Abstract

We study far-field angular radiation patterns of second harmonic generation (SHG) from gold nanosphere, nanocube, nanorod, and nanocup illuminated by tightly focused linearly and radially polarized beams, respectively. It is found that under linearly polarized illumination, far-field forward-scattering SHG (FSHG) dominates second harmonic (SH) responses generated by those gold particles. On the contrary, it is amazing that significant backward-scattering SHG (BSHG) can be observed when those gold nanoparticles are excited by a focused radially polarized beam. For the case of gold nanosphere, the effective point dipole systems are developed to reasonably elucidate this interesting difference. Our investigations suggest that for SHG microscopy with backward detection scheme, tightly focused radially polarized beam could be a promising excitation field to improve the backward SH signal.

© 2016 Optical Society of America

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References

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2016 (1)

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

2015 (2)

M. A. Tyrk, S. A. Zolotovskaya, W. A. Gillespie, and A. Abdolvand, “Radially and azimuthally polarized laser induced shape transformation of embedded metallic nanoparticles in glass,” Opt. Express 23(18), 23394–23400 (2015).
[Crossref] [PubMed]

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (3)

2012 (2)

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

2011 (2)

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express 19(15), 13750–13756 (2011).
[Crossref] [PubMed]

2010 (3)

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

2009 (1)

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

2008 (2)

K. Şendur, W. Challener, and O. Mryasov, “Interaction of spherical nanoparticles with a highly focused beam of light,” Opt. Express 16(5), 2874–2886 (2008).
[Crossref] [PubMed]

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]

2007 (2)

X. Huang, W. Qian, I. H. El-Sayed, and M. A. El-Sayed, “The potential use of the enhanced nonlinear properties of gold nanospheres in photothermal cancer therapy,” Lasers Surg. Med. 39(9), 747–753 (2007).
[Crossref] [PubMed]

D. Débarre, N. Olivier, and E. Beaurepaire, “Signal epidetection in third-harmonic generation microscopy of turbid media,” Opt. Express 15(14), 8913–8924 (2007).
[Crossref] [PubMed]

2006 (1)

2004 (1)

2003 (1)

2002 (1)

2001 (2)

J. Mertz and L. Moreaux, “Second-harmonic generation by focused excitation of inhomogeneously distributed scatterers,” Opt. Commun. 196(1–6), 325–330 (2001).
[Crossref]

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref] [PubMed]

2000 (1)

1989 (1)

Y. R. Shen, “Surface properties probed by second-harmonic and sum-frequency generation,” Nature 337(6207), 519–525 (1989).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Abdolvand, A.

Ayala-Orozco, C.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Bachelier, G.

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

Bautista, G.

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Beaurepaire, E.

Benichou, E.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

Bertorelle, F.

Brasselet, S.

Brevet, P.-F.

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

Brown, T.

Butet, J.

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13(4), 1787–1792 (2013).
[Crossref] [PubMed]

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

Challener, W.

Chang, S.-J.

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

Chen, H.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Cheng, J. X.

J. X. Cheng and X. S. Xie, “Green’s function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19(7), 1604–1610 (2002).
[Crossref]

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Dadap, J. I.

Débarre, D.

Duboisset, J.

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

El-Sayed, I. H.

X. Huang, W. Qian, I. H. El-Sayed, and M. A. El-Sayed, “The potential use of the enhanced nonlinear properties of gold nanospheres in photothermal cancer therapy,” Lasers Surg. Med. 39(9), 747–753 (2007).
[Crossref] [PubMed]

El-Sayed, M. A.

X. Huang, W. Qian, I. H. El-Sayed, and M. A. El-Sayed, “The potential use of the enhanced nonlinear properties of gold nanospheres in photothermal cancer therapy,” Lasers Surg. Med. 39(9), 747–753 (2007).
[Crossref] [PubMed]

Eng, L. M.

Fleischer, M.

Gachet, D.

Gillespie, W. A.

Gollmer, D. A.

Grady, N. K.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Halas, N. J.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Heinz, T. F.

Hille, A.

Horneber, A.

Huang, X.

X. Huang, W. Qian, I. H. El-Sayed, and M. A. El-Sayed, “The potential use of the enhanced nonlinear properties of gold nanospheres in photothermal cancer therapy,” Lasers Surg. Med. 39(9), 747–753 (2007).
[Crossref] [PubMed]

Huttunen, M. J.

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Jin, J.

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]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Jonin, C.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

Kauranen, M.

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Kern, D. P.

Kim, S.

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]

Kim, S.-W.

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]

Kim, Y.

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]

Kim, Y.-J.

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]

Kitamura, K.

Kontio, J. M.

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Lascoux, N.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Maillard, V.

Mäkitalo, J.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Martin, O. J. F.

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13(4), 1787–1792 (2013).
[Crossref] [PubMed]

Meixner, A. J.

Mertz, J.

J. Mertz and L. Moreaux, “Second-harmonic generation by focused excitation of inhomogeneously distributed scatterers,” Opt. Commun. 196(1–6), 325–330 (2001).
[Crossref]

Mihaljevic, J.

Ming, T.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Moreaux, L.

J. Mertz and L. Moreaux, “Second-harmonic generation by focused excitation of inhomogeneously distributed scatterers,” Opt. Commun. 196(1–6), 325–330 (2001).
[Crossref]

Mryasov, O.

Nguyen, N.

Noda, S.

Olivier, N.

Park, I.-Y.

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]

Peng, C.

Qian, W.

X. Huang, W. Qian, I. H. El-Sayed, and M. A. El-Sayed, “The potential use of the enhanced nonlinear properties of gold nanospheres in photothermal cancer therapy,” Lasers Surg. Med. 39(9), 747–753 (2007).
[Crossref] [PubMed]

Reichenbach, P.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Russier-Antoine, I.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

Sakai, K.

Schäfer, C.

Sendur, I.

Sendur, K.

Shan, J.

Shen, H.

Shen, Y. R.

Y. R. Shen, “Surface properties probed by second-harmonic and sum-frequency generation,” Nature 337(6207), 519–525 (1989).
[Crossref]

Sheppard, C.

Simonen, J.

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Sun, J.-W.

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

Sun, L.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Thyagarajan, K.

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13(4), 1787–1792 (2013).
[Crossref] [PubMed]

Toury, T.

Tyrk, M. A.

Volkmer, A.

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref] [PubMed]

Wang, J.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Wang, X.-H.

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Xie, X. S.

J. X. Cheng and X. S. Xie, “Green’s function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19(7), 1604–1610 (2002).
[Crossref]

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref] [PubMed]

Yan, C.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Yang, Z.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Yew, E.

Youngworth, K.

Zeng, M.

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

Zhang, D.

Zhang, N.

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

Zhang, Y.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Zhao, L.

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Zolotovskaya, S. A.

ACS Nano (1)

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

Chin. Phys. B (1)

J.-W. Sun, X.-H. Wang, S.-J. Chang, M. Zeng, and N. Zhang, “Second harmonic generation of metal nanoparticles under tightly focused illumination,” Chin. Phys. B 25(3), 037803 (2016).
[Crossref]

J. Opt. Soc. Am. B (2)

Lasers Surg. Med. (1)

X. Huang, W. Qian, I. H. El-Sayed, and M. A. El-Sayed, “The potential use of the enhanced nonlinear properties of gold nanospheres in photothermal cancer therapy,” Lasers Surg. Med. 39(9), 747–753 (2007).
[Crossref] [PubMed]

Nano Lett. (6)

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13(4), 1787–1792 (2013).
[Crossref] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

T. Ming, L. Zhao, Z. Yang, H. Chen, L. Sun, J. Wang, and C. Yan, “Strong polarization dependence of plasmon-enhanced fluorescence on single gold nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Nature (2)

Y. R. Shen, “Surface properties probed by second-harmonic and sum-frequency generation,” Nature 337(6207), 519–525 (1989).
[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,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Opt. Commun. (1)

J. Mertz and L. Moreaux, “Second-harmonic generation by focused excitation of inhomogeneously distributed scatterers,” Opt. Commun. 196(1–6), 325–330 (2001).
[Crossref]

Opt. Express (11)

W. Challener, I. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11(23), 3160–3170 (2003).
[Crossref] [PubMed]

E. Yew and C. Sheppard, “Effects of axial field components on second harmonic generation microscopy,” Opt. Express 14(3), 1167–1174 (2006).
[Crossref] [PubMed]

D. Débarre, N. Olivier, and E. Beaurepaire, “Signal epidetection in third-harmonic generation microscopy of turbid media,” Opt. Express 15(14), 8913–8924 (2007).
[Crossref] [PubMed]

K. Şendur, W. Challener, and O. Mryasov, “Interaction of spherical nanoparticles with a highly focused beam of light,” Opt. Express 16(5), 2874–2886 (2008).
[Crossref] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[Crossref] [PubMed]

K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express 19(15), 13750–13756 (2011).
[Crossref] [PubMed]

H. Shen, N. Nguyen, D. Gachet, V. Maillard, T. Toury, and S. Brasselet, “Nanoscale optical properties of metal nanoparticles probed by Second Harmonic Generation microscopy,” Opt. Express 21(10), 12318–12326 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

P. Reichenbach, A. Horneber, D. A. Gollmer, A. Hille, J. Mihaljevic, C. Schäfer, D. P. Kern, A. J. Meixner, D. Zhang, M. Fleischer, and L. M. Eng, “Nonlinear optical point light sources through field enhancement at metallic nanocones,” Opt. Express 22(13), 15484–15501 (2014).
[Crossref] [PubMed]

M. A. Tyrk, S. A. Zolotovskaya, W. A. Gillespie, and A. Abdolvand, “Radially and azimuthally polarized laser induced shape transformation of embedded metallic nanoparticles in glass,” Opt. Express 23(18), 23394–23400 (2015).
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K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
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Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

Phys. Rev. Lett. (1)

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

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A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of SH response from single metal nanoparticle excited by a focused beam. ϕp and θp are the azimuthal and polar angles of the point rp. Θ and Φ are the polar and azimuthal angles of the detection point R, respectively

Fig. 2
Fig. 2

Normalized intensity distributions of different electric field components in the focal plane for (a) linear and (b) radial polarizations.

Fig. 3
Fig. 3

Near-field electric field distributions around a 150nm gold nanosphere in the xz plane for (a) linear and (b) radial polarizations.

Fig. 4
Fig. 4

Far-field SH angular radiation patterns for a 150nm gold nanosphere under focused (a) linear and (b) radial illuminations. (c) SH power as a function of Θ when Φ = 0. The black and red curves refer to the results for linear and radial polarizations, respectively.

Fig. 5
Fig. 5

(a) Surface SH polarization for a 150nm gold nanosphere under focused linear illumination. The black arrow denotes the direction of the nonlinear polarization at the local surface. (b) An effective system composed of four coherent dipolar sources in the xz plane. (c) Far-field SH radiation pattern generated by the effective four-dipole system.

Fig. 6
Fig. 6

(a) Surface SH polarization for a 150nm gold nanosphere under focused radial illumination. The black arrow denotes the direction of the nonlinear polarization at the local surface. (b) An effective system composed of two coherent dipolar sources located at the z axis. (c) Far-field SH radiation pattern generated by the effective two-dipole system.

Fig. 7
Fig. 7

Near-field distributions of the fundamental field in the xz plane and far-field SHG angular radiation diagrams are presented in (a) and (c) for linear polarization and in (b) and (d) for radial polarization. (e) SH power as a function of Θ when Φ = 0. The black and red curves refer to the results for linear and radial polarizations, respectively.

Tables (1)

Tables Icon

Table 1 IB/IF for particles with different shapes

Equations (6)

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

[ E inc,L x E inc,L y E inc,L z ]=[ iA[ I 0 + I 2 cos(2 ϕ p )] iA I 2 sin(2 ϕ p ) 2A I 1 cos( ϕ p ) ], [ E inc,R x E inc,R y E inc,R z ]=[ A I 3 cos( ϕ p ) A I 3 sin( ϕ p ) 2iA I 4 ],
I 0 = 0 α cosθ sinθ(1+cosθ) J 0 (k r p sinθsin θ p ) M L ( r p ) dθ, I 1 = 0 α cosθ sin 2 θ J 1 (k r p sinθsin θ p ) M L ( r p ) dθ, I 2 = 0 α cosθ sinθ(1cosθ) J 2 (k r p sinθsin θ p ) M L ( r p ) dθ, I 3 = 0 α cosθ sin2θ J 1 (2 β 0 sinθ/sinα) J 1 (k r p sinθsin θ p ) M R ( r p ) dθ, I 4 = 0 α cosθ si n 2 θ J 1 (2 β 0 sinθ/sinα) J 0 (k r p sinθsin θ p ) M R ( r p ) dθ,
P (2ω) ( r s )= χ s (2) : E ex (ω) ( r s ) E ex (ω) ( r s )δ( r s h( r s )),
P (2ω) ( r s )= ε 0 χ δ( r s h( r s ))[ E x (ω) ( r s ) E x (ω) ( r s ) sin 2 θ s cos 2 φ s + E y (ω) ( r s ) E y (ω) ( r s ) sin 2 θ s sin 2 φ s + E z (ω) ( r s ) E z (ω) ( r s ) cos 2 θ s + E x (ω) ( r s ) E y (ω) ( r s ) sin 2 θ s sin2 φ s + E x (ω) ( r s ) E z (ω) ( r s )sin2 θ s cos φ s + E y (ω) ( r s ) E z (ω) ( r s )sin2 θ s sin φ s ],
E (2ω) (R)= μ 0 ω 2 exp(iKR) πR V dV exp( iKR r s R )                 [ 0 0 0 cosΘcosΦ cosΘsinΦ sinΘ sinΦ cosΦ 0 ][ P x (2ω) ( r s ) P y (2ω) ( r s ) P z (2ω) ( r s ) ]
I F = 0 β dΘ 0 2π dΦ | Ε (2ω) (R) | 2 | R | 2 sinΘ , I B = π-β π dΘ 0 dΦ | E (2ω) (R) | 2 | R | 2 sinΘ ,

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