic diffraction imaging¹⁷, laser ablation mass spectroscopy¹⁸, and solid-based plasmonic HHG⁶. In the gas medium, the phase matching of the non-collinear geometry has been investigated as an efficient scheme for generation of polarization controlled attosecond pulse¹⁹, cavity-assisted EUV^20,21, and optical vortex^22-24. A photon carrying non-zero orbital angular momentum (OAM) is versatile for wavefront multiplexing of communication systems²⁵, micromanipulation of particle spins^26-28, and ghost imaging²⁹. Particularly, the EUV vortices can be used for observing interactions between electron orbits and high-energy photons³⁰. More recently, it has been theoretically predicted that strong chiral responses driven by electric-dipole interactions can be resolved by divergence angles of non-collinearly generated high order harmonics³¹. Nonetheless, these precedent reports of wavefront manipulation have been based on static control by using the geometrical shape of HHG medium and passive optics, lacking dynamic control of EUV wavefronts including orbital angular momentum, which will open new vista for precision EUV spectroscopy and metrology applications.

Herein, we investigate a solid-based HHG scheme devised to irradiate MgO crystal by means of non-collinear illumination to focus EUV harmonics spatially separated from the driving laser by the principles of conservation of momentum, parity, and orbital angular momentum. In addition, such non-collinear illumination permits EUV harmonics to be focused behind the rear surface of the solid specimen, which is subsequently steered by wavefront manipulation of the driving laser field via a spatial light modulator. Further, our non-collinear HHG scheme is extended to a 3-dimensional configuration by using two annular driver beams to convert EUV harmonics to Bessel beams for beam focusing to a spot size of a few wavelengths without extra EUV optics. We show that the nano-focusing EUV Bessel beam can carry helical wavefronts over a long depth-of-focus by using double-annular vortex drivers. Our study presents a reliable route to control coherent EUV radiation in the spatial domain, offering an efficient tool for ultrafast spectroscopy as well as coherent diffraction imaging.

Non-collinear high-harmonic generation in solids.

The non-collinear HHG is a well-accepted scheme that gives additional controllability on wavefront^{22–24, 32}, polarization^19,33,34, and spectrum³⁵ especially in gaseous atomic medium. The similar approach is the HHG using an annular driver to separate driver while keeping radial symmetry of the harmonic beams^36–38. Meanwhile, the non-collinear scheme has not been introduced to this recent field of solid HHG, so in-depth understanding on its key advantages has not been addressed to date. In this study, we devised a common-optics setup mediating wavefront control of the EUV high-harmonics from a solid medium. Figure 1a illustrates the experimental setup configured in this investigation to generate EUV high harmonics from a thin wafer of magnesium oxide (MgO) crystal. Our non-collinear HHG is implemented by irradiating the crystal sample with a pair of beams symmetrically split from a single driving laser. With identical vertical polarization, the two beams undergo non-collinear propagation through a series of optical components, including a Wollaston prism, a Glan polarizer, a half-wave plate, a triangular optical wedge, and a collimating lens (see Methods for details). The driving laser delivers infrared (IR) short pulses via a spatial light modulator (SLM) that is inserted to induce a sequence of linearly varying phase slopes across the laser wavefront. The driving laser is accordingly steered up and down, by the phase modulation using the SLM, vertically along the x-axis with respect to the x-y-z coordinate system embedded in the experimental setup (Fig. 1a). The oblique beams finally converging to the crystal sample, with a crossing angle of ${2\theta }_{d}$as projected on the y-z plane, are distinguished as k₁ and k₂ in terms of their wavevectors.

Note that our non-collinear illumination causes generated EUV harmonics to diverge on the y-z plane as shown in our experimental data (Fig. 1c) obtained from a 150-µm thick MgO (100) crystal. In fact, the divergence angle of the q-th harmonic, measured from the surface normal of the crystal sample, varies with the harmonic order q in compliance with the conservation of two physical quantities; parity and momentum. First, the rule of parity conservation dictates the equality of q = q₁ + q₂ with q₁ and q₂ being the individual number of IR photons contributed by k₁ and k₂, respectively³². This shared multi-photon excitation leads to a multiplicity of possible sets of (q₁, q₂) for a given harmonic order q, i.e. {(0, q), (1, q-1), (2, q-2), … (q-1,1), (q,0)}, as observed in our experimental data of the 7-th (H7) and 9-th (H9) harmonics (Fig. 1d). Second, for each set of (q₁, q₂), the rule of momentum conservation holds as k_q = q₁ k₁ + q₂k₂ with k_q being the wavevector of the q-th harmonic. Third, in solid-based HHG, generated EUV harmonics are subject to strong reabsorption during the travel within the specimen, thereby leaving no concern about phase matching. More specifically, for MgO crystal, the optical penetration depth is known to be as short as about one wavelength (Fig. 1a inset) for the whole EUV spectrum ranging from 20 to 120 nm³⁹. This implies that the main portion of EUV harmonics escaping from the crystal originates from just a few hundreds of atomic layers on the rear-side surface. Fourth, the momentum conservation indicates that the smallest value of ${\theta }_{q}$ for the q-th harmonic, propagating closest to the z-axis, satisfies the relation of $\text{t}\text{a}\text{n}{\theta }_{q}=\text{t}\text{a}\text{n}{\theta }_{d}/q$ as verified in our experimental data (Fig. 1b). Fifth, all the non-collinear divergence of generated EUV harmonics remain uninfluenced, being not much affected by driving laser intensities up to 23 TW/cm² (Fig. 1e). Lastly, it is worthwhile to note that the divergent character of non-collinear harmonics generation can also be scrutinized by dealing with the wave interference pattern of the two driving beams as an active grating formed on the rear surface of the specimen, in compliance with the well-established far-field wave diffraction theory ^40,41.

Figure 2 presents our test results showing the dependence of measured EUV harmonic spectra upon the crystal orientation as well as the driving laser intensity under non-collinear illumination. The measured spectra of H7 – H17 all exhibit four-fold symmetry when the crystal sample is rotated with respect to the polarization direction of the driving laser (Fig. 2a), which is attributable to the face-centred cubic crystal structure of the MgO sample. Meanwhile, the yield of generated EUV harmonics becomes higher when the driving laser polarization coincides with the Γ-X direction of the crystal (Fig. 2b), which is known as the case of offering strong dipole-allowed coupling between the conduction and valence bands⁴². In addition, with increasing the driving laser intensity I, the yield of generated EUV harmonics builds up in proportion to ${I}^{q}$ for intensities up to 15–20 TW/cm² (Fig. 2c). This perturbative growth of EUV harmonics however begins to weaken as the crystal sample is subject to thermal damage with increasing the driving laser intensity, and eventually ceases due to the occurrence of ablation near 30 TW/cm². This observation indicates that EUV harmonics emitted by non-collinear irradiation exhibit similar behaviours to the normal illumination of single-beam HHG⁴³, except generated EUV harmonics isolate from the driving laser under the conservation rule of parity and momentum.

Facile wavefront control of EUV harmonic beams

Figure 3 illustrates how our scheme of non-collinear illumination separates the EUV harmonics spatially from the driving laser in the horizonal y-z plane on the exit side of the crystal sample (Fig. 3a). Note that phase-modulation of the driving laser wavefront using the SLM permits the EUV harmonics to be steered in the vertical x-z plane (Fig. 3b), in which θ_diff denotes the tilt angle of the driving laser wavefront brought on the x-z plane by the SLM. The source driving laser has a beam diameter of 2.5 mm and the MgO crystal sample is placed at a defocused position inward by an offset of 7 mm from the focal point. The focusing lens has a 50 mm focal length. The beam profile of the 7-th harmonic (H7) is measured along the Rayleigh length (1.63 mm) of the driving laser beam by adopting the knife-edge method (see Methods for details). The measured beam profile yields an elliptical cross-section with a beam diameter of 12 µm and 18 µm along the x-axis and y-axis, respectively (Fig. 3c & 3d). When θ_diff varies in the range of -4 to 4 mrad by activating the SLM (Fig. 3b), the H7 harmonic makes a linear-scanning motion on the focal plane along the x-direction following the multifold phase conversion condition of ${\varPhi }_{EUV}={q\varPhi }_{IR}$, leading to a significant lateral range of -2 to 2 mm (Fig. 3e). This EUV beam scanning appears to be highly repeatable in response to the θ_diff input command, with no significant variation in the spot size of the EUV beam. Accordingly, without use of extra EUV-scanning optics, elaborate dynamic control can be achieved simply by modulating the θ_diff input command (Fig. 3f).

EUV Bessel vortex generation

Figure 4 shows another experimental scheme implemented in this investigation to focus EUV harmonics in the form of interferometric Bessel-like beams. The SLM screen was separated into two sections in radial direction to afford two different helical wavefronts to the driver beams. Next, the driving laser beam is spatially masked to form double-annular beams carrying a different topological charge l, the number of $2\pi$ phase-shift around the azimuthal direction. Then, around-z-axis-symmetric non-collinear irradiation is made on the MgO crystal through an axicon lens combined with an aspheric focusing lens (Fig. 4a). The resulting EUV harmonic beam profile is monitored by moving a microchannel plate (MCP) 2-D detector along the z-axis direction (Fig. 4b). For the 7th harmonic (H7), two parity sets (q₁:q₂ = 3:4 and 4:3) are seen most dominant with distinct converging angles (${\theta }_{b}$). Therefore, the propagation of two annular EUV beams is observed along the z-axis. Note that an annular aperture is inserted before the MCP to block the IR driving laser, while letting only the H7 EUV harmonic be received. Our scheme is almost free from EUV harmonic power loss from a spectral filter (such as an aluminium membrane) owing to the non-collinear focusing configuration. With the driving laser intensity being set at 27 TW/cm², the temporal stability of our optical configuration (Fig. 4a) was verified during a relatively long observation period of 20 min with respect to the EUV beam profile as well as the photon flux (Fig. 4c & 4d). These stable test results confirm that our Bessel-beam conversion scheme based on solid-based HHG is robust to environmental noises and less sensitive to phase matching. As a result, a stable interferometric Bessel beam of the H7 harmonic was well grown along the optical axis over a few millimetres of focal depth.

The single pixel size of our MCP detector was as large as 80 µm, being not adequate for accurate determination of the focused Bessel beam diameter. Alternatively, a ptychographic technique⁴⁴ was adopted to retrieve the intensity profile of the EUV Bessel beams (Fig. 4e, see Methods for details). Figure 4g shows the retrieved beam profile with the phase map applied to the SLM. The result with an uniform phase indicates that the central lobe is well concentrated on a spot size of 390 nm in FWHM, equivalent to 3.4 times the H7 wavelength of 115 nm (Fig. 4g). Note that side lobes of lower intensities are seen not purely concentric, as they are found disturbed by the aperture stop of annular shape installed to block the IR driving laser using four suspension-legs. When the SLM applied the counter rotating topological charges of l₁ = 1and l₂ = -1 for each annular beam, the topological charge of the q-th harmonic Bessel beam was determined by the conservation rules of parity and orbital angular momentum: l_q = q₁ l₁ + q₂l₂, thus l_q = ± 1. The interference of the two driving beams with the non-zero azimuthal phase leads to formation of a spiral phase, which is transferred to the high-harmonic beams. Again, the intensity and phase distributions were disturbed by the IR beam blocks. Nonetheless, we can infer that the interference of the two driving beams with the non-zero azimuthal phase leads to formation of a spiral phase, which is transferred to the high-harmonic beams. The singularity of the spiral phase at the centre of the beam leads to the zero intensity, thereby demonstrating the EUV Bessel vortex for the first time.

Our non-collinear scheme of solid-based HHG demonstrated in this investigation proves to be an effective, robust way of focusing EUV harmonics, while spatially isolating IR driving laser beams. The spatial phase modulation of the driving laser enabled active manipulation of the EUV harmonic beams. Generated EUV harmonics can readily be steered to perform lateral linear scanning on a target sample, without using extra EUV-designated optical components, simply by wavefront modulation of the IR driving laser via a spatial light modulator in accordance with the multi-fold phase conversion. Our results hint that the high-harmonic beam propagation is rarely influenced by nonlinear phase shifts which are susceptible to the carrier-envelope phase and driving intensity. Because we introduced non-structured surfaces, long-term damage issues due to local hot spots around the sharp edges are negligible, proving coherent manipulation of driving laser in spatial domain as a reliable and compelling method for high-harmonic beam control. Our non-collinear scheme of solid-based HHG is extended to convert EUV harmonics to pencil-like Bessel beams, achieving a lateral resolution of a few wavelengths. Combined with the unprecedented focusing power, the EUV Bessel vortices may open a new avenue for dynamic nanomanipulation of electrons and atoms.

The instantaneous peak intensity of the H7 Bessel beam is estimated to be 2.7×10⁸ W/cm² (see Methods), which is about two orders of magnitude below the minimum level of intensities required for coherent EUV-based material processing^45,46. In fact, the achievable yield of EUV harmonics from a solid medium by HHG is known greatly reduced by strong reabsorption of generated EUV radiation by the medium itself. Besides, the maximum driving laser power must be severely restrained in order to avoid thermal damage of the medium’s atomic structure. Despite the inherent restrictions of solid-based HHG, the EUV yield may be enhanced, up to one order of magnitude⁴⁷, by compensating the propagation effects of the driving laser within the solid medium. Further, selecting a crystal material with temperature-dependent band-gap structure is recently known to lead to yield enhancement up to three orders of magnitude at low temperature (50 K) compared to the case of room temperature⁴⁸. Also, the power loss occurring in the interferometric conversion to Bessel beams may be mitigated by modulating the driving laser beam using a spatial phase mask so as to suppress side-lobe intensities⁴⁹. In conclusion, our investigation paves an efficient way to control coherent EUV radiation in the spatial domain, offering an efficient tool for ultrafast, coherent EUV imaging and spectroscopy.

Non-collinear illumination. In Fig. 1a, the driving laser pulses were emitted from a Ti:Sapphire regenerated amplifier (Astrella, Coherent) of a centre 805 nm wavelength with 40 fs pulse duration at a 1 kHz repetition rate. The spatial light modulator (SLM) was used to steer the propagation direction of the driving laser, as used in experiments of Fig. 3, by inducing a linearly-varying spatial phase distribution across the laser wavefront. The Wollaston prism was used to split the linearly polarized driving laser beam into two orthogonally polarized beams of equal intensity, of which the polarization was controlled subsequently by the polariser of Glan type and the half-wave plate shown in Fig. 1a. Further, the wedged delay line was set to adjust the spatiotemporal overlap of the split driving pulses converged on the MgO crystal through a collimating lens.

Knife-edge method. In Fig. 3c & 3d, the beam diameter of the 7-th harmonic (H7) was measured using a knife-edge fabricated on a sapphire blade of a 0.2 mm thickness (Single edge lancet, WPI). With mechanical scanning of the knife edge across the beam diameter, the transmitted optical power (P_N) was fitted to the error function of ${P}_{N}\left(x,z\right)=\frac{1}{2}\left[1+\text{e}\text{r}\text{f}\left(\frac{\sqrt{2}x}{w\left(z\right)}\right)\right], \text{w}\text{i}\text{t}\text{h}$x being the scanning position of the knife-edge position, z being the optical axis, and $w\left(z\right)$ denoting the $1/{e}^{2}$ beam radius. The measured cross-sectional intensity profile was assumed a Gaussian shape so as to be quantified by differentiating the fitted error function⁵⁰.

EUV Bessel beam generation. In Fig. 4a, the driving IR beam was shaped into two concentric annular beams, through an annular aperture in combination with an axicon, and spatiotemporally overlapped in the MgO crystal through the aspheric focusing lens. Distance between the aspheric lens and the outer Bessel beam spot (light red) was set larger than the focal length so as to obtain converging EUV annular beams from the sample surface. The IR beam block, made on a stainless-steel foil supported with three or four bridges, was positioned behind the MgO sample to selectively extract EUV harmonic beams. For direct imaging of H7 harmonic, a fused silica axicon with an apex angle ${\theta }_{a}=2.79 \text{r}\text{a}\text{d} (160^\circ$) was used with a collimating lens of a 50 mm focal length to obtain a large working distance. On the other hand, for the diffraction imaging using a single slit for Fig. 4f, a different axicon with ${\theta }_{a}=2.97 \text{r}\text{a}\text{d} (170^\circ )$ was used to increase the converging angle under a millimetre-scale working distance.

Ptychographic wavefront retrieval. The cross-sectional intensity profiles of Fig. 4f&g were obtained by employing a ptychographic method of microscopic diffraction imaging (Fig. 4e). A slit with a single rectangular aperture fabricated by femtosecond laser patterning with 20 µm width and 3 mm length on a 15 µm thick stainless-steel foil was used to scan across the EUV harmonic radiation. The far-field diffraction pattern was recorded while scanning along the x-axis and y-axis sequentially, with the slit being held vertically along the scanning axis. The MCP screen was positioned at a distance of 49–55 mm away from the slit. The single slit was moved at five points spaced 1.6 µm apart in the x and y directions. Thus, we only obtained 10 diffraction patterns (i.e. five patterns in each scanning direction) for field retrieval. To increase the spatial resolution, zero padding was implemented outside the diffraction patterns after noise was removed. The PIE algorithm³⁴ used in our study is expressed as

$${P}_{g,n+1}\left(\mathbf{r}\right)={P}_{g,n}\left(\mathbf{r}\right)+\frac{\beta \left|O\left(\mathbf{r}-\mathbf{R}\right)\right|{O}^{*}(\mathbf{r}-\mathbf{R})\left({\psi }_{c,n}\right(\mathbf{r},\mathbf{R})-{\psi }_{g,n}(\mathbf{r},\mathbf{R}\left)\right)}{\left|{O}_{max}\left(\mathbf{r}-\mathbf{R}\right)\right|({\left|O\left(\mathbf{r}-\mathbf{R}\right)\right|}^{2}+\alpha )}$$

where $P$, $O$, and $\psi$ are the probe, object, and exit field immediately after the slit, respectively. The slit position $\mathbf{R}$ changes in Cartesian coordinates $\mathbf{r}=(x,y)$. Subscripts $g$ and $c$ indicate whether a field would be guessed or corrected, respectively, and superscript $n$ denotes the iteration number. In consideration of the algorithm’s convergence, the parameters $\alpha$ and $\beta$ were optimised as 0.001 and 0.85, respectively. After 200 iterations, the sum squared error was of the order of 10^− 6.

Quantification of EUV Bessel beam. In Fig. 4, the instantaneous peak intensity of the focused Bessel beam of H7 was estimated by measuring the EUV photon flux using a copper-beryllium oxide (Cu-BeO) electron multiplier tube (EMT, R5150-10, Hamamatsu Photonics). Specifically, the photon flux $N$ was first quantified, in units of photons/s, through the formula of $N=C/(q\times Q\times G)$ with $C, q, Q$, and $G$ being the measured photocurrent, the electron charge (1.6 × 10⁻¹⁹ C), the quantum conversion efficiency (0.17), and the EMT’s amplification gain, respectively⁷. The resulting photon flux N was about 5.00 × 10⁸ photons/s (green line, Fig. 4d). Then, assuming that the photon flux N was contributed mostly by the dominating harmonic order of H7 (115 nm, photon energy $ϵ=$ 10.8 eV), the corresponding EUV power P was worked out 8.64 × 10^− 10 W by the formula of $P=N\times ϵ$. Thirdly, from the intensity profile retrieved using the ptychographic method (Fig. 4f), the concentration factor $\eta$ of the EUV power on the central lobe was evaluated to be ~ 6.0 ×10⁻³ as a ratio to the total power. Fourthly, the instantaneous peak intensity was calculated by ${I}_{peak}= P\times \eta /\left(A{\times t}_{EUV}\times {f}_{rep}\right)$ with $A, {t}_{EUV}$ and ${f}_{rep}$ denoting the central lobe area($={\pi }{r}^{2}/4$, $r=$ 390 nm), the EUV pulse duration (20 fs) and the repetition rate (1 kHz), respectively, leading to the final result of ${I}_{peak}=$ 2.7×10⁸ W/cm².

Acknowledgement

This work was supported by the National Research Foundation of the Republic of Korea (NRF-2012R1A3A1050386, 2020R1A2C2102338, and 2021R1A4A1031660).

Authors contribution

Under the supervision of S.-W.K. and Y.-J.K., B.K. and S.C. equally performed experiments and data analysis with the support of S.J.W. and Y.W.K. All authors contributed to the preparation of the manuscript.

Declaration of competing interest

The authors declare no competing financial interests.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Baltuška, A. et al. Attosecond control of electronic processes by intense light fields. Nature 421, 611-615, doi:10.1038/nature01414 (2003).
Li, J. et al. Attosecond science based on high harmonic generation from gases and solids. Commun. 11, 1-13, doi:10.1038/s41467-020-16480-6 (2020).
Popmintchev, T. et al. Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum. Natl Acad. Sci. U.S.A. 106, 10516-10521, doi:10.1073/pnas.0903748106 (2009).
Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Phys. 7, 138-141, doi:10.1038/nphys1847 (2010).
Garg, M., Kim, H. Y. & Goulielmakis, E. Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz. Photonics 12, 291-296, doi:10.1038/s41566-018-0123-6 (2018).
Sivis, M. et al. Tailored semiconductors for high-harmonic optoelectronics. Science 357, 303-306, doi:10.1126/science.aan2395 (2017).
Han, S. et al. High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure. Commun. 7, 13105, doi:10.1038/ncomms13105 (2016).
Luu, T. T. et al. Extreme-ultraviolet high-harmonic generation in liquids. Commun. 9, 3723, doi:10.1038/s41467-018-06040-4 (2018).
Siemens, M. E. et al. Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. Mater. 9, 26-30, doi:10.1038/nmat2568 (2010).
Gardner, D. F. et al. Subwavelength coherent imaging of periodic samples using a 13.5 nm tabletop high-harmonic light source. Photonics 11, 259-263, doi:10.1038/nphoton.2017.33 (2017).
Tadesse, G. K. et al. Wavelength-scale ptychographic coherent diffractive imaging using a high-order harmonic source. Rep. 9, 1-7, doi:10.1038/s41598-019-38501-1 (2019).
Zhang, B. et al. High contrast 3D imaging of surfaces near the wavelength limit using tabletop EUV ptychography. Ultramicroscopy 158, 98-104, doi:10.1016/j.ultramic.2015.07.006 (2015).
Sie, E. J., Rohwer, T., Lee, C. & Gedik, N. Time-resolved XUV ARPES with tunable 24-33 eV laser pulses at 30 meV resolution. Commun. 10, 3535, doi:10.1038/s41467-019-11492-3 (2019).
Mimura, H. et al. Breaking the 10 nm barrier in hard-X-ray focusing. Phys. 6, 122-125, doi:10.1038/nphys1457 (2010).
Drescher, L. et al. Extreme-ultraviolet refractive optics. Nature 564, 91-94, doi:10.1038/s41586-018-0737-3 (2018).
Quintard, L. et al. Optics-less focusing of XUV high-order harmonics. Adv. 5, eaau7175, doi:10.1126/sciadv.aau7175 (2019).
Nashed, Y. S. et al. Parallel ptychographic reconstruction. Express 22, 32082-32097, doi:10.1364/OE.22.032082 (2014).
Kuznetsov, I. et al. Three-dimensional nanoscale molecular imaging by extreme ultraviolet laser ablation mass spectrometry. Commun. 6, 1-6, doi:10.1038/ncomms7944 (2015).
Hickstein, D. D. et al. Non-collinear generation of angularly isolated circularly polarized high harmonics. Photonics 9, 743-750, doi:10.1038/nphoton.2015.181 (2015).
Ozawa, A. et al., Non-collinear high harmonic generation: a promising outcoupling method for cavity-assisted XUV generation. Exp. 16, 6233-6239, doi: 10.1364/OE.16.006233 (2008)
Högner, M. et al., Cavity-enhanced noncollinear high-harmonic generation. Exp. 27, 19675-19691, doi: 10.1364/OE.27.019675 (2019)
Dorney, K. M. et al., Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation, Photonics 13, 123-130 (2019).
Gauthier, D. et al., Tunable orbital angular momentum in high-harmonic generation. Commun. 8, 14971 (2017).
Kong, F. Q. et al., Controlling the orbital angular momentum of high harmonic vortices. Commun. 8, 14970 (2017).
Lei, T., Zhang, M., Li, Y. et al. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light Sci Appl 4, e257 (2015).
He, H. et al., Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity. Rev. Lett. 75, 826 (1995)
Paterson, L. et al., Controlled Rotation of Optically Trapped Microscopic Particles. Science 292, 5518 (2001)
Grier, D., A revolution in optical manipulation. Nature 424, 810–816 (2003).
Chen, L., Lei, J. & Romero, J. Quantum digital spiral imaging. Light Sci Appl 3, e153 (2014)
de las Heras, A. et al., Extreme-ultraviolet vector-vortex beams from high harmonic generation. Optica 9, 71-79, doi: 10.1364/OPTICA.442304 (2022)
Ayuso, D. et al., Strong chiral response in non-collinear high harmonic generation driven by purely electric-dipole interactions. Exp. 30, 4659-4667, doi: 10.1364/OE.444210 (2022)
Heyl, C. et al. Macroscopic effects in noncollinear high-order harmonic generation. Physical review letters 112, 143902 (2014).
Fleischer, A. et al., Spin angular momentum and tunable polarization in high-harmonic generation. Photon. 8, 543–549, doi: 10.1038/nphoton.2014.108 (2014)
Neufeld, O. et al., Ultrasensitive Chiral Spectroscopy by Dynamical Symmetry Breaking in High Harmonic Generation. Rev. X 9, 03100 (2019)
Bertrand, J. B. et al., Ultrahigh-Order Wave Mixing in Noncollinear High Harmonic Generation. Rev. Lett. 106, 023001 (2011)
Peatross, J. et al., High-order harmonic generation with an annular laser beam. Lett. 19, 942-944 (1994)
Klas, R. et al., Annular beam driven high harmonic generation for high flux coherent XUV and soft X-ray radiation. Exp. 26, 19318-19327 (2018)
Gaumnitz, T. et al., Extreme-ultraviolet high-order harmonic generation from few-cycle annular beams. Lett. 43, 4506-4509 (2018)
Henke, B. L. et al. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E= 50-30,000 eV, Z= 1-92. Data Nucl. Data Tables 54, 181-342 (1993).
Chappuis, C., Bresteau, D., Auguste, T., Gobert, O. & Ruchon, T. High-order harmonic generation in an active grating. Rev. A 99, doi:10.1103/PhysRevA.99.033806 (2019).
Ellis, J. L. et al. Phase matching of noncollinear sum and difference frequency high harmonic generation above and below the critical ionization level. Optics express 25, 10126-10144 (2017).
You, Y. S. et al. Laser waveform control of extreme ultraviolet high harmonics from solids. Lett. 42, 1816-1819, doi:10.1364/OL.42.001816 (2017).
Han, S. et al. Extraction of higher-order nonlinear electronic response in solids using high harmonic generation. Nature communications 10, 1-6 (2019).
Faulkner, H. M. & Rodenburg, J. M. Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. Rev. Lett. 93, 023903, doi:10.1103/PhysRevLett.93.023903 (2004)
Maznev, A. A. et al. Generation of coherent phonons by coherent extreme ultraviolet radiation in a transient grating experiment. Phys. Lett. 113, 221905, doi:/10.1063/1.5048023
Chalupský, J. et al. Non-thermal desorption/ablation of molecular solids induced by ultra-short soft x-ray pulses. Exp. 17, 1, 208-217, doi:10.1364/OE.17.000208 (2009)
Kim, Y. W. et al. Compensation of laser propagation effects within solids for high harmonic generation of extreme ultraviolet radiation. Laser Technol. 145, 107507, doi: 10.1016/j.optlastec.2021.107507 (2022)
Uchida, K. et al. High-order Harmonic Generation and its Unconventional Scaling Law in the Mott-insulating Ca₂RuO₄. arXiv:2106.15478, doi: 10.48550/arXiv.2106.15478 (2021) .
He, F. et al. Tailoring femtosecond 1.5-μm Bessel beams for manufacturing high-aspect-ratio through-silicon vias. Rep. 7, 40785 doi: 10.1038/srep40785 (2017)
Suzaki, Y. & Tachibana, A. Measurement of the μm sized radius of Gaussian laser beam using the scanning knife-edge. Opt. 14, 2809-2810, doi: 10.1364/AO.14.002809 (1975).

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Coherent manipulation of extreme-ultraviolet Bessel vortex beam from solids by active wavefront shaping of driving fundamental beam

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Abstract

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Introduction

Results

Facile wavefront control of EUV harmonic beams

EUV Bessel vortex generation

Discussion

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