Abstract

We study high-order harmonic generation (HHG) resulting from the illumination of plasmonic nanostructures with a short laser pulse of long wavelength. We demonstrate that both the confinement of the electron motion and the inhomogeneous character of the laser electric field play an important role in the HHG process and lead to a significant increase of the harmonic cutoff. In particular, in bow-tie nanostructures with small gaps, electron trajectories with large excursion amplitudes experience significant confinement and their contribution is essentially suppressed. In order to understand and characterize this feature, we combine the numerical solution of the time-dependent Schrödinger equation (TDSE) with the electric fields obtained from 3D finite element simulations. We employ time-frequency analysis to extract more detailed information from the TDSE results and classical tools to explain the extended harmonic spectra. The spatial inhomogeneity of the laser electric field modifies substantially the electron trajectories and contributes also to cutoff increase.

© 2012 OSA

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2012 (7)

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A85(1), 013416 (2012).
[CrossRef]

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A85(3), 033828 (2012).
[CrossRef]

T. Shaaran, M. F. Ciappina, and M. Lewenstein, “Quantum-orbit analysis of high-order-harmonic generation by resonant plasmon field enhancement,” Phys. Rev. A86(2), 023408 (2012).
[CrossRef]

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature485(7397), E1–E3 (2012).
[CrossRef] [PubMed]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “Kim et al. reply,” Nature485(7397), E1–E3 (2012).
[CrossRef]

M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B45(7), 074006 (2012).
[CrossRef]

G. Herink, D. R. Solli, M. Gulde, and C. Ropers, “Field-driven photoemission from nanostructures quenches the quiver motion,” Nature483(7388), 190–193 (2012).
[CrossRef] [PubMed]

2011 (7)

I.-Y. Park, S. Kim, J. Choi, D.-H. L. Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Phot.5(11), 677–681 (2011).
[CrossRef]

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. A83(4), 043839 (2011).
[CrossRef]

M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature475(7354), 78–81 (2011).
[CrossRef] [PubMed]

A. Thai, M. Hemmer, P. Bates, O. Chalus, and J. Biegert, “Sub-250-mrad, passively carrierenvelope-phase-stable mid-infrared OPCPA source at high repetition rate,” Opt. Lett.36(19), 3918–3920 (2011).
[CrossRef] [PubMed]

S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
[CrossRef]

F. Süßmann and M. F. Kling, “Attosecond nanoplasmonic streaking of localized fields near metal nanospheres,”, Phys. Rev. B84(12), 121406(R) (2011).

S. Zherebtsov and , “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys.7(8), 656–662 (2011).
[CrossRef]

2010 (2)

C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A81(3), 033412 (2010).
[CrossRef]

M. Schenk, M. Krüger, and P. Hommelhoff, “Strong-field above-threshold photoemission from sharp metal tips,” Phys. Rev. Lett.105(2), 257601 (2010).
[CrossRef]

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009).
[CrossRef]

2008 (1)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

2007 (2)

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys.3(6), 381–387 (2007).
[CrossRef]

M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. B40(16), R135–R173 (2007).
[CrossRef]

2006 (1)

P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, and M. A. Kasevich, “Field emission tip as a nanometer source of free electron femtosecond pulses,” Phys. Rev. Lett.96(7), 077401 (2006).
[CrossRef] [PubMed]

2005 (3)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94(19) 193201 (2005).
[CrossRef] [PubMed]

2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys.72(2), 545–591 (2000).
[CrossRef]

1999 (1)

P. Salières, A. L’Huillier, P. Antoine, and M. Lewenstein,“Study of the spatial and temporal coherence of high-order harmonics,” Advances in Atomic, Molecular and Optical Physics, eds. B. Bederson and H. Walther41, 83–142 (1999).
[CrossRef]

1997 (2)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys.60(4), 389–486 (1997).
[CrossRef]

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett.78(4), 638–641 (1997).
[CrossRef]

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. A49(3) 2117–2132 (1994).
[CrossRef] [PubMed]

1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett.71(13), 1994–1997 (1993).
[CrossRef] [PubMed]

1992 (1)

J. L. Krause, K. J. Schafer, and K. C. Kulander, “Calculation of photoemission from atoms subject to intense laser fields,” Phys. Rev. A45(7), 4998–5010 (1992).
[CrossRef] [PubMed]

1991 (1)

Q. Su and J. H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A44(9), 5997–6008 (1991).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP64(6), 1191–1194 (1986).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP20(5), 1307–1314 (1965).

1946 (1)

D. Gabor, “Theory of communication,” J. Inst. Electr. Eng.93, 429–441 (1946).

Abel, B.

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature485(7397), E1–E3 (2012).
[CrossRef] [PubMed]

Aghajani-Talesh, A.

P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, and M. A. Kasevich, “Field emission tip as a nanometer source of free electron femtosecond pulses,” Phys. Rev. Lett.96(7), 077401 (2006).
[CrossRef] [PubMed]

Altun, Z.

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A85(1), 013416 (2012).
[CrossRef]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP64(6), 1191–1194 (1986).

Antoine, P.

P. Salières, A. L’Huillier, P. Antoine, and M. Lewenstein,“Study of the spatial and temporal coherence of high-order harmonics,” Advances in Atomic, Molecular and Optical Physics, eds. B. Bederson and H. Walther41, 83–142 (1999).
[CrossRef]

Baffou, G.

G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser & Photon. Rev. (in press) (2012).
[CrossRef]

Balcou, P.

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. A49(3) 2117–2132 (1994).
[CrossRef] [PubMed]

Bates, P.

Biegert, J.

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A85(3), 033828 (2012).
[CrossRef]

A. Thai, M. Hemmer, P. Bates, O. Chalus, and J. Biegert, “Sub-250-mrad, passively carrierenvelope-phase-stable mid-infrared OPCPA source at high repetition rate,” Opt. Lett.36(19), 3918–3920 (2011).
[CrossRef] [PubMed]

Bleda, E. A.

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A85(1), 013416 (2012).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys.72(2), 545–591 (2000).
[CrossRef]

Chalus, O.

Chirila, C. C.

C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A81(3), 033412 (2010).
[CrossRef]

Choi, J.

I.-Y. Park, S. Kim, J. Choi, D.-H. L. Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Phot.5(11), 677–681 (2011).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Ciappina, M. F.

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A85(3), 033828 (2012).
[CrossRef]

T. Shaaran, M. F. Ciappina, and M. Lewenstein, “Quantum-orbit analysis of high-order-harmonic generation by resonant plasmon field enhancement,” Phys. Rev. A86(2), 023408 (2012).
[CrossRef]

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond Carbon K-edge harmonic emission using spatial and temporal synthesized laser field,”, arXiv:1207.4653v1 (2012).

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys.3(6), 381–387 (2007).
[CrossRef]

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. A49(3) 2117–2132 (1994).
[CrossRef] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett.71(13), 1994–1997 (1993).
[CrossRef] [PubMed]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP64(6), 1191–1194 (1986).

Dreissigacker, I.

C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A81(3), 033412 (2010).
[CrossRef]

Durach, M.

S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
[CrossRef]

Duwe, M.

M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature485(7397), E1–E3 (2012).
[CrossRef] [PubMed]

Eberly, J. H.

Q. Su and J. H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A44(9), 5997–6008 (1991).
[CrossRef] [PubMed]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Förster, M.

M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B45(7), 074006 (2012).
[CrossRef]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, “Theory of communication,” J. Inst. Electr. Eng.93, 429–441 (1946).

Gulde, M.

G. Herink, D. R. Solli, M. Gulde, and C. Ropers, “Field-driven photoemission from nanostructures quenches the quiver motion,” Nature483(7388), 190–193 (2012).
[CrossRef] [PubMed]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Hemmer, M.

Herink, G.

G. Herink, D. R. Solli, M. Gulde, and C. Ropers, “Field-driven photoemission from nanostructures quenches the quiver motion,” Nature483(7388), 190–193 (2012).
[CrossRef] [PubMed]

Herrmann, J.

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. A83(4), 043839 (2011).
[CrossRef]

Hommelhoff, P.

M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B45(7), 074006 (2012).
[CrossRef]

M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature475(7354), 78–81 (2011).
[CrossRef] [PubMed]

M. Schenk, M. Krüger, and P. Hommelhoff, “Strong-field above-threshold photoemission from sharp metal tips,” Phys. Rev. Lett.105(2), 257601 (2010).
[CrossRef]

P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, and M. A. Kasevich, “Field emission tip as a nanometer source of free electron femtosecond pulses,” Phys. Rev. Lett.96(7), 077401 (2006).
[CrossRef] [PubMed]

Husakou, A.

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. A83(4), 043839 (2011).
[CrossRef]

Im, S.-J.

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. A83(4), 043839 (2011).
[CrossRef]

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009).
[CrossRef]

Ivanov, M. Y.

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. A49(3) 2117–2132 (1994).
[CrossRef] [PubMed]

Jin, J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “Kim et al. reply,” Nature485(7397), E1–E3 (2012).
[CrossRef]

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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005).
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R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94(19) 193201 (2005).
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S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “Kim et al. reply,” Nature485(7397), E1–E3 (2012).
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I.-Y. Park, S. Kim, J. Choi, D.-H. L. Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Phot.5(11), 677–681 (2011).
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S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
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J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond Carbon K-edge harmonic emission using spatial and temporal synthesized laser field,”, arXiv:1207.4653v1 (2012).

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P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
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M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys.60(4), 389–486 (1997).
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S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
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P. Salières, A. L’Huillier, P. Antoine, and M. Lewenstein,“Study of the spatial and temporal coherence of high-order harmonics,” Advances in Atomic, Molecular and Optical Physics, eds. B. Bederson and H. Walther41, 83–142 (1999).
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K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett.78(4), 638–641 (1997).
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M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B45(7), 074006 (2012).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005).
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S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
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T. Shaaran, M. F. Ciappina, and M. Lewenstein, “Quantum-orbit analysis of high-order-harmonic generation by resonant plasmon field enhancement,” Phys. Rev. A86(2), 023408 (2012).
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M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature485(7397), E1–E3 (2012).
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G. Herink, D. R. Solli, M. Gulde, and C. Ropers, “Field-driven photoemission from nanostructures quenches the quiver motion,” Nature483(7388), 190–193 (2012).
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P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, and M. A. Kasevich, “Field emission tip as a nanometer source of free electron femtosecond pulses,” Phys. Rev. Lett.96(7), 077401 (2006).
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S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
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I.-Y. Park, S. Kim, J. Choi, D.-H. L. Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Phot.5(11), 677–681 (2011).
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S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
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R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94(19) 193201 (2005).
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R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94(19) 193201 (2005).
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J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond Carbon K-edge harmonic emission using spatial and temporal synthesized laser field,”, arXiv:1207.4653v1 (2012).

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P. Salières, A. L’Huillier, P. Antoine, and M. Lewenstein,“Study of the spatial and temporal coherence of high-order harmonics,” Advances in Atomic, Molecular and Optical Physics, eds. B. Bederson and H. Walther41, 83–142 (1999).
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Nat. Phot. (1)

I.-Y. Park, S. Kim, J. Choi, D.-H. L. Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Phot.5(11), 677–681 (2011).
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P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys.3(6), 381–387 (2007).
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S. Zherebtsov and , “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys.7(8), 656–662 (2011).
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Nature (5)

G. Herink, D. R. Solli, M. Gulde, and C. Ropers, “Field-driven photoemission from nanostructures quenches the quiver motion,” Nature483(7388), 190–193 (2012).
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S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature475(7354), 78–81 (2011).
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M. Sivis, M. Duwe, B. Abel, and C. Ropers, “Nanostructure-enhanced atomic line emission,” Nature485(7397), E1–E3 (2012).
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New Journal of Physics (1)

S. L. Stebbings, F. Süßmann, 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 Journal of Physics13(7), 073010 (2011).
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Opt. Lett. (1)

Phys. Rev. A (8)

C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A81(3), 033412 (2010).
[CrossRef]

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[CrossRef] [PubMed]

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I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A85(1), 013416 (2012).
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M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A85(3), 033828 (2012).
[CrossRef]

T. Shaaran, M. F. Ciappina, and M. Lewenstein, “Quantum-orbit analysis of high-order-harmonic generation by resonant plasmon field enhancement,” Phys. Rev. A86(2), 023408 (2012).
[CrossRef]

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. A49(3) 2117–2132 (1994).
[CrossRef] [PubMed]

Phys. Rev. B (2)

F. Süßmann and M. F. Kling, “Attosecond nanoplasmonic streaking of localized fields near metal nanospheres,”, Phys. Rev. B84(12), 121406(R) (2011).

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Phys. Rev. Lett. (6)

P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, and M. A. Kasevich, “Field emission tip as a nanometer source of free electron femtosecond pulses,” Phys. Rev. Lett.96(7), 077401 (2006).
[CrossRef] [PubMed]

M. Schenk, M. Krüger, and P. Hommelhoff, “Strong-field above-threshold photoemission from sharp metal tips,” Phys. Rev. Lett.105(2), 257601 (2010).
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Figures (8)

Fig. 1
Fig. 1

Schematic representation of the geometry of the considered nanostructure. A gold bow-tie antenna resides on glass substrate (refractive index n = 1.52) with superstate medium of air (n = 1). The characteristic dimensions of the system and the coordinate system used in the 1D-TDSE simulations are shown.

Fig. 2
Fig. 2

High-order harmonic generation (HHG) spectra for Ar with ionization potential GS = −0.58 a.u., laser wavelength λ = 1800 nm and intensity I = 8 × 1013 W·cm−2 at the center of the gap x = 0. We use a trapezoidal shaped pulse, Eq. (7), with non = 3, noff = 3 and np = 4 (about 60 fs). The gold bow-tie nanostructure has a gap g = 12 nm (226 a.u.). The black line indicates the homogeneous case while the red line indicates the nonhomogeneous case. The arrow indicates the cutoff predicted by the semiclassical model for the homogeneous case [7]. The top left inset shows the functional form of the electric field E(x,t), where the solid lines are the raw data obtained from the finite element simulations and the dashed line is a nonlinear fitting. The top right inset shows the intensity enhancement in the gap region of the gold bow-tie nanostructure.

Fig. 3
Fig. 3

Idem Fig. 2, except that now the gold bow-tie nanostructure has a gap g of 15 nm (283 a.u.) and the laser intensity is I = 1.25 × 1014 W·cm−2 at the center of the gap x = 0.

Fig. 4
Fig. 4

Gabor analysis for the harmonic spectra of Figs. 2 and 3. Panels (a) and (b) correspond to the Fig. 2 for the homogeneous and nonhomogeneous case, respectively. While panels (c) and (d) correspond to the Fig. 3 for the homogeneous and nonhomogeneous case, respectively. In all panels, the zoomed regions show a time interval during the laser pulse (Ref. [38] for details).

Fig. 5
Fig. 5

Total energy of the free electron (in terms of the harmonic order) in the laser field when it recollides with its parent ion obtained from Newton’s second law and plotted as a function of the ionization time (green filled circles) or the recollision time (red open circles). Panel (a) homogeneous case without restriction in the electron motion, (b) non-homogeneous case without restriction in the electron motion, (c) idem (a) restricting the electron motion to the region [−α0, α0] and (d) idem (b) restricting the electron motion to the region [−α0, α0]. The laser parameters are I = 8 × 1013 W·cm−2, λ = 1800 nm and a trapezoidal shaped pulse with non = 3, np = 4 and noff = 3. The nonhomogeneous electric field is that corresponding to a bow-tie shaped nanostructure with g = 12 nm.

Fig. 6
Fig. 6

Idem Fig. 5 but with I = 1.25 × 1014 W·cm−2 and the nonhomogeneous electric field is that corresponding to a bow-tie shaped nanostructure with g = 15 nm.

Fig. 7
Fig. 7

Dependence of the semiclassical trajectories on the ionization and recollision times. Non confined case panel (a); confined case panel (b). Blue squares ( oe----i001.gif), homogeneous case; red circles ( oe----i002.gif) nonhomogeneous case. The laser parameters are I = 8×1013 W·cm−2, λ = 1800 nm and a trapezoidal pulse with non = 3, np = 4 and noff = 3. The nonhomogeneous electric field is that corresponding to a bow-tie shaped nanostructure with g = 12 nm.

Fig. 8
Fig. 8

Idem Fig. 7 but with I = 1.25 × 1014 W·cm−2. The nonhomogeneous electric field is that corresponding to a bow-tie shaped nanostructure with g = 15 nm.

Equations (16)

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i Ψ ( x , t ) t = ( t ) Ψ ( x , t )
= [ 1 2 2 x 2 + V atom ( x ) + V laser ( x , t ) ] Ψ ( x , t )
V atom ( x ) = 1 x 2 + ξ 2
V laser ( x , t ) = E ( x , t ) x .
E ( x , t ) = E 0 f ( t ) ( 1 + h ( x ) ) sin ω t ,
h ( x ) = i = 1 N b i x i
f ( t ) = { t t 1 for 0 t < t 1 1 for t 1 t t 2 ( t t 3 ) ( t 3 t 2 ) for t 2 < t t 3 0 elsewhere
D ( ω ) = | 1 τ 1 ω 2 d t e i ω t a ( t ) | 2
a ( t ) = d 2 x d t 2 = Ψ ( t ) | [ ( t ) , [ ( t ) , x ] ] | Ψ ( t ) .
a G ( Ω , t ) = d t a ( t ) exp [ ( t t 2 / 2 σ 2 ] σ 2 π exp ( i Ω t )
n c = ( 3.17 U p + I p ) / ω
x ( t 0 ) = 0
x ˙ ( t 0 ) = 0 .
x ( t 1 ) = 0 .
E k ( t 1 ) = x ˙ ( t 1 ) 2 2
x ¨ ( t ) = x V laser ( x , t ) = E ˜ ( x , t )

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