Abstract

We present a novel method for controlling the transverse positions and relative powers of multiple high-order harmonic beams. A phase-only spatial light modulator is used to produce multiple infrared foci, the positions and intensities of which can be controlled programmably, enabling the generation and control of multiple HHG beams. To demonstrate the utility of this method we perform Fourier transform holography with separate illumination of the object and reference pinhole by a pair of HHG beams, which makes optimal use of the available photon flux. The programmable control of the spatial distribution of HHG beams demonstrated here offers new opportunities for experiments at extreme ultraviolet (XUV) wavelengths, particularly for photon intensive applications such as imaging.

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2019 (4)

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13(1), 54–59 (2019).
[Crossref]

F. Wiegandt, P. N. Anderson, F. Yu, D. J. Treacher, D. T. Lloyd, P. J. Mosley, S. M. Hooker, and I. A. Walmsley, “Quasi-phase-matched high-harmonic generation in gas-filled hollow-core photonic crystal fiber,” Optica 6(4), 442–447 (2019).
[Crossref]

L. Jian, E. F. Cunningham, Y. S. You, D. A. Reis, and S. Ghimire, “Interferometry of dipole phase in high harmonics from solids,” Nat. Photonics 13(2), 96–100 (2019).
[Crossref]

G. Xia, W. Fan, D. Huang, H. Cheng, J. Guo, and X. Wang, “High damage threshold liquid crystal binary mask for laser beam shaping,” High Power Laser Sci. Eng. 7, e9 (2019).
[Crossref]

2018 (2)

G. K. Tadesse, W. Eschen, R. Klas, V. Hilbert, D. Schelle, A. Nathanael, M. Zilk, M. Steinert, F. Schrempel, T. Pertsch, A. Tünnermann, J. Limpert, and J. Rothhardt, “High resolution XUV Fourier transform holography on a table top,” Sci. Rep. 8(1), 8677 (2018).
[Crossref]

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
[Crossref]

2017 (1)

P. Anderson, F. Wiegandt, D. Treacher, M. Mang, I. Gianani, A. Schiavi, D. Lloyd, K. O’Keeffe, S. Hooker, and I. Walmsley, “Blind digital holographic microscopy,” Proc. SPIE 10127, 101270H (2017).
[Crossref]

2016 (2)

2015 (1)

2014 (4)

Y. Qin, T. Nakajima, H. Zen, X. Wang, T. Kii, and H. Ohgaki, “Characterization of non-Gaussian mid-infrared free-electron laser beams by the knife-edge method,” Infrared Phys. Technol. 66, 146–151 (2014).
[Crossref]

K. O’Keeffe, D. Lloyd, and S. Hooker, “Quasi-phase-matched high-order harmonic generation using tunable pulse trains,” Opt. Express 22(7), 7722–7732 (2014).
[Crossref]

Q. Huang, M. de Boer, J. Barreaux, R. van der Meer, E. Louis, and F. Bijkerk, “High efficiency structured EUV multilayer mirror for spectral filtering of long wavelengths,” Opt. Express 22(16), 19365–19374 (2014).
[Crossref]

M. E. Couprie, “New generation of light sources: Present and future,” J. Electron Spectrosc. Relat. Phenom. 196, 3–13 (2014).
[Crossref]

2013 (2)

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref]

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103(17), 171105 (2013).
[Crossref]

2012 (1)

2011 (2)

J. C. Petersen, S. Kaiser, N. Dean, A. Simoncig, H. Y. Liu, A. L. Cavalieri, C. Cacho, I. C. E. Turcu, E. Springate, F. Frassetto, L. Poletto, S. S. Dhesi, H. Berger, and A. Cavalleri, “Clocking the melting transition of charge and lattice order in 1t-tas$_2$2 with ultrafast extreme-ultraviolet angle-resolved photoemission spectroscopy,” Phys. Rev. Lett. 107(17), 177402 (2011).
[Crossref]

E. Louis, A. Yakshin, T. Tsarfati, and F. Bijkerk, “Nanometer interface and materials control for multilayer euv-optical applications,” Prog. Surf. Sci. 86(11-12), 255–294 (2011).
[Crossref]

2010 (3)

S. Hädrich, J. Rothhardt, M. Krebs, F. Tavella, A. Willner, J. Limpert, and A. Tünnermann, “High harmonic generation by novel fiber amplifier based sources,” Opt. Express 18(19), 20242–20250 (2010).
[Crossref]

E. L. Falcão-Filho, C.-J. Lai, K.-H. Hong, V.-M. Gkortsas, S.-W. Huang, L.-J. Chen, and F. X. Kärtner, “Scaling of high-order harmonic efficiencies with visible wavelength drivers: A route to efficient extreme ultraviolet sources,” Appl. Phys. Lett. 97(6), 061107 (2010).
[Crossref]

Y. H. Jiang, T. Pfeifer, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, M. Lezius, and M. F. Kling, “Temporal coherence effects in multiple ionization of N 2 via XUV pump-probe autocorrelation,” Phys. Rev. A 82(4), 041403 (2010).
[Crossref]

2009 (2)

R. L. Sandberg, D. A. Raymondson, C. La-o-vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009).
[Crossref]

T. Popmintchev and M.-C. Chen, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U. S. A. 106(26), 10516–10521 (2009).
[Crossref]

2008 (3)

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At., Mol. Opt. Phys. 41(13), 132001 (2008).
[Crossref]

A. Ozawa, J. Rauschenberger, C. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and T. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008).
[Crossref]

G. Genoud, O. Guilbaud, E. Mengotti, S.-G. Pettersson, E. Georgiadou, E. Pourtal, C.-G. Wahlström, and A. L’Huillier, “Xuv digital in-line holography using high-order harmonics,” Appl. Phys. B: Lasers Opt. 90(3-4), 533–538 (2008).
[Crossref]

2007 (2)

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-x-ray beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15(26), 17592–17612 (2007).
[Crossref]

2006 (2)

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, C. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89(16), 163112 (2006).
[Crossref]

A.-S. Morlens, J. Gautier, G. Rey, P. Zeitoun, J.-P. Caumes, M. Kos-Rosset, H. Merdji, S. Kazamias, K. Cassou, and M. Fajardo, “Submicrometer digital in-line holographic microscopy at 32 nm with high-order harmonics,” Opt. Lett. 31(21), 3095–3097 (2006).
[Crossref]

2003 (2)

1998 (1)

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C.-G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

1993 (1)

B. Henke, E. Gullikson, and J. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[Crossref]

1992 (1)

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[Crossref]

1982 (1)

W. O. Saxton and W. Baumeister, “The correlation averaging of a regularly arranged bacterial cell envelope protein,” J. Microsc. 127(2), 127–138 (1982).
[Crossref]

Anderson, E. H.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[Crossref]

Anderson, P.

P. Anderson, F. Wiegandt, D. Treacher, M. Mang, I. Gianani, A. Schiavi, D. Lloyd, K. O’Keeffe, S. Hooker, and I. Walmsley, “Blind digital holographic microscopy,” Proc. SPIE 10127, 101270H (2017).
[Crossref]

Anderson, P. N.

Andrews, L.

L. Andrews, Special Functions of Mathematics for Engineers, Oxford science publications. (SPIE Optical Engineering Press, 1998). Page 110.

Apolonski, A.

A. Ozawa, J. Rauschenberger, C. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and T. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008).
[Crossref]

Auguste, T.

Azoury, D.

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13(1), 54–59 (2019).
[Crossref]

Bandrauk, A. D.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
[Crossref]

Barreaux, J.

Bates, M.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref]

Baumeister, W.

W. O. Saxton and W. Baumeister, “The correlation averaging of a regularly arranged bacterial cell envelope protein,” J. Microsc. 127(2), 127–138 (1982).
[Crossref]

Bellini, M.

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C.-G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Berger, H.

J. C. Petersen, S. Kaiser, N. Dean, A. Simoncig, H. Y. Liu, A. L. Cavalieri, C. Cacho, I. C. E. Turcu, E. Springate, F. Frassetto, L. Poletto, S. S. Dhesi, H. Berger, and A. Cavalleri, “Clocking the melting transition of charge and lattice order in 1t-tas$_2$2 with ultrafast extreme-ultraviolet angle-resolved photoemission spectroscopy,” Phys. Rev. Lett. 107(17), 177402 (2011).
[Crossref]

Bian, X.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
[Crossref]

Bijkerk, F.

Q. Huang, M. de Boer, J. Barreaux, R. van der Meer, E. Louis, and F. Bijkerk, “High efficiency structured EUV multilayer mirror for spectral filtering of long wavelengths,” Opt. Express 22(16), 19365–19374 (2014).
[Crossref]

E. Louis, A. Yakshin, T. Tsarfati, and F. Bijkerk, “Nanometer interface and materials control for multilayer euv-optical applications,” Prog. Surf. Sci. 86(11-12), 255–294 (2011).
[Crossref]

Boutu, W.

Bruner, B. D.

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13(1), 54–59 (2019).
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Springate, E.

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L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
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Y. Qin, T. Nakajima, H. Zen, X. Wang, T. Kii, and H. Ohgaki, “Characterization of non-Gaussian mid-infrared free-electron laser beams by the knife-edge method,” Infrared Phys. Technol. 66, 146–151 (2014).
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L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
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R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
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Nature (1)

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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-x-ray beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. a) Schematic diagram of the experimental beamline downstream of the SLM. The labels are as follows: SLM is the spatial light modulator, $\theta$ is the angle of incidence to the SLM which was $<5^{\circ}$, L is the IR focusing lens, GC is the nickel gas cell and M is a mirror that when in place, deflects the driver beam onto a CCD through a 4-f unitary magnification reimaging line that allows inspection of the focal plane. F represents Aluminium filters, MLO represents a pair of multilayered XUV optics and XYZ represents a 3 axis optically encoded translation stage. The object and detection planes are denoted ‘O’ and ‘D’ respectively. b) Reflectance curve of both MLO.
Fig. 2.
Fig. 2. a) Measured transverse intensity profile of the infrared radiation after transmission through the phase mask shown in b) and focusing by a $f=50\:$cm lens. The numbers shown next to the foci in a) indicate the corresponding annulus responsible for their creation in b), numbered in order of increasing annulus radius. Beams 6 and 7 in (a) are lacking in circular symmetry because the mask in (b) assumes a perfect incident Gaussian driver beam with no asymmetry, imperfections or clipping. This discrepancy could be accounted for using a priori information about the incident intensity profile.
Fig. 3.
Fig. 3. a) Measured transverse intensity profile (red dots) in the driver focal plane ($\hat {x}$) of the IR focus produced by a $N=2$ SLM mask with parameters given in the text. The simulated intensity (red, solid) and simulated phase (black, dashed) profiles are overlaid. b) Measured variation of the harmonic signal as a function of the position of a knife edge inserted in the beam with its edge parallel to $\hat {y}'$ coordinates in the harmonic focal plane shown by green points, along with the fit (dashed green line). Only every third data point is shown, however the fit was made to the complete dataset. The transverse fluence profile of the harmonic beam in the $\hat {x}'$ dimension (solid black line) was calculated by differentiating [37] the corresponding fit. c) Shows the counterpart data to (b) but in the perpendicular transverse dimension.
Fig. 4.
Fig. 4. Scanning electron microscope image of the FTH sample that comprises the object to the left and two reference holes outlined by white squares. The faint horizontal grey line is a ruler drawn on the SEM image in the focussed ion beam software.
Fig. 5.
Fig. 5. Schematic illustrations of: a) Illumination of the object and reference hole R$_2$ by a pair of harmonic beams; and b) Illumination of the object and reference hole R$_1$ by a single beam. The labels ‘Obj’, R$_1$ and R$_2$ refer to the object, near reference and far reference respectively. More detail is in the text.
Fig. 6.
Fig. 6. Detected holograms on a log scale for normalised exposures of $120$ for $N=1$ (a) and $N=2$ (b) beams. Recovered images for normalised exposures of $120$ for $N=1$ (c) and $N=2$ (d) beams. e) Variation of the S:N ratio as a function of normalized exposure time for the case of $N=1$ (open blue squares) and $N=2$ (full red triangles) beams.

Equations (4)

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ϕ ˙ trans = 2 π λ f ( Δ X x + Δ Y y )
0 2 π r n r n + 1 I 0 e 2 ( r w ) 2 r d r d θ = 1 N 0 2 π 0 I 0 e 2 ( r w ) 2 r d r d θ .
r n + 1 = w 1 2 log e [ 1 exp { 2 ( r n w ) 2 } 1 N ] ,
w Δ z = d 1 2 log e ( 1 α ) ,

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