## Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles |

Optics Express, Vol. 19, Issue 23, pp. 22999-23007 (2011)

http://dx.doi.org/10.1364/OE.19.022999

Acrobat PDF (1056 KB)

### Abstract

A fast and general technique to investigation the interaction between a fast electron and nonlinear materials consisting of centrosymmetric spheres is presented by means of multiple scattering of electromagnetic multipole fields. Two kinds of new effect, the negative electron energy loss caused by the second-harmonic field and the second-harmonic Smith-Purcell radiation using finite chain of nonlinear spheres, are predicted for the first time. It is shown that these new effects can be probed by the electron energy loss spectrum, suggesting their possible applications in tunable light sources for the second-harmonic generation.

© 2011 OSA

1. F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. **82**(1), 209–275 (2010). [CrossRef]

2. R. García-Molina, A. Gras-Marti, and R. H. Ritchie, “Excitation of edge modes in the interaction of electron beams with dielectric wedges,” Phys. Rev. B Condens. Matter **31**(1), 121–126 (1985). [CrossRef] [PubMed]

12. J. Xu and X. Zhang, “Cloaking radiation of moving electron beam and relativistic energy loss spectra,” Opt. Express **17**(6), 4758–4772 (2009). [CrossRef] [PubMed]

13. S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. **92**(4), 1069–1069 (1953). [CrossRef]

16. N. Yamamoto, K. Araya, and F. J. Garcia de Abajo, “Photon emission from silver particles induced by a high-energy electron beam,” Phys. Rev. B **64**(20), 205419 (2001). [CrossRef]

1. F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. **82**(1), 209–275 (2010). [CrossRef]

16. N. Yamamoto, K. Araya, and F. J. Garcia de Abajo, “Photon emission from silver particles induced by a high-energy electron beam,” Phys. Rev. B **64**(20), 205419 (2001). [CrossRef]

23. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. **105**(7), 077401 (2010). [CrossRef] [PubMed]

18. J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B **21**(7), 1328–1347 (2004). [CrossRef]

24. V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. **104**(12), 127401 (2010). [CrossRef] [PubMed]

25. Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B **70**(24), 245434 (2004). [CrossRef]

7. F. J. García de Abajo, “Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam,” Phys. Rev. B **59**(4), 3095–3107 (1999). [CrossRef]

7. F. J. García de Abajo, “Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam,” Phys. Rev. B **59**(4), 3095–3107 (1999). [CrossRef]

8. F. J. García de Abajo, “Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach,” Phys. Rev. Lett. **82**(13), 2776–2779 (1999). [CrossRef]

18. J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B **21**(7), 1328–1347 (2004). [CrossRef]

27. F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B **80**(23), 233402 (2009). [CrossRef]

18. J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B **21**(7), 1328–1347 (2004). [CrossRef]

**21**(7), 1328–1347 (2004). [CrossRef]

7. F. J. García de Abajo, “Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam,” Phys. Rev. B **59**(4), 3095–3107 (1999). [CrossRef]

8. F. J. García de Abajo, “Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach,” Phys. Rev. Lett. **82**(13), 2776–2779 (1999). [CrossRef]

6. F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. **80**(23), 5180–5183 (1998). [CrossRef]

8. F. J. García de Abajo, “Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach,” Phys. Rev. Lett. **82**(13), 2776–2779 (1999). [CrossRef]

6. F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. **80**(23), 5180–5183 (1998). [CrossRef]

**82**(13), 2776–2779 (1999). [CrossRef]

30. M. A. Ordal, R. J. Bell, R. W. Alexander Jr, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. **24**(24), 4493–4499 (1985). [CrossRef] [PubMed]

31. D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. **96**(7), 3626–3634 (2004). [CrossRef]

1. F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. **82**(1), 209–275 (2010). [CrossRef]

**82**(13), 2776–2779 (1999). [CrossRef]

_{3}Li

_{2}Nb

_{5}O

_{15}(KLN). The dielectric constant of the KLN is

**82**(13), 2776–2779 (1999). [CrossRef]

15. F. J. García de Abajo; “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **61**(55B), 5743–5752 (2000). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. |

2. | R. García-Molina, A. Gras-Marti, and R. H. Ritchie, “Excitation of edge modes in the interaction of electron beams with dielectric wedges,” Phys. Rev. B Condens. Matter |

3. | T. L. Ferrell and P. M. Echenique, “Generation of surface excitations on dielectric spheres by an external electron beam,” Phys. Rev. Lett. |

4. | A. Rivacoba, N. Zabala, and P. M. Echenique, “Theory of energy loss in scanning transmission electron microscopy of supported small particles,” Phys. Rev. Lett. |

5. | J. B. Pendry and L. Martín-Moreno, “Energy loss by charged particles in complex media,” Phys. Rev. B Condens. Matter |

6. | F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. |

7. | F. J. García de Abajo, “Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam,” Phys. Rev. B |

8. | F. J. García de Abajo, “Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach,” Phys. Rev. Lett. |

9. | F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, “Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals,” Phys. Rev. B |

10. | T. Ochiai and K. Ohtaka, “Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals.I. Formalism and surface plasmon polariton,” Phys. Rev. B |

11. | J. Xu, Y. Dong, and X. Zhang, “Electromagnetic interactions between a fast electron beam and metamaterial cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

12. | J. Xu and X. Zhang, “Cloaking radiation of moving electron beam and relativistic energy loss spectra,” Opt. Express |

13. | S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. |

14. | G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, “First observation of Smith-Purcell radiation from relativistic electrons,” Phys. Rev. Lett. |

15. | F. J. García de Abajo; “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

16. | N. Yamamoto, K. Araya, and F. J. Garcia de Abajo, “Photon emission from silver particles induced by a high-energy electron beam,” Phys. Rev. B |

17. | T. F. Heinz, in |

18. | J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B |

19. | P. C. Ray, “Size and shape dependent second order nonlinear optical properties of nanomaterials and their application in biological and chemical sensing,” Chem. Rev. |

20. | S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. |

21. | Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. |

22. | J. U. Furst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. |

23. | J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. |

24. | V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. |

25. | Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B |

26. | J. D. Jackson, |

27. | F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B |

28. | D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, |

29. | M. Abramowitz and I. A. Stegun, |

30. | M. A. Ordal, R. J. Bell, R. W. Alexander Jr, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. |

31. | D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. |

32. | E. D. Palik, |

33. | D. N. Nikogosyan, |

**OCIS Codes**

(160.4330) Materials : Nonlinear optical materials

(260.2110) Physical optics : Electromagnetic optics

(300.2140) Spectroscopy : Emission

**ToC Category:**

Materials

**History**

Original Manuscript: August 18, 2011

Revised Manuscript: September 30, 2011

Manuscript Accepted: October 10, 2011

Published: October 28, 2011

**Citation**

Jinying Xu and Xiangdong Zhang, "Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles," Opt. Express **19**, 22999-23007 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-22999

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### References

- F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82(1), 209–275 (2010). [CrossRef]
- R. García-Molina, A. Gras-Marti, and R. H. Ritchie, “Excitation of edge modes in the interaction of electron beams with dielectric wedges,” Phys. Rev. B Condens. Matter31(1), 121–126 (1985). [CrossRef] [PubMed]
- T. L. Ferrell and P. M. Echenique, “Generation of surface excitations on dielectric spheres by an external electron beam,” Phys. Rev. Lett.55(14), 1526–1529 (1985). [CrossRef] [PubMed]
- A. Rivacoba, N. Zabala, and P. M. Echenique, “Theory of energy loss in scanning transmission electron microscopy of supported small particles,” Phys. Rev. Lett.69(23), 3362–3365 (1992). [CrossRef] [PubMed]
- J. B. Pendry and L. Martín-Moreno, “Energy loss by charged particles in complex media,” Phys. Rev. B Condens. Matter50(8), 5062–5073 (1994). [CrossRef] [PubMed]
- F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett.80(23), 5180–5183 (1998). [CrossRef]
- F. J. García de Abajo, “Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam,” Phys. Rev. B59(4), 3095–3107 (1999). [CrossRef]
- F. J. García de Abajo, “Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach,” Phys. Rev. Lett.82(13), 2776–2779 (1999). [CrossRef]
- F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, “Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals,” Phys. Rev. B68(20), 205105 (2003). [CrossRef]
- T. Ochiai and K. Ohtaka, “Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals.I. Formalism and surface plasmon polariton,” Phys. Rev. B69(12), 125106 (2004). [CrossRef]
- J. Xu, Y. Dong, and X. Zhang, “Electromagnetic interactions between a fast electron beam and metamaterial cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(4), 046601 (2008). [CrossRef] [PubMed]
- J. Xu and X. Zhang, “Cloaking radiation of moving electron beam and relativistic energy loss spectra,” Opt. Express17(6), 4758–4772 (2009). [CrossRef] [PubMed]
- S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev.92(4), 1069–1069 (1953). [CrossRef]
- G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, “First observation of Smith-Purcell radiation from relativistic electrons,” Phys. Rev. Lett.69(12), 1761–1764 (1992). [CrossRef] [PubMed]
- F. J. García de Abajo; “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics61(55B), 5743–5752 (2000). [CrossRef] [PubMed]
- N. Yamamoto, K. Araya, and F. J. Garcia de Abajo, “Photon emission from silver particles induced by a high-energy electron beam,” Phys. Rev. B64(20), 205419 (2001). [CrossRef]
- T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, edited by H.-E. Ponath and G. I. Stegeman (North-Holland, Amsterdam, 1991).
- J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B21(7), 1328–1347 (2004). [CrossRef]
- P. C. Ray, “Size and shape dependent second order nonlinear optical properties of nanomaterials and their application in biological and chemical sensing,” Chem. Rev.110(9), 5332–5365 (2010). [CrossRef] [PubMed]
- S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett.98(16), 167403 (2007). [CrossRef] [PubMed]
- Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett.104(20), 207402 (2010). [CrossRef] [PubMed]
- J. U. Furst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010). [CrossRef] [PubMed]
- J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett.105(7), 077401 (2010). [CrossRef] [PubMed]
- V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett.104(12), 127401 (2010). [CrossRef] [PubMed]
- Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B70(24), 245434 (2004). [CrossRef]
- J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
- F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B80(23), 233402 (2009). [CrossRef]
- D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1972), p. 363.
- M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt.24(24), 4493–4499 (1985). [CrossRef] [PubMed]
- D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys.96(7), 3626–3634 (2004). [CrossRef]
- E. D. Palik, Handbook of optical constants of solids (Academic, Orlando, 1985).
- D. N. Nikogosyan, Nonlinear optical crystals: A complete survey, Springer New York, USA (2003).

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