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

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    [CrossRef] [PubMed]
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2010 (6)

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

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]

2009 (2)

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]

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]

2008 (1)

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]

2007 (1)

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]

2004 (4)

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 69(12), 125106 (2004).
[CrossRef]

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

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]

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]

2003 (1)

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 68(20), 205105 (2003).
[CrossRef]

2001 (1)

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]

2000 (1)

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]

1999 (2)

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]

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]

1998 (1)

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]

1994 (1)

J. B. Pendry and L. Martín-Moreno, “Energy loss by charged particles in complex media,” Phys. Rev. B Condens. Matter 50(8), 5062–5073 (1994).
[CrossRef] [PubMed]

1992 (2)

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]

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]

1985 (3)

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]

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]

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]

1953 (1)

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]

Ahorinta, R.

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]

Aktsipetrov, O. A.

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]

Albers, W. M.

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]

Alexander, R. W.

Andersen, U. L.

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]

Araya, K.

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]

Bachelier, G.

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]

Bell, R. J.

Benichou, E.

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]

Brevet, P.-F.

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]

Butet, J.

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]

Canfield, B. K.

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]

Dadap, J. I.

Dong, Y.

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]

Doucas, G.

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]

Echenique, P. M.

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 68(20), 205105 (2003).
[CrossRef]

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]

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]

Elser, D.

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]

Ferrell, T. L.

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]

Furst, J. U.

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]

Garcia de Abajo, F. J.

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]

García de Abajo, F. J.

F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. 82(1), 209–275 (2010).
[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. B 68(20), 205105 (2003).
[CrossRef]

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]

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, “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]

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]

García-Molina, R.

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]

Gillijns, W.

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]

Grange, R.

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]

Gras-Marti, A.

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]

Heinz, T. F.

Howie, A.

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]

Hsieh, C.-L.

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]

Hubner, W.

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

Jonin, C.

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]

Kauranen, M.

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]

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]

Kimmitt, M. F.

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]

Krause, D.

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]

Kujala, S.

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]

Lassen, M.

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]

Leuchs, G.

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]

Long, L. L.

Marquardt, C.

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]

Martín-Moreno, L.

J. B. Pendry and L. Martín-Moreno, “Energy loss by charged particles in complex media,” Phys. Rev. B Condens. Matter 50(8), 5062–5073 (1994).
[CrossRef] [PubMed]

Moshchalkov, V. V.

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]

Mulvey, J. H.

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]

Ochiai, T.

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 69(12), 125106 (2004).
[CrossRef]

Ohtaka, K.

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 69(12), 125106 (2004).
[CrossRef]

Omori, M.

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]

Ordal, M. A.

Pavlyukh, Y.

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

Pendry, J. B.

J. B. Pendry and L. Martín-Moreno, “Energy loss by charged particles in complex media,” Phys. Rev. B Condens. Matter 50(8), 5062–5073 (1994).
[CrossRef] [PubMed]

Psaltis, D.

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]

Pu, Y.

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]

Purcell, E. M.

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]

Querry, M. R.

Ray, P. C.

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]

Ritchie, R. H.

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]

Rivacoba, A.

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 68(20), 205105 (2003).
[CrossRef]

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]

Rodríguez, F. J.

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]

Rogers, C. T.

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]

Russier-Antoine, I.

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]

Shan, J.

Silhanek, A. V.

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]

Sipe, J. E.

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]

Smith, S. J.

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]

Strekalov, D. V.

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]

Svirko, Y.

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]

Teplin, C. W.

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]

Turunen, J.

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]

Valev, V. K.

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]

Van Dorpe, P.

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]

Vandenbosch, G. A. E.

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]

Verbiest, T.

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]

Verellen, N.

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]

Walsh, J.

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]

Wang, F. X.

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]

Xu, J.

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]

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]

Yamamoto, N.

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]

Zabala, N.

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 68(20), 205105 (2003).
[CrossRef]

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]

Zhang, X.

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]

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]

Appl. Opt. (1)

Chem. Rev. (1)

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]

J. Appl. Phys. (1)

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]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Phys. Rev. (1)

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]

Phys. Rev. B (6)

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]

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 68(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. B 69(12), 125106 (2004).
[CrossRef]

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]

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]

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

Phys. Rev. B Condens. Matter (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]

J. B. Pendry and L. Martín-Moreno, “Energy loss by charged particles in complex media,” Phys. Rev. B Condens. Matter 50(8), 5062–5073 (1994).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

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]

Phys. Rev. Lett. (10)

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]

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]

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

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]

Rev. Mod. Phys. (1)

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

Other (6)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, edited by H.-E. Ponath and G. I. Stegeman (North-Holland, Amsterdam, 1991).

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).

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.

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Figures (3)

Fig. 1
Fig. 1

(a) and (d): Energy loss probabilities (solid lines) and photon-emission probabilities (dashed lines) without nonlinear effects for a moving electron with v = 0.7c passing at b = 1.1a from Ag spheres with a = 10nm and d = 22nm. (a) one sphere; (d) four spheres. (b) and (e) correspond to energy loss probabilities caused by the SH field; (c) and (f) to photon-emission probabilities caused by the SH field.

Fig. 2
Fig. 2

Energy loss and photon-emission probabilities for an electron moving with v = 0.7c parallel to a finite periodic chain of 15 aligned spheres consisting of the KLN, as shown in (a). Here a = 10nm, d = 22nm and b = 1.1a. (b) Energy loss probability for the FF field (the same curve for the emission probability without absorptions); (c) Energy loss probability caused by the SH field; (d) photon-emission probabilities caused by the SH field.

Fig. 3
Fig. 3

Probability of photon emission for an electron moving parallel to a finite chain of N aligned spheres as a function of photon energy and polar angle θ . (a), (b) and (c) correspond to the cases for the FF, while (d), (e) and (f) to those of the SH. The values of N under consideration are 1, 5 and 15, respectively. Here a = 50nm and d = 120nm. The other parameters are identical with those in Fig. 2.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

E ext ( x n )= lm { i k 2 a nlm ext,E × j l ( k 2 r ) X lm ( r ^ )+ a nlm ext,H j l ( k 2 r ) X lm ( r ^ ) } ,
E out (2ω) ( x n )= lm { A nlm out,E H Elm (2ω) ( x n )+ A nlm out,H H Hlm (2ω) ( x n ) }
A nlm out,E = 4πi G E,nlm r [ r j l ( K 1 r) ]4π l(l+1) G r,nlm j l ( K 1 r) ε 1 (2ω) K 2 j l ( K 1 r) r [r h l (1) ( K 2 r)] ε 2 (2ω) K 2 h l (1) ( K 2 r) r [r j l ( K 1 r)] | r=a ,
A nlm out,H = 8πω c G M,nlm j l ( K 1 r) ε 2 (2ω) K 2 r j l ( K 1 r) r [r h l (1) ( K 2 r)] ε 1 (2ω) K 1 r h l (1) ( K 2 r) r [r j l ( K 1 r)] | r=a ,
χ s (2) = χ r ^ r ^ r ^ + χ r ^ ( θ ^ θ ^ + φ ^ φ ^ )+ χ ( θ ^ r ^ θ ^ + φ ^ r ^ φ ^ + θ ^ θ ^ r ^ + φ ^ φ ^ r ^ ).
P s (2ω) = r ^ ( χ E r (ω) E r (ω) + χ E t (ω) E r (ω) )+2 χ E r (ω) E t (ω) .
G r,nlm = χ b nlm + χ b nlm ,
G M,nlm = χ b ,M nlm ,
G E,nlm = χ b ,E nlm .
b nlm = l 1 , m 1 l 2 , m 2 A n l 1 m 1 (1) A n l 2 m 2 (1) C l 1 , m 1 , l 2 , m 2 ,l,m (1,1) ,
b nlm = l 1 , m 1 l 2 , m 2 ( A n l 1 m 1 (1) A n l 2 m 2 (1) C l 1 , m 1 , l 2 , m 2 ,l,m (1,1) + A n l 1 m 1 (0) A ln l 2 m 2 (0) C l 1 , m 1 , l 2 , m 2 ,l,m (0,0) ) ,
b ,M nlm =2 l 1 , m 1 l 2 , m 2 ( A n l 1 m 1 (0) A n l 2 m 2 (1) C l 1 , m 1 , l 2 , m 2 ,l,m (1,1) + A n l 1 m 1 (1) A ln l 2 m 2 (1) C l 1 , m 1 , l 2 , m 2 ,l,m (0,1) ) ,
b ,E nlm =2i l 1 , m 1 l 2 , m 2 ( A n l 1 m 1 (0) A n l 2 m 2 (1) C l 1 , m 1 , l 2 , m 2 ,l,m (1,0) + A n l 1 m 1 (1) A n l 2 m 2 (1) C l 1 , m 1 , l 2 , m 2 ,l,m (1,1) )
A nlm (1) = 1 k 1 a d[r j l ( k 1 r)] dr | r=a a nlm ext,E ,
A nlm (0) = j l ( k 1 a) a nlm ext,H ,
A nlm (1) = ε 1 l(l+1) k 1 a j l ( k 1 a) a nlm ext,E .
E sca (2ω) ( x n )= lm { A nlm sca,E H Elm (2ω) ( x n )+ A nlm sca,H H Hlm (2ω) ( x n ) } ,
E loc (2ω) ( x n )= n n lm { ( A nlm out,E + A n lm sca,E ) H Elm (2ω) ( x n )+( A nlm out,H + A n lm sca,H ) H Hlm (2ω) ( x n ) } .
n l m [ δ n n δ l l δ m m T l E ( Ω nlm, n l m EE A n l m sca,E + Ω nlm, n l m EH A n l m sca,H ) ] = n l m T l E [ Ω nlm, n l m EE A n l m out,E + Ω nlm, n l m EH A n l m out,H ] ,
n l m [ δ n n δ l l δ m m T l H ( Ω nlm, n l m HE A n l m sca,E + Ω nlm, n l m HH A n l m sca,H ) ] = n l m T l H [ Ω nlm, n l m EE A n l m out,E + Ω nlm, n l m EH A n l m out,H ] ,
Γ loss (2ω)= 1 πϖ dtRe{ e i2ωt v E (2ω) ( r t ,2ω)}
Γ rad (2ω,Ω)= lim r r 2 4 π 2 k Re{[ E (2ω) (2ω)× H (2ω) (2ω)] r ^ }.

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