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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 14879–14890
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Optimization of plasmonic nanostructure for nanoparticle trapping

Jingzhi Wu and Xiaosong Gan  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 14879-14890 (2012)
http://dx.doi.org/10.1364/OE.20.014879


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Abstract

We present a detailed analysis of nanoparticle trapping using plasmonic nanostructures, which predicts an improvement of two orders of magnitude in trapping force obtained by optimizing the plasmon resonance of the nanostructures. As the result, a total of four orders of magnitude enhancement in trapping force can be achieved comparing to the case without the nanostructures. In addition, it is illustrated that tuning the resonance wavelength is achievable by varying the diameter and/or the height of the nanorods.

© 2012 OSA

1. Introduction

Accurate three-dimensional (3D) manipulation of nanoparticles is a highly desirable technique for a range of applications such as single molecule spectroscopy, colloidal dynamics, particle assembly, and lab-on-a-chip technology [1

1. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

3

3. B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12(2), 796–801 (2012). [CrossRef] [PubMed]

]. However, trapping nanoparticles is challenging because the magnitude of optical trapping force decreases with the cube of the diameter of the nanoparticles, and the Brownian motion becomes increasingly affecting the trapping performance. For nanoparticle of size significantly smaller than the optical wavelength, the optical trapping force can be approximated as the linearly proportion to the gradient of electromagnetic (EM) field [1

1. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

3

3. B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12(2), 796–801 (2012). [CrossRef] [PubMed]

]. Therefore in order to improve the field gradient, one can either increase the strength or the confinement of the EM field. Inducing surface plasmon resonance in metallic nanostructures is a well-known technique that produces strongly enhanced and spatially confined EM field [4

4. X. Gao and X. Gan, “Modulation of evanescent focus by localized surface plasmons waveguide,” Opt. Express 17(25), 22726–22734 (2009). [CrossRef] [PubMed]

9

9. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

] and therefore attracts wide attention in producing plasmon-based nano-optical tweezers for nanoparticle trapping [1

1. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

, 10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

]. For example, plasmonic antennas [1

1. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

, 11

11. A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008). [CrossRef]

, 12

12. W. Zhang, L. Huang, C. Santschi, and O. J. F. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10(3), 1006–1011 (2010). [CrossRef] [PubMed]

] and nanoholes in metallic thin film [13

13. Y. Pang and R. Gordon, “Optical trapping of 12 nm dielectric spheres using double-nanoholes in a gold film,” Nano Lett. 11(9), 3763–3767 (2011). [CrossRef] [PubMed]

15

15. C. Chen, M. L. Juan, Y. Li, G. Maes, G. Borghs, P. Van Dorpe, and R. Quidant, “Enhanced optical trapping and arrangement of nano-objects in a plasmonic nanocavity,” Nano Lett. 12(1), 125–132 (2012). [CrossRef] [PubMed]

] have been demonstrated for trapping metallic and dielectric nanospheres. Periodic arrays of gold nanopillars on a metal film [7

7. B. Päivänranta, H. Merbold, R. Giannini, L. Büchi, S. Gorelick, C. David, J. F. Löffler, T. Feurer, and Y. Ekinci, “High aspect ratio plasmonic nanostructures for sensing applications,” ACS Nano 5(8), 6374–6382 (2011). [CrossRef] [PubMed]

, 16

16. A. E. Cetin, A. A. Yanik, C. Yilmaz, S. Somu, A. Busnaina, and H. Altug, “Monopole antenna arrays for optical trapping, spectroscopy, and sensing,” Appl. Phys. Lett. 98(11), 111110 (2011). [CrossRef]

, 17

17. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun. 2, 469 (2011). [CrossRef] [PubMed]

] have been presented for sensing applications. It is worth to be mentioned that under the laser excitation at wavelength close to the plasmon resonance wavelength, plasmonic nanostructures efficiently couple to the incident optical field and generate considerable amount of heat [1

1. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

, 18

18. D. Lapotko, “Optical excitation and detection of vapor bubbles around plasmonic nanoparticles,” Opt. Express 17(4), 2538–2556 (2009). [CrossRef] [PubMed]

, 19

19. P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107(3), 037401 (2011). [CrossRef] [PubMed]

]. The thermally induced forces can strongly affect motions of nanoparticles and should be taken into consideration when designing efficient nano-tweezers [20

20. R. T. Schermer, C. C. Olson, J. P. Coleman, and F. Bucholtz, “Laser-induced thermophoresis of individual particles in a viscous liquid,” Opt. Express 19(11), 10571–10586 (2011). [CrossRef] [PubMed]

, 21

21. X. Miao, B. K. Wilson, and L. Y. Lin, “Localized surface plasmon assisted microfluidic mixing,” Appl. Phys. Lett. 92(12), 124108 (2008). [CrossRef]

].

Plasmonic nanorods or nanowires are interesting for the design of optical resonators [22

22. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

, 23

23. J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10(9), 3596–3603 (2010). [CrossRef] [PubMed]

]. It has been demonstrated previously that strong EM field enhancement and confinement in the plasmonic nano-waveguides structure provides up to two orders of magnitude stronger optical forces for trapping nanoparticles comparing with the optical trapping without the nanostructure [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

]. In this work, the effects of structure parameters on plasmon resonance are studied in detail in order to further improve the trapping force of nanoparticles.

2. Trapping scheme and plasmonic nanostructure layout

The nanoparticle trapping approach is based on a plasmonic nanostructure comprising of two vertically aligned silver nanorods suspended in water (refractive index nm = 1.33), as shown in Fig. 1
Fig. 1 Schematic diagram of the nanostructure of two silver nanorods with height h, diameter d and separation s. Incident field is x-polarized and propagates in the z direction from the substrate (refractive index 1.78) into water (refractive index nm = 1.33). The origin of the coordinate system is at the center of the gap on the interface.
. The geometrical parameters of the nanostructure are the diameter d and height h of the nanorods, and the separation s between them. Plasmonic absorption and field distributions of the plasmonic nanostructures are calculated using a commercial Finite Difference Time Domain (FDTD) solver (Lumerical Inc, with material data for silver reported in Ref [24

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

], mesh size 1 nm x 1 nm x 1 nm) [25

25. “FDTD Solutions,” Lumerical Solutions Inc., www.lumerical.com.

]. The electric field E, magnetic field H and wavevector k of the excitation light, oriented along the x, y and z directions, are illustrated in Fig. 1. The excitation light is x-polarized plane wave and propagates from the substrate. For electric field calculations throughout the paper, the amplitude of the incident illumination is set as |E| = 1 V m−1.

While dielectric nanoparticles are of size significantly smaller than optical wavelength, the electromagnetic trapping force is proportional to the gradient of the localized field, F=nm2αE2, here αis the polarizability of the nanoparticle [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

, 14

14. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]

, 26

26. H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002). [CrossRef] [PubMed]

]. Due to the fact that the nanoparticle is small and of a refractive index of 1.5, which close to that of the surrounding medium (water, nw = 1.33), the disturbance in the EM field caused by the presence of the nanoparticle is negligible. It has been shown that the gradient force agrees well with rigorous force calculations using Maxwell stress tensor method for nanoparticles more than 20 nm away from plasmonic nanostructures [14

14. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]

]. The scattering force on a 20 nm nanoparticle is about three orders magnitude smaller than the gradient force. While the nanoparticle is in the immediate vicinity of the nanostructure (e.g. <10 nm), the trapping force calculated with the perturbative method using gradient of the field is slightly smaller than that obtained with the rigorous method using the Maxwell stress tensor [14

14. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]

].

For low concentration of nanoparticles, the net thermal force f [27

27. H.-R. Jiang, H. Wada, N. Yoshinaga, and M. Sano, “Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient,” Phys. Rev. Lett. 102(20), 208301 (2009). [CrossRef] [PubMed]

30

30. S. Duhr and D. Braun, “Why molecules move along a temperature gradient,” Proc. Natl. Acad. Sci. U.S.A. 103(52), 19678–19682 (2006). [CrossRef] [PubMed]

] acting on the particle by the solvent due to the present of the temperature gradient can be approximated as proportional to the temperature gradient T [29

29. R. Piazza and A. Parola, “Thermophoresis in colloidal suspensions,” J. Phys. Condens. Matter 20(15), 153102 (2008). [CrossRef]

], f=STT/β,where ST is the Soret coefficient, β=1/kBT,kB is the Boltzmann constant, T is the temperature [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

]. The temperature increase around the plasmonic nanostructure can be obtained by ΔT(r)=14πKm(Vqr1dVKsKmKs+KmVqr2dV), where q is the heat generation density which is determined by energy absorption of the nanostructure [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

], r1, r2 are the distance from the heat source element dV in the nanostructure (with volume V) and its image heat source in the substrate, to a position r. Km, Ks are the thermal conductivity of the surrounding medium and the substrate respectively (Km = 0.6 W K−1 m−1 and Ks = 1.1 W K−1 m−1 is assumed for our simulation) [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

, 31

31. G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: Influence of morphology,” Appl. Phys. Lett. 94(15), 153109 (2009). [CrossRef]

].

We start by considering the optical response of the nanostructure with two silver nanorods having diameter d of 70 nm, height h of 820 nm, and separation s of 100 nm. Fig. 2(a)
Fig. 2 (a) Absorption spectrum of the nanostructure with separation s of 100 nm, diameter d of 70 nm and height h of 820 nm. (b) An oscillator model for the optical response of the nanostructure.
shows the absorption spectrum of the nanostructure. Two strong absorption peaks at wavelengths of 430 nm and 455 nm can be observed, which arise from localized surface plasmon resonance. This is because that the light polarization direction is normal to the long axis of the nanorods, only transverse plasmon modes in the plasmonic nanorods can be excited efficiently. As a result of the finite length of the nanorods, standing plasmon wave can be formed along the long axis of the nanorods [23

23. J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10(9), 3596–3603 (2010). [CrossRef] [PubMed]

].

The absorption spectrum can be explained by using a simple oscillator model [32

32. C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70(1), 37–41 (2002). [CrossRef]

] as shown in Fig. 2(b). Each nanorod is modeled by two harmonic oscillators (m1, m2) and (m3, m4), that are all attached to walls by springs of spring constants k1, k2, k3 and k4. The four oscillators are also interconnected with springs of spring constants K1, K2, K3 and K4. Harmonic forces F=Fexp(iωSt) are applied to oscillators m1 and m3. For simplicity, we choose m1 = m2 = m3 = m4 = 1, k1 = k2 = k3 = k4 = k, K1 = K2 = K, andΩ2=K/m. Also usingΩc2=K3/m, Ωc22=K4/m for the coupling between the two nanorods, we can derive the motion equations of oscillators m1, m2, m3, and m4 as a function of displacements x1, x2, x3 and x4, from their respective equilibrium positions as,
x1+γ1x1+ω12x1Ω2x2Ωc2x3=Fmexp(iωSt),x2+γ2x2+ω22x2Ω2x1Ωc22x4=0,x3+γ3x3+ω32x3Ω2x4Ωc2x1=Fmexp(iωSt),x4+γ4x4+ω42x4Ω2x3Ωc22x2=0.
(1)
here γ1, γ2, γ3 and γ4 are the friction constants associated with the energy dissipation, andω1, ω2, ω3 and ω4 are oscillation frequencies corresponding to m1, m2, m3, and m4, respectively. The absorption spectrum can be derived from the solutions of the motion equations (Eq. (1)), and we can fit the absorption spectrum obtained from FDTD simulation (Fig. 2(a)) by using the following set of parameters, i.e., ω1 = ω2 = ω3 = ω4 = 2.86 eV, γ1 = γ3 = 2 x10−2, γ2 = γ4 = 2.3 x10−1, Ω = 0.78, Ωc = 0.6, Ωc2 = 0.61.

The time-averaged intensity distributions in the central cross section (zx plane) for different wavelengths are illustrated in Fig. 3
Fig. 3 Intensity distributions of the nanostructure with diameter d of 70 nm, height h of 820 nm, separation s of 100 nm at excitation wavelengths λ of (a) λ: 430 nm, (b) λ: 455 nm and (c) λ: 532 nm, in the zx cross section. The white line indicates the interface. Colorbar is in unit of V2 m−2.
, which shows that the enhancement of the EM field is more significant at the peak absorption wavelength, e.g. 430 nm, comparing to a non-resonance wavelength, i.e. 532 nm. The resonance intensity at the center of the gap is plotted along the z direction (Fig. 4
Fig. 4 Comparison of intensity distributions of the nanostructure with diameter d of 70 nm, height h of 820 nm, separation s of 100 nm at different wavelengths at the center of the gap along the z direction.
). It is noted that the electric field intensity at wavelength 430 nm is approximately 2.3 times stronger than the intensity at the non-resonance absorption wavelength of 532 nm.

One of the major concerns of plasmonic trapping is the considerable heat generated from plasmonic absorption, in which case the thermal force acting on the nanoparticles can be significant [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

]. The thermal force acting on the 20 nm nanosphere in a plane 690 nm above the interface is shown in Fig. 6
Fig. 6 Comparison of the thermal force in the nanostructure with diameter d of 70 nm, height h of 820 nm, separation s of 100 nm at different wavelengths, at the center of the gap. (a) Fy, (b) Fz. The intensity of the incident light is taken as 0.1 mW·μm−2. The Soret coefficient ST used for calculation is 2 x 10−4 (K −1).
. The Soret coefficient is assumed as ST = 2 × 10−4 K −1 according to reported experimental data [27

27. H.-R. Jiang, H. Wada, N. Yoshinaga, and M. Sano, “Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient,” Phys. Rev. Lett. 102(20), 208301 (2009). [CrossRef] [PubMed]

29

29. R. Piazza and A. Parola, “Thermophoresis in colloidal suspensions,” J. Phys. Condens. Matter 20(15), 153102 (2008). [CrossRef]

]. It should be pointed out that vapor bubbles may form around the plasmonic nanostructure under high laser power excitation [18

18. D. Lapotko, “Optical excitation and detection of vapor bubbles around plasmonic nanoparticles,” Opt. Express 17(4), 2538–2556 (2009). [CrossRef] [PubMed]

]. For the plasmonic nanoparticle trapping, bubbles formation can be avoided by controlling the incident power or wavelength. The maximum temperature increase at wavelength of 455 nm is 11 K for incident intensity of 0.1 mW·μm−2. Under such moderate temperature increase in the surrounding medium [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

] and the constant ST, the thermal force at the peak absorption wavelength (e.g. 455 nm) is approximately five times stronger than that at the non-peak absorption wavelength (e.g. 532 nm) in either the transverse force Fy or the axial forces Fz due to strong plasmonic absorption. Because the thermal force is far greater than the EM force in the region outside of the nanostructure, the significant increase makes it strong enough to vary transport of nanoparticles [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

].

3. Optimization of the nanostructure

3.1 The separation

It is demonstrated in the last section that the plasmonic nano-waveguides structure exhibits significantly stronger enhancement of the resonance field at absorption peaks (e.g. 430 nm or 455 nm). It is expected that the absorption peak is associated with the geometric parameters such as the size (diameter and height) of the rods, and the separation between them. Firstly we fix the size of each rod, i.e. diameter d: 70 nm, height h: 820 nm, and vary the separation s. Figure 7
Fig. 7 Absorption spectra of the nanostructure with different separations s, for fixed diameter d of 70 nm and height h of 820 nm.
shows the absorption spectra of the two silver nanorods nanostructures with different separations of 40 nm, 70 nm and 100 nm. It is noted that the absorption peaks are red-shifted while decreasing the separation s.

The overall electric field enhancement of the nanostructure is strong at the peak absorption wavelength because of the large dimension of height of the nanorods. In Figs. 8(a-c)
Fig. 8 Intensity distributions in the central cross section (zx plane) of the nanostructure with different separations s at the corresponding peak absorption wavelengths λ. (a) s = 40 nm at λ = 470 nm, (b) s = 70 nm at λ = 461 nm, and (c) s = 100 nm at λ = 455 nm. Colorbar is in unit of V2 m−2.
the field intensity distributions of the nanostructures with different separations at wavelengths corresponding to the absorption peaks are shown. It is apparent that the field intensity at the gap can be enhanced by decreasing the separation between the two nanorods. The intensity distribution at the center of the gap along the z direction is plotted in Fig. 9
Fig. 9 Comparison of intensity distributions at the center of the gap along the z direction for the nanostructures with different separations s at the corresponding peak absorption wavelengths λ of 470 nm, 461 nm and 455 nm.
. It shows that by reducing the separation size from 100 nm to 40 nm, the field intensity at the center the gap is increased almost by one order of magnitude.

3.2 Effect of the diameter of the nanorod

The absorption spectra of the nanostructure with different diameters of nanorods are shown in Fig. 12
Fig. 12 Absorption spectra of the nanostructure with different diameters d at fixed separation s of 70 nm and height h of 820 nm.
. There is a significant shift of peak absorption wavelength (i.e. Δλ: 53 nm) when the diameter of the nanorods changes from 40 nm to 100 nm. It is shown in Fig. 13(a)
Fig. 13 Intensity distributions of the nanostructure with different diameters d at the corresponding peak absorption wavelengths λ. (a) d = 40 nm at λ = 427 nm, (b) d = 70 nm at λ = 461 nm, and (c) d = 100 nm at λ = 480 nm, in the zx plane. Colorbar is in unit of V2 m−2.
that the field intensity in the nanostructure with diameter of 40 nm nanorods becomes very weak even at the peak absorption wavelength of 427 nm. For thin nanowires, it is difficult to excite plasmon resonance by the incident light with polarization direction normal to the long axis of the nanorods [23

23. J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10(9), 3596–3603 (2010). [CrossRef] [PubMed]

] due to the fact that the radius of the nanorods (20 nm) is close to the skin depth (~14 nm). Under the circumstance, although the absorption is strong, the plasmon resonance is weak.

The comparison of the intensity distributions at the center of the gap along the z direction is illustrated in Fig. 14
Fig. 14 Comparison of intensity distributions of the nanostructure at the center of the gap along the z direction with different diameters d at the corresponding peak absorption wavelengths λ of 427 nm, 461 nm and 480 nm.
. For the nanorods with diameter larger than 70 nm, the field intensity at the center of the gap does not change noticeably, however accompanied by a peak absorption wavelength shift of 19 nm. Such feature indicates a possible fine tuning capability for plasmon resonance by varying the diameter of the nanorods.

3.3 Effect of the height of the nanorod

The absorption spectra of the nanostructures with different heights of 700 nm, 760 nm and 820 nm are shown in Fig. 15
Fig. 15 Absorption spectra of the nanostructure with different heights h of 700 nm, 760 nm and 820 nm, at fixed separation s of 70 nm and diameter d of 70 nm.
. The diameter of the nanorods and their separation are kept the same (70 nm). It is noticed that the absorption peak wavelength for the same order of plasmon resonance shifts from 461 nm to 437 nm with the height of the nanorods decreased from 820 nm to 700 nm (Fig. 16
Fig. 16 Intensity distributions of the nanostructure in the zx plane with different heights h at the corresponding peak absorption wavelengths λ. (a) h = 700 nm at λ = 437 nm, (b) h = 760 nm at λ = 450 nm, and (c) h = 820 nm at λ = 461 nm. Colorbar is in unit of V2 m−2.
). The association of plasmon resonance of with the cavity length can be expressed as,
4πλsph=2mπ+φ.
(2)
where m is the order of plasmon resonance, λsp is the plasmon wavelength, φ is the phase shift induced by reflections on the ends of the nanorods [22

22. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

, 23

23. J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10(9), 3596–3603 (2010). [CrossRef] [PubMed]

].

The variation of the nanorod length h induces changes in both the plasmon wavelength λsp and the phase shift φ. The distance between two intensity maxima of the plasmon modes is λsp/2, which changes according to the height of the nanorods (Fig. 17(a)
Fig. 17 Comparisons of (a) the intensity distributions, and (b) the EM force, in the nanostructure with different heights h at the center of the gap along the z direction. The corresponding peak absorption wavelengths λ for nanorods of diameter 700 nm, 760 nm and 820 nm are 437 nm, 450 nm and 461 nm, respectively. The intensity of the incident light is taken as 0.1 mW·μm−2 for force calculation.
). It is also noted that the field intensity around the end of the nanorods exhibits significant variations. This is because that the phase change φ induced by reflections at the ends of nanorods with different heights has a strong effect on the intensity distribution along the nanorods. From Eq. (2), the phase change φ and plasmon wavelength λsp for nanorods with h = 700 nm, 760 nm, 820 nm, can be obtained as, φ = 0.37π, 0.13π, 0.25π, and λsp = 270 nm, 300 nm, 320 nm, respectively. When φ = π/4, the field intensity at the end the nanorods (h = 820 nm) is much stronger than the other two cases. As a result, the EM trapping force strength around the end of the nanorods with h = 820 nm, is approximately four times stronger than that of the nanorods with h = 700 nm, as shown in Fig. 17(b). Additionally, the equilibrium trapping positions change with the height of the nanorods under excitations at the peak absorption wavelengths.

4. Discussion

We predict that an improvement of two orders of magnitude in trapping force can be obtained by optimizing the plasmon resonance of the nanostructures. Therefore a total of four orders of magnitude improvement in trapping force can be obtained comparing to the case without the nanostructures [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

]. Optical trapping force can be greatly enhanced by tuning the excitation wavelength towards the peak absorption wavelengths of the nanostructure. But such an enhancement in EM force is also accompanied with greater enhancement in the thermally induced forces. As indicated previously [10

10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

], the thermal effects are important for plasmonic nanoparticle trapping due to the fact that it has a much wider working range compared to EM force. Reducing the separation between the nanorods can greatly improve the EM trapping force without strongly affecting the thermal force, and this provides us the mechanism to tune the balance between the EM force and the thermal force in order to achieve best nanoparticle trapping performance. The fact that the peak absorption wavelength of the nanostructure is strongly dependent on the diameter of the nanorods offers us the fine tuning capability of the plasmon resonance in practice.

The present results should be of significant importance to attempts to manipulate nanoparticles using plasmonic nanostructures. The high aspect ratio of plasmonic nanostructures is useful for applications such as increasing the packaging density of plasmonic sensors, single molecule assays and nanospectroscopy [5

5. X. Miao and L. Y. Lin, “Trapping and manipulation of biological particles through a plasmonic platform,” IEEE J. Sel. Top. Quantum Electron. 13(6), 1655–1662 (2007). [CrossRef]

, 9

9. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

, 16

16. A. E. Cetin, A. A. Yanik, C. Yilmaz, S. Somu, A. Busnaina, and H. Altug, “Monopole antenna arrays for optical trapping, spectroscopy, and sensing,” Appl. Phys. Lett. 98(11), 111110 (2011). [CrossRef]

]. Well-defined high aspect ratio plasmonic nanostructures can be fabricated using top-down fabrication processes [7

7. B. Päivänranta, H. Merbold, R. Giannini, L. Büchi, S. Gorelick, C. David, J. F. Löffler, T. Feurer, and Y. Ekinci, “High aspect ratio plasmonic nanostructures for sensing applications,” ACS Nano 5(8), 6374–6382 (2011). [CrossRef] [PubMed]

, 33

33. S. Buzzi, M. Galli, M. Agio, and J. F. Loffler, “Silver high-aspect-ratio micro- and nanoimprinting for optical applications,” Appl. Phys. Lett. 94(22), 223115 (2009). [CrossRef]

]. The optimization results of this work can be utilized to improve sensing sensitivity and trapping capability using the nanorod plasmonic nanostructures.

References and links

1.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

2.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008). [CrossRef] [PubMed]

3.

B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12(2), 796–801 (2012). [CrossRef] [PubMed]

4.

X. Gao and X. Gan, “Modulation of evanescent focus by localized surface plasmons waveguide,” Opt. Express 17(25), 22726–22734 (2009). [CrossRef] [PubMed]

5.

X. Miao and L. Y. Lin, “Trapping and manipulation of biological particles through a plasmonic platform,” IEEE J. Sel. Top. Quantum Electron. 13(6), 1655–1662 (2007). [CrossRef]

6.

X. Miao, B. K. Wilson, S. H. Pun, and L. Y. Lin, “Optical manipulation of micron/submicron sized particles and biomolecules through plasmonics,” Opt. Express 16(18), 13517–13525 (2008). [CrossRef] [PubMed]

7.

B. Päivänranta, H. Merbold, R. Giannini, L. Büchi, S. Gorelick, C. David, J. F. Löffler, T. Feurer, and Y. Ekinci, “High aspect ratio plasmonic nanostructures for sensing applications,” ACS Nano 5(8), 6374–6382 (2011). [CrossRef] [PubMed]

8.

M. Bora, B. J. Fasenfest, E. M. Behymer, A. S. P. Chang, H. T. Nguyen, J. A. Britten, C. C. Larson, J. W. Chan, R. R. Miles, and T. C. Bond, “Plasmon resonant cavities in vertical nanowire arrays,” Nano Lett. 10(8), 2832–2837 (2010). [CrossRef] [PubMed]

9.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

10.

J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010). [CrossRef] [PubMed]

11.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008). [CrossRef]

12.

W. Zhang, L. Huang, C. Santschi, and O. J. F. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10(3), 1006–1011 (2010). [CrossRef] [PubMed]

13.

Y. Pang and R. Gordon, “Optical trapping of 12 nm dielectric spheres using double-nanoholes in a gold film,” Nano Lett. 11(9), 3763–3767 (2011). [CrossRef] [PubMed]

14.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]

15.

C. Chen, M. L. Juan, Y. Li, G. Maes, G. Borghs, P. Van Dorpe, and R. Quidant, “Enhanced optical trapping and arrangement of nano-objects in a plasmonic nanocavity,” Nano Lett. 12(1), 125–132 (2012). [CrossRef] [PubMed]

16.

A. E. Cetin, A. A. Yanik, C. Yilmaz, S. Somu, A. Busnaina, and H. Altug, “Monopole antenna arrays for optical trapping, spectroscopy, and sensing,” Appl. Phys. Lett. 98(11), 111110 (2011). [CrossRef]

17.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun. 2, 469 (2011). [CrossRef] [PubMed]

18.

D. Lapotko, “Optical excitation and detection of vapor bubbles around plasmonic nanoparticles,” Opt. Express 17(4), 2538–2556 (2009). [CrossRef] [PubMed]

19.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107(3), 037401 (2011). [CrossRef] [PubMed]

20.

R. T. Schermer, C. C. Olson, J. P. Coleman, and F. Bucholtz, “Laser-induced thermophoresis of individual particles in a viscous liquid,” Opt. Express 19(11), 10571–10586 (2011). [CrossRef] [PubMed]

21.

X. Miao, B. K. Wilson, and L. Y. Lin, “Localized surface plasmon assisted microfluidic mixing,” Appl. Phys. Lett. 92(12), 124108 (2008). [CrossRef]

22.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

23.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10(9), 3596–3603 (2010). [CrossRef] [PubMed]

24.

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

25.

“FDTD Solutions,” Lumerical Solutions Inc., www.lumerical.com.

26.

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002). [CrossRef] [PubMed]

27.

H.-R. Jiang, H. Wada, N. Yoshinaga, and M. Sano, “Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient,” Phys. Rev. Lett. 102(20), 208301 (2009). [CrossRef] [PubMed]

28.

M. Braibanti, D. Vigolo, and R. Piazza, “Does thermophoretic mobility depend on particle size?” Phys. Rev. Lett. 100(10), 108303 (2008). [CrossRef] [PubMed]

29.

R. Piazza and A. Parola, “Thermophoresis in colloidal suspensions,” J. Phys. Condens. Matter 20(15), 153102 (2008). [CrossRef]

30.

S. Duhr and D. Braun, “Why molecules move along a temperature gradient,” Proc. Natl. Acad. Sci. U.S.A. 103(52), 19678–19682 (2006). [CrossRef] [PubMed]

31.

G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: Influence of morphology,” Appl. Phys. Lett. 94(15), 153109 (2009). [CrossRef]

32.

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70(1), 37–41 (2002). [CrossRef]

33.

S. Buzzi, M. Galli, M. Agio, and J. F. Loffler, “Silver high-aspect-ratio micro- and nanoimprinting for optical applications,” Appl. Phys. Lett. 94(22), 223115 (2009). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: March 9, 2012
Revised Manuscript: April 28, 2012
Manuscript Accepted: June 5, 2012
Published: June 19, 2012

Virtual Issues
Vol. 7, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Jingzhi Wu and Xiaosong Gan, "Optimization of plasmonic nanostructure for nanoparticle trapping," Opt. Express 20, 14879-14890 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-14879


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References

  1. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011). [CrossRef]
  2. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem.77(1), 205–228 (2008). [CrossRef] [PubMed]
  3. B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint., “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett.12(2), 796–801 (2012). [CrossRef] [PubMed]
  4. X. Gao and X. Gan, “Modulation of evanescent focus by localized surface plasmons waveguide,” Opt. Express17(25), 22726–22734 (2009). [CrossRef] [PubMed]
  5. X. Miao and L. Y. Lin, “Trapping and manipulation of biological particles through a plasmonic platform,” IEEE J. Sel. Top. Quantum Electron.13(6), 1655–1662 (2007). [CrossRef]
  6. X. Miao, B. K. Wilson, S. H. Pun, and L. Y. Lin, “Optical manipulation of micron/submicron sized particles and biomolecules through plasmonics,” Opt. Express16(18), 13517–13525 (2008). [CrossRef] [PubMed]
  7. B. Päivänranta, H. Merbold, R. Giannini, L. Büchi, S. Gorelick, C. David, J. F. Löffler, T. Feurer, and Y. Ekinci, “High aspect ratio plasmonic nanostructures for sensing applications,” ACS Nano5(8), 6374–6382 (2011). [CrossRef] [PubMed]
  8. M. Bora, B. J. Fasenfest, E. M. Behymer, A. S. P. Chang, H. T. Nguyen, J. A. Britten, C. C. Larson, J. W. Chan, R. R. Miles, and T. C. Bond, “Plasmon resonant cavities in vertical nanowire arrays,” Nano Lett.10(8), 2832–2837 (2010). [CrossRef] [PubMed]
  9. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater.8(11), 867–871 (2009). [CrossRef] [PubMed]
  10. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express18(26), 27619–27626 (2010). [CrossRef] [PubMed]
  11. A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics2(6), 365–370 (2008). [CrossRef]
  12. W. Zhang, L. Huang, C. Santschi, and O. J. F. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett.10(3), 1006–1011 (2010). [CrossRef] [PubMed]
  13. Y. Pang and R. Gordon, “Optical trapping of 12 nm dielectric spheres using double-nanoholes in a gold film,” Nano Lett.11(9), 3763–3767 (2011). [CrossRef] [PubMed]
  14. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys.5(12), 915–919 (2009). [CrossRef]
  15. C. Chen, M. L. Juan, Y. Li, G. Maes, G. Borghs, P. Van Dorpe, and R. Quidant, “Enhanced optical trapping and arrangement of nano-objects in a plasmonic nanocavity,” Nano Lett.12(1), 125–132 (2012). [CrossRef] [PubMed]
  16. A. E. Cetin, A. A. Yanik, C. Yilmaz, S. Somu, A. Busnaina, and H. Altug, “Monopole antenna arrays for optical trapping, spectroscopy, and sensing,” Appl. Phys. Lett.98(11), 111110 (2011). [CrossRef]
  17. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun.2, 469 (2011). [CrossRef] [PubMed]
  18. D. Lapotko, “Optical excitation and detection of vapor bubbles around plasmonic nanoparticles,” Opt. Express17(4), 2538–2556 (2009). [CrossRef] [PubMed]
  19. P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett.107(3), 037401 (2011). [CrossRef] [PubMed]
  20. R. T. Schermer, C. C. Olson, J. P. Coleman, and F. Bucholtz, “Laser-induced thermophoresis of individual particles in a viscous liquid,” Opt. Express19(11), 10571–10586 (2011). [CrossRef] [PubMed]
  21. X. Miao, B. K. Wilson, and L. Y. Lin, “Localized surface plasmon assisted microfluidic mixing,” Appl. Phys. Lett.92(12), 124108 (2008). [CrossRef]
  22. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95(25), 257403 (2005). [CrossRef] [PubMed]
  23. J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett.10(9), 3596–3603 (2010). [CrossRef] [PubMed]
  24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  25. “FDTD Solutions,” Lumerical Solutions Inc., www.lumerical.com .
  26. H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett.89(24), 246802 (2002). [CrossRef] [PubMed]
  27. H.-R. Jiang, H. Wada, N. Yoshinaga, and M. Sano, “Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient,” Phys. Rev. Lett.102(20), 208301 (2009). [CrossRef] [PubMed]
  28. M. Braibanti, D. Vigolo, and R. Piazza, “Does thermophoretic mobility depend on particle size?” Phys. Rev. Lett.100(10), 108303 (2008). [CrossRef] [PubMed]
  29. R. Piazza and A. Parola, “Thermophoresis in colloidal suspensions,” J. Phys. Condens. Matter20(15), 153102 (2008). [CrossRef]
  30. S. Duhr and D. Braun, “Why molecules move along a temperature gradient,” Proc. Natl. Acad. Sci. U.S.A.103(52), 19678–19682 (2006). [CrossRef] [PubMed]
  31. G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: Influence of morphology,” Appl. Phys. Lett.94(15), 153109 (2009). [CrossRef]
  32. C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys.70(1), 37–41 (2002). [CrossRef]
  33. S. Buzzi, M. Galli, M. Agio, and J. F. Loffler, “Silver high-aspect-ratio micro- and nanoimprinting for optical applications,” Appl. Phys. Lett.94(22), 223115 (2009). [CrossRef]

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