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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 4 — May. 22, 2013
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Reversal of optical binding force by Fano resonance in plasmonic nanorod heterodimer

Q. Zhang, J. J. Xiao, X. M. Zhang, Y. Yao, and H. Liu  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 6601-6608 (2013)
http://dx.doi.org/10.1364/OE.21.006601


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Abstract

We present calculations of the optical force on heterodimer of two gold nanorods aligned head-to-tail, under plane wave illumination that is polarized along the dimer axis. It is found that near the dipole-quadrupole Fano resonance, the optical binding force between the nanorods reverses, indicating an attractive to repulsive transition. This is in contrast to homodimer which in similar configuration shows no negative binding force. Moreover, the force spectrum features asymmetric line shape and shifts accordingly when the Fano resonance is tuned by varying the nanorods length or their gap. We show that the force reversal is associated with the strong phase variation between the hybridized dipole and quadrupole modes near the Fano dip. The numerical results may be demonstrated by a near-field optical tweezer and shall be useful for studying “optical matters” in plasmonics.

© 2013 OSA

1. Introduction

It is of great interest to examine opto-mechanical effects when optical resonances happen in photonic nanostructures and metamaterials. Effects of various optical and photonic resonances on the optical forces and optical micromanipulations have been reported [1

1. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). [CrossRef]

7

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

]. Near the resonances, despite of the increase of force magnitude by the strong field enhancement, the force direction can also be tuned via the relative phase delay between the constituting optical fields. In some cases, the interacting force between nanostructures changes from positive to negative, indicating mutual attraction or repulsion of nearby nano-objects. For instance, two adjacent silicon waveguides may repel or attract each other by controlling the phase relationship of the guided modes [1

1. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). [CrossRef]

]. A pair of photonic crystal slabs can be optically tuned to attract or repel each other [2

2. V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express 17(24), 21897–21909 (2009). [CrossRef] [PubMed]

]. A metallic parallel plate cavity exhibits enhanced and reversed optical pressure by an anomalous magnetic resonance [3

3. S. B. Wang, J. Ng, H. Liu, H. H. Zheng, Z. H. Hang, and C. T. Chan, “Sizable electromagnetic forces in parallel-plate metallic cavity,” Phys. Rev. B 84(7), 075114 (2011). [CrossRef]

, 4

4. H. Liu, J. Ng, S. B. Wang, Z. F. Lin, Z. H. Hang, C. T. Chan, and S. N. Zhu, “Strong light-induced negative optical pressure arising from kinetic energy of conduction electrons in plasmon-type cavities,” Phys. Rev. Lett. 106(8), 087401 (2011). [CrossRef] [PubMed]

]. Moreover, a pair of side-by-side nanorods could generate attractive or repulsive forces by electric or magnetic resonances [5

5. R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18(25), 25665–25676 (2010). [CrossRef] [PubMed]

].

Recently, many works have revealed a variety of plasmonic nanostructures that sustain Fano resonances, including single asymmetric particles, core-shell structures, nanoholes, metal-dielectric-metal waveguides, and particle clusters and chains [8

8. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

21

21. H. Lu, X. Liu, D. Mao, and G. Wang, “Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators,” Opt. Lett. 37(18), 3780–3782 (2012). [CrossRef] [PubMed]

]. The Fano resonances in such plasmonic nanostructures are simply regarded as the photonic analogies to the original one in quantum systems [22

22. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

]. Classical oscillator model [13

13. Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano 6(2), 1830–1838 (2012). [CrossRef] [PubMed]

], phenomenological mode [14

14. V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: A parameter-free modeling approach,” Nano Lett. 11(7), 2835–2840 (2011). [CrossRef] [PubMed]

], coupled-mode formalism [15

15. L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: A coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett. 108(8), 083902 (2012). [CrossRef] [PubMed]

], as well as ab initio theory [16

16. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83(23), 235427 (2011). [CrossRef]

] have been developed to analysis them. However, to the best of our knowledge, there is by far no report of the Fano resonance effect on the optical forces among such plasmonic systems.

In this work, we present such a study and show that a dipole-quadrupole (DQ) Fano resonance [17

17. J. M. Reed, H. Wang, W. Hu, and S. Zou, “Shape of Fano resonance line spectra calculated for silver nanorods,” Opt. Lett. 36(22), 4386–4388 (2011). [CrossRef] [PubMed]

, 18

18. Z. J. Yang, Z. S. Zhang, L. H. Zhang, Q. Q. Li, Z. H. Hao, and Q. Q. Wang, “Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers,” Opt. Lett. 36(9), 1542–1544 (2011). [CrossRef] [PubMed]

] can dramatically affect the optical binding force, in both magnitude and direction. We numerically examine the optical forces on a gold nanorod heterodimer which is designated to support a DQ Fano resonance (see Fig. 1
Fig. 1 The geometry of the system and the incoming light configuration. The plasmonic dimer consists of two nanorods with L1=100nm, L2=280 nm, and gap g=10nm. The diameter of the nanorods is d=40nm.
) by simultaneously overlapping a dipole mode and a quadrupole mode spectrally and spatially. The dipole mode of the short nanorod can act as a continuum while the relatively high-Q quadrupole mode in the long nanorod as the sub-radiative discrete level (e.g, dark mode) [8

8. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

, 17

17. J. M. Reed, H. Wang, W. Hu, and S. Zou, “Shape of Fano resonance line spectra calculated for silver nanorods,” Opt. Lett. 36(22), 4386–4388 (2011). [CrossRef] [PubMed]

, 18

18. Z. J. Yang, Z. S. Zhang, L. H. Zhang, Q. Q. Li, Z. H. Hao, and Q. Q. Wang, “Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers,” Opt. Lett. 36(9), 1542–1544 (2011). [CrossRef] [PubMed]

]. Interestingly, near the Fano dip, the binding force between the two nanorods becomes negative, indicating an attraction to repulsion transition and possible equilibrium configuration. We stress that this is not possible for a homodimer under the parallel configuration. It is because that the anti-parallel mode is totally “dark” in such case and not excitable by a normal incidence plane wave polarized along the dimer axes [7

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

,23

23. V. D. Miljković, T. Pakizeh, B. Sepulveda, P. Johansson, and M. Käll, “Optical forces in plasmonic nanoparticle dimers,” J. Phys. Chem. C 114(16), 7472–7479 (2010). [CrossRef]

].

2. Numerical approaches and benchmark

The numerical calculations are performed by employing an electromagnetic computational tool based on the finite integral technique (FIT) [24

24. Commercial software CST Microwave Studio, http://www.cst.com.

]. We use the optical constant of gold from Ref [25

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

]. The interested volume is meshed with a resolution of 2nm along all the three coordinates and the edge and gap region is fine-meshed to 0.5nm. A Gaussian time pulse with appropriate central frequency and bandwidth coming from the y^direction (i.e., transverse to the dimer axis as shown in Fig. 1) illuminates the dimer with E field z^-polarized. The spatial distribution of the light fields in the frequency domain is obtained by the Fourier transformation of the FIT time-domain results. The optical force F(i)on each individual object is then evaluated via a surface integral
F(i)=SiTn^ds
(1)
where the time-averaged Maxwell stress tensor (MST) Treads [23

23. V. D. Miljković, T. Pakizeh, B. Sepulveda, P. Johansson, and M. Käll, “Optical forces in plasmonic nanoparticle dimers,” J. Phys. Chem. C 114(16), 7472–7479 (2010). [CrossRef]

]

T=12Re[εε0EE+μμ0HHI2(εε0|Ε|2+μμ0|H|2)].
(2)

In Eq. (1), S(i) must be a closed surface exclusively containing the i-th object and n^is the outward normal vector on S(i). For convenience, we have chosen a rectangular parallelepiped box to enclose the target nanorod i(i=1,2), with walls along the principle coordinate axis. In all calculations, the optical forces were monitored by changing the size of the box and regarded as convergence when the fluctuation is below 1%.

Additionally, to justify the calculations by this FIT plus MST (FIT-MST) method, we have compared the results to the ones (dots in Fig. 1) by the method of discrete dipole approximation (DDA), in which the optical forces are calculated by the Lorentz formula [23

23. V. D. Miljković, T. Pakizeh, B. Sepulveda, P. Johansson, and M. Käll, “Optical forces in plasmonic nanoparticle dimers,” J. Phys. Chem. C 114(16), 7472–7479 (2010). [CrossRef]

, 26

26. M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011). [CrossRef]

]. The total dipole number isN=60040 (~8nm3/dipole) for the DDA calculations. Good agreements of the results by the FIT-MST (curves) and DDA (symbols) are seen for both the optical cross sections and the optical forces in Figs. 2(a)
Fig. 2 Optical features associated with the DQ Fano resonance. (a) Optical extinction cross sections and optical scattering cross sections. (b) Optical forces between the two nanorods and along the k-direction.
and 2(b), respectively. With respect to the force magnitude in this work, our calculations are effectively in accord to an illuminating plane wave with intensity I0=1mW/µm2.

3. Results and discussion

Figure 2(a) shows the scattering cross section (dashed line) and the extinction cross section (solid line) of the plasmonic heterodimer shown in Fig. 1. The geometry parameters are listed in the figure caption. The peaks around the wavelength ofλ=715 nm (fDQ=420THz) and λ=635nm (fDQ+=473THz) come from the hybridized DQ plasmon modes. The plasmonic DQ Fano resonance featuring an asymmetric line shape in the optical cross section is spectrally between these two modes and can also be regarded as a result from the interference of the fundamental plasmonic modes of the two nanorods [17

17. J. M. Reed, H. Wang, W. Hu, and S. Zou, “Shape of Fano resonance line spectra calculated for silver nanorods,” Opt. Lett. 36(22), 4386–4388 (2011). [CrossRef] [PubMed]

, 18

18. Z. J. Yang, Z. S. Zhang, L. H. Zhang, Q. Q. Li, Z. H. Hao, and Q. Q. Wang, “Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers,” Opt. Lett. 36(9), 1542–1544 (2011). [CrossRef] [PubMed]

]. The identification of the Fano resonance is confirmed by the optical spectrum of individual nanorods (figures not shown here). The dipole resonance of the short nanorod is at fD(s)=463THz and that of the long nanorod is at much lower frequency fD(l)=262THz. However, the quadrupole (or second-order) resonance of the long nanorod is around fQ(l)=443THz, very close to fD(s). The situation can be further corroborated by the current distributions as shown in Fig. 3
Fig. 3 Snapshot of steady-state current density in the yzplane through the nanorod center. (a)–(d) are for the frequencies of 473 THz, 448 THz, 420 THz, and 385 THz, respectively, corresponding to the positions marked with (A), (B), (C), and (D) in Fig. 2(b). The contour is for the dominatingzcomponent of the current.
which shows the current density (arrows) in the yzplane through the nanorod center. By the polarization of the incoming light, the current is dominated by its z^-component and we show it as the contour in the figures. It is clearly seen in Fig. 3 that inside the investigated frequency range, there is no (one) node in the short (long) nanorod. This is actually true for all frequencies between fDQ and fDQ+. It is noteworthy that in some cases, the mode excited in the long nanorod is not strictly a quadrupole but rather a general high-order mode. However, for convenience we retain the notation of quadrupole throughout this paper.

The key part of our results is contained in Fig. 2(b) where the k-direction scattering force Fscat=Fy(1)+Fy(2)on the whole dimer and the inter-particle force Fbind=Fz(1)Fz(2)between the two nanorods are plotted against the light frequency. Notice that we have labeled the short nanorod in the left as 1 and the other one as 2 (see Fig. 1). It is straightforward to see that with respect to the defined coordinates, positive (negative) Fbindrepresents attraction (repulsion) of the two nanorods in the z^-direction.

Figure 2(b) demonstrates that the k-direction scattering force spectrum (black solid curve) has a line shape similar to the extinction cross section (black solid curve) shown in Fig. 2(a). This is a consequence of usual radiation pressure which is basically determined by the total extinction cross section and the differential cross section [27

27. J. J. Xiao and C. T. Chan, “Calculation of optical force on an infinite cylinder with arbitrary cross-section by the boundary element method,” J. Opt. Soc. Am. B 25(9), 1553–1561 (2008). [CrossRef]

]. The binding force spectrum (red dashed curve), however, looks much more similar to the scattering cross section, particularly around the Fano dip near f=448THz. These similarities are reasonable since the definedFbindis dominated by the scattering process whereas Fscatis more directly relevant to both light scattering and absorption. As a matter fact, optical force can be regard as a quantity explicitly determined by the near-field properties which are correlated to the far-field features at Fano resonances [10

10. B. Gallinet and O. J. F. Martin, “Relation between near-field and far-field properties of plasmonic Fano resonances,” Opt. Express 19(22), 22167–22175 (2011). [CrossRef] [PubMed]

].

Figure 2(b) further shows that near the low-frequency resonance fDQ=420THz (marked as C), the two nanorods attract each other due to bonding hybridization where the electric currents at the nanorod ends across the gap are in phase [see Fig. 3(c)]. On the other hand, around the Fano dip (near the point marked as B), the Fbind spectrum develops an asymmetric line shape which, more importantly, crosses the zero point. In other words, the binding force is reversed. Particularly, the two nanorods repel each other in a frequency window as marked by the vertical dashed lines which fall in between fDQ and fDQ+ . We attribute this to the fact that inside this regime, the excitations in the two nanorods are nearly out-of-phase, resulting from the Fano interference. Indeed, Fig. 3(a) shows that the currents across the gap is basically out-of-phase at f=473THz. Figure 3(b) shows a rather similar but dipole-weakened version of Fig. 3(a) when the frequency goes down tof=448THz. These two cases correspond respectively to the points A and B as marked in Fig. 2(b), for which the binding force vanishes (Fbind0). For frequencies between these two points, the binding forces are all negative. We notice that at a frequency much lower than fDQ[marked as D in Fig. 2(b)], the binding force also reverses slightly. This is due to the destructive interference effect of a dipole-dipole configuration [17

17. J. M. Reed, H. Wang, W. Hu, and S. Zou, “Shape of Fano resonance line spectra calculated for silver nanorods,” Opt. Lett. 36(22), 4386–4388 (2011). [CrossRef] [PubMed]

]. Figure 3(d) shows such a case for f=385THz where the current in the long nanorod represents the first-order mode.

To examine how the forces are mediated by the DQ Fano resonance, we plot in Fig. 4
Fig. 4 Spectra of optical forces for nanorod heterodimers in the parallel configuration. (a) The total scattering force and (b) the relative interparticle force. The lengths are kept as L1=100nm and L2=250nm.
the force spectra for different gap distance gbetween the two nanorods. Actually, introducing a variation of the gap gis to spatially tune the separation of dipole and quadrupole resonances. We note that the peaks on the force spectra shift in consistent with the plasmon hybridization prediction [13

13. Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano 6(2), 1830–1838 (2012). [CrossRef] [PubMed]

]. As the gap gincreases, the multiple scattering interactions between the nanorods are expected to weaken. One of the consequences is that the two DQ-hybridized modes come closer in their spectral positions, converging to the nearly-overlapped dipole and quadrupole resonances of the individual nanorods, which is around f=463THz. Accompanying such shifting, the k-direction force Fscatincreases because the spectrum sharpens [see Fig. 4(b)] and becomes the simple summation of those on individual (isolated)nanorod. Meanwhile, the binding force [see Fig. 4(a)] gradually diminishes and the force reversal phenomenon finally disappears for g50nm as the Fano resonance is killed in absence of strong interaction.

Figure 5
Fig. 5 Same as Fig. 2 while keeping the gap g=10nm but varying the nanorod length. (a) and (c) for L1=100 nm and variousL2; (b) and (d) for L2=250nm and variousL1.
shows the force spectrum variation when one of the nanorod’s length changes. ChangingL1is to spectrally tune the dipole resonance while changing L2for the quadrupole one. We have kept the gap g=10nm in such processes during the calculation. Note that the dipole resonance shifts faster than the quadrupole one does when the nanorod length is varied [19

19. F. López-Tejeiral, R. Paniagua-Domínguez, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Fano-like interference of plasmon resonances at a single rod-shaped nanoantenna,” New J. Phys. 14(2), 023035 (2012).

]. Not surprisingly, as the dipole and quadrupole resonances are spectrally separated, their interaction (hybridization) is modulated. As a consequence, the optical force spectra vary accordingly. For instance, when the quadrupole resonance is red-shifted by increasing L2 from 260nm to 300 nm, i.e., tuning fQ(l)from 455THz to 431THz, the force spectra redshift as a whole and the force reversal survives robustly (see the left column of Fig. 5). This is partially because of the rather broad dipole continuum which persistently overlaps with the quadrupole resonance. However, when the dipole resonance is red-shifted by increasing L1(e.g., tuning fD(s)from 450THz to 400THz with fixed fQ(l)=462THz forL2=250nm), the binding force reversal weakens and becomes almost invisible for L1=150nm [see Fig. 5(b)]. This is because that the spectral separation for the case of fD(s)=400THz and fQ(l)=462THz is quite large and the DQ interference becomes negligible.

4. Conclusion

We have shown that dipole-quadrupole Fano resonance can dramatically affect the optical binding force and even lead to a reversal. The binding force spectrum features asymmetric line shape and therefore represents an important consequence of plasmonic Fano resonance. The results we obtained are relevant to near-field optical micromanipulation and to the study of “optical matters” in plasmonics. It is possible to experimentally fabricate the long nanorod as the tip of a fixed near-field optical tweezer over a substrate and use it to control other particles which are like the short nanorod in our model [7

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

]. The attraction-to-repulsion transition may be easily observed by measuring the particles relative motion to the tip. Flexible control of magnitude and direction of the optical binding force opens the door for the observation of collective phenomena of nanoparticles and the design of new materials and devices.

Acknowledgments

This work was supported in part by the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. HIT.NSFIR.2010131), NSFC (11004043 and 11274083), and SZMSTP (Nos. JC201005260185A, JC201105160592A, JC201105160592A, JCYJ20120613114137248, and 2011PTZZ048), and in part by the PIIER of Guangdong No. 2010B090400306. Helps from the Key Lab of IOT Terminal and the National Supercomputing Center in Shenzhen (NSCCSZ) are acknowledged.

References and links

1.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). [CrossRef]

2.

V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express 17(24), 21897–21909 (2009). [CrossRef] [PubMed]

3.

S. B. Wang, J. Ng, H. Liu, H. H. Zheng, Z. H. Hang, and C. T. Chan, “Sizable electromagnetic forces in parallel-plate metallic cavity,” Phys. Rev. B 84(7), 075114 (2011). [CrossRef]

4.

H. Liu, J. Ng, S. B. Wang, Z. F. Lin, Z. H. Hang, C. T. Chan, and S. N. Zhu, “Strong light-induced negative optical pressure arising from kinetic energy of conduction electrons in plasmon-type cavities,” Phys. Rev. Lett. 106(8), 087401 (2011). [CrossRef] [PubMed]

5.

R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18(25), 25665–25676 (2010). [CrossRef] [PubMed]

6.

J. J. Xiao, H. H. Zheng, Y. X. Sun, and Y. Yao, “Bipolar optical forces on dielectric and metallic nanoparticles by evanescent wave,” Opt. Lett. 35(7), 962–964 (2010). [CrossRef] [PubMed]

7.

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

8.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

9.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonance in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

10.

B. Gallinet and O. J. F. Martin, “Relation between near-field and far-field properties of plasmonic Fano resonances,” Opt. Express 19(22), 22167–22175 (2011). [CrossRef] [PubMed]

11.

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photonics Rev. advanced online paper, (2012).

12.

Y. Zhang, T. Q. Jia, H. M. Zhang, and Z. Z. Xu, “Fano resonances in disk-ring plasmonic nanostructure: strong interaction between bright dipolar and dark multipolar mode,” Opt. Lett. 37(23), 4919–4921 (2012). [CrossRef] [PubMed]

13.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano 6(2), 1830–1838 (2012). [CrossRef] [PubMed]

14.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: A parameter-free modeling approach,” Nano Lett. 11(7), 2835–2840 (2011). [CrossRef] [PubMed]

15.

L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: A coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett. 108(8), 083902 (2012). [CrossRef] [PubMed]

16.

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83(23), 235427 (2011). [CrossRef]

17.

J. M. Reed, H. Wang, W. Hu, and S. Zou, “Shape of Fano resonance line spectra calculated for silver nanorods,” Opt. Lett. 36(22), 4386–4388 (2011). [CrossRef] [PubMed]

18.

Z. J. Yang, Z. S. Zhang, L. H. Zhang, Q. Q. Li, Z. H. Hao, and Q. Q. Wang, “Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers,” Opt. Lett. 36(9), 1542–1544 (2011). [CrossRef] [PubMed]

19.

F. López-Tejeiral, R. Paniagua-Domínguez, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Fano-like interference of plasmon resonances at a single rod-shaped nanoantenna,” New J. Phys. 14(2), 023035 (2012).

20.

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Polarization-independent Fano resonances in arrays of core-shell nanoparticles,” Phys. Rev. B 86(8), 081407 (2012). [CrossRef]

21.

H. Lu, X. Liu, D. Mao, and G. Wang, “Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators,” Opt. Lett. 37(18), 3780–3782 (2012). [CrossRef] [PubMed]

22.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

23.

V. D. Miljković, T. Pakizeh, B. Sepulveda, P. Johansson, and M. Käll, “Optical forces in plasmonic nanoparticle dimers,” J. Phys. Chem. C 114(16), 7472–7479 (2010). [CrossRef]

24.

Commercial software CST Microwave Studio, http://www.cst.com.

25.

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

26.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011). [CrossRef]

27.

J. J. Xiao and C. T. Chan, “Calculation of optical force on an infinite cylinder with arbitrary cross-section by the boundary element method,” J. Opt. Soc. Am. B 25(9), 1553–1561 (2008). [CrossRef]

OCIS Codes
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(250.5403) Optoelectronics : Plasmonics
(120.4880) Instrumentation, measurement, and metrology : Optomechanics

ToC Category:
Optics at Surfaces

History
Original Manuscript: January 3, 2013
Manuscript Accepted: February 27, 2013
Published: March 8, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Q. Zhang, J. J. Xiao, X. M. Zhang, Y. Yao, and H. Liu, "Reversal of optical binding force by Fano resonance in plasmonic nanorod heterodimer," Opt. Express 21, 6601-6608 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-5-6601


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