## Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures |

Optics Express, Vol. 20, Issue 24, pp. 26261-26274 (2012)

http://dx.doi.org/10.1364/OE.20.026261

Acrobat PDF (8720 KB)

### 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

## 1. Introduction

1. 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]

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

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

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

5. M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. B **40**(16), R135–R173 (2007). [CrossRef]

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

7. 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**(3) 2117–2132 (1994). [CrossRef] [PubMed]

^{13}W·cm

^{−2}, two orders of magnitude larger than the output of the current femtosecond oscillators. Nowadays, chirped-pulse amplification is employed to reach the threshold intensity. In addition, improving the efficiency and duty cycle of XUV radiation based on HHG is challenging.

8. 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**(7196), 757–760 (2008). [CrossRef] [PubMed]

9. 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]

10. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science **308**(5728), 1607–1609 (2005). [CrossRef] [PubMed]

11. 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]

^{th}(114 nm) to the 17

^{th}(47 nm) harmonics while the pulse repetition rate remains unaltered without any extra pumping or cavity attachment (for cavity enhancement production of XUV radiation see e.g. [12

12. 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]

8. 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**(7196), 757–760 (2008). [CrossRef] [PubMed]

*λ*= 800 nm and

*λ*= 1800 nm and compared them with the absorption of a 50-nm-thick continuous gold film [19

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

*λ*= 800 nm, with intensity 1.4×10

^{11}W·cm

^{−2}, the absorbed power per unit volume of nanoantennas and continuous film are 6.14×10

^{4}nW/nm

^{3}and 1.16×10

^{3}nW/nm

^{3}, respectively; while for

*λ*= 1800 nm they are 3.83×10

^{4}nW/nm

^{3}and 1.07×10

^{3}nW/nm

^{3}, respectively. Our results show that the heat produced by nanoantennas engineered to resonate at

*λ*= 1800 nm is smaller compared to those that resonate at

*λ*= 800 nm. This lower absorbency, combined with the lower electric field enhancements required to observe the same harmonics, make infrared antennas particularly advantageous compared to visible antennas. Alternative approaches employing different kinds of metallic nanostructures, e.g. nanoparticles (see e.g. [20

20. 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 Physics **13**(7), 073010 (2011). [CrossRef]

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

23. 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]

27. G. Herink, D. R. Solli, M. Gulde, and C. Ropers, “Field-driven photoemission from nanostructures quenches the quiver motion,” Nature **483**(7388), 190–193 (2012). [CrossRef] [PubMed]

**E**(

**r**,

*t*)) and its vector potential associated (

**A**(

**r**,

*t*)) are spatially homogeneous in the region where the electron dynamics takes place, i.e.

**E**(

**r**,

*t*) =

**E**(

*t*) and

**A**(

**r**,

*t*) =

**A**(

*t*) [1

1. 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]

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

28. 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. Walther**41**, 83–142 (1999). [CrossRef]

15. M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A **85**(3), 033828 (2012). [CrossRef]

14. 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. A **85**(1), 013416 (2012). [CrossRef]

15. M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A **85**(3), 033828 (2012). [CrossRef]

8. 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**(7196), 757–760 (2008). [CrossRef] [PubMed]

## 2. Theoretical method

1. 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]

*V*(

_{atom}*x*) is the atomic potential and

*V*(

_{laser}*x*,

*t*) represents the potential due to the laser electric field. In here, we use for

*V*(

_{atom}*x*) the quasi-Coulomb potential which first was introduced in [31

31. Q. Su and J. H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A **44**(9), 5997–6008 (1991). [CrossRef] [PubMed]

*ξ*in Eq. (3). The potential

*V*(

_{laser}*x,t*) due to the laser electric field

*E*(

*x,t*), is given by In here the spatial dependency of

*E*(

*x,t*) can be defined in terms of a perturbation to the dipole approximation and it reads: which is linearly polarized along the

*x*-axis. In Eq. (5),

*E*

_{0},

*ω*and

*f*(

*t*) are the peak amplitude, the frequency of the coherent electromagnetic radiation and the pulse envelope, respectively. Furthermore,

*h*(

*x*) represents the functional form of the nonhomogeneous electric field and it can be written as a series of the form where the coefficients

*b*are obtained by fitting the real electric field that results from a finite element simulation considering the real geometry of different nanostructures. In this work we use for the laser pulse a trapezoidal envelope given by where

_{i}*t*

_{1}= 2

*πn*/

_{on}*ω*,

*t*

_{2}=

*t*

_{1}+ 2

*πn*/

_{p}*ω*, and

*t*

_{3}=

*t*

_{2}+ 2

*πn*/

_{off}*ω*. In here,

*n*,

_{on}*n*and

_{p}*n*are the number of cycles of turn on, plateau and turn off, respectively.

_{off}*ξ*= 1.18 in Eq. (3) such that the binding energy of the ground state of the 1D Hamiltonian coincides with the (negative) ionization potential of Argon, i.e. ℰ

*= −15.7596 eV (−0.58 a.u.). Moreover, we assume that the noble gas atom is in its initial state (ground state (GS)) before we turning the laser (*

_{GS}*t*= −∞) on. Equation (1) is then solved numerically by using the Crank-Nicolson scheme [1

**60**(4), 389–486 (1997). [CrossRef]

32. J. L. Krause, K. J. Schafer, and K. C. Kulander, “Calculation of photoemission from atoms subject to intense laser fields,” Phys. Rev. A **45**(7), 4998–5010 (1992). [CrossRef] [PubMed]

*a*(

*t*) of its active electron [33

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

*a*(

*t*) is obtained by using the following commutator relation In here, ℋ(

*t*) and Ψ(

*x,t*) are the Hamiltonian and the electron wave function defined in Eq. (1), respectively. The function

*D*(

*ω*) is called the dipole spectrum, which gives the spectral profile measured in HHG experiments. For solving Eq. (1), the gap size

*g*of the gold bow-tie nanostructure is taken into account by restricting the spatial grid size (see Fig. 1 for a sketch of the gold bow-tie nanostructure including the typical dimensions and the geometry).

## 3. Results and discussion

### 3.1. Nanostructure

*g*(as shown in Fig. 1). The apices at corners were rounded (10 nm radius of curvature) to account for limitation of current fabrication techniques and avoid nonphysical fields enhancement due to tip-effect. The out of plane thickness is set to 25 nm. These parameters yield to a dipolar bonding resonance centered at around

*λ*= 1800 nm. This particular value of

*λ*was chosen according to the availability of laser sources [34

34. 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]

*α*

_{0}, which is

*I*is the laser intensity. For instance, in here, for intensities

*I*of ∼ 10

^{14}W·cm

^{−2},

*α*

_{0}can have a value about ±80 a.u. (±4.5 nm).

35. S. S. Aćimović, “Introduction to nanoparticle characterization in COMSOL” (available from http://srdjancomsol.weebly.com, 2011).

36. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

*g*= 10 nm and

*g*= 20 nm. In particular, we study HHG for the cases with

*g*= 12 nm and

*g*= 15 nm.

*x*-axis) plane wave at 1800 nm for

*g*= 12 nm and

*g*= 15 nm, respectively. The field-enhancement profile is extracted for the bow-tie long axis through the middle of the gap, so the successive problem is reduced to 1D. Additionally we normalize the electric field by setting

*E*(0,

*t*) = 1. We observe amplifications of about 39 and 37 dB, between the input intensity and the intensity at center of the gap for

*g*= 12 nm and

*g*= 15 nm, respectively.

### 3.2. Spectra and time analysis

**453**(7196), 757–760 (2008). [CrossRef] [PubMed]

*g*= 12 nm case and 30 dB for the

*g*= 15. We use a reduction factor to account for the difference between the plasmonic field enhancement obtained in the finite elements results and the one experimentally observed at

*λ*= 800 nm and not at

*λ*= 1800 nm, which is the value used in our simulations. Obviously, the reduction factors obtained for

*λ*= 800 nm not necessarily apply for

*λ*= 1800 nm. Nevertheless, we think that our estimations are very conservative and that, in fact, potential wavelength dependence of the discrepancy between experimental and theoretical observations should be less pronounced at longer wavelengths. For instance, if e.g. the quality of the nanostructuring process was responsible for this discrepancy at

*λ*= 800 nm, this will be less severe at

*λ*= 1800 nm, where the structures are larger and the field enhancement less sensitive to small fabrication deviations. We will consider a laser with initial input intensities of 1×10

^{11}W·cm

^{−2}which would lead to enhanced field of

*I*= 8×10

^{13}W·cm

^{−2}and

*I*= 1.25×10

^{14}W·cm

^{−2}at the center of the spot (

*x*= 0), for the former and later cases, respectively. In order to be consistent with our finite-element calculation, in which we used a monochromatic field, we used a trapezoidal shaped pulse with three optical cycles during the ramp up (

*n*= 3) and the ramp down (

_{on}*n*= 3), with a plateau with 4 optical cycles (

_{off}*n*= 4), i.e. 10 optical cycles in total which is roughly 60 fs for a wavelength

_{p}*λ*= 1800 nm.

*E*(

*x,t*) =

*E*(

*t*), and a nonhomogeneous electric field, using Eq. (5). These results are displayed in Figs. 2 and 3 for

*g*= 12 nm and

*g*= 15, respectively.

*ω*and 204

*ω*as shown by the arrows in Figs. 2 and 3, respectively. In fact, our calculation are in excellent agreement with the semiclassical model [7

7. 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**(3) 2117–2132 (1994). [CrossRef] [PubMed]

15. M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A **85**(3), 033828 (2012). [CrossRef]

38. C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A **81**(3), 033412 (2010). [CrossRef]

*a*(

*t*) of Eq. (9), the Gabor transform is defined as where the integration is usually taken over the pulse duration. In our studies we use

*σ*= 1/3

*ω*, with

*ω*being the central laser frequency. The chosen value of

*σ*allows us to achieve an adequate balance between the time and frequency resolutions (see Ref. [38

38. C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A **81**(3), 033412 (2010). [CrossRef]

### 3.3. Classical analysis

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

7. 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**(3) 2117–2132 (1994). [CrossRef] [PubMed]

**85**(3), 033828 (2012). [CrossRef]

*n*is the harmonic order at the cutoff,

_{c}*ω*the laser frequency,

*U*the ponderomotive energy (defined by

_{p}*U*=

_{p}*I*/4

*ω*

^{2},

*I*being the laser intensity in a.u.) and

*I*the ionization potential of the atom or molecule.

_{p}*x*-axis, electric oscillating field under the following initial conditions: (i) the electron starts at position zero at time

*t*=

*t*

_{0}with zero velocity, i.e. Here,

*t*

_{0}is known as the birth or ionization time; (ii) when the electric field reverses its direction, the electron returns to its initial position (i.e the electron

*recollides*or recombines with the parent ion) at a later time

*t*=

*t*

_{1}, i.e. In Eq. (14)

*t*

_{1}defines the recollision or recombination time. The electron kinetic energy at the

*t*

_{1}time is calculated from and finding the value of

*t*

_{1}(as a function of

*t*

_{0}) that maximizes this energy, Eq. (11) is fulfilled.

*Ẽ*(

*x,t*) is the effective electric field along the electron trajectory

*x*(

*t*). In Eq. (16)

*V*(

_{laser}*x,t*) and

*E*(

*x,t*) are defined by Eqs. (4) and (5), respectively. Fixing the value of ionization time

*t*

_{0}it is possible to compute the classical trajectories and to numerically calculate the recollision times

*t*

_{1}, i.e. the

*t*

_{1}when

*x*(

*t*

_{1}) = 0.

*t*

_{0}the electron trajectory is completely determined. For comparison purposes we present here the following set of results, namely, (i) calculations with

*E*(

*x,t*) =

*E*(

*t*), i.e. the homogeneous case and without restriction in the electron motion; (ii) calculations with the nonhomogeneous fields

*E*(

*x,t*) of Eq. (5) and without restriction in the electron motion; (iii) idem (i) but restricting the electron motion to the region [−

*α*

_{0},

*α*

_{0}],

*α*

_{0}being the quiver radius defined by

*α*

_{0}=

*E*

_{0}/

*ω*

^{2}; (iv) idem (ii) but restricting the electron motion to the region [−

*α*

_{0},

*α*

_{0}].

*t*

_{0}) and recollision time (

*t*

_{1}), calculated from

*n*= (

*E*(

_{k}*t*) +

_{i}*I*)/

_{p}*ω*, with

*i*= 0 and

*i*= 1, respectively, and for the first case presented in Sec. 3.2, i.e. for

*g*= 12 nm. Panel (a) is the homogeneous case without restriction in the electron motion (case (i)); (panel b) is the nonhomogeneous case without restriction in the electron motion (case (ii)); (panel c) is the homogeneous case, but now restricting the electron motion (case (iii)); and (panel d) is the nonhomogeneous case by including the restriction in the electron motion (case (iv)). From panel (a) it is possible to observe that the maximum kinetic energy of the returning electron is in perfect agreement with Eq. (11) (no harmonic order beyond

*n*∼ 140 is reached). On the other hand panel (b) shows how the nonhomogeneities of the field modify the electron trajectories and that no clear high-order harmonic cutoff is observed. This behaviour is consistent with the predictions of the 1D-TDSE simulations presented in [15

_{c}**85**(3), 033828 (2012). [CrossRef]

*g*= 15 nm. We present the results in Fig. 6. From panels (a)–(d) similar conclusions to the previous case can be extracted.

*t*

_{1}of the electron as a function of the ionization time

*t*

_{0}for all the cases considered above. Panels (a) (of both Figs. 7 and 8) represent the

*free space*case, i.e. the electron motion is not restricted, and in panels (b) we confine the electron motion into the region [−

*α*

_{0},

*α*

_{0}]. The long trajectories are those with recollision times

*t*

_{1}≳ 4.25 optical cycles and only for the homogeneous case (blue squares ( )) these trajectories are clearly visible. On the other hand, short trajectories are characterized by

*t*

_{1}≲ 4.25 optical cycles and these are present for both the homogeneous and nonhomogeneous cases. Our results are consistent with those shown in [14

14. 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. A **85**(1), 013416 (2012). [CrossRef]

**85**(3), 033828 (2012). [CrossRef]

*homogeneous*long trajectories (blue squares ( )) with ionization times

*t*

_{0}around the 3.25 and 3.75 optical cycles

*merge*into unique trajectories ( ). Additionally the branch with

*t*

_{0}∼ 3.75 has now ionization times smaller; hence, the time spent by the electron in the continuum increase and consequently a higher amount of kinetic energy is acquired [14

14. 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. A **85**(1), 013416 (2012). [CrossRef]

*modified*short trajectories shows an extended cutoff.

## 4. Conclusions and outlook

## Acknowledgments

## References and links

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2. | T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. |

3. | F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. |

4. | P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. |

5. | M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. B |

6. | P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. |

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8. | 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 |

9. | 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. |

10. | P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science |

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32. | J. L. Krause, K. J. Schafer, and K. C. Kulander, “Calculation of photoemission from atoms subject to intense laser fields,” Phys. Rev. A |

33. | K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. |

34. | 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. |

35. | S. S. Aćimović, “Introduction to nanoparticle characterization in COMSOL” (available from http://srdjancomsol.weebly.com, 2011). |

36. | P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B |

37. | D. Gabor, “Theory of communication,” J. Inst. Electr. Eng. |

38. | C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A |

39. | L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP |

40. | 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. JETP |

**OCIS Codes**

(320.7120) Ultrafast optics : Ultrafast phenomena

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: September 25, 2012

Revised Manuscript: October 24, 2012

Manuscript Accepted: October 25, 2012

Published: November 6, 2012

**Citation**

M. F. Ciappina, Srdjan S. Aćimović, T. Shaaran, J. Biegert, R. Quidant, and M. Lewenstein, "Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures," Opt. Express **20**, 26261-26274 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26261

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