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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 25 — Dec. 3, 2012
  • pp: 27941–27952
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Plasmonic resonances in diffractive arrays of gold nanoantennas: near and far field effects

Andrey G. Nikitin, Andrei V. Kabashin, and Hervé Dallaporta  »View Author Affiliations


Optics Express, Vol. 20, Issue 25, pp. 27941-27952 (2012)
http://dx.doi.org/10.1364/OE.20.027941


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Abstract

We examine the excitation of plasmonic resonances in arrays of periodically arranged gold nanoparticles placed in a uniform refractive index environment. Under a proper periodicity of the nanoparticle lattice, such nanoantenna arrays are known to exhibit narrow resonances with asymmetric Fano-type spectral line shape in transmission and reflection spectra having much better resonance quality compared to the single nanoparticle case. Using numerical simulations, we first identify two distinct regimes of lattice response, associated with two-characteristic states of the spectra: Rayleigh anomaly and lattice plasmon mode. The evolution of the electric field pattern is rigorously studied for these two states revealing different configurations of optical forces: the first regime is characterized by the concentration of electric field between the nanoparticles, yielding to almost complete transparency of the array, whereas the second regime is characterized by the concentration of electric field on the nanoparticles and a strong plasmon-related absorption/scattering. We present electric field distributions for different spectral positions of Rayleigh anomaly with respect to the single nanoparticle resonance and optimize lattice parameters in order to maximize the enhancement of electric field on the nanoparticles. Finally, by employing collective plasmon excitations, we explore possibilities for electric field enhancement in the region between the nanoparticles. The presented results are of importance for the field enhanced spectroscopy as well as for plasmonic bio and chemical sensing.

© 2012 OSA

1. Introduction

Metallic nanostructures are now in the research focus of many studies due to their capability of supporting collective electron oscillations (plasmons), yielding to a number of effects including spectrally tunable absorption and scattering, electromagnetic coupling to nanoscale objects, local enhancement and strong confinement of electromagnetic field at length scales much smaller than the optical diffraction limit [l]. Such unique properties can provide decisive advantages for many important applications such Surface Enhanced Raman Scattering [2

2. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef] [PubMed]

,3

3. K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications, (Springer, 2006).

], imaging and guiding beyond the diffraction limit [4

4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

,5

5. S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and super lensing,” Nat. Photonics 3(7), 388–394 (2009). [CrossRef]

], plasmonic emitters [6

6. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).

], active plasmonic devices [7

7. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]

,8

8. V. G. Kravets, G. Zoriniants, C. P. Burrows, F. Schedin, C. Casiraghi, P. Klar, A. K. Geim, W. L. Barnes, and A. N. Grigorenko, “Cascaded optical field enhancement in composite plasmonic nanostructures,” Phys. Rev. Lett. 105(24), 246806 (2010). [CrossRef] [PubMed]

], biosensors [9

9. B. Liedberg, C. Nylander, and I. Lundström, “Biosensing with surface plasmon resonance-how it all started,” Biosens. Bioelectron. 10(8), i–ix (1995). [CrossRef] [PubMed]

11

11. 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]

].

Regular plasmonic arrays are of particular interest for these applications as they enable controllable collective mechanisms of interaction between array constituents yielding to a local concentration/manipulation of electric field. It is well known for many years that periodicity may be employed for excitation of surface waves (later called surface plasmon polaritons (SPPs)) on metallic gratings. A century ago Wood observed anomalous patterns in the reflection spectrum of metallic gratings [12

12. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4(21), 396–402 (1902). [CrossRef]

]. The spectra presented rapid variations of intensity with a succession of maxima and minima in certain narrow wavelength bands. A first explanation of these anomalies was proposed by Rayleigh [13

13. L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond. A79, 399 (1907).

], who derived the characteristic wavelength that corresponds to the edge of diffraction when one diffraction order passes from evanescent to radiative state. Fano [14

14. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's Waves),” J. Opt. Soc. Am. 31(3), 213 (1941). [CrossRef]

] explained the asymmetric shape of observed spectral features by the manifestation of two distinct anomalies: (i) Rayleigh anomaly (RA) corresponding to the edge of diffraction [13

13. L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond. A79, 399 (1907).

]; and (ii) Resonant anomaly associated with the excitation of surface waves, which is red-shifted with respect to RA. A rigorous theory of grating anomalies on the basis of numerical treatment was presented by Hessel and Oliner [15

15. A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 4(10), 1275 (1965). [CrossRef]

]. They developed the general theoretical approach that allowed to derive the locations and detailed shapes for variety of cases of resonant anomalies. It was shown that at the resonance the evanescent diffraction order couples to the complex guided wave that is supported by the periodic structure. At this condition the amplitude of this order undergoes a sharp increase while the other orders exhibit a maximum on one side of the resonance and a minimum on the other. An asymmetric shape of the spectral profile at the resonance is called Fano-type resonance [16

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

,17

17. 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]

,23

23. M. Sarrazin and J. P. Vigneron, “Bounded modes to the rescue of optical transmission,” Europhys. News 38(3), 27–31 (2007). [CrossRef]

]. Anomalies with Fano spectral profile in optical response of metallic gratings have been investigated for many years [12

12. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4(21), 396–402 (1902). [CrossRef]

,14

14. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's Waves),” J. Opt. Soc. Am. 31(3), 213 (1941). [CrossRef]

,15

15. A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 4(10), 1275 (1965). [CrossRef]

,18

18. D. Maystre, in Electromagnetic Surface Modes edited by A. D. Boardman (Wiley, 1982), chap.17.

]. However, more recently, Fano-like resonances have been identified in various types of periodic plasmon structures including nanohole arrays [19

19. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

23

23. M. Sarrazin and J. P. Vigneron, “Bounded modes to the rescue of optical transmission,” Europhys. News 38(3), 27–31 (2007). [CrossRef]

], photonic crystal slabs [24

24. A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: Strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003). [CrossRef] [PubMed]

,25

25. A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: Experiment and theory,” Phys. Rev. B 70(12), 1–15 (2004). [CrossRef]

] etc.

Collective plasmonic effects in ensembles of metal nanoparticles present a particular case. The arrangement of these nanoparticles in periodic arrays under conditions of diffractive coupling can lead to a drastic improvement of the resonant quality, as it was first suggested theoretically [26

26. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]

29

29. S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121(24), 12606–12612 (2004). [CrossRef] [PubMed]

] and then observed experimentally [30

30. S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403(1–3), 62–67 (2005). [CrossRef]

39

39. W. Zhou and T. W. Odom, “Tunable subradiant lattice plasmons by out-of-plane dipolar interactions,” Nat. Nanotechnol. 6(7), 423–427 (2011). [CrossRef] [PubMed]

], as well as higher electric field enhancement factors [30

30. S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403(1–3), 62–67 (2005). [CrossRef]

,33

33. Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008). [CrossRef]

,39

39. W. Zhou and T. W. Odom, “Tunable subradiant lattice plasmons by out-of-plane dipolar interactions,” Nat. Nanotechnol. 6(7), 423–427 (2011). [CrossRef] [PubMed]

] can be achieved compared to single nanoparticle case due to controllable collective mechanisms of optical interaction. Most studies observed narrow resonances in transmission spectra for metal nanoparticle array placed in uniform refractive index environment with characteristic asymmetric Fano profile under the normal incidence [32

32. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]

,34

34. G. Vecchi, V. Giannini, and J. Gomez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009). [CrossRef]

,38

38. P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gómez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5(6), 5151–5157 (2011). [CrossRef] [PubMed]

,43

43. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012). [CrossRef]

] (see, also [40

40. E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223{230 (2009).

42

42. B. Auguié, X. Bendaña, W. Barnes, and F. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: Critical role of the substrate,” Phys. Rev. B 82(15), 155447 (2010). [CrossRef]

] where the effect of environment asymmetry is addressed and [44

44. W. Hu and Sh. Zou, “Remarkable radiation efficiency through leakage modes in two-dimensional silver nanoparticle arrays,” J. Phys. Chem. C 115(35), 17328–17333 (2011). [CrossRef]

] where inclined incidence and effect of finite array are considered). This spectral line shape can be explained by the interference between directly transmitted light and light scattered by the array [32

32. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]

]. Although conditions of excitation and properties of collective plasmon resonances in metallic arrays were already studied, mechanisms and regimes of interaction of nanoparticles in the lattice are not yet well understood. In particular, it is still important to clarify the interference effects and electric field enhancement distributions under different array parameters, as well as to optimize resonances for particular applications.

In this paper, we examine near and far field distributions of electromagnetic field for characteristic states of Fano spectral profile of ordered gold nanoparticle arrays: Rayleigh Anomaly and Lattice Plasmon Mode (LPM). In addition, we investigate the electric field behavior for different spectral positions of Rayleigh anomaly with respect to single nanoparticle resonance.

2. Method

In this work FDTD realization on the basis of sine/cosine plane wave method with Flocket type phase shift periodic boundary conditions (PBC) [45

45. “FDTD method for periodic structures,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), Chap. 6.

] is employed to study periodically arranged sub-wavelength nanoparticles. Computational domain is excited by two simultaneously incident plane waves: the first one (E1,H1) with a cos(ωt) time dependence and the second one E2,H2 with a sin(ωt) dependence. The conventional Yee algorithm is used to update these two sets of fields separately. To apply the PBC the fields at the boundary are combined as follows Ec=E1+iE1,, Hc=H1+iH2. According to Flocket theory for periodic scattering problems in frequency domain, PBC along the x and y directions for electric and magnetic field:
Ec(x,y,z)=Ec(x+ax,y,z)eikxax
Hc(x,y,z)=Hc(x+ax,y,z)eikxax
Ec(x,y,z)=Ec(x,y+ay,z)eikyay
Hc(x,y,z)=Hc(x,y+ay,z)eikyay
where ax and ay are periodicities in x and y directions, kx and ky are horizontal wave vector projections. These conditions are applicable since the combined fields are excited by eiωt=cos(ωt)+isin(ωt). Finally two sets of fields are extracted from the combined field:
(E1,H1)=Re(Ec,Hc)
(E2,H2)=Im(Ec,Hc)
This procedure is repeated each time step until the steady state is reached.

In each simulation, monochromatic electromagnetic plane wave is launched into-a computational domain in the positive direction of the z axis. Periodic boundary conditions are applied along the x and y axis. The gold nanoparticles are arranged in periodic manner with unit cell of rectangular shape, as shown in the inset of Fig. 1(a)
Fig. 1 Simulated total (blue) and 0-order (green) transmission and reflection spectra of a rectangular array of gold nanoparticles with lattice constants ax = 450 nm and ay = 250 nm (a) as well as ± 1 order power function (b). Transmission and reflection spectra for a single gold nanoparticle (red) (a). Inset shows schematic representation of the studied array.
. Perfectly Matched Layers (PML) are used above top and below bottom z-boundaries of the unit cell simulation domain to absorb the transmitted and reflected electromagnetic waves (we define simulation domain as a volume of space where E and H fields are calculated excluding region of PMLs). To find reflected E and H fields values, the incident fields are subtracted from the total fields. Fraction of the power that is reflected or transmitted into individual order of diffraction is defined as ratio of its energy flux through the simulation area in the (x, y) plane to the incident field energy flux through the same area. The results are normalized such that summation of all these power fractions gives unity. The integrated transmitted and reflected power is the sum of individual components above and below nanoparticle array respectively. Convergence is reached calculating the fields at narrow width resonances after less than 100 cycles (each cycle means that the wave oscillates one period in time). In our simulations refractive index of surrounding medium is equal to 1.5 and optical constants of gold are taken from [46

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

]. In all simulations, the gold nanoparticles have an ellipsoidal shape with the dimensions of 120nm,120nm,and 75nm along x, y and z directions respectively. The structures are studied for the light polarized along y axis under the condition of normal incidence.

3. Results

3.1 Transmission and reflection spectra of nanoparticle array

A periodic 2D array of nanoparticles generates a number of diffracted orders if the wavelength of incident light in the medium is comparable with the spacing between array constituents. The wave vector projection in the (x, y) plane determined as: km1,m2=kxex+kyey+m1Gxex+m2Gyey, where kx and ky are wave number components along x and y directions, Gx=2π/ax and Gy=2π/ay are reciprocal lattice vectors along x and y directions, m1 and m2 are integers that correspond to the order of diffraction. For the modeled structure only the orders characterized by m1=±1,m2=0 change their state from evanescent to propagating in the spectral vicinity of the undisturbed single particle localized plasmon resonance (LPR). In the case of normal incidence the value of k±1,0 is determined only by the reciprocal lattice vector Gx and these two orders have equal amplitudes due to the degeneracy in frequency. The component along z axis is determined as: κz=k2km1,m22, where k=n2πλ is the magnitude of the wave vector in a medium having refractive index n. There is a threshold wavelength λRA=nax (Rayleigh anomaly wavelength), above which the order is attenuating along z due to the change of the sign in the expression under square root. To understand the physics of collective resonance phenomena in regular nanoparticle arrays, we present in Fig. 1 calculated fraction of light power reflected and transmitted into the 0-order and ± 1-order, as well as total reflection and transmission, for an array with lattice constants of ax = 450 nm and ay = 250 nm. As shown in Fig. 1(a), the excitation of collective resonances in such array leads to the appearance of asymmetric Fano-like line shape in transmission and reflection spectra, which is absent in the case of single nanoparticle LPR (the latter was calculated by replacing PBC with PML along the x and y axis). In this case, one can see a clear correlation in the evolution of spectral features in transmission and reflection. The first maximum in transmission, which coincides with minimum in reflectivity is observed at λ = 675 nm, which corresponds to RA for the ± 1 diffraction order. Under this condition ± 1-order passes from evanescent to propagating state and the slope of its power function is almost 90 degrees (Fig. 1(b)). In addition, under a certain wavelength (λ= 730 nm), red-shifted with respect to λRA, a clearlydistinguishable resonant dip in transmission and peak in reflection take place. At this condition, according to modeling, localized plasmons of the nanoparticle array are excited collectively (this plasmon wave will be later denoted as the Lattice Plasmon Mode (LPM)). In this case, the in-plane light momentum of the evanescent diffraction order matches the one of LPM and the energy is coupled into the array of metal nanoparticles [34

34. G. Vecchi, V. Giannini, and J. Gomez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009). [CrossRef]

]. For λ>λRA all diffraction orders (except 0-order) are evanescent waves bounded to the lattice. Therefore, under this condition only 0-order contributes to the total transmitted and reflected power. In contrast, for λ<λRA the total transmitted and reflected power is redistributed between 0- and ± 1-orders in considered wavelength range (Fig. 1).

3.2 Electric field patterns for RA and LPM

3.3 Transmission and reflection spectra at different regimes of electromagnetic far field coupling

In order to clarify regimes of collective interaction in the nanoparticle lattice and their dependence on lattice periodicity, we calculated transmission and reflection spectra for different lattice constants along the x axis (ax changes from 300 nm to 750 nm with 50 nm step), whereas the constant along the y axis was fixed at ay = 250 nm (Fig. 4
Fig. 4 Simulated total transmission and reflection spectra of the rectangular arrays of gold nanoparticles with fixed periodicity in y direction aY = 250 and changing periodicity in x direction from 300 nm (bottom) to 750 nm (top) with 50 nm step. For clarity individual spectra are shifted by 0.1 units along y axis
). Our calculations show that both coupling efficiency and resonant line shape critically depend on spectral position of λRA with respect to the one of the single nanoparticle LPR λLPR (as shown in Fig. 1(a), the single particle LPR is reached at λLPR = 625 nm for the used nanoparticles).

3.4 Electric field patterns at characteristic regimes of electromagnetic far field coupling

As follows from Table 1, in the limit of large separations (ay = 450 nm) the enhancement between nanoparticles is negligible for strong and weak coupling regimes as near field coupling is almost absent. In contrast, for ay below 250 nm, |Ey|mid in the regime of strong coupling rise above |Ey|max of the weak coupling regime. Under the lattice parameter of ay = 120 nm, the gap between metal surfaces in y direction becomes very small (10 nm) and electric field can be localized in tiny volume between two nanoparticles. As it was shown for 1D arrays of nanoparticle dimers [30

30. S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403(1–3), 62–67 (2005). [CrossRef]

], long range (far field) coupling can lead to the improvement of electric field enhancement factor in the gap between two metal nanoparticles compared to single dimer case. In this paper, we observed a similar effect for 2D infinite arrays. This case may be described as far field coupling between infinite chains (external electric field is parallel to the axis of the chain). According to our results the far field coupling leads to a near 2-fold increase of |Ey|mid in the gap in comparison with uncoupled chains (Table 1).

4. Discussion

Thus, we determined conditions of excitation of ultra-narrow Fano-type resonances (the smallest width of the resonance is 7 nm compared to 115 nm that is of the single nanoparticle resonance) of plasmonic nanoantenna lattices and obtained electric field distributions for different lattice parameters in characteristic points of light-lattice interaction. Our calculations show that for the given size of nanoparticles the maximal amplitude of electric field on the nanoparticles is reached under relatively large lattice parameter (600-650nm) and this phenomenon is accompanied by the extension of enhancement region to the space between nanoparticles. The effect of delocalization of field enhancement due to non-locality of electron response in nanoscale metallic structures has been discussed recently [48

48. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337,1072–1074 (2012).

]. Indeed, charges cannot be squeezed into a layer of infinitesimal thickness along the nanoparticle surface but occupy some volume in a case of real metal structures. This effect should be taken into consideration in theoretical modeling of field enhancements near sharp corners of metal nanostructures or within the subnanometer gap formed between plasmonic metal nanoparticle aggregates. However delocalization of enhancement region in diffractive metallic arrays studied here has different origin and arises from photonic-like behavior of the studied modes [34

34. G. Vecchi, V. Giannini, and J. Gomez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009). [CrossRef]

]. We believe that these data can be important for many plasmonic applications relying on locally enhanced electric field.

One prominent example is Surface Enhanced Raman Scattering (SERS). The electric field enhancement near rough metal surfaces and metal nanoparticles determines the electromagnetic enhancement in SERS [49

49. M. Kerker, “Electromagnetic model for surface-enhanced Raman scattering (SERS) on metal colloids,” Acc. Chem. Res. 17(8), 271–277 (1984). [CrossRef]

,50

50. P. K. Aravind and H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74(2), 301–305 (1980). [CrossRef]

]. The enhancement factor in SERS is proportional to the forth power of the localized field intensity. Two types of enhancement present interest: the average of electric field over the region of enhancement and the peak value of electric field which is important in single molecule SERS [51

51. E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimers,” J. Chem. Phys. 120(1), 357–366 (2004). [CrossRef] [PubMed]

]. Although the latter phenomenon have received recently a lot of attention, the design and optimization of variety of SERS based chemical sensors for which the average electric field enhancement plays an essential role is still an important issue [3

3. K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications, (Springer, 2006).

]. For this case, large volume of electric field enhancement is desirable, and, therefore, collective plasmon excitation that results in an increase of electric field enhancement region (characteristic length is a few hundred nanometers) may be useful.

5. Conclusion

We report a study of optical response of ordered ensembles of gold nanoparticles employing FDTD method with Bloch Flocket boundary conditions. We first analyzed the evolution of the electric near and far field for two characteristic states of Fano-like transmission and reflection spectra: RA and LPM. The former regime of optical excitation is characterized by almost zero amplitude of the electric field in the sites of the metal nanoparticles, while the latter regime is characterized by the collective excitation of localized plasmons in the nanoparticle lattice. Then, we investigated the behavior of electric field at different regimes of LPM excitation, obtaining the parameters of the periodic array that provide the highest factor of electric field enhancement. Finally, we studied the conditions of optical coupling that provide the extension of electric near field enhancement region to the space between metal nanoparticles.

Acknowledgments

This work is funded through the Nanobioplasmon ANR project.

References and links

1.

S. A. Maier Plasmonics: Fundamentals and Applications (Springer Science + Business Media LLC, 2007).

2.

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef] [PubMed]

3.

K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications, (Springer, 2006).

4.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

5.

S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and super lensing,” Nat. Photonics 3(7), 388–394 (2009). [CrossRef]

6.

G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).

7.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]

8.

V. G. Kravets, G. Zoriniants, C. P. Burrows, F. Schedin, C. Casiraghi, P. Klar, A. K. Geim, W. L. Barnes, and A. N. Grigorenko, “Cascaded optical field enhancement in composite plasmonic nanostructures,” Phys. Rev. Lett. 105(24), 246806 (2010). [CrossRef] [PubMed]

9.

B. Liedberg, C. Nylander, and I. Lundström, “Biosensing with surface plasmon resonance-how it all started,” Biosens. Bioelectron. 10(8), i–ix (1995). [CrossRef] [PubMed]

10.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with Plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

11.

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]

12.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4(21), 396–402 (1902). [CrossRef]

13.

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond. A79, 399 (1907).

14.

U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's Waves),” J. Opt. Soc. Am. 31(3), 213 (1941). [CrossRef]

15.

A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 4(10), 1275 (1965). [CrossRef]

16.

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

17.

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]

18.

D. Maystre, in Electromagnetic Surface Modes edited by A. D. Boardman (Wiley, 1982), chap.17.

19.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

20.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000). [CrossRef]

21.

N. Bonod, S. Enoch, L. Li, P. Evgeny, and M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11(5), 482–490 (2003). [CrossRef] [PubMed]

22.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003). [CrossRef]

23.

M. Sarrazin and J. P. Vigneron, “Bounded modes to the rescue of optical transmission,” Europhys. News 38(3), 27–31 (2007). [CrossRef]

24.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: Strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003). [CrossRef] [PubMed]

25.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: Experiment and theory,” Phys. Rev. B 70(12), 1–15 (2004). [CrossRef]

26.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]

27.

V. A. Markel, “Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one dimensional periodic arrays of nanospheres,” J. Phys. B.: Mol. Opt. 38(7), L115–L121 (2005). [CrossRef]

28.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120(23), 10871–10875 (2004). [CrossRef] [PubMed]

29.

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121(24), 12606–12612 (2004). [CrossRef] [PubMed]

30.

S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403(1–3), 62–67 (2005). [CrossRef]

31.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008). [CrossRef] [PubMed]

32.

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]

33.

Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008). [CrossRef]

34.

G. Vecchi, V. Giannini, and J. Gomez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009). [CrossRef]

35.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009). [CrossRef] [PubMed]

36.

V. G. Kravets, F. Schedin, A. V. Kabashin, and A. N. Grigorenko, “Sensitivity of collective plasmon modes of gold nanoresonators to local environment,” Opt. Lett. 35(7), 956–958 (2010). [CrossRef] [PubMed]

37.

V. Giannini, G. Vecchi, and J. Gómez Rivas, “Lighting up multipolar surface plasmon polaritons by collective resonances in arrays of nanoantennas,” Phys. Rev. Lett. 105(26), 266801 (2010). [CrossRef] [PubMed]

38.

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gómez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5(6), 5151–5157 (2011). [CrossRef] [PubMed]

39.

W. Zhou and T. W. Odom, “Tunable subradiant lattice plasmons by out-of-plane dipolar interactions,” Nat. Nanotechnol. 6(7), 423–427 (2011). [CrossRef] [PubMed]

40.

E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223{230 (2009).

41.

E. Simsek, “Full analytical model for obtaining surface plasmon resonance modes of metal nanoparticle structures embedded in layered media,” Opt. Express 18(2), 1722–1733 (2010). [CrossRef] [PubMed]

42.

B. Auguié, X. Bendaña, W. Barnes, and F. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: Critical role of the substrate,” Phys. Rev. B 82(15), 155447 (2010). [CrossRef]

43.

B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012). [CrossRef]

44.

W. Hu and Sh. Zou, “Remarkable radiation efficiency through leakage modes in two-dimensional silver nanoparticle arrays,” J. Phys. Chem. C 115(35), 17328–17333 (2011). [CrossRef]

45.

“FDTD method for periodic structures,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), Chap. 6.

46.

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

47.

A. Taflove and S. C. Hagness, “Computational Electrodynamics: The Finite Difference Time-Domain Method,” (Artech House Publishers, 2005), Chap. 8.

48.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337,1072–1074 (2012).

49.

M. Kerker, “Electromagnetic model for surface-enhanced Raman scattering (SERS) on metal colloids,” Acc. Chem. Res. 17(8), 271–277 (1984). [CrossRef]

50.

P. K. Aravind and H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74(2), 301–305 (1980). [CrossRef]

51.

E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimers,” J. Chem. Phys. 120(1), 357–366 (2004). [CrossRef] [PubMed]

52.

A. V. Kabashin and P. I. Nikitin, “Surface plasmon resonance interferometer for bio- and chemical sensors,” Opt. Commun. 150(1-6), 5–8 (1998). [CrossRef]

53.

A. V. Kabashin, V. E. Kochergin, and P. I. Nikitin, “Surface plasmon resonance bio- and chemical sensors with phase-polarisation contrat,” Sens. Actuators B Chem. 54(1-2), 51–56 (1999). [CrossRef]

54.

N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, “Phase jumps and interferometric surface plasmon resonance imaging,” Appl. Phys. Lett. 75(25), 3917–3919 (1999). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(260.5740) Physical optics : Resonance
(290.5850) Scattering : Scattering, particles
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 18, 2012
Revised Manuscript: October 29, 2012
Manuscript Accepted: November 5, 2012
Published: November 30, 2012

Virtual Issues
Vol. 8, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Andrey G. Nikitin, Andrei V. Kabashin, and Hervé Dallaporta, "Plasmonic resonances in diffractive arrays of gold nanoantennas: near and far field effects," Opt. Express 20, 27941-27952 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-25-27941


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References

  1. S. A. Maier Plasmonics: Fundamentals and Applications (Springer Science + Business Media LLC, 2007).
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  11. 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]
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  18. D. Maystre, in Electromagnetic Surface Modes edited by A. D. Boardman (Wiley, 1982), chap.17.
  19. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998). [CrossRef]
  20. E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B62(23), 16100–16108 (2000). [CrossRef]
  21. N. Bonod, S. Enoch, L. Li, P. Evgeny, and M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express11(5), 482–490 (2003). [CrossRef] [PubMed]
  22. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67(8), 085415 (2003). [CrossRef]
  23. M. Sarrazin and J. P. Vigneron, “Bounded modes to the rescue of optical transmission,” Europhys. News38(3), 27–31 (2007). [CrossRef]
  24. A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: Strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett.91(18), 183901 (2003). [CrossRef] [PubMed]
  25. A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: Experiment and theory,” Phys. Rev. B70(12), 1–15 (2004). [CrossRef]
  26. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys.79(4), 1267–1290 (2007). [CrossRef]
  27. V. A. Markel, “Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one dimensional periodic arrays of nanospheres,” J. Phys. B.: Mol. Opt.38(7), L115–L121 (2005). [CrossRef]
  28. S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys.120(23), 10871–10875 (2004). [CrossRef] [PubMed]
  29. S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys.121(24), 12606–12612 (2004). [CrossRef] [PubMed]
  30. S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett.403(1–3), 62–67 (2005). [CrossRef]
  31. V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett.101(8), 087403 (2008). [CrossRef] [PubMed]
  32. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett.101(14), 143902 (2008). [CrossRef] [PubMed]
  33. Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett.93(18), 181108 (2008). [CrossRef]
  34. G. Vecchi, V. Giannini, and J. Gomez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B80(20), 201401 (2009). [CrossRef]
  35. G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett.102(14), 146807 (2009). [CrossRef] [PubMed]
  36. V. G. Kravets, F. Schedin, A. V. Kabashin, and A. N. Grigorenko, “Sensitivity of collective plasmon modes of gold nanoresonators to local environment,” Opt. Lett.35(7), 956–958 (2010). [CrossRef] [PubMed]
  37. V. Giannini, G. Vecchi, and J. Gómez Rivas, “Lighting up multipolar surface plasmon polaritons by collective resonances in arrays of nanoantennas,” Phys. Rev. Lett.105(26), 266801 (2010). [CrossRef] [PubMed]
  38. P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gómez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano5(6), 5151–5157 (2011). [CrossRef] [PubMed]
  39. W. Zhou and T. W. Odom, “Tunable subradiant lattice plasmons by out-of-plane dipolar interactions,” Nat. Nanotechnol.6(7), 423–427 (2011). [CrossRef] [PubMed]
  40. E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223{230 (2009).
  41. E. Simsek, “Full analytical model for obtaining surface plasmon resonance modes of metal nanoparticle structures embedded in layered media,” Opt. Express18(2), 1722–1733 (2010). [CrossRef] [PubMed]
  42. B. Auguié, X. Bendaña, W. Barnes, and F. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: Critical role of the substrate,” Phys. Rev. B82(15), 155447 (2010). [CrossRef]
  43. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B85(24), 245411 (2012). [CrossRef]
  44. W. Hu and Sh. Zou, “Remarkable radiation efficiency through leakage modes in two-dimensional silver nanoparticle arrays,” J. Phys. Chem. C115(35), 17328–17333 (2011). [CrossRef]
  45. “FDTD method for periodic structures,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), Chap. 6.
  46. P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  47. A. Taflove and S. C. Hagness, “Computational Electrodynamics: The Finite Difference Time-Domain Method,” (Artech House Publishers, 2005), Chap. 8.
  48. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337,1072–1074 (2012).
  49. M. Kerker, “Electromagnetic model for surface-enhanced Raman scattering (SERS) on metal colloids,” Acc. Chem. Res.17(8), 271–277 (1984). [CrossRef]
  50. P. K. Aravind and H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett.74(2), 301–305 (1980). [CrossRef]
  51. E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimers,” J. Chem. Phys.120(1), 357–366 (2004). [CrossRef] [PubMed]
  52. A. V. Kabashin and P. I. Nikitin, “Surface plasmon resonance interferometer for bio- and chemical sensors,” Opt. Commun.150(1-6), 5–8 (1998). [CrossRef]
  53. A. V. Kabashin, V. E. Kochergin, and P. I. Nikitin, “Surface plasmon resonance bio- and chemical sensors with phase-polarisation contrat,” Sens. Actuators B Chem.54(1-2), 51–56 (1999). [CrossRef]
  54. N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, “Phase jumps and interferometric surface plasmon resonance imaging,” Appl. Phys. Lett.75(25), 3917–3919 (1999). [CrossRef]

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