## Polarization gating and circularly-polarized high harmonic generation using plasmonic enhancement in metal nanostructures |

Optics Express, Vol. 19, Issue 25, pp. 25346-25354 (2011)

http://dx.doi.org/10.1364/OE.19.025346

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### Abstract

We investigate possibilities to utilize field enhancement by specifically designed metal nanostructures for the generation of single attosecond pulses using the polarization gating technique. We predict the generation of isolated 59-attosecond-long pulses using 15-fs pump pulses with only a 0.6 TW/cm^{2} intensity. Our simulations also indicate the possibility to generate previously inaccessible high-harmonics with circular polarization by using an ensemble of vertically and horizontally orientated bow-tie structures. In the numerical simulation we used an extended Lewenstein model, which includes the spatial inhomogeneity in the hot spots and collisions of electrons with the metal surface.

© 2011 OSA

1. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature **414**, 509–513 (2001). [CrossRef] [PubMed]

8. G. Sansone, G. Sansone, F. Kelkensberg, J. F. Perez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lepine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L. Huillier, M. Yu. Ivanov, M. Nisoli, F. Martin, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature **465**, 763–766 (2010). [CrossRef] [PubMed]

1. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature **414**, 509–513 (2001). [CrossRef] [PubMed]

9. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecod pulses,” Opt. Lett. **19**, 1870–1872 (1994). [CrossRef] [PubMed]

13. I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating”, Nat. Phys. **2**, 319–322 (2006). [CrossRef]

^{2}– the generation of high-order harmonics relies on femtosecond laser amplifiers with typical repetition rates in the range of a few kHz. At present many groups follow different approaches with the aim to increase the repetition rate of HHG sources to the MHz range. One of the possibilities to realize this aim is based on the utilization of plasmonic field enhancement by metallic nanostructures. Kim

*et al.*[14

14. 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]

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

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

17. 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 J. Phys. **13**, 073010 (2011). [CrossRef]

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

^{2}intensity. Additionally, we predict that specially designed metal nanostructure arrays enable the previously unattainable generation of circularly-polarized harmonics from circularly-polarized pumpi laser pulses.

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

**E**(

*t*) of the driving pulse ionizes an atom at a time

*t*and creates a free electron in the continuum. The free electron is accelerated by the oscillating field and for a linearly polarized field is driven back to the parent ion after the field changes its direction. In the last step the recombination with the parent ion at a moment

_{s}*t*leads to the emission of a high-energy photon. Neglecting the Coulomb potential, one can represent the time-dependent high-harmonic dipole moment in the direction of the field polarization

_{f}*x*as [18

18. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne 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]

*t*,

_{s}*d*(

_{x}*p*–

*eA*(

*t*)) is the dipole moment for a transition from the ground state to the continuum with a kinetic momentum

_{s}*p*–

*eA*(

*t*),

_{s}*p*=

*m*+

_{e}v*eA*is the canonical momentum,

*A*(

*t*) is the vector potential with

*Ȧ*≡

*dA*(

*t*)/

*dt*=

*E*(

*t*),

*S*(

*t*,

_{f}*t*) =

_{s}*S*

_{0}(

*t*,

_{f}*t*) =

_{s}*I*Δ

_{p}*t*– 0.5

*e*

^{2}(Δ

*B*

^{2}/Δ

*t*+ Δ

*C*)/

*m*is the classical action of an electron in the field, where

_{e}*Ċ*(

*t*) =

*A*

^{2}(

*t*) and

*I*is the ionization potential. The canonical momentum

_{p}*p*is given by

_{st}*p*=

_{st}*e*Δ

*B*/Δ

*t*with

*Ḃ*(

*t*) =

*A*(

*t*), Δ

*t*≡

*t*–

_{f}*t*,

_{s}*ɛ*is an arbitrary small regularization parameter,

*ω*

_{0}is the central laser frequency and

*m*the electron mass. For any function

_{e}*F*we define Δ

*F*≡

*F*(

*t*) –

_{f}*F*(

*t*). For the ground state of a hydrogenlike atom the dipole matrix element is

_{s}*H*(

*t*,

_{f}*t*) ≡ 1; in the modified case it can take other values as discussed below.

_{s}**83**, 043839 (2011). [CrossRef]

*E*(

*t,x*) =

*E*(

*t*)(1 +

*x/d*), In other words, a linear spatial variation of the electric field strength along the diretion of the polarization is included, which is described by a scaling parameter

_{inh}*d*. Considering this derivative term as a perturbation, we get a correction

_{inh}*x*

^{(0)}(

*t*). As a result, the expressions for the momentum

*p*and

_{st}*S*(

*t*,

_{f}*t*) are modified as follows [16

_{s}**83**, 043839 (2011). [CrossRef]

*Ḋ*(

*t*) =

*C*(

*t*),

*Ḟ*(

*t*) =

*C*(

*t*)

*E*(

*t*),

*Ġ*(

*t*) =

*B*(

*t*),

*β*=

*e*/(

*m*). Another modification of the model is described by the function

_{e}d_{inh}*H*(

*t,t*) under the integral in Eq. (2). This function is equal to 1 unless the electron hits during the motion the metal surface positioned at

_{s}*d*, otherwise we assume that the electron is absorbed by the surface and set

_{sur}*H*(

*t,t*) = 0.

_{s}*ɛ*|

_{Ag}^{2}∼ 0.01 to values below 5 TW/cm

^{2}. Therefore we can assume that for the considered parameters the damage threshold of metal or metal nanostructures of about 0.1 J/cm

^{2}is not reached. For moderate laser intensities lower than 10 GW/cm

^{2}even and odd harmonics up to the fifth order can be generated from the metal surface but with an efficiency very rapidly decreasing with the harmonic order [19

19. Gy. Farkas, Cs. Toth, S. D. Moustaizis, N. A. Papadogiannis, and C. Fotakis, “Observation of multiple-harmonic radiation induced from a gold surface by picosecond neodymium-doped yttrium aluminum garnet laser pulses,” Phys. Rev. A **46**, R3605 (1992). [CrossRef] [PubMed]

14. 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]

20. P. Biagioni, J. S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. **102**, 256801 (2009). [CrossRef] [PubMed]

*y*=

*x*and

*y*= −

*x*lines. This assures that for both polarizations the enhancement values will be the same, and a circularly polarized incident beam will excite circularly polarized local fields in the “hot spots”. Such a translation of the polarization state could fail outside of these hot spots; fortunately, only the hot spots are relevant for HHG.

21. 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]

*λ*/4 waveplate. The optical axis of the first plate is at 45 degrees with respect to the (initial) linear polarization while the second plate is turned 45 degrees with respect to the first. Next the one of the two orthogonal polarizations (

*x*and

*y*) is attenuated as if the pulse would be passed through a plate at Brewster angle. Group velocity dispersion of the three plates is compensated. In Fig. 2, we show the temporal profile of the

*x*and

*y*components of the optimized pulse in the center of the “hot spot”. Note how the almost-circular polarization at the leading edge goes over into a linear polarization near the center of the pulse, enabling efficient HHG only during a short time and leading to the generation of a single attosecond pulse. The wavelength-dependent phase contributions in the local fields, as well as the depolarization effects of the nanostructure do not have a strong influence on the shape of the pulse in the hot spot and on the generated harmonics.

*x*- and

*y*-polarized pump components can be utilized for the generation of circularly-polarized harmonics by using a circularly-polarized pump. Each of the components is highly enhanced in the gap of half of the nanoantennas for which the axis is parallel to the polarization vector. The local field in the nanoantennas normal to this field component is barely influenced. Therefore the field in the vicinity of each element is (almost) linearly polarized, permitting high harmonic generation with high efficiency, not hindered by the circular polarization. Since the phase offset between the harmonic components is the phase offset between the pump components multiplied by the harmonic number, the output radiation will form a circularly polarized harmonic beam in the far field of the nanoelement array. Note that the rotation direction of the 4

*N*+ 1th (fifth, ninth, etc.) harmonics will coincide with that of the pump, while the 4

*N*+ 3th (third, seventh, etc.) harmonics will also be circularly polarized but rotate in the opposite direction. From this it follows that these harmonics would be a suitable source for circular dichroism measurements, where the handedness of the incident circular polarization controls the handedness of the harmonics generated. In Fig. 7, the output spectrum of the emitted circularly-polarized harmonics is shown by the red crosses for a 0.3-TW/cm

^{2}continuous-wave pump at 800 nm for 1 atm argon pressure surrounding the nanoantennae. One can see a typical plateau-and-cutoff behavior which is characteristic for a linearly polarized pump. The conversion efficiency is about 10

^{−10}in the middle of the plateau. We conclude that this arrangement of nanoantennae can be used for an efficient circular-polarization HHG. The high-harmonic dipole moment of such nanoparticle ensemble leads to the emission of circularly polarized harmonics within a narrow emission angle which depends on the ensemble size. Note that the radiation emitted at larger angles could have other polarization properties. In Fig. 7 the conversion efficiency for the linearly-polarized pump is shown for comparison by the green squares, showing values lower by a factor of roughly 4.

## Conclusion

^{2}pump pulses has been predicted. Additionally, we studied the possibility to generate high harmonics with circular polarization which is impossible in the traditional generation method. We predict that arrays consisting of equal numbers of mutually normally-oriented nanostructures allow the generation of circularly polarized harmonics from circularly polarized pump pulses, which can be used for circular dichroism measurements. The results are obtained using a finite-element method for the calculation of the field enhancement and an extended Lewenstein model which includes the field inhomogeneity in the hot spots and the possible collisions of the electrons with the metal surface.

## References and links

1. | M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature |

2. | A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi phase matched generation of coherent extreme ultraviolet light,” Nature |

3. | X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum path control of high-harmonic generation using counterpropagating light,” Nat. Phys. |

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

5. | H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science |

6. | M. F. Kling and M. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem. |

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

8. | G. Sansone, G. Sansone, F. Kelkensberg, J. F. Perez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lepine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L. Huillier, M. Yu. Ivanov, M. Nisoli, F. Martin, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature |

9. | P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecod pulses,” Opt. Lett. |

10. | O. Tcherbakoff, E. Mevel, D. Descamps, J. Plumridge, and E. Constant, “Time gated high order harmonic generation,” Phys. Rev. A |

11. | M. Kovacev, Y. Mairesse, E. Priori, H. Merdji, O. Tcherbakoff, P. Monchicourt, P. Breger, E. Mevel, E. Constant, P. Salieres, B. Carre, and P. Agostini, “Temporal confinement of the harmonic emission through polarization gating,” Eur. Phys. J. D |

12. | D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, “Efficient polarization gating of high-order harmonic generation by polarization-shaped ultrashort pulses,” Phys. Rev. A |

13. | I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating”, Nat. Phys. |

14. | 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 |

15. | I.-Y. Park, S. Kim, J. Choi, D.-H. Lee, Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photon. |

16. | A. Husakou, S.-J. Im, and J. Herrmann, “Theory of plasmon-enhanced high-harmonic generation in the vicinity of metal nanostructures in noble gases,” Phys. Rev. A. |

17. | 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 J. Phys. |

18. | M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L. Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A |

19. | Gy. Farkas, Cs. Toth, S. D. Moustaizis, N. A. Papadogiannis, and C. Fotakis, “Observation of multiple-harmonic radiation induced from a gold surface by picosecond neodymium-doped yttrium aluminum garnet laser pulses,” Phys. Rev. A |

20. | P. Biagioni, J. S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. |

21. | 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 |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 17, 2011

Revised Manuscript: November 15, 2011

Manuscript Accepted: November 15, 2011

Published: November 28, 2011

**Citation**

A. Husakou, F. Kelkensberg, J. Herrmann, and M. J. J. Vrakking, "Polarization gating and circularly-polarized high harmonic generation using plasmonic enhancement in metal nanostructures," Opt. Express **19**, 25346-25354 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25346

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### References

- M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature414, 509–513 (2001). [CrossRef] [PubMed]
- A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi phase matched generation of coherent extreme ultraviolet light,” Nature421, 51–54 (2003). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum path control of high-harmonic generation using counterpropagating light,” Nat. Phys.3, 270–275 (2007). [CrossRef]
- P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys.3, 381–387 (2007). [CrossRef]
- H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science317, 775–778 (2007). [CrossRef] [PubMed]
- M. F. Kling and M. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem.59, 463–492 (2008). [CrossRef]
- F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009). [CrossRef]
- G. Sansone, G. Sansone, F. Kelkensberg, J. F. Perez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lepine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L. Huillier, M. Yu. Ivanov, M. Nisoli, F. Martin, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature465, 763–766 (2010). [CrossRef] [PubMed]
- P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecod pulses,” Opt. Lett.19, 1870–1872 (1994). [CrossRef] [PubMed]
- O. Tcherbakoff, E. Mevel, D. Descamps, J. Plumridge, and E. Constant, “Time gated high order harmonic generation,” Phys. Rev. A68, 043804 (2003). [CrossRef]
- M. Kovacev, Y. Mairesse, E. Priori, H. Merdji, O. Tcherbakoff, P. Monchicourt, P. Breger, E. Mevel, E. Constant, P. Salieres, B. Carre, and P. Agostini, “Temporal confinement of the harmonic emission through polarization gating,” Eur. Phys. J. D26, 79–82 (2003). [CrossRef]
- D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, “Efficient polarization gating of high-order harmonic generation by polarization-shaped ultrashort pulses,” Phys. Rev. A72, 063816 (2006). [CrossRef]
- I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating”, Nat. Phys.2, 319–322 (2006). [CrossRef]
- 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, 757–760 (2008). [CrossRef] [PubMed]
- I.-Y. Park, S. Kim, J. Choi, D.-H. Lee, Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photon.5, 677–681 (2011). [CrossRef]
- A. Husakou, S.-J. Im, and J. Herrmann, “Theory of plasmon-enhanced high-harmonic generation in the vicinity of metal nanostructures in noble gases,” Phys. Rev. A.83, 043839 (2011). [CrossRef]
- 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 J. Phys.13, 073010 (2011). [CrossRef]
- M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L. Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49, 2117–2132 (1994). [CrossRef] [PubMed]
- Gy. Farkas, Cs. Toth, S. D. Moustaizis, N. A. Papadogiannis, and C. Fotakis, “Observation of multiple-harmonic radiation induced from a gold surface by picosecond neodymium-doped yttrium aluminum garnet laser pulses,” Phys. Rev. A46, R3605 (1992). [CrossRef] [PubMed]
- P. Biagioni, J. S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett.102, 256801 (2009). [CrossRef] [PubMed]
- 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,” Science314, 443–446 (2006). [CrossRef] [PubMed]

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