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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 19214–19225
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Anomalously-large photo-induced magnetic response of metallic nanocolloids in aqueous solution using a solar simulator

N. D. Singh, M. Moocarme, B. Edelstein, N. Punnoose, and L. T. Vuong  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 19214-19225 (2012)
http://dx.doi.org/10.1364/OE.20.019214


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Abstract

We experimentally, analytically, and numerically demonstrate the nonlinear photo-induced plasmon-assisted magnetic response that occurs with metallic nanoparticles in aqueous solution. We measure the scattered spectra from solutions of gold nanospheres (10−7 fill factor) and observe appreciable changes when simultaneously applying DC magnetic fields and illuminating samples with light. The magnetic response is achieved using light from a solar simulator at unprecedented low illumination intensities (< 1W/cm2) and is sustained when the magnetic field is removed. Distinctly different behavior is observed depending on the circular-polarization handedness given a fixed magnetic field. Nanoparticle aggregation is more likely to occur when the circular-polarization trajectory opposes the solenoid current that produces the magnetic field. Using Mie’s theoretical solution, we show how vortex orbital surface currents lead to an increased and anisotropic electrical conductivity, which shifts the scattered spectra in agreement with experimental results. The single-nanoparticle plasmon-induced magnetization, which couples the scattered and incident electric fields, changes sign with orthogonal circular-polarization handedness.

© 2012 OSA

1. Introduction

When light illuminates metallic sub-wavelength structures, vortex energy flows and phase singularities are produced [1

1. J. Meixner, “The behavior of electromagnetic fields at edges,” Antennas Propaga. 20, 442–446 (1972). [CrossRef]

]. The associated whirlpool energy flows manifest near sharp edges and as hydrodynamic effects [2

2. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” J. Exp. Theor. Phys. Lett. 33, 195–199 (1981).

, 3

3. D. Rozas, C. T. Law, and G. A. Swartzlander Jr., “Propagation dynamics of optical vortices,” J. Opt. Soc. Amer. B 14, 3054–3065 (1997). [CrossRef]

], which are strongly coupled to surface plasmons. It is well-known that such coiled electron currents and vortex energy flows give rise to magnetic fields and that an appreciable photo-induced magnetic response occurs via the excitation of plasmons on metallic sub-wavelength structures [4

4. A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90, 107404 (2003). [CrossRef] [PubMed]

9

9. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” 328, 1135–1138 (2010).

]. Observations of phase singularities coincide with the conditions associated with large pulse delays [10

10. P. N. Stavrinou and L. Solymar, “Pulse delay and propagation through subwavelength metallic slits,” Phys. Rev. E 68, 066604 (2003). [CrossRef]

], enhanced transmission [11

11. D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 13, 7760–7771 (2005). [CrossRef] [PubMed]

], and optical activity in plasmonic structures [7

7. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” App. Phys. Lett. 83, 2713–2715 (2003). [CrossRef]

, 12

12. V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7, 1996–1999 (2007). [CrossRef]

]. Selective plasmon control using external magnetic fields and ferromagnetic materials currently provides a means for manipulating non-metallic nanoparticles [13

13. H. Yu, M. Chen, P. M. Rice, S. X. Wang, R. L. White, and S. H. Sun, “Dumbbell-like bifunctional Au-Fe3O4 nanoparticles,” Nano Lett. 5, 379–382 (2005). [CrossRef] [PubMed]

, 14

14. H. Deng, J. Liu, W. Zhao, W. Zhang, X. Lin, T. Sun, Q. Dai, L. Wu, S. Lan, and A. V. Gopal, “Enhancement of switching speed by laser-induced clustering of nanoparticles in magnetic fluids,” App. Phys. Lett. 92, 233103 (2008). [CrossRef]

], which has applications in active plasmonics and metamaterial bottom-up synthesis [15

15. S. Mühlig, C. Rockstuhl, V. Yannopapas, T. Burgi, N. Shalkevich, and F. Lederer, “Optical properties of a fabricated self-assembled bottom-up bulk metamaterial,” Opt. Express 19, 9607–9616 (2011). [CrossRef] [PubMed]

]. Our understanding of the photo-induced plasmon dynamics underpins the design of electromagnetic metamaterials and will aid the development of new photocatalytic materials, photovoltaic devices, and sensors [16

16. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mat. 9, 193–204 (2010). [CrossRef]

].

Optical vortex dynamics and plasmon-induced magnetic fields characterize the energy flow in nanostructured geometries. In prior research, a magnetic resonance arises due to the ring-shaped arrangement of nanoparticles [8

8. A. Alu, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14, 1557–1567 (2006). [CrossRef] [PubMed]

, 9

9. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” 328, 1135–1138 (2010).

] when each individual particle dipole is oriented in the azimuthal direction. From another perspective, the phase vortices in the scattered electromagnetic fields, which are coupled to the surface waves, reveal that the spin angular momentum of incident circularly-polarized light excites plasmons with orbital angular momentum via scattering [17

17. L. T. Vuong, A. J. L. Adam, J. M. Brok, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of sub-wavelength apertures,” Phys. Rev. Lett. 104, 083903 (2010). [CrossRef] [PubMed]

].

Although the control of plasmon angular momenta and the subsequent magnetic fields is possible via the design of the illuminating polarization and illuminated nanostructure [17

17. L. T. Vuong, A. J. L. Adam, J. M. Brok, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of sub-wavelength apertures,” Phys. Rev. Lett. 104, 083903 (2010). [CrossRef] [PubMed]

, 18

18. S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B.K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009). [CrossRef]

], the dynamics have been shown to be highly nonlinear. Within the ring-arrangement of nanoparticles, the electric and magnetic plasmon resonances are coupled and highly dependent on the uniform spacing between particles [19

19. S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmonic resonances,” Nano Lett. 11, 3927–3934 (2011). [CrossRef] [PubMed]

]. Near a plasmon resonance, small changes in the boundary conditions lead to sharp changes in the Poynting vector [20

20. B. S. Luk’yanchuk and V. Ternovsky, “Light scattering by a thin wire with a surface-plasmon resonance: bifurcations of the Poynting vector eld,” Phys. Rev. B 73, 235432 (2006). [CrossRef]

] and in fact, opposite vortex energy flows are predicted above and below a plasmon resonance [21

21. M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express 13, 8372–8379 (2005). [CrossRef] [PubMed]

, 22

22. S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale 4, 76–90 (2012). [CrossRef]

]. Future metamaterials will reliably control or leverage these nonlinear plasmon vortex dynamics, which are the focus of this report.

Here, we demonstrate nanocolloid self-assembly and aggregation dynamics that occur in response to DC magnetic fields when samples are illuminated with light, and to the best of our knowledge, we are the first to demonstrate the nonlinear chiral behavior of the associated photo-induced magnetic response. The underlying physical principles are not novel and are associated with a photo-induced drift, photo-galvanic, or photon drag effect [23

23. M. Durach, A. Rusina, and M. I. Stockman, “Giant surface-plasmon-induced drag effect in metal nanowires,” Phys. Rev. Lett. 103, 186801 (1990). [CrossRef]

28

28. N. Noginova, A. V. Yakim, J. Soimo, L. Gu, and M. A. Noginov, “Light-to-current and current-to-light coupling in plasmonic systems,” Phys. Rev. B 84, 035447 (2011). [CrossRef]

], which lead to the production of magnetic fields and a measurable inverse Faraday effect [29

29. Y. Gu and K. G. Kornev, “Plasmon enhanced direct and inverse Faraday effects in non-magnetic nanocomposites,” J. Opt. Soc. Am. B. 27, 2165–2173 (2010). [CrossRef]

,30

30. R. Hertel, “Theory of the inverse Faraday effect in metals,” Journal of Magnetism and Magnetic Materials 303, L1–L4 (2006). [CrossRef]

]. However, the transfer of momentum from photon to electron has the signature of being polarization-dependent. Subsequently and crucially, the nonlinear vortex flows that reverse direction with incident circular polarization handedness cannot be numerically simulated by assuming a linear superposition of orthogonal linear polarizations. Another distinction is that these polarization-dependent vortex dynamics do not flip direction with wavelength “detuning” at the plasmonic resonance. This nondispersive behavior, in addition to the anomalously-large sustained response, may lead to robust self-assembly dynamics for broad-band photonics applications.

In our experiments, we measure the scattered light spectra before and after applying DC magnetic fields and show consistent changes in the scattering intensity. The magnetic response occurs on minute-time scales, is concentration-dependent, and nonlinear with respect to the applied magnetic field. Moreover, the polarization-dependence of the photo-induced magnetic response is drastic; we show that, depending on the circular-polarization handedness of the incident light and magnetic field, samples either aggregate, resulting in a reduction of light scattering or the samples undergo polarization-dependent pattern formation that results in enhanced scattering at the plasmon absorption wavelengths.

The photo-induced magnetic response is particularly remarkable given the low particle fill-factor of our solution samples (≈10−7), the unprecedented low illumination intensities (<1W/cm2), and the use of incoherent unpolarized light from a broad-band lamp or solar simulator in our experiments. Our results indicate that 1) the surrounding aqueous solution plays a strong role in the collective dynamics and 2) the interaction between particles is nonnegligible.

This manuscript is organized as follows. In Sec. 2 we describe the experimental setup and we present our experimental measurements. In Sec. 3 we show how DC orbital surface currents or plasmonic loops lead to an increased effective conductivity, in agreement with our experimental results. In Sec. 4 we present the single-nanoparticle plasmon-induced nonlinear magnetization Mnli(E × E*). We numerically evaluate the first-order correction using Mie theory, which changes sign with orthogonal circular-polarization handedness. In Sec. 5 we put our experimental and numerical results in context and summarize our results.

2. Experimental set-up and results

Our experimental setup is shown in Fig. 1(a). Light from a 150-W halogen-xenon lamp is collimated onto sealed 2.5cm-diameter samples containing dispersed polyvinylpyrrolidone(PVP)-coated 80nm-diameter gold nanospheres in aqueous solution (0.025–0.05mg/mL) with a plasmon resonance wavelength λ = 546 nm (NanoXact from Nanocomposix). The lamp intensity is less than 1W/cm2 at the sample. The sample containers sit at the center of a solenoid whose axis is aligned with the incident lamp light. A visible-wavelength anti-reflection-coated polarizer and achromatic waveplate are placed to produce left- and right-handed circularly-polarized (LHCP and RHCP) or linearly-polarized (LINP) light. A fiber-coupled spectrometer measures the scattered light spectra at approximately 135° from the incident angle. The convention we use assumes that the helical direction of the LHCP (RHCP) electric field vector rotates clockwise (counter-clockwise) when viewed in the direction of the light propagation. The magnetic field produced by the solenoid points in the direction of light propagation.

Fig. 1 (a) Experimental setup. The magnetic field produced by the solenoid points in the direction of light propagation. (b) Relative changes in the sample transmission intensity as the sample settles when illuminated with circularly-polarized light.

Within 30 minutes of placing the container in the collimated beam, the scattering spectra stabilizes and we observe <0.3% variation between minute-lapsed measurements. Figure 1(b) shows changes in the transmission spectra over this time interval as the circularly-polarized light illuminates the gold nanocolloid solution. Since the samples take less time to stabilize when heated prior to the experiment, it is likely that the scattering spectra stabilizes when samples reach thermal equilibrium with the incident light. However, as the appreciable blue-shift in the plasmon resonance over this time suggests, there may also be a coincident melting or reduction in the PVP coating that lowers the refractive index surrounding the gold nanoparticle.

The stabilized spectrum serves as the reference for subsequent measurements. Figure 2 shows top-to-bottom minute-lapsed measurements of the relative scattered spectra of 0.025mg/mL-concentration samples before, during, and after a 0.8-mT magnetic field is applied and when samples are illuminated with LHCP and RHCP. In Fig. 2(a) we observe that the scattering spectra of the sample illuminated by LHCP increases at the plasmon resonance as a result of the applied magnetic field, while the sample illuminated with RHCP exhibits a decrease in scattering over the same conditions. These effects are visible immediately after conducting the experiment. While LHCP and the applied magnetic field results in a slight discoloration of the sample, the sample illuminated with RHCP is clear due to near-complete aggregation of the nanocolloid [Fig. 2(c)].

Fig. 2 Effect of an external DC magnetic field on the scattering spectra of 80nm-diameter gold nanocolloids in aqueous solution. Relative scattering spectra before (blue), during (red), and after (green) application of a 0.8-mT magnetic field. Scattering spectra is shown for (a) left-handed and (b) right-handed circularly-polarized light, where consistent and distinct differences are associated with each orthogonal polarization, given the fixed direction of the magnetic field. Note different vertical scales for these plots. (c) Cropped photos of the sample before and after illumination with left and right-handed circularly-polarized light. On the left, the sample exhibits slight discoloration but on the right, the sample is clear because the nanocolloidal gold has aggregated and fallen to the bottom of the sample.

While the crystal structures of self-assembled metal nanoparticles have been studied [31

31. D. Nykypanchuk, M. M. Mayer, D. van der Lelie, and O. Gang, “DNA-guided crystallization of colloidal nanoparticles,” Nature 451, 549–552 (2008). [CrossRef] [PubMed]

], the magnetic-field induced and polarization-dependent self-assembly shown here is novel. An intuitive explanation for the response is as follows. Firstly, circularly-polarized light produces surface current loops whose directions depend on the light polarization handedness. These plasmons with orbital angular momentum induce a DC magnetization that is either aligned (LHCP) or anti-aligned (RHCP) with the external magnetic field [See Sec. 4]. We assert that the disperse nanocolloid solution undergoes self-assembly because the applied external magnetic fields align the orbital motion of plasmons, effectively aligning the plasmon-induced magnetic moment of each nanoparticle. The photo-induced magnetic response occurs on minute timescales because the metal nanoparticles, which are not perfectly spherical, reorient themselves in a direction that maximizes this orbital surface current. In the case of LHCP, a local crystal order may be achieved, along with the selective excitation of plasmon modes with orbital angular momentum, and a subsequent increase in the effective electrical conductivity [See Sec 3]. In the case with RHCP, electron-phonon collisions increase and lead to the appreciable heating and melting of the PVP coating and subsequent aggregation of the nanocolloids.

When smaller magnetic fields are applied to the sample, the subsequent changes in the scattered spectra are broader and require more time to stabilize. Figure 3(a) shows the nonlinear changes that occur in the relative scattering using μT magnetic fields when samples are illuminated with LHCP. Above the application of a 200-μT magnetic field, the relative changes in scattering spectra have similar shapes. If the nanoparticles do not aggregate, they reorient and undergo self-assembly, the signature of which is a relative increase in scattering intensity at the plasmon resonance.

Fig. 3 (a) Nonlinear changes in the relative scattering when smaller (μT) magnetic fields are applied. (b) Top-to-bottom minute-lapsed changes in the relative scattering when samples are illuminated with unpolarized light and (c) stabilized scattered spectra, without offset, when samples are illuminated with left-handed circularly-polarized light. The spectra before (blue), during (red), and after (green) application of a 1.5-mT DC magnetic field show a relative increase in the scattered light at the plasmonic resonance. The scattered spectra broadens when the incident light is subsequently changed to linear polarization (yellow).

Since the photo-induced magnetic responses are strongly polarization-dependent, it is remarkable that the self-assembly observed with LHCP [Fig. 2(a)] also occurs when samples are illuminated with unpolarized light [Fig. 3(b)]. Figure 3(b) shows minute-lapsed measurements (from the top, offset 0.015/measurement) when samples are illuminated with unpolarized light using 0.05mg/mL solutions. The scattered spectra stabilizes along the timescale of minutes and changes by as much as 4% after application of a 1.5-mT magnetic field. This result points to the appreciable pattern formation and interaction between nanoparticles in this disperse nanoparticle solution [See Sec. 5].

Another indication of self-assembly or pattern formation of the disperse nanocolloid solution is the polarization-dependent response that arises after the sample has settled. Figure 3(c) shows the stabilized scattered spectra when 0.05mg/mL sample solutions are illuminated with LHCP light. The curves show the relative scattering before, during, and after a 1.5-mT magnetic field is applied, as well as the subsequent scattered spectra when the quarter waveplate is rotated to align its fast optical axis with the polarizer, producing LINP angled 45° to the plane of incidence.

The relative scattering intensity increases 6.3% with LHCP and increases to 20% after a magnetic field is applied when the sample is illuminated with LINP. The spectrum is notably twice as broad with LINP than with LHCP. The measured changes in the scattering spectra that occur as a result of a changed polarization are stable and repeatable, show memory of the magnetic field and are sustained by light after its removal.

In all experiments we confirm two things: that the magnetic response is photo-induced (when the magnetic field is applied and the light is instead simultaneously blocked for one minute, there is no appreciable change in the scattered spectra) and that the change is sustained (particles showed no indication of re-alignment even after several hours). Similar responses at the plasmonic resonance are measured using dispersed silver nanospheres in solution. Experiments using polystyrene spheres are inconclusive in identifying a similar photo-induced magnetic response.

The prominent features in our experimental results are demonstrated analytically and numerically in the following Secs. In Sec. 3 we show how the existence of electrical surface current loops or nanoparticle plasmons with orbital angular momentum lead to increased conductivity in the theoretical Mie scattering solutions [32

32. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999), pp. 760–771.

]. Our analysis explains why the measured change in the disperse-solution scattering spectra [Fig. 3] resemble that of the single-particle scattering spectra. In the Sec. 4, we evaluate the first-order contribution of the nonlinear magnetization Mnli(E × E*) where E is the total electric field, which illustrates how a rotating electric field magnetizes a non-magnetic conducting nanoparticle by producing plasmons with orbital angular momentum.

3. Analysis of the scattering due to orbital surface currents

However, in an important departure from [30

30. R. Hertel, “Theory of the inverse Faraday effect in metals,” Journal of Magnetism and Magnetic Materials 303, L1–L4 (2006). [CrossRef]

], we do not assume that the time-averaged velocity v0 is zero; in fact, we assert that the orbital DC currents manifest in the optical scattering as a signature of the photo-induced magnetic fields measured here. The incident circularly-polarized plane wave in spherical coordinates is
Ei,r=1(kbr)2l=1il1(2l+1)ψl(kbr)Pl(cosθ)(e±iϕ),Ei,θ=1kbrl=1il(2l+1)ψl(kbr)Pl(cosθ)cosθ(e±iϕ),Ei,ϕ=±1kbrl=1il+1(2l+1)ψl(kbr)Pl(cosθ)(e±iϕ),
(3)
where kb=2πεb/λ is the wavenumber, λ is the wavelength, εb is the permittivity of the material surrounding the conducting sphere, and the ± sign determines the orthogonal polarization handedness of the circularly-polarized light. The polarization-dependent geometric phase exp(±) gives rise to polarization-dependent vortex flows in the scattered fields [17

17. L. T. Vuong, A. J. L. Adam, J. M. Brok, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of sub-wavelength apertures,” Phys. Rev. Lett. 104, 083903 (2010). [CrossRef] [PubMed]

]. Substituting the modified relation for the current density [Eq. (1)] into Mie’s solution [32

32. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999), pp. 760–771.

] with incident circularly-polarized light, the scattered electric fields remain
Es,r=e±iϕ(kbr)2l=1l(l+1)BTMlξl(kbr)Pl(cosθ),Es,θ=e±iϕkbrsinθl=1BTMlξ(kbr)Pl(cosθ)sin2θiBTElξl(kbr)Pl(cosθ),Es,ϕ=±e±iϕkbrsinθl=1BTMlξ(kbr)Pl(cosθ)iBTElξ(kbr)Pl(cosθ)sin2θ,
(4)
where Pl is the first associated Legendre polynomial of order l, ξ is the Riccati-Hankel function of the first kind, and ′ denotes differentiation with respect to the argument. The coefficients TEB and TMB are determined by the TE and TM boundary conditions of the problem, respectively
BTMl=il+1(2l+1)l(l+1)kak2bψl(kaa)ψl(kba)k2akbψl(kaa)ψl(kba)k2bkaψl(kaa)ζl(kba)kbk2aζl(kba)ψl(kaa)BTEl=il+1(2l+1)l(l+1)kak2bψl(kba)ψl(kaa)k2akbψl(kaa)ψl(kba)k2bkaζl(kba)ψl(kaa)kbk2aψl(kaa)ζl(kba)
(5)
where k2b=k2a=i2πλ and ka=2πλεa4πσiω for a non-magnetic sphere, where ε is the permittivity and σ is the specific conductivity. The superscripts (a) and (b) identify the conducting sphere and the surrounding material, respectively.

By including the relation for [Eq. (1)] in Maxwell’s equations, we see that loops of azimuthal electrical currents and nonzero v0 on the surface of the nanoparticles lead to modified, anisotropic coefficients for ka. If we assume that v0 = v0ϕ̂, then the corresponding conductivity tensor σj,k becomes
σr,r=(v1r^n0)qE1r^,
(6)
σθ,θ=(v1θ^n0)qE1θ^,
(7)
σϕ,ϕ=(v1ϕ^n0+v0n1)qE1ϕ^.
(8)
The conductivity tensor increases anisotropically due to the existence of surface current loops. We do not provide a closed solution to the analytical scattering problem, however our claim of an increased effective conductivity agrees with our experimental measurements. In Fig. 4 we plot the scattering cross-section of the nanocolloid solution with varying electrical conductivity. The corresponding changes in the scattering spectra that arise due to an increased effective conductivity agree with experimental results.

Fig. 4 Scattering cross-section of 80-nm gold nanospheres surrounded by PVP with different values for the gold electrical conductivity. With increased conductivity, the scattering spectra increases at the plasmon resonance, in agreement with experimental results.

4. The nonlinear magnetization Mnl

Hertel [30

30. R. Hertel, “Theory of the inverse Faraday effect in metals,” Journal of Magnetism and Magnetic Materials 303, L1–L4 (2006). [CrossRef]

] derives a tractable analytic expression for the DC or low-frequency nonlinear magnetization Mnl from the nonlinear current density Jnl(r, t) = ∇ × Mnl, where
Jnl[i(E*)E+c.c.]
(9)
=i[(E*)Ec.c.]
(10)
=i×(E×E*)+i[(E)E*(E*)E]
(11)
Equation 9 points to the source of Jnl: the evanescent electric fields associated with the oscillating surface charge density. Even when there are no free charges, Jnl is nonzero because ∇ · E ≠ 0. By evaluating individual terms numerically, we observe that the right square-bracketed term of Eq. (11), which is associated with a ponderomotive force, has a significantly weaker contribution compared to the first term, from which Hertel extracts the plasmon-induced magnetization,
Mnli(E×E*),
(12)
where E is the total electric field. In Fig. 5 we evaluate Eq. (12) using the incident Ei = (Ei,r, Ei,θ, Ei,ϕ) [Eq. (3)] and scattered Es = (Es,r, Es,θ, Es,ϕ) [Eq. (4)] electric fields, i.e.,
Mnli(Es×Es*+Ei×Es*+Es×Ei*),
(13)
and where Ei×Ei* is neglected because it is constant-valued and therefore does not contribute to Jnl. The evaluation of Eq. (13) yields a pure real-valued numerical result, which represents the first-order non-zero nonlinear DC correction to Maxwell’s equations.

Fig. 5 Numerical evaluation of the nonlinear magnetization at the surface of an 80nm-diameter gold nanosphere in water when illuminated with circularly-polarized light at wavelength λ = 540nm. The “plus”-circular polarization is shown, with the orthogonal “minus”-circular polarization inset at half-scale. (a) Mnl,r, (b) Mnl,θ, (c) Mnl,ϕ.

When the incident circular-polarization handedness changes, the polarity of the nonlinear magnetization flips sign. The longitudinal magnetization,
Mnl,z=cos(θ)Mnl,rsin(θ)Mnl,θ,
(14)
is polarization-dependent while in contrast, the direction of the azimuthal magnetization Mnl,ϕ is not polarization-dependent [See Fig. 5]. The vortex energy flows associated with the azimuthal magnetization receive considerable attention [21

21. M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express 13, 8372–8379 (2005). [CrossRef] [PubMed]

, 22

22. S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale 4, 76–90 (2012). [CrossRef]

] but carry a smaller role with the nonlinear response that is studied here. In comparison with [21

21. M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express 13, 8372–8379 (2005). [CrossRef] [PubMed]

] where the vortex flows associated with the azimuthal magnetization reverse direction at the plasmon resonance wavelength, we find that the longitudinal nonlinear magnetization and associated vortex flows maintain the same polarity across wavelengths; there is qualitatively little change in the nonlinear magnetization as a function of wavelength. Instead, the strength of the nonlinear magnetization is larger at wavelengths closer to the plasmonic resonance.

The application of a DC longitudinal magnetic field results in the selective removal of terms from Eq. (13). Only contributions coupling the incident electric fields with the TM-scattered electric fields contribute to a longitudinal magnetization, i.e.,
Mnl,zi(Ei×ETMS*+ETMS×Ei*),
(15)
where the TM-scattered electric fields TMEs only include the TMB-coefficient modes [Eq. (5)]. We deduce this claim by inspection of Eqs. 3 and 4, knowing that the magnetic longitudinal dipole decomposes into the odd-valued radial and the even-valued polar magnetization vectors [Eq. (14)]. The product of two even or two odd-order Legendre polynomials yields an even-ordered Legendre polynomial, the product of an even and odd-ordered Legendre polynomial yields an odd-ordered Legendre polynomial, and multiplication or division by sinθ changes the order from even to odd or vice versa.

In Fig. 6 we show the first-order perturbation correction of the nanoparticle nonlinear magnetization after a longitudinal magnetic field is applied [Eq. (15)]. Our analysis indicates that the incident electric field strongly couples to the TM-scattered electric fields as a result of the applied magnetic field. Although the contribution of TE-scattered fields is relatively small, the selective excitation of scattering modes leads to decreased electron-electron collisions that further increase the electrical conductivity and azimuthal surface currents illustrated in Sec. 3. Subsequent changes in the DC-magnetic fields and electric fields are necessary in order to satisfy Maxwell’s equations.

Fig. 6 Numerical evaluation of the nonlinear magnetization on the surface of the nanosphere from Fig. 5 after applying a DC longitudinal magnetic field. (a) Mnl,r, (b) Mnl,θ, (c) Mnl,ϕ. The “plus”-circular polarization is shown, with the orthogonal “minus”-circular polarization inset at half-scale.

The nonlinear photo-induced magnetization shown here points to the magnetic forces that may underlie gold nanocolloid crystallization [31

31. D. Nykypanchuk, M. M. Mayer, D. van der Lelie, and O. Gang, “DNA-guided crystallization of colloidal nanoparticles,” Nature 451, 549–552 (2008). [CrossRef] [PubMed]

] and photo-induced coagulation dynamics [33

33. N. Satoh, H. Hasegawa, K. Tsujii, and K. Kimura, “Photoinduced coagulation of Au nanocolloids,” J. Phys. Chem. 98, 2143–2147 (1994). [CrossRef]

]. Incident circularly-polarized light produces surface electrical current loops that induce a DC nanoparticle magnetization. The longitudinal magnetization changes direction with orthogonal polarization handedness. LINP and unpolarized light also demonstrate a similar– but perhaps more complicated– photo-induced magnetic response.

5. Conclusion and additional discussion

In conclusion, we have measured a photo-induced magnetic response of highly-disperse gold nanocolloids in aqueous solution using polarized and unpolarized light. When illuminating samples with broad-band non-laser light at sunlight intensities and simultaneously applying μT-strength DC magnetic fields, we observe relative changes in the scattering spectra that indicate an increase in the nanoparticle electrical conductivity. The subsequent scattering from the self-assembled nanocolloid is highly polarization-dependent. When samples are illuminated with circular-polarized light whose trajectory is aligned opposite to the solenoid current that produces the magnetic field, samples aggregate.

Our analysis shows that the existence of electrical surface current loops leads to an increased anisotropic effective conductivity. The associated longitudinal component of the nonlinear magnetization changes sign with incident polarization handedness. Our work points to the significance of observing phase singularities and vortex flows with nanostructured materials; the chiral nonlinear response that we measure and investigate is easily overlooked if one assumes that the photo-induced response from circularly-polarized light is simply a superposition of two orthogonal linear polarizations.

We speculate that when the plasmon-induced magnetization is aligned with the applied DC magnetic field, the electron-electron scattering lifetime increases and leads to local organization of the nanocolloid. When the plasmon-induced magnetization of the nanoparticle is anti-aligned with the applied magnetic field, then electron-phonon collisions increase, leading to heating and accelerated damage to the PVP coating. With similar insight, it has been proposed that incident circularly-polarized light selectively excites plasmons with angular momentum [34

34. C. Timm and K. H. Bennemann, “Response theory for time-resolved second-harmonic generation and two-photon photoemission,” J. Phys.: Cond. Matt. 16, 661–694 (2004). [CrossRef]

]. Evidence of an increased plasmon lifetime with LHCP as a result of the nanocolloid pattern formation and photo-induced magnetic response is seen in Fig. 3(c) where the scattered spectra from LINP is at least twice as broad.

Here, we demonstrate experimentally an anomalously-large and sustained response to DC magnetic fields from solutions of gold nanospheres. Since the photo-induced magnetic response of individual nanospheres is considered too small to be significant at room temperatures [29

29. Y. Gu and K. G. Kornev, “Plasmon enhanced direct and inverse Faraday effects in non-magnetic nanocomposites,” J. Opt. Soc. Am. B. 27, 2165–2173 (2010). [CrossRef]

] and because the photo-induced magnetic response is sustained by incident light after the applied magnetic field is removed, it is inferred that the roles of the surrounding aqueous solution and the interactions between adjacent particles are non-negligible. Although it is an open question how the polar molecules in the solution respond to the photo-induced magnetic DC dipole, a degree of synchronization and pattern formation associated within the disperse nanocolloid solution is expected. The photo-induced magnetic response studied here is sustained by disperse nanoparticle interactions that are not yet completely understood.

To the best of our knowledge, we provide the first demonstration of a chiral polarization-dependent plasmon-assisted magnetic response that occurs with non-ferromagnetic metallic nanoparticles and moreover, the first demonstration of any such plasmonic magnetic response of metal nanocolloids using unpolarized incoherent light. Our research builds on prior work aimed at the bottom-up synthesis of 3D metamaterials and highlights the potential for broad-band solar applications with nanocomposites. Our investigation points to new routes for nonlinear optics research with nanostructures and underlines considerations that should be relevant for high-sensitivity force measurements. Finally, our demonstration indicates vast untapped potential of solution-based 3D nanocomposite metamaterials using electrophoretic and external magnetic-field self-assembly techniques.

References and links

1.

J. Meixner, “The behavior of electromagnetic fields at edges,” Antennas Propaga. 20, 442–446 (1972). [CrossRef]

2.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” J. Exp. Theor. Phys. Lett. 33, 195–199 (1981).

3.

D. Rozas, C. T. Law, and G. A. Swartzlander Jr., “Propagation dynamics of optical vortices,” J. Opt. Soc. Amer. B 14, 3054–3065 (1997). [CrossRef]

4.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90, 107404 (2003). [CrossRef] [PubMed]

5.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005). [CrossRef] [PubMed]

6.

V.P. Drachev, W. D. Bragg, V. A. Podolskiy, V. P. Safonov, W.-T. Kim, Z. C. Ying, R. L. Armstrong, and V. M. Shalaev, “Large local optical activity in fractal aggregates of nanoparticles,” J. Opt. Soc. Amer. B 18, 1896–1903 (2001). [CrossRef]

7.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” App. Phys. Lett. 83, 2713–2715 (2003). [CrossRef]

8.

A. Alu, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14, 1557–1567 (2006). [CrossRef] [PubMed]

9.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” 328, 1135–1138 (2010).

10.

P. N. Stavrinou and L. Solymar, “Pulse delay and propagation through subwavelength metallic slits,” Phys. Rev. E 68, 066604 (2003). [CrossRef]

11.

D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 13, 7760–7771 (2005). [CrossRef] [PubMed]

12.

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7, 1996–1999 (2007). [CrossRef]

13.

H. Yu, M. Chen, P. M. Rice, S. X. Wang, R. L. White, and S. H. Sun, “Dumbbell-like bifunctional Au-Fe3O4 nanoparticles,” Nano Lett. 5, 379–382 (2005). [CrossRef] [PubMed]

14.

H. Deng, J. Liu, W. Zhao, W. Zhang, X. Lin, T. Sun, Q. Dai, L. Wu, S. Lan, and A. V. Gopal, “Enhancement of switching speed by laser-induced clustering of nanoparticles in magnetic fluids,” App. Phys. Lett. 92, 233103 (2008). [CrossRef]

15.

S. Mühlig, C. Rockstuhl, V. Yannopapas, T. Burgi, N. Shalkevich, and F. Lederer, “Optical properties of a fabricated self-assembled bottom-up bulk metamaterial,” Opt. Express 19, 9607–9616 (2011). [CrossRef] [PubMed]

16.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mat. 9, 193–204 (2010). [CrossRef]

17.

L. T. Vuong, A. J. L. Adam, J. M. Brok, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of sub-wavelength apertures,” Phys. Rev. Lett. 104, 083903 (2010). [CrossRef] [PubMed]

18.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B.K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009). [CrossRef]

19.

S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmonic resonances,” Nano Lett. 11, 3927–3934 (2011). [CrossRef] [PubMed]

20.

B. S. Luk’yanchuk and V. Ternovsky, “Light scattering by a thin wire with a surface-plasmon resonance: bifurcations of the Poynting vector eld,” Phys. Rev. B 73, 235432 (2006). [CrossRef]

21.

M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express 13, 8372–8379 (2005). [CrossRef] [PubMed]

22.

S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale 4, 76–90 (2012). [CrossRef]

23.

M. Durach, A. Rusina, and M. I. Stockman, “Giant surface-plasmon-induced drag effect in metal nanowires,” Phys. Rev. Lett. 103, 186801 (1990). [CrossRef]

24.

V. L. Gurevich, R. Laiho, and A. V. Lashkul, “Photomagnetism of metals,” Phys. Rev. Lett. 69, 180–183 (1992). [CrossRef] [PubMed]

25.

V. L. Gurevich and R. Laiho, “Photomagnetism of metals: microscopic theory of the photoinduced surface current,” Phys. Rev. B 48, 8307–8316 (1993). [CrossRef]

26.

O. Keller and G. Wang, “Angular momentum photon drag in a mesoscopic ring,” Opt. Commun. 138, 75–80 (1997). [CrossRef]

27.

A. S. Vengurlekar and T. Ishihara, “Surface plasmon enhanced photon drag in metal films,” App. Phys. Lett. 87, 091118 (2005). [CrossRef]

28.

N. Noginova, A. V. Yakim, J. Soimo, L. Gu, and M. A. Noginov, “Light-to-current and current-to-light coupling in plasmonic systems,” Phys. Rev. B 84, 035447 (2011). [CrossRef]

29.

Y. Gu and K. G. Kornev, “Plasmon enhanced direct and inverse Faraday effects in non-magnetic nanocomposites,” J. Opt. Soc. Am. B. 27, 2165–2173 (2010). [CrossRef]

30.

R. Hertel, “Theory of the inverse Faraday effect in metals,” Journal of Magnetism and Magnetic Materials 303, L1–L4 (2006). [CrossRef]

31.

D. Nykypanchuk, M. M. Mayer, D. van der Lelie, and O. Gang, “DNA-guided crystallization of colloidal nanoparticles,” Nature 451, 549–552 (2008). [CrossRef] [PubMed]

32.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999), pp. 760–771.

33.

N. Satoh, H. Hasegawa, K. Tsujii, and K. Kimura, “Photoinduced coagulation of Au nanocolloids,” J. Phys. Chem. 98, 2143–2147 (1994). [CrossRef]

34.

C. Timm and K. H. Bennemann, “Response theory for time-resolved second-harmonic generation and two-photon photoemission,” J. Phys.: Cond. Matt. 16, 661–694 (2004). [CrossRef]

OCIS Codes
(190.5940) Nonlinear optics : Self-action effects
(260.0260) Physical optics : Physical optics
(160.4236) Materials : Nanomaterials

ToC Category:
Metamaterials

History
Original Manuscript: May 2, 2012
Revised Manuscript: June 29, 2012
Manuscript Accepted: July 25, 2012
Published: August 8, 2012

Citation
N. D. Singh, M. Moocarme, B. Edelstein, N. Punnoose, and L. T. Vuong, "Anomalously-large photo-induced magnetic response of metallic nanocolloids in aqueous solution using a solar simulator," Opt. Express 20, 19214-19225 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-19214


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References

  1. J. Meixner, “The behavior of electromagnetic fields at edges,” Antennas Propaga.20, 442–446 (1972). [CrossRef]
  2. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” J. Exp. Theor. Phys. Lett.33, 195–199 (1981).
  3. D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Amer. B14, 3054–3065 (1997). [CrossRef]
  4. A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett.90, 107404 (2003). [CrossRef] [PubMed]
  5. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett.95, 227401 (2005). [CrossRef] [PubMed]
  6. V.P. Drachev, W. D. Bragg, V. A. Podolskiy, V. P. Safonov, W.-T. Kim, Z. C. Ying, R. L. Armstrong, and V. M. Shalaev, “Large local optical activity in fractal aggregates of nanoparticles,” J. Opt. Soc. Amer. B18, 1896–1903 (2001). [CrossRef]
  7. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” App. Phys. Lett.83, 2713–2715 (2003). [CrossRef]
  8. A. Alu, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express14, 1557–1567 (2006). [CrossRef] [PubMed]
  9. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” 328, 1135–1138 (2010).
  10. P. N. Stavrinou and L. Solymar, “Pulse delay and propagation through subwavelength metallic slits,” Phys. Rev. E68, 066604 (2003). [CrossRef]
  11. D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express13, 7760–7771 (2005). [CrossRef] [PubMed]
  12. V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett.7, 1996–1999 (2007). [CrossRef]
  13. H. Yu, M. Chen, P. M. Rice, S. X. Wang, R. L. White, and S. H. Sun, “Dumbbell-like bifunctional Au-Fe3O4 nanoparticles,” Nano Lett.5, 379–382 (2005). [CrossRef] [PubMed]
  14. H. Deng, J. Liu, W. Zhao, W. Zhang, X. Lin, T. Sun, Q. Dai, L. Wu, S. Lan, and A. V. Gopal, “Enhancement of switching speed by laser-induced clustering of nanoparticles in magnetic fluids,” App. Phys. Lett.92, 233103 (2008). [CrossRef]
  15. S. Mühlig, C. Rockstuhl, V. Yannopapas, T. Burgi, N. Shalkevich, and F. Lederer, “Optical properties of a fabricated self-assembled bottom-up bulk metamaterial,” Opt. Express19, 9607–9616 (2011). [CrossRef] [PubMed]
  16. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mat.9, 193–204 (2010). [CrossRef]
  17. L. T. Vuong, A. J. L. Adam, J. M. Brok, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of sub-wavelength apertures,” Phys. Rev. Lett.104, 083903 (2010). [CrossRef] [PubMed]
  18. S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B.K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A79, 043819 (2009). [CrossRef]
  19. S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmonic resonances,” Nano Lett.11, 3927–3934 (2011). [CrossRef] [PubMed]
  20. B. S. Luk’yanchuk and V. Ternovsky, “Light scattering by a thin wire with a surface-plasmon resonance: bifurcations of the Poynting vector eld,” Phys. Rev. B73, 235432 (2006). [CrossRef]
  21. M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express13, 8372–8379 (2005). [CrossRef] [PubMed]
  22. S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale4, 76–90 (2012). [CrossRef]
  23. M. Durach, A. Rusina, and M. I. Stockman, “Giant surface-plasmon-induced drag effect in metal nanowires,” Phys. Rev. Lett.103, 186801 (1990). [CrossRef]
  24. V. L. Gurevich, R. Laiho, and A. V. Lashkul, “Photomagnetism of metals,” Phys. Rev. Lett.69, 180–183 (1992). [CrossRef] [PubMed]
  25. V. L. Gurevich and R. Laiho, “Photomagnetism of metals: microscopic theory of the photoinduced surface current,” Phys. Rev. B48, 8307–8316 (1993). [CrossRef]
  26. O. Keller and G. Wang, “Angular momentum photon drag in a mesoscopic ring,” Opt. Commun.138, 75–80 (1997). [CrossRef]
  27. A. S. Vengurlekar and T. Ishihara, “Surface plasmon enhanced photon drag in metal films,” App. Phys. Lett.87, 091118 (2005). [CrossRef]
  28. N. Noginova, A. V. Yakim, J. Soimo, L. Gu, and M. A. Noginov, “Light-to-current and current-to-light coupling in plasmonic systems,” Phys. Rev. B84, 035447 (2011). [CrossRef]
  29. Y. Gu and K. G. Kornev, “Plasmon enhanced direct and inverse Faraday effects in non-magnetic nanocomposites,” J. Opt. Soc. Am. B.27, 2165–2173 (2010). [CrossRef]
  30. R. Hertel, “Theory of the inverse Faraday effect in metals,” Journal of Magnetism and Magnetic Materials303, L1–L4 (2006). [CrossRef]
  31. D. Nykypanchuk, M. M. Mayer, D. van der Lelie, and O. Gang, “DNA-guided crystallization of colloidal nanoparticles,” Nature451, 549–552 (2008). [CrossRef] [PubMed]
  32. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999), pp. 760–771.
  33. N. Satoh, H. Hasegawa, K. Tsujii, and K. Kimura, “Photoinduced coagulation of Au nanocolloids,” J. Phys. Chem.98, 2143–2147 (1994). [CrossRef]
  34. C. Timm and K. H. Bennemann, “Response theory for time-resolved second-harmonic generation and two-photon photoemission,” J. Phys.: Cond. Matt.16, 661–694 (2004). [CrossRef]

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