Abstract

Plasmon resonances are known to amplify the electromagnetic fields near metallic nanostructures, providing a promising scheme to generate extreme-ultraviolet harmonics using low power drivings. During high-order harmonic generation (HHG), the driving and harmonic fields accumulate a phase difference as they propagate through the target. In a typical set-up –a laser focused into a gas jet– the propagation distances amount to several wavelengths, and the cumulative phase-mismatch affects strongly the efficiency and properties of the harmonic emission. In contrast, HHG in metallic nanostructures is considered to overcome these limitations, as the common sources of phase mismatch –optical density and focusing geometry– are negligible for subwavelength propagation distances. We demonstrate that phase matching still plays a relevant role in HHG from nanostructures due to the non-perturbative character of HHG, that links the harmonic phase to the intensity distribution of the driving field. Our computations show that widely used applications of phase matching control, such as quantum path selection and the increase of contrast in attosecond pulse generation, are also feasible at the nanoscale.

© 2017 Optical Society of America

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2017 (3)

G. Vampa, B. G. Ghamsari, S. Siadat Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 64, 39–45 (2017).

M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, W. A. Okell, S. Zherebtsov, B. Förg, J. Schöz, L. Seiffert, T. Fennel, T. Shaaran, T. Zimmermann, A. Chacón, R. Guichard, A. Zaïr, J. W. G. Tisch, J. P. Marangos, T. Witting, A. Braun, S. A. Maier, L. Roso, M. Krüger, P. Hommelhoff, M. F. Kling, F. Krausz, and M. Lewenstein, “Attosecond physics at the nanoscale,” Rep. Prog. Phys. 80, 054401 (2017).
[Crossref] [PubMed]

E. N. Osika, A. Chacón, L. Ortmann, N. Suárez, J. A. Pérez-Hernández, B. Szafran, M. F. Ciappina, F. Sols, A. S. Landsman, and M. Lewenstein, “Wannier-bloch approach to localization in high-harmonics generation in solids,” Phys. Rev. X 7, 021017 (2017).

2016 (2)

S. Han, H. Kim, Y. W. Kim, Y.-J. Kim, S. Kim, I.-Y. Park, and S.-W. Kim, “High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure,” Nat. Commun. 7, 13105 (2016).
[Crossref] [PubMed]

C. Hernández-García, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, L. Plaja, A. Becker, and A. Jaron-Becker, “Group velocity matching in high-order harmonic generation driven by mid-infrared lasers,” New J. Phys. 18, 073031 (2016).
[Crossref]

2015 (3)

C. Hernández-García, W. Holgado, L. Plaja, B. Alonso, F. Silva, M. Miranda, H. Crespo, and I. J. Sola, “Carrier-envelope-phase insensitivity in high-order harmonic generation driven by few-cycle laser pulses,” Opt. Express 23, 21497–21508 (2015).
[Crossref] [PubMed]

C. Hernández-García, J. S. Román, L. Plaja, and A. Picón, “Quantum-path signatures in attosecond helical beams driven by optical vortices,” New J. Phys. 17, 093029 (2015).
[Crossref]

A. Chacón, M. F. Ciappina, and M. Lewenstein, “Numerical studies of light-matter interaction driven by plasmonic fields: The velocity gauge,” Phys. Rev. A 92, 063834 (2015).
[Crossref]

2014 (2)

A. M. Summers, A. S. Ramm, G. Paneru, M. F. Kling, B. N. Flanders, and C. A. Trallero-Herrero, “Optical damage threshold of au nanowires in strong femtosecond laser fields,” Opt. Express 22, 4235–4246 (2014).
[Crossref] [PubMed]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photon. 8, 178–186 (2014).
[Crossref]

2013 (5)

N. Pfullmann, C. Waltermann, M. Noack, S. Rausch, T. Nagy, C. Reinhardt, M. Kovačev, V. Knittel, R. Bratschitsch, D. Akemeier, A. Hütten, A. Leitenstorfer, and U. Morgner, “Bow-tie nano-antenna assisted generation of extreme ultraviolet radiation,” New J. Phys. 15, 093027 (2013).
[Crossref]

C. Hernández-García, J. A. Pérez-Hernández, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, A. Jaron-Becker, A. Becker, and L. Plaja, “Zeptosecond high harmonic kev x-ray waveforms driven by midinfrared laser pulses,” Phys. Rev. Lett. 111, 033002 (2013).
[Crossref] [PubMed]

R. A. Fonseca, J. Vieira, F. Fiuza, A. Davidson, F. S. Tsung, W. B. Mori, and L. O. Silva, “Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators,” Plasma Phys. Control. Fusion 55, 124011 (2013).
[Crossref]

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Extreme-ultraviolet light generation in plasmonic nanostructures,” Nat. Phys. 9, 304–309 (2013).
[Crossref]

C. Hernández-García, I. J. Sola, and L. Plaja, “Signature of the transversal coherence length in high-order harmonic generation,” Phys. Rev. A 88, 043848 (2013).
[Crossref]

2012 (6)

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A 85, 033828 (2012).
[Crossref]

C. Hernández-García and L. Plaja, “Off-axis compensation of attosecond pulse chirp,” J. Phys. B 45, 074021 (2012).
[Crossref]

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature 485, E1–E3 (2012).
[Crossref] [PubMed]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. Murnane, and H. Kapteyn, “Bright coherent ultrahigh harmonics in the kev x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “Kim et al. reply,” Nature 485, E1–E3 (2012).
[Crossref]

J. Choi, S. Kim, I.-Y. Park, D.-H. Lee, S. Han, and S.-W. Kim, “Generation of isolated attosecond pulses using a plasmonic funnel-waveguide,” New J. Phys. 14, 103038 (2012).
[Crossref]

2011 (2)

A. Husakou, S.-J. Im, and J. Herrmann, “Theory of plasmon-enhanced high-order harmonic generation in the vicinity of metal nanostructures in noble gases,” Phys. Rev. A 83, 043839 (2011).
[Crossref]

S. L. Stebbings, F. S. mann, Y.-Y. Yang, A. Scrinzi, M. Durach, A. Rusina, M. I. Stockman, and M. F. Kling, “Generation of isolated attosecond extreme ultraviolet pulses employing nanoplasmonic field enhancement: optimization of coupled ellipsoids,” New J. Phys. 13, 073010 (2011).
[Crossref]

2010 (1)

C. Hernández-García, J. A. Pérez-Hernández, J. Ramos, E. C. Jarque, L. Roso, and L. Plaja, “High-order harmonic propagation in gases within the discrete dipole approximation,” Phys. Rev. A 82, 033432 (2010).
[Crossref]

2009 (2)

2008 (4)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

R. A. Fonseca, S. F. Martins, L. O. Silva, J. W. Tonge, F. S. Tsung, and W. B. Mori, “One-to-one direct modeling of experiments and astrophysical scenarios: pushing the envelope on kinetic plasma simulations,” Plasma Phys. Control. Fusion 50, 124034 (2008).
[Crossref]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum path interferences in high-order harmonic generation,” Phys. Rev. Lett. 100, 143902 (2008).
[Crossref] [PubMed]

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

2006 (1)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

2003 (1)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[Crossref] [PubMed]

2001 (2)

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292, 902–905 (2001).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

1997 (1)

W. Becker, A. Lohr, M. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: Application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[Crossref]

1995 (2)

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
[Crossref] [PubMed]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
[Crossref] [PubMed]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

1993 (2)

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

1980 (1)

H. R. Reiss, “Effect of an intense electromagnetic field on a weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[Crossref]

1973 (1)

F. H. M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89 (1973).
[Crossref]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh. Eksp. Teor. Fiz. 47, 1945 (1965).

Abel, B.

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Extreme-ultraviolet light generation in plasmonic nanostructures,” Nat. Phys. 9, 304–309 (2013).
[Crossref]

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature 485, E1–E3 (2012).
[Crossref] [PubMed]

Adam, J. C.

R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, and J. C. Adam, OSIRIS: A Three-Dimensional, Fully Relativistic Particle in Cell Code for Modeling Plasma Based Accelerators (Springer, 2002), pp. 342–351.

Agostini, P.

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Silva, L. O.

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M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, W. A. Okell, S. Zherebtsov, B. Förg, J. Schöz, L. Seiffert, T. Fennel, T. Shaaran, T. Zimmermann, A. Chacón, R. Guichard, A. Zaïr, J. W. G. Tisch, J. P. Marangos, T. Witting, A. Braun, S. A. Maier, L. Roso, M. Krüger, P. Hommelhoff, M. F. Kling, F. Krausz, and M. Lewenstein, “Attosecond physics at the nanoscale,” Rep. Prog. Phys. 80, 054401 (2017).
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Nature (3)

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Figures (7)

Fig. 1
Fig. 1

(a) Interaction scheme considered in this paper: a few-cycle NIR beam is focused into a gold bow-tie nano antenna. Harmonics are generated from argon gas by the enhanced driving field at the antenna’s gap. (b) Field amplitude profile across the gap, at the antenna’s center, induced at the peak of the driving field at the time tmax.

Fig. 2
Fig. 2

(a) Violet: Harmonic spectrum from the volume-integrated propagated signal emitted by the argon gas enclosed in the antenna’s gap (linear scale), for the antena’s design depicted in Fig. 1a. . Blue: emission by the same number of atoms positioned at the coordinate origin (referred in the text as effective single-atom emission). (b) EUV field emitted by the antenna, after filtering the harmonic orders below 10 (c) Time-frequency analysis of the emission of the effective single-atom (d) the same for the volume-integrated propagated signal.

Fig. 3
Fig. 3

Left column: Absolute value of the field amplitude at the planes (a) z = 0, (b) y = 0 and (c) x = 0 at the time tmax. Right column: Time-dependent amplitudes at three points in each of the planes (white crosses in the left-column plots).

Fig. 4
Fig. 4

Intensity (color) and phase (arrows) maps of the spatial contributions to the 17th harmonic far field plotted along the planes shown in Fig. 3 a to c, respectively.

Fig. 5
Fig. 5

Results for the spectrum emitted by a bow-tie antenna structure with the same geometry as the considered in the main text (Fig. 1, main text) but with its thickness increased by a factor two (100 nm). The driving field parameters are also those used in the main text, except for the driver’s intensity, that has been increased by a factor 1.5, to match the peak field amplitude at the center of the gap in both cases. (a) Spectrum of the gap’s volume harmonic emission in comparison with the 50 nm thickness case, shown in Fig. 2 (main text). (b) Attosecond pulses after selecting the higher frequencies of the harmonic spectra (harmonic orders > 10), in comparison with the 50 nm thickness case. (c) Map of the 17th harmonic intensity (color background) and phases (arrows) for the 100 nm thick antenna, that can be compared with the 50 nm thick case shown in Fig. 4 (main text). The white double arrow indicates the coherence length.

Fig. 6
Fig. 6

Results for the HHG emitted by a bow-tie antenna structure with the same geometry as the considered in the main text (Fig. 1) but with the gap size increased by a factor two (40 nm). The driving field parameters are also those used in the main text, except for the driver’s intensity, that has been increased by a factor 1.77, to match the peak field amplitude in the gap in both cases. (a) Spectrum of the gap’s volume harmonic emission in comparison with the 20 nm gap case, shown in Fig. 2 (main text). (b) Attosecond pulses after selecting the higher frequencies of the harmonic spectra (harmonic orders > 10), in comparison with the 20 nm gap case. (c) Map of the 17th harmonic intensity (color background) and phases (arrows) for the antenna with 40 nm gap, that can be compared with the 20 nm gap case shown in Fig. 4.

Fig. 7
Fig. 7

(a) Red line: field amplitude profile along the nanoantenna’s gap as shown in Fig. 1, at the antenna’s center, during the peak of the driving field (t = tmax) Green line: Inhomogeneity parameter (field amplitude gradient in atomic units) along the antenna’s gap. (b) Single-atom harmonic spectra generated, blue solid line: without inhomogeneity; green solid line: with = 5.3 × 10−5 corresponding to the maximum value shown in (a); and various inhomogeneity parameters above this value. The position of the spectral cut-off for the homogeneous case is shown as a black dashed vertical line.

Equations (1)

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E j ( r d , t ) = q j s d c 2 | r d r j | × [ s d × a j ( t | r d r j | c ) ]

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