OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 18611–18623
« Show journal navigation

Plasmonic enhancement of second harmonic generation on metal coated nanoparticles

Sarina Wunderlich and Ulf Peschel  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 18611-18623 (2013)
http://dx.doi.org/10.1364/OE.21.018611


View Full Text Article

Acrobat PDF (1287 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Second Harmonic Generation (SHG) is a widely used tool to study surfaces. Here we investigate SHG from spherical nanoparticles consisting of a dielectric core (radius 100 nm) and a metallic shell of variable thickness. Plasmonic resonances occur that depend on the thickness of the nanoshells and boost the intensity of the Second Harmonic (SH) signal. The origin of the resonances is studied for the fundamental harmonic and the second harmonic frequencies. Mie resonances at the fundamental harmonic frequency dominate resonant effects of the SH-signal at low shell thickness. Resonances excited by a dipole emitting at SH frequency close to the surface explain the enhancement of the SHG-process at a larger shell thickness. All resonances are caused by surface plasmon polaritons, which run on the surface of the spherical particle and are in resonance with the circumference of the sphere. Because their wavelength critically depends on the properties of the metallic layer SHG resonances of core-shell nanoparticles can be easily tuned by varying the thickness of the shell.

© 2013 OSA

1. Introduction

Surface science relies on probing and characterization techniques. Second Harmonic Generation (SHG) has proven to be a surface sensitive measurement tool, hence it has been used for in situ investigations for several decades [1

1. Y. Shen, “Surface 2nd harmonic-generation - a new technique for surface studies,” Annu. Rev. Mater. Sci. 16(1), 69–86 (1986). [CrossRef]

]. For centrosymmetric materials SH is generated at the surface of nano-particles, because symmetry is broken at that interface as Wang has demonstrated experimentally for the first time [2

2. H. Wang, E. C. Y. Yan, E. Borguet, and K. B. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett. 259(1-2), 15–20 (1996). [CrossRef]

]. SHG has been applied to study the surface and buried micro-structure of colloidal nano-particles [3

3. E. C. Y. Yan, Y. Liu, and K. B. Eisenthal, “New method for determination of surface potential of microscopic particles by second harmonic generation,” J. Chem. Phys. B 102(33), 6331–6336 (1998). [CrossRef]

13

13. L. H. Haber, S. J. J. Kwok, M. Semeraro, and K. B. Eisenthal, “Probing the colloidal gold nanoparticle/aqueous interface with second harmonic generation,” Chem. Phys. Lett. 507(1-3), 11–14 (2011). [CrossRef]

] or as probing technique in bio-physical experiments [14

14. J. Griffin, A. K. Singh, D. Senapati, E. Lee, K. Gaylor, J. Jones-Boone, and P. C. Ray, “Sequence-Specific HCV RNA Quantification Using the Size-Dependent Nonlinear Optical Properties of Gold Nanoparticles,” Small 5(7), 839–845 (2009). [CrossRef] [PubMed]

18

18. G. Gonella and H.-L. Dai, “Determination of adsorption geometry on spherical particles from nonlinear Mie theory analysis of surface second harmonic generation,” Phys. Rev. B 84(12), 121402 (2011). [CrossRef]

]. We have used SHG to determine the nonlinear susceptibility χ(2) of a thin layer of Malachite Green [19

19. S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B 84(23), 235403 (2011). [CrossRef]

], to study the layer of oriented water near polystyrene particles [20

20. B. Schürer, S. Wunderlich, C. Sauerbeck, U. Peschel, and W. Peukert, “Probing colloidal interfaces by angle-resolved second harmonic light scattering,” Phys. Rev. B 82(24), 241404 (2010). [CrossRef]

] and the organization of polyelectrolyte chains, depending on the salt concentration of the solvent [21

21. B. Schürer, M. Hoffmann, S. Wunderlich, L. Harnau, U. Peschel, M. M. Ballauff, and W. Peukert, “Second harmonic light scattering from spherical polyelectrolyte brushes,” J. Phys. Chem. C 115(37), 18302–18309 (2011). [CrossRef]

].

SHG has also been used to investigate the surface of metals, where surface plasmons can be excited. First experimental and theoretical studies were performed on plane surfaces [22

22. J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4(12), 4274–4290 (1971). [CrossRef]

27

27. J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980). [CrossRef]

]. Recently studies on SHG or Hyper Rayleigh [28

28. S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem. 63(1), 353–378 (2012). [CrossRef] [PubMed]

] scattering were performed on colloidal metallic nanoparticles [29

29. F. W. Vance, B. I. Lemon, and J. T. Hupp, “Enormous hyper-Rayleigh scattering from nanocrystalline gold particle suspensions,” J. Chem. Phys. B 102(50), 10091–10093 (1998). [CrossRef]

36

36. M. Chandra and P. K. Das, “Size dependence and dispersion behavior of the first hyperpolarizability of copper nanoparticles,” Chem. Phys. Lett. 476(1-3), 62–64 (2009). [CrossRef]

] as well as on particles embedded in a matrix [37

37. R. Antoine, M. Pellarin, B. Palpant, M. Broyer, B. Prevel, P. Galletto, P. F. Brevet, and H. H. Girault, “Surface plasmon enhanced second harmonic response from gold clusters embedded in an alumina matrix,” J. Appl. Phys. 84(8), 4532–4536 (1998). [CrossRef]

,38

38. 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]

] and more complex plasmonic structures [39

39. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008). [CrossRef] [PubMed]

42

42. H. Lu, X. Liu, R. Zhou, Y. Gong, and D. Mao, “Second-harmonic generation from metal-film nanohole arrays,” Appl. Opt. 49(12), 2347–2351 (2010). [CrossRef] [PubMed]

].

There exist several theoretical models for SHG from spherical nano-particles. The response of small particles can be modeled by Second-Harmonic Rayleigh Scattering [43

43. G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun. 41(6), 499–501 (1982). [CrossRef]

46

46. B. S. Mendoza and W. L. Mochán, “Second harmonic surface response of a composite,” Opt. Mater. 29(1), 1–5 (2006). [CrossRef]

]. For small particles of low refractive index contrast, which do not significantly perturb the incident field, also the Rayleigh-Gans-Debye approximation can be used [47

47. J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55(6), 4520–4525 (1997). [CrossRef]

51

51. J. I. Dadap, “Optical second-harmonic scattering from cylindrical particles,” Phys. Rev. B 78(20), 205322 (2008). [CrossRef]

]. Larger spheres or such with a high refractive index contrast require the application of a full Mie theory, based on which several numerical models have been developed for solid particles [18

18. G. Gonella and H.-L. Dai, “Determination of adsorption geometry on spherical particles from nonlinear Mie theory analysis of surface second harmonic generation,” Phys. Rev. B 84(12), 121402 (2011). [CrossRef]

,19

19. S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B 84(23), 235403 (2011). [CrossRef]

,52

52. D. Östling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear optical properties of small metallic spheres,” Z. Phys. D 28, 169–175 (1993). [CrossRef]

54

54. S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B 70(11), 115106 (2004). [CrossRef]

]. Only recently, a nonlinear Mie model for core-shell particles has been applied to describe the wavelength-dependence of SHG on nanoparticles with up to 100 nm outer diameter and with fixed gold and silver shells of 10 nm thickness [55

55. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Nonlinear Mie theory for the second harmonic generation in metallic nanoshells,” J. Opt. Soc. Am. B 29(8), 2213–2221 (2012). [CrossRef]

,56

56. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Effect of the dielectric core and embedding medium on the second harmonic generation from plasmonic nanoshells: tunability and sensing,” J. Phys. Chem. C 117(2), 1172–1177 (2013). [CrossRef]

]. Simulations were used to investigate the dependence of the SH signal on the refractive indices of the core and the surrounding.

Here, we apply a refined nonlinear Mie model [19

19. S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B 84(23), 235403 (2011). [CrossRef]

] to investigate in detail the nature of the various plasmonic resonances, which influence the SHG process from dielectric-metallic core-shell particles with variable shell thickness. We analyze the resonant behavior of the Second Harmonic intensity when varying the geometry and the material parameters of the nanoparticle. We find that even the nonlinear response is solely dominated by plasmonic resonances at fundamental harmonic (FH) and the second harmonic (SH) frequencies.

As the aim of our paper is to enable an analysis of experimentally obtained scattering data a typical experimental set-up is introduced at the beginning. This allows introducing experimentally relevant parameters, which will later be discussed in more detail. After that the general behavior of SHG and its dependence on particle parameters is discussed. Because plasmonic resonances play a decisive role in SHG we discuss the excitation and propagation of plasmons.

2. Nonlinear Mie model

In most other nonlinear Mie models second harmonic generation is assumed to take place in a nonlinear core or at an interface, which all have spherical symmetry. Solutions for the scattering coefficients are than obtained by decomposing nonlinear products of vector spherical harmonics into the basis functions of the Mie model and by evaluating respective boundary conditions [52

52. D. Östling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear optical properties of small metallic spheres,” Z. Phys. D 28, 169–175 (1993). [CrossRef]

,53

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

]. Here we use a different approach and start from a molecular Mie model that we have introduced earlier [19

19. S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B 84(23), 235403 (2011). [CrossRef]

]: The nonlinear polarization
Pi(2)j,kχijk(2)EjFHEkFH
(1.1)
is calculated from the fundamental harmonic fieldsEFH and the surface susceptibility χ(2), which depends on the materials. Similar to the Rayleigh-Gans-Debye-theory, where the polarization is modeled as a dipole density, we interpret P(2) as an ensemble of dipoles on a discrete grid rd. The second harmonic is driven by this ensemble of nonlinear dipoles. . rd. Although the distribution of the dipoles need not obey spherical symmetry all electric fields can be calculated using classical Mie theory with a plane wave as incident field. The model also takes into account the correct influence of the sphere on the emission of the nonlinearly induced dipoles into the SH. The effective fields of the individual dipoles are calculated using generalized Mie theory, with the field of a dipole, placed at any position rd [57

57. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, 1969).

]. One advantage of our approach is that it is in general not limited to nonlinear configurations with spherical symmetry. For example it can also account for particles, which are covered with incomplete layers of second harmonic generating molecules. Only the linear index distribution must have spherical symmetry.

Mie theory, which is the basis of our model, relies on the expansion of all fields into a set of vector spherical harmonics Mm,n(j) and Nm,n(j) j=1j=3with expansion coefficients am,n, bm,n, cm,n, and dm,n:
EFH(r)=n=1Nm=nnam,nNm,n(1)(r)+bm,nNm,n(1)(r)+cm,nNm,n(3)(r)+dm,nMm,n(3)(r).
(1.2)
Each vector component of these is a product of Bessel function (j = 1) or Hankel function (j = 3) of r, associated Legendre function of θ and exponential function of ϕ. Only the Bessel or Hankel functions that describe the radial dependence finally enter the continuity-conditions. Inside the sphere, Hankel functions diverge, so that cm,n and dm,n are zero. The scattered field outside the particle is described as an outgoing wave, so that only Hankel functions are used (fields with j=3) are used.

Standard Mie theory only evaluates one boundary condition for the incident electric field and scattered fields inside and outside the sphere
Eθ,ϕinc(R)+Eθ,ϕsc, out(R)=Eθ,ϕsc, in(R)
(1.3)
and a respective continuity condition for the magnetic fields. To apply the Mie model to a sphere with L layers, the continuity conditions have to be modified. For several layers, denoted by l=1L+1, there exist L continuity conditions for the scattered electric fields Esc, l in the layers l and l+1 at the boundaries with radius Rl:
Eθ,ϕsc, l(Rl)=Eθ,ϕsc, l+1(Rl).
(1.4)
The Mie scattering process of the fundamental harmonic fields involves a plane wave Epw(r) that enters the boundary condition at the outer radius RL [58

58. M. Sitarski, “Internal heating of multilayered aerosol particles by electromagnetic radiation,” Langmuir 3(1), 85–93 (1987). [CrossRef]

]:
Eθ,ϕsc, l(RL)=Eθ,ϕsc, l+1(RL)+Eθ,ϕpw(RL).
(1.5)
The 4L expansion coefficients in the different layers l=1L+1 are obtained from two sets of linear equations with 2L×2L matrices that have to be solved for every expansion order n [58

58. M. Sitarski, “Internal heating of multilayered aerosol particles by electromagnetic radiation,” Langmuir 3(1), 85–93 (1987). [CrossRef]

].

For metallic particles it is essential, that some modifications are added to Mie theory for stability [59

59. J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Develop. 13(3), 302–313 (1969). [CrossRef]

,60

60. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19(9), 1505–1509 (1980). [CrossRef] [PubMed]

]. The refractive index, which has a dominant imaginary part in case of metals, enters the equations through the argument of the Bessel functions. Bessel functions of an imaginary argument diverge exponentially and therefore make Mie scattering unstable for highly absorbing particles. In the original equations for the boundary conditions in Mie-Theory, the Bessel functions and their derivatives are therefore replaced by ratios of Bessel functions and logarithmic derivatives for which stable recursion formulas exist [58

58. M. Sitarski, “Internal heating of multilayered aerosol particles by electromagnetic radiation,” Langmuir 3(1), 85–93 (1987). [CrossRef]

].

The polarization P(2)(rd) is resembled by dipoles at discrete positions rd. The electric fields of a dipole at position rd are calculated from a dipole at the origin EDipole(r)=N0,1(j=3)(r) by a translation theorem [61

61. J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I: multipole expansion and ray-optical solutions,” IEEE Trans. Antenn. Propag. 19(3), 378–390 (1971). [CrossRef]

]. This results in different expansions, depending on r:
EDipole(r)={E(j=3),Dipole(r)=m,nam,n(j=3)Nm,n(j=3)(r)+bm,n(j=3)Nm,n(j=3)(r)if|r|>if|rd|.E(j=1),Dipole(r)=m,nam,n(j=1)Nm,n(j=1)(r)+bm,n(j=1)Nm,n(j=1)(r)if|r|<|rd|
(1.6)
If the dipole is positioned inside layer l (Rl1<|rd|<Rl), EDipole(r) enters the boundary conditions at Rl1 and Rl:

Eθ,ϕsc, l1(Rl1)=Eθ,ϕDipole,(1)(Rl1)+Eθ,ϕsc, l(Rl1),
(1.7)
Eθ,ϕsc, l(Rl)+Eθ,ϕDipole,(3)(Rl)=Eθ,ϕsc, l+1(Rl).
(1.8)

3. Results and discussion

In typical experiments [20

20. B. Schürer, S. Wunderlich, C. Sauerbeck, U. Peschel, and W. Peukert, “Probing colloidal interfaces by angle-resolved second harmonic light scattering,” Phys. Rev. B 82(24), 241404 (2010). [CrossRef]

] the SH fields, generated at the surface of nanoparticles, are measured as a function of the scattering angle θ and for the polarizations of the incident and the detected light being either parallel (p) or perpendicular (s) to the scattering plane (Fig. 1
Fig. 1 a) typical experimental setup for angle-resolved SHG from colloidal core-shell particles. b) Angular scattering pattern Isp(θ) (FH s-polarized, SH p-polarized) and Ipp(θ) (FH and SH p-polarized) for a silica particle (radius 100 nm) with a silver shell of 6.3 nm thickness (compare Fig. 2).
). As high power pulses are required we assume the FH to be generated by a Ti:Sa-Laser at 800 nm wavelength. The intensity and the polarization of the scattered SH light at 400 nm is detected. The respective intensities are given for example by Isp(θ), if the incident fundamental harmonic is s-polarized and the p-polarized second harmonic is detected under an angle θ with respect to the exciting laser pulse. Ipp(θ) is measured if both beams are p-polarized. Due to symmetry reasons Ips(θ) and Iss(θ) are identical to zero for spherical particles.

Here we simulated the SH-intensities Ipp(θ) and Isp(θ) for a nano-particle consisting of a silica core (radius 100 nm) and a silver shell, which is suspended in water. Dielectric constants are taken from Johnson and Christy [62

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

]. In addition we first assume a dominating χzzz(2) [55

55. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Nonlinear Mie theory for the second harmonic generation in metallic nanoshells,” J. Opt. Soc. Am. B 29(8), 2213–2221 (2012). [CrossRef]

,63

63. 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]

65

65. G. Gonella, W. Gan, B. Xu, and H.-L. Dai, “The effect of composition, morphology, and susceptibility on nonlinear light scattering from metallic and dielectric nanoparticles,” J. Phys. Chem. Lett. 3(19), 2877–2881 (2012). [CrossRef]

] for the nonlinear surface susceptibility of the silica-silver and the silver-water interfaces. We will later investigate the effect of the nonlinear coefficient on the SH-signal.

A typical angular dependent emission spectrum is displayed in Fig. 1. For symmetry reasons the SH emission in forward direction is always zero (but a nonzero intensity might be measured in the experiment due to a finite aperture and detector size), but characteristic peaks emerge for higher angles. Varying the thickness of the shell between 0 nm and 30 nm causes changes in the angular emission pattern, but mainly influences the total efficiency of SHG (Fig. 2
Fig. 2 Angle-resolved SH-intensity Ipp(θ) and Isp(θ) (a,b) and mean intensity, averaged over the detection angle (c,d) for a growing silver shell on a silica particle. For the metallic shell either idealized silver without plasmon losses ϵshell400 nm=4.4, ϵshell800 nm=30.8 (a,b,c) or realistic values, including plasmon losses ϵshell400 nm=4.4+0.2i, ϵshell800 nm=30.8+0.4i, are used (d).
). Resonances occur e.g. at 4 nm, 7 nm or 25 nm thickness and are even more pronounced, if an idealized material without losses is assumed for the metallic shell. When plasmon losses are included (ϵshell400 nm=4.4+0.2i, ϵshell800 nm=30.8+0.4i), the resonant enhancement is reduced and the resonance at 25 nm shell thickness even disappears (Fig. 2).

To understand these resonances, we have to keep in mind that SHG takes place in two steps. The first one includes the formation of the nonlinear polarization at the inner and outer interface of the core-shell particle. The nonlinear polarization is directly proportional to the square of the scattered FH wave that excites the particle. Hence, plasmonic resonances at FH frequency lead to a higher SH-intensity due to the increased field strength at the two interfaces.

The second step is calculating the electromagnetic field at SH frequency that is produced by the nonlinear polarization. To this end we decompose the nonlinear polarization into an ensemble of dipolar point sources each emitting an electromagnetic field at SH frequency. This emission process is again heavily determined by resonances of the particle, but now at SH frequency.

Field enhancement at such Mie resonances happens for both the radial |Er|2 and azimuthal |Eϑ|2, |Eϕ|2 components of the electric field simultaneously. Also the inner (core-shell) and the outer (shell-surrounding) interfaces of the shell (Fig. 3
Fig. 3 Mean electric field Er(ϑ)ϑ induced by a scattered plane wave (fundamental harmonic wavelength) at the inner (rin) and outer (rout) interface of a sphere with silica core of radius 100 nm and a silver shell of variable thickness with (ϵshell800 nm=30.8+0.4i) and without (ϵshell800 nm=30.8) damping. Additionally, the extinction at λ=800 nm is given as a function of the shell thickness.
) experience qualitatively the same field strength. Strength and width of resonances are heavily influenced by the shell thickness. FH resonances occur for a shell thickness below 10 nm. Their spectral position is equally reproduced by peaks of the SH-intensity. In contrast the linear extinction spectrum, which is usually measured does not show such a significant dependence on the shell thickness because the farfield is much less sensitive to resonant effects compared with the the fundamental harmonic nearfield at the surface of the sphere which finally causes the SH emission. For metals with higher plasmon losses, like gold, this difference between linear extinction spectra and field enhancement at the surface of the sphere becomes even more pronounced.

A second possible reason for enhancement of SHG is the excitation of a resonance at SH frequency. The emission of a dipole is influenced by the sphere (Fig. 4
Fig. 4 Field distribution log10|E|2 emitted by a dipole radiating at 400 nm wavelength (a) and respective field distribution log10|Eϑ|2 modified by the presence of a sphere (b,c). The sphere has a silica core of radius 100 nm, and silver shell of thickness D=25 nm. The shell thickness is tuned for the resonance K=5 with 10 lobes. For the metallic shell either idealized silver without plasmon losses ϵshell400 nm=4.4 (b) or realistic ϵshell400 nm=4.4+0.2i is used (c).
). This influence can be very dramatic in the case of a plasmonic resonance: The emitting dipole is hardly visible and all radiation seems to emerge from the particle in a star-like pattern. For dipoles with radial orientation the generated tangential field distribution shows a minimum at the position of the dipole and on the opposite site of the sphere. When the dipole is parallel to the surface, maxima and minima switch places, so that a maximum is observed at the position of the dipole and on the opposite site of the sphere. Obviously the near-field of the dipole is imaged onto the opposite side of the sphere, showing that a spherical surface has perfect imaging properties even on a sub wavelength scale.

The situation of a single dipole close to a sphere is similar to single molecule spectroscopy performed near a metallic surface in order to profit from the enhanced local fields as they are employed in surface enhanced Raman scattering (SERS). Here, the environment influences the molecular emission properties [66

66. K. H. Drexhage, “IV Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1974), Vol. 12, pp. 163–232.

]. Kuhn et al. [67

67. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

] even used a spherical gold nanoparticle as an optical nanoantenna to enhance the fluorescence signal.

Although FH resonances are excited by a plane wave, but SH resonances by localized dipoles the respective field pattern are quite similar. In both cases each resonance exhibits a star-like pattern with a certain number of lobes. For decreasing shell thickness two more lobes arise at every new resonance (Fig. 5
Fig. 5 Tangential component of the intensity of a dipole (second harmonic wavelength) placed at the surface of a spherical particle with silica core of radius 100 nm and a silver shell (with and without damping) of variable thickness (compare Fig. 4 for the geometry). a) Intensity |Eϑ(ϑ)|2 of a dipole at the outer surface (without plasmonic losses, ϵshell400 nm=4.4). The intensity is detected 20 nm above the surface of the sphere and shown as a function of the scattering angle ϑ. b, c: Intensity |Eϑ(ϑ)|2ϑ of a dipole, which is placed at the inner and outer interface of a sphere, without (b) and with (c) plasmonic losses (ϵshell400 nm=4.4+0.2i), detected in 2 cm distance.
). This suggests that resonances are caused by surface plasmon polaritons running around the sphere. A resonance with 2K lobes occurs, whenever a multiple of the effective wavelength of the plasmon fits to the circumference of the sphere: 2πR=KλSPP. Hence, resonances depend on both the diameter of the sphere and the effective wavelength of the plasmon. The latter one is mainly determined by the shell thickness. In our case the resonance corresponding to the longest plasmon wavelength at SH frequency occurs for D=25 nm and explains the respective enhancement of the total SHG. For smaller shell thicknesses the plasmon wavelength decreases and further resonances are observed, at least for the lossless case (Fig. 5). But, plasmons are guided waves and do only interact with the farfield due to the curvature of the surface. The thinner the shell, the shorter is the plasmon wavelength and the stronger is the guidance. Therefore resonances at smaller shell thickness can be excited by nonlinear dipoles, but they are only visible close to the surface of the sphere (Fig. 5), but do not significantly contribute to an emission to the farfield.

To test our assumption that resonances are caused by running plasmons we shortly discuss the case of a solid metallic particle because the wavelength of plasmons propagating at a pure metal interface is known analytically as
λSPP=λDipoleεSphere+εSurroundingεSphereεSurrounding
(1.9)
Resonance positions in fact occur almost exactly when the circumference of the sphere coincides with multiples of λSPP even though the interface is highly curved (Fig. 6
Fig. 6 Resonances with 2K lobes occurring at certain values of the permittivity εNSphere of a solid metallic sphere in comparison to the model based on the planar plasmon for R=100 nm and λDipole=400 nm.
).

Hence, any enhancement of SHG on core-shell nanoparticles is solely based on resonances at FH or SH wavelength, which both are caused by plasmons running along the metallic film. As the plasmon wavelength critically depends on the shell thickness SHG provides an extremely sensitive tool to determine the thickness of nanoshells by in situ scattering experiments and by evaluating the spectral position of respective peaks (Fig. 7
Fig. 7 SH-intensity (a) and extinction spectrum (b) as a function of the fundamental harmonic wavelength. The dashed lines show the SH-scattering cross section Cextm,n(2n+1)k2(|am,nSH|2+|bm,nSH|2). Three systems of silica particles with silver shell (including plasmon losses) of 5 nm, 7.5 nm, and 10 nm thickness are shown.
). This sensitivity is based on the strong response of SHG on the local near fields at the surface of the sphere. As discussed earlier conventional linear extinction spectra cannot provide this information with a comparable contrast in particular in case of metals with higher losses.

4. Conclusion

We have successfully refined the nonlinear Mie model to account for metallo-dielectric core-shell particles. We found that for certain shell thicknesses SHG is extremely enhanced. We attribute this to the occurrence of plasmonic resonances at either the FH or SH frequency. Resonances at a low shell thickness arise from Mie-resonances of the nanoshells-particle excited the scattered FH plain wave. Enhancement of SHG at larger shell thicknesses is caused by resonances excited by the nonlinear dipoles oscillating at SH frequency. All resonances are caused by surface plasmons, which run on the surface of the spherical particle and are in resonance with the circumference of the sphere. Because the plasmon wavelength critically depends on the properties of the metallic layer SHG resonances of core-shell nanoparticles can be easily tuned by varying the thickness of the shell. In turn SHG might therefore become a convenient tool to study the growth and the evolution of the thickness of metallic shells on particles with much higher sensitivity than it can be provided by linear scattering experiments. Our simulations have also shown that the actual composition of the nonlinear tensor mainly influences the strength of the interaction with χzzz(2) playing the dominant role, but does not influence the resonance positions. In contrast the angular distribution of the scattered SH field is affected, which in principal allows to deduce also individual tensor elements from angularly resolved SHG scattering data.

Acknowledgments

The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of the excellence initiative

References and links

1.

Y. Shen, “Surface 2nd harmonic-generation - a new technique for surface studies,” Annu. Rev. Mater. Sci. 16(1), 69–86 (1986). [CrossRef]

2.

H. Wang, E. C. Y. Yan, E. Borguet, and K. B. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett. 259(1-2), 15–20 (1996). [CrossRef]

3.

E. C. Y. Yan, Y. Liu, and K. B. Eisenthal, “New method for determination of surface potential of microscopic particles by second harmonic generation,” J. Chem. Phys. B 102(33), 6331–6336 (1998). [CrossRef]

4.

H. Wang, T. Troxler, A.-G. Yeh, and H.-L. Dai, “In situ, nonlinear optical probe of surfactant adsorption on the durface of microparticles in colloids,” Langmuir 16(6), 2475–2481 (2000). [CrossRef]

5.

S. Roke, O. Berg, J. Buitenhuis, A. van Blaaderen, and M. Bonn, “Surface molecular view of colloidal gelation,” Proc. Natl. Acad. Sci. U.S.A. 103(36), 13310–13314 (2006). [CrossRef] [PubMed]

6.

M. Subir, J. Liu, and K. B. Eisenthal, “Protonation at the Aqueous Interface of Polymer Nanoparticles with Second Harmonic Generation,” J. Phys. Chem. C 112(40), 15809–15812 (2008). [CrossRef]

7.

A. G. F. de Beer, H. B. de Aguiar, J. F. W. Nijsen, and S. Roke, “Detection of buried microstructures by nonlinear light scattering spectroscopy,” Phys. Rev. Lett. 102(9), 095502 (2009). [CrossRef] [PubMed]

8.

H. B. Aguiar, A. G. F. de Beer, M. L. Strader, and S. Roke, “The interfacial tension of nanoscopic oil droplets in water is hardly affected by SDS surfactant,” J. Am. Chem. Soc. 132(7), 2122–2123 (2010). [CrossRef] [PubMed]

9.

H. B. de Aguiar, M. L. Strader, A. G. F. de Beer, and S. Roke, “Surface structure of sodium dodecyl sulfate surfactant and oil at the oil-in-water droplet liquid/liquid interface: a manifestation of a nonequilibrium surface state,” J. Phys. Chem. B 115(12), 2970–2978 (2011). [CrossRef] [PubMed]

10.

A. G. F. de Beer and S. Roke, “Obtaining molecular orientation from second harmonic and sum frequency scattering experiments in water: Angular distribution and polarization dependence,” J. Chem. Phys. 132(23), 234702 (2010). [CrossRef] [PubMed]

11.

W. Gan, B. Xu, and H.-L. Dai, “Activation of Thiols at a Silver Nanoparticle Surface,” Angew. Chem. Int. Ed. Engl. 50(29), 6622–6625 (2011). [CrossRef] [PubMed]

12.

R. Vácha, S. W. Rick, P. Jungwirth, A. G. F. de Beer, H. B. de Aguiar, J.-S. Samson, and S. Roke, “The orientation and charge of water at the hydrophobic oil droplet-water interface,” J. Am. Chem. Soc. 133(26), 10204–10210 (2011). [CrossRef] [PubMed]

13.

L. H. Haber, S. J. J. Kwok, M. Semeraro, and K. B. Eisenthal, “Probing the colloidal gold nanoparticle/aqueous interface with second harmonic generation,” Chem. Phys. Lett. 507(1-3), 11–14 (2011). [CrossRef]

14.

J. Griffin, A. K. Singh, D. Senapati, E. Lee, K. Gaylor, J. Jones-Boone, and P. C. Ray, “Sequence-Specific HCV RNA Quantification Using the Size-Dependent Nonlinear Optical Properties of Gold Nanoparticles,” Small 5(7), 839–845 (2009). [CrossRef] [PubMed]

15.

C.-L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Bioconjugation of barium titanate nanocrystals with immunoglobulin G antibody for second harmonic radiation imaging probes,” Biomaterials 31(8), 2272–2277 (2010). [CrossRef] [PubMed]

16.

J. Jiang, K. B. Eisenthal, and R. Yuste, “Second harmonic generation in neurons: electro-optic mechanism of membrane potential sensitivity,” Biophys. J. 93(5), L26–L28 (2007). [CrossRef] [PubMed]

17.

Y. Liu, E. C. Y. Yan, and K. B. Eisenthal, “Effects of bilayer surface charge density on molecular adsorption and transport across liposome bilayers,” Biophys. J. 80(2), 1004–1012 (2001). [CrossRef] [PubMed]

18.

G. Gonella and H.-L. Dai, “Determination of adsorption geometry on spherical particles from nonlinear Mie theory analysis of surface second harmonic generation,” Phys. Rev. B 84(12), 121402 (2011). [CrossRef]

19.

S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B 84(23), 235403 (2011). [CrossRef]

20.

B. Schürer, S. Wunderlich, C. Sauerbeck, U. Peschel, and W. Peukert, “Probing colloidal interfaces by angle-resolved second harmonic light scattering,” Phys. Rev. B 82(24), 241404 (2010). [CrossRef]

21.

B. Schürer, M. Hoffmann, S. Wunderlich, L. Harnau, U. Peschel, M. M. Ballauff, and W. Peukert, “Second harmonic light scattering from spherical polyelectrolyte brushes,” J. Phys. Chem. C 115(37), 18302–18309 (2011). [CrossRef]

22.

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4(12), 4274–4290 (1971). [CrossRef]

23.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974). [CrossRef]

24.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Second harmonic generation with surface plasmons in alkali metals,” Opt. Commun. 13(3), 294–298 (1975). [CrossRef]

25.

H. J. Simon and J. K. Guha, “Directional surface plasmon scattering from silver films,” Opt. Commun. 18(3), 391–394 (1976). [CrossRef]

26.

D. L. Mills, “Theory of second harmonic generation by surface polaritons on metals,” Solid State Commun. 24(9), 669–671 (1977). [CrossRef]

27.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980). [CrossRef]

28.

S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem. 63(1), 353–378 (2012). [CrossRef] [PubMed]

29.

F. W. Vance, B. I. Lemon, and J. T. Hupp, “Enormous hyper-Rayleigh scattering from nanocrystalline gold particle suspensions,” J. Chem. Phys. B 102(50), 10091–10093 (1998). [CrossRef]

30.

R. C. Johnson, J. Li, J. T. Hupp, and G. C. Schatz, “Hyper-Rayleigh scattering studies of silver, copper, and platinum nanoparticle suspensions,” Chem. Phys. Lett. 356(5-6), 534–540 (2002). [CrossRef]

31.

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117(13), 5963 (2002). [CrossRef]

32.

J.-P. Abid, J. Nappa, H. H. Girault, and P.-F. Brevet, “Pure surface plasmon resonance enhancement of the first hyperpolarizability of gold core-silver shell nanoparticles,” J. Chem. Phys. 121(24), 12577–12582 (2004). [CrossRef] [PubMed]

33.

J. Nappa, I. Russier-Antoine, E. Benichou, Ch. Jonin, and P.-F. Brevet, “Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response,” J. Chem. Phys. 125(18), 184712 (2006). [CrossRef] [PubMed]

34.

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005). [CrossRef]

35.

M. Chandra and P. K. Das, ““Small-particle limit” in the second harmonic generation from noble metal nanoparticles,” Chem. Phys. 358(3), 203–208 (2009). [CrossRef]

36.

M. Chandra and P. K. Das, “Size dependence and dispersion behavior of the first hyperpolarizability of copper nanoparticles,” Chem. Phys. Lett. 476(1-3), 62–64 (2009). [CrossRef]

37.

R. Antoine, M. Pellarin, B. Palpant, M. Broyer, B. Prevel, P. Galletto, P. F. Brevet, and H. H. Girault, “Surface plasmon enhanced second harmonic response from gold clusters embedded in an alumina matrix,” J. Appl. Phys. 84(8), 4532–4536 (1998). [CrossRef]

38.

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]

39.

N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008). [CrossRef] [PubMed]

40.

F. B. P. Niesler, N. Feth, S. Linden, J. Niegemann, J. Gieseler, K. Busch, and M. Wegener, “Second-harmonic generation from split-ring resonators on a GaAs substrate,” Opt. Lett. 34(13), 1997–1999 (2009). [CrossRef] [PubMed]

41.

N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010). [CrossRef] [PubMed]

42.

H. Lu, X. Liu, R. Zhou, Y. Gong, and D. Mao, “Second-harmonic generation from metal-film nanohole arrays,” Appl. Opt. 49(12), 2347–2351 (2010). [CrossRef] [PubMed]

43.

G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun. 41(6), 499–501 (1982). [CrossRef]

44.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999). [CrossRef]

45.

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, “Second-harmonic generation in arrays of spherical particles,” Phys. Rev. B 68(8), 085318 (2003). [CrossRef]

46.

B. S. Mendoza and W. L. Mochán, “Second harmonic surface response of a composite,” Opt. Mater. 29(1), 1–5 (2006). [CrossRef]

47.

J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55(6), 4520–4525 (1997). [CrossRef]

48.

S. Roke, W. G. Roeterdink, J. E. G. J. Wijnhoven, A. V. Petukhov, A. W. Kleyn, and M. Bonn, “Vibrational sum frequency scattering from a submicron suspension,” Phys. Rev. Lett. 91(25), 258302 (2003). [CrossRef] [PubMed]

49.

S. Viarbitskaya, V. Kapshai, P. van der Meulen, and T. Hansson, “Size dependence of second-harmonic generation at the surface of microspheres,” Phys. Rev. A 81(5), 053850 (2010). [CrossRef]

50.

S.-H. Jen, H.-L. Dai, and G. Gonella, “The effect of particle size in second harmonic generation from the surface of spherical colloidal particles. II: The nonlinear Rayleigh−Gans−Debye model,” J. Phys. Chem. C 114(10), 4302–4308 (2010). [CrossRef]

51.

J. I. Dadap, “Optical second-harmonic scattering from cylindrical particles,” Phys. Rev. B 78(20), 205322 (2008). [CrossRef]

52.

D. Östling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear optical properties of small metallic spheres,” Z. Phys. D 28, 169–175 (1993). [CrossRef]

53.

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

54.

S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B 70(11), 115106 (2004). [CrossRef]

55.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Nonlinear Mie theory for the second harmonic generation in metallic nanoshells,” J. Opt. Soc. Am. B 29(8), 2213–2221 (2012). [CrossRef]

56.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Effect of the dielectric core and embedding medium on the second harmonic generation from plasmonic nanoshells: tunability and sensing,” J. Phys. Chem. C 117(2), 1172–1177 (2013). [CrossRef]

57.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, 1969).

58.

M. Sitarski, “Internal heating of multilayered aerosol particles by electromagnetic radiation,” Langmuir 3(1), 85–93 (1987). [CrossRef]

59.

J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Develop. 13(3), 302–313 (1969). [CrossRef]

60.

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19(9), 1505–1509 (1980). [CrossRef] [PubMed]

61.

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I: multipole expansion and ray-optical solutions,” IEEE Trans. Antenn. Propag. 19(3), 378–390 (1971). [CrossRef]

62.

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

63.

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]

64.

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]

65.

G. Gonella, W. Gan, B. Xu, and H.-L. Dai, “The effect of composition, morphology, and susceptibility on nonlinear light scattering from metallic and dielectric nanoparticles,” J. Phys. Chem. Lett. 3(19), 2877–2881 (2012). [CrossRef]

66.

K. H. Drexhage, “IV Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1974), Vol. 12, pp. 163–232.

67.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(240.0240) Optics at surfaces : Optics at surfaces
(290.0290) Scattering : Scattering

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 10, 2013
Revised Manuscript: June 19, 2013
Manuscript Accepted: June 22, 2013
Published: July 29, 2013

Citation
Sarina Wunderlich and Ulf Peschel, "Plasmonic enhancement of second harmonic generation on metal coated nanoparticles," Opt. Express 21, 18611-18623 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-18611


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. Shen, “Surface 2nd harmonic-generation - a new technique for surface studies,” Annu. Rev. Mater. Sci.16(1), 69–86 (1986). [CrossRef]
  2. H. Wang, E. C. Y. Yan, E. Borguet, and K. B. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.259(1-2), 15–20 (1996). [CrossRef]
  3. E. C. Y. Yan, Y. Liu, and K. B. Eisenthal, “New method for determination of surface potential of microscopic particles by second harmonic generation,” J. Chem. Phys. B102(33), 6331–6336 (1998). [CrossRef]
  4. H. Wang, T. Troxler, A.-G. Yeh, and H.-L. Dai, “In situ, nonlinear optical probe of surfactant adsorption on the durface of microparticles in colloids,” Langmuir16(6), 2475–2481 (2000). [CrossRef]
  5. S. Roke, O. Berg, J. Buitenhuis, A. van Blaaderen, and M. Bonn, “Surface molecular view of colloidal gelation,” Proc. Natl. Acad. Sci. U.S.A.103(36), 13310–13314 (2006). [CrossRef] [PubMed]
  6. M. Subir, J. Liu, and K. B. Eisenthal, “Protonation at the Aqueous Interface of Polymer Nanoparticles with Second Harmonic Generation,” J. Phys. Chem. C112(40), 15809–15812 (2008). [CrossRef]
  7. A. G. F. de Beer, H. B. de Aguiar, J. F. W. Nijsen, and S. Roke, “Detection of buried microstructures by nonlinear light scattering spectroscopy,” Phys. Rev. Lett.102(9), 095502 (2009). [CrossRef] [PubMed]
  8. H. B. Aguiar, A. G. F. de Beer, M. L. Strader, and S. Roke, “The interfacial tension of nanoscopic oil droplets in water is hardly affected by SDS surfactant,” J. Am. Chem. Soc.132(7), 2122–2123 (2010). [CrossRef] [PubMed]
  9. H. B. de Aguiar, M. L. Strader, A. G. F. de Beer, and S. Roke, “Surface structure of sodium dodecyl sulfate surfactant and oil at the oil-in-water droplet liquid/liquid interface: a manifestation of a nonequilibrium surface state,” J. Phys. Chem. B115(12), 2970–2978 (2011). [CrossRef] [PubMed]
  10. A. G. F. de Beer and S. Roke, “Obtaining molecular orientation from second harmonic and sum frequency scattering experiments in water: Angular distribution and polarization dependence,” J. Chem. Phys.132(23), 234702 (2010). [CrossRef] [PubMed]
  11. W. Gan, B. Xu, and H.-L. Dai, “Activation of Thiols at a Silver Nanoparticle Surface,” Angew. Chem. Int. Ed. Engl.50(29), 6622–6625 (2011). [CrossRef] [PubMed]
  12. R. Vácha, S. W. Rick, P. Jungwirth, A. G. F. de Beer, H. B. de Aguiar, J.-S. Samson, and S. Roke, “The orientation and charge of water at the hydrophobic oil droplet-water interface,” J. Am. Chem. Soc.133(26), 10204–10210 (2011). [CrossRef] [PubMed]
  13. L. H. Haber, S. J. J. Kwok, M. Semeraro, and K. B. Eisenthal, “Probing the colloidal gold nanoparticle/aqueous interface with second harmonic generation,” Chem. Phys. Lett.507(1-3), 11–14 (2011). [CrossRef]
  14. J. Griffin, A. K. Singh, D. Senapati, E. Lee, K. Gaylor, J. Jones-Boone, and P. C. Ray, “Sequence-Specific HCV RNA Quantification Using the Size-Dependent Nonlinear Optical Properties of Gold Nanoparticles,” Small5(7), 839–845 (2009). [CrossRef] [PubMed]
  15. C.-L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Bioconjugation of barium titanate nanocrystals with immunoglobulin G antibody for second harmonic radiation imaging probes,” Biomaterials31(8), 2272–2277 (2010). [CrossRef] [PubMed]
  16. J. Jiang, K. B. Eisenthal, and R. Yuste, “Second harmonic generation in neurons: electro-optic mechanism of membrane potential sensitivity,” Biophys. J.93(5), L26–L28 (2007). [CrossRef] [PubMed]
  17. Y. Liu, E. C. Y. Yan, and K. B. Eisenthal, “Effects of bilayer surface charge density on molecular adsorption and transport across liposome bilayers,” Biophys. J.80(2), 1004–1012 (2001). [CrossRef] [PubMed]
  18. G. Gonella and H.-L. Dai, “Determination of adsorption geometry on spherical particles from nonlinear Mie theory analysis of surface second harmonic generation,” Phys. Rev. B84(12), 121402 (2011). [CrossRef]
  19. S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B84(23), 235403 (2011). [CrossRef]
  20. B. Schürer, S. Wunderlich, C. Sauerbeck, U. Peschel, and W. Peukert, “Probing colloidal interfaces by angle-resolved second harmonic light scattering,” Phys. Rev. B82(24), 241404 (2010). [CrossRef]
  21. B. Schürer, M. Hoffmann, S. Wunderlich, L. Harnau, U. Peschel, M. M. Ballauff, and W. Peukert, “Second harmonic light scattering from spherical polyelectrolyte brushes,” J. Phys. Chem. C115(37), 18302–18309 (2011). [CrossRef]
  22. J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B4(12), 4274–4290 (1971). [CrossRef]
  23. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett.33(26), 1531–1534 (1974). [CrossRef]
  24. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Second harmonic generation with surface plasmons in alkali metals,” Opt. Commun.13(3), 294–298 (1975). [CrossRef]
  25. H. J. Simon and J. K. Guha, “Directional surface plasmon scattering from silver films,” Opt. Commun.18(3), 391–394 (1976). [CrossRef]
  26. D. L. Mills, “Theory of second harmonic generation by surface polaritons on metals,” Solid State Commun.24(9), 669–671 (1977). [CrossRef]
  27. J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B21(10), 4389–4402 (1980). [CrossRef]
  28. S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem.63(1), 353–378 (2012). [CrossRef] [PubMed]
  29. F. W. Vance, B. I. Lemon, and J. T. Hupp, “Enormous hyper-Rayleigh scattering from nanocrystalline gold particle suspensions,” J. Chem. Phys. B102(50), 10091–10093 (1998). [CrossRef]
  30. R. C. Johnson, J. Li, J. T. Hupp, and G. C. Schatz, “Hyper-Rayleigh scattering studies of silver, copper, and platinum nanoparticle suspensions,” Chem. Phys. Lett.356(5-6), 534–540 (2002). [CrossRef]
  31. E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys.117(13), 5963 (2002). [CrossRef]
  32. J.-P. Abid, J. Nappa, H. H. Girault, and P.-F. Brevet, “Pure surface plasmon resonance enhancement of the first hyperpolarizability of gold core-silver shell nanoparticles,” J. Chem. Phys.121(24), 12577–12582 (2004). [CrossRef] [PubMed]
  33. J. Nappa, I. Russier-Antoine, E. Benichou, Ch. Jonin, and P.-F. Brevet, “Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response,” J. Chem. Phys.125(18), 184712 (2006). [CrossRef] [PubMed]
  34. J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B71(16), 165407 (2005). [CrossRef]
  35. M. Chandra and P. K. Das, ““Small-particle limit” in the second harmonic generation from noble metal nanoparticles,” Chem. Phys.358(3), 203–208 (2009). [CrossRef]
  36. M. Chandra and P. K. Das, “Size dependence and dispersion behavior of the first hyperpolarizability of copper nanoparticles,” Chem. Phys. Lett.476(1-3), 62–64 (2009). [CrossRef]
  37. R. Antoine, M. Pellarin, B. Palpant, M. Broyer, B. Prevel, P. Galletto, P. F. Brevet, and H. H. Girault, “Surface plasmon enhanced second harmonic response from gold clusters embedded in an alumina matrix,” J. Appl. Phys.84(8), 4532–4536 (1998). [CrossRef]
  38. 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]
  39. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett.33(17), 1975–1977 (2008). [CrossRef] [PubMed]
  40. F. B. P. Niesler, N. Feth, S. Linden, J. Niegemann, J. Gieseler, K. Busch, and M. Wegener, “Second-harmonic generation from split-ring resonators on a GaAs substrate,” Opt. Lett.34(13), 1997–1999 (2009). [CrossRef] [PubMed]
  41. N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express18(7), 6545–6554 (2010). [CrossRef] [PubMed]
  42. H. Lu, X. Liu, R. Zhou, Y. Gong, and D. Mao, “Second-harmonic generation from metal-film nanohole arrays,” Appl. Opt.49(12), 2347–2351 (2010). [CrossRef] [PubMed]
  43. G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun.41(6), 499–501 (1982). [CrossRef]
  44. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett.83(20), 4045–4048 (1999). [CrossRef]
  45. W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, “Second-harmonic generation in arrays of spherical particles,” Phys. Rev. B68(8), 085318 (2003). [CrossRef]
  46. B. S. Mendoza and W. L. Mochán, “Second harmonic surface response of a composite,” Opt. Mater.29(1), 1–5 (2006). [CrossRef]
  47. J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A55(6), 4520–4525 (1997). [CrossRef]
  48. S. Roke, W. G. Roeterdink, J. E. G. J. Wijnhoven, A. V. Petukhov, A. W. Kleyn, and M. Bonn, “Vibrational sum frequency scattering from a submicron suspension,” Phys. Rev. Lett.91(25), 258302 (2003). [CrossRef] [PubMed]
  49. S. Viarbitskaya, V. Kapshai, P. van der Meulen, and T. Hansson, “Size dependence of second-harmonic generation at the surface of microspheres,” Phys. Rev. A81(5), 053850 (2010). [CrossRef]
  50. S.-H. Jen, H.-L. Dai, and G. Gonella, “The effect of particle size in second harmonic generation from the surface of spherical colloidal particles. II: The nonlinear Rayleigh−Gans−Debye model,” J. Phys. Chem. C114(10), 4302–4308 (2010). [CrossRef]
  51. J. I. Dadap, “Optical second-harmonic scattering from cylindrical particles,” Phys. Rev. B78(20), 205322 (2008). [CrossRef]
  52. D. Östling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear optical properties of small metallic spheres,” Z. Phys. D28, 169–175 (1993). [CrossRef]
  53. Y. Pavlyukh and W. Hübner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B70(24), 245434 (2004). [CrossRef]
  54. S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B70(11), 115106 (2004). [CrossRef]
  55. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Nonlinear Mie theory for the second harmonic generation in metallic nanoshells,” J. Opt. Soc. Am. B29(8), 2213–2221 (2012). [CrossRef]
  56. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Effect of the dielectric core and embedding medium on the second harmonic generation from plasmonic nanoshells: tunability and sensing,” J. Phys. Chem. C117(2), 1172–1177 (2013). [CrossRef]
  57. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, 1969).
  58. M. Sitarski, “Internal heating of multilayered aerosol particles by electromagnetic radiation,” Langmuir3(1), 85–93 (1987). [CrossRef]
  59. J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Develop.13(3), 302–313 (1969). [CrossRef]
  60. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt.19(9), 1505–1509 (1980). [CrossRef] [PubMed]
  61. J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I: multipole expansion and ray-optical solutions,” IEEE Trans. Antenn. Propag.19(3), 378–390 (1971). [CrossRef]
  62. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  63. 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]
  64. 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. B82(23), 235403 (2010). [CrossRef]
  65. G. Gonella, W. Gan, B. Xu, and H.-L. Dai, “The effect of composition, morphology, and susceptibility on nonlinear light scattering from metallic and dielectric nanoparticles,” J. Phys. Chem. Lett.3(19), 2877–2881 (2012). [CrossRef]
  66. K. H. Drexhage, “IV Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1974), Vol. 12, pp. 163–232.
  67. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett.97(1), 017402 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited