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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 23 — Nov. 5, 2012
  • pp: 25201–25212
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A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone

Aitzol García-Etxarri, Peter Apell, Mikael Käll, and Javier Aizpurua  »View Author Affiliations


Optics Express, Vol. 20, Issue 23, pp. 25201-25212 (2012)
http://dx.doi.org/10.1364/OE.20.025201


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Abstract

We introduce a design strategy to maximize the Near Field (NF) enhancement near plasmonic antennas. We start by identifying and studying the basic electromagnetic effects that contribute to the electric near field enhancement. Next, we show how the concatenation of a convex and a concave surface allows merging all the effects on a single, continuous nanoantenna. As an example of this NF maximization strategy, we engineer a nanostructure, the indented nanocone. This structure, combines all the studied NF maximization effects with a synergistic boost provided by a Fano-like interference effect activated by the presence of the concave surface. As a result, the antenna exhibits a NF amplitude enhancement of ∼ 800, which transforms into ∼1600 when coupled to a perfect metallic surface. This strong enhancement makes the proposed structure a robust candidate to be used in field enhancement based technologies. Further elaborations of the concept may produce even larger and more effective enhancements.

© 2012 OSA

1. Introduction

The rational design of effective optical antennas [1

1. L. Novotny and N. Van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011). [CrossRef]

] is challenging and necessary to push the limits of several emerging technologies such as field-enhanced spectroscopies [2

2. H. Xu, E. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of Single hemoglobin molecules by surface enhanced raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999). [CrossRef]

, 3

3. F. Neubrech, A. Pucci, T. Cornelius, S. Karim, A. Garcia-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101, 2–5 (2008). [CrossRef]

], plasmonic biosensing [4

4. T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Höök, D. S. Sutherland, and M. Käll, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335 (2005). [CrossRef] [PubMed]

, 5

5. A. Dmitriev, C. Hägglund, S. Chen, H. Fredriksson, T. Pakizeh, M. Käll, and D. S. Sutherland, “Enhanced nanoplasmonic optical sensors with reduced substrate effect,” Nano Lett. 8, 3893 (2008). [CrossRef] [PubMed]

], and plasmon enhanced photovoltaics and photocatalysis [6

6. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mat. 9, 205–213 (2010). [CrossRef]

8

8. Z. Liu, W. Hou, P. Pavaskar, M. Aykol, and S. B. Cronin, “Plasmon resonant enhancement of carbon monoxide catalysis,” Nano Lett. 11, 1111–1116 (2011). [CrossRef] [PubMed]

]. Various structures, such as dimers [9

9. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]

, 10

10. P. Nordlander and C. Oubre, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004). [CrossRef]

] and plasmonic lenses [11

11. K. Li, M. Stockman, and D. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003). [CrossRef] [PubMed]

] have been proposed and adopted to obtain electromagnetic hot-spots with very large field enhancements of up to 1000 times the incident electromagnetic field amplitude. These huge enhancements are obtained mainly through electromagnetic coupling of metallic nanoparticles. The field-enhancements produced by isolated nanostructures are less spectacular, typically not higher than 100 in amplitude. In this contribution, we first introduce the elementary strategies for maximizing the near-field enhancement around metallic structures and secondly, we combine these building blocks on a single continuous nanostructure, the indented nanocone, to show the potential of combining all the enhancing effects in one single continuous nanostructure.

2. Ingredients of the field enhancement

To gain insights about the nature of the different near field enhancing effects, we first introduce a simple non-retarded analytical model and later verify the identified effects with numerical simulations obtained by using the Boundary Element Method (BEM) [15

15. F. J. García, De Abajo, and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002). [CrossRef]

, 16

16. F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180–5183 (1998). [CrossRef]

] to solve Maxwell’s equations.

Let us assume the generic polarizability tensor components αjj of an ellipsoidal particle (P) of volume V in a medium (M) [17

17. C. F. Bohren and D. R. Huffman, “Absorption and Scattering of Light by Small Particles” (Wiley, New York, 1983).

]
αjj(ω)=4πε0VLjεP(ω)εM(ω)εP(ω)εM(ω)+εM(ω)/Lj=α0f(ω),
(1)
where εP/εM/ε0 are the dielectric functions of the particle/medium/vacuum respectively, and Lj is the so called depolarization factor, corresponding to the direction of the component j of the applied field, that only depends on the shape of the particle. α0 = 4πε0V/Lj is the static polarizability of the particle.

Material: Taking Eq. 3 as a reference, it is easy to conclude that the resonant value of the field enhancement is correlated with the Drude damping of the material (γ). Smaller γ factors give rise to sharper resonances and thus, to higher values of the maximum field enhancement in the surroundings of the spheroid.

Fig. 1(a) illustrates this dependence. We calculate the field enhancement spectra of three 5 nm spheres 1 nm away from their surface for 3 different materials with different Drude damping factors. We choose Coper, Gold and Silver as an example. The Drude damping factors of these materials are γCu = 0.0955 eV, γAu = 0.07088 eV and γAg = 0.02125 eV [18

18. E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory study of surface enhancement factors for Ag, Au, Cu, Li, Na, AI, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987). [CrossRef]

]. The maximum value of the near field increases as the Drude damping factor of the material decreases. Note that the resonant wavelength is also modified due to the different bulk plasma frequencies (ωp) of the materials. Based on this argument and in the spirit of trying to maximize the near field response of a nanostructure, we will choose silver as the material to use for the rest of the study.

Fig. 1 Evolution of the near-field amplitude enhancement spectra 1 nm above the surface of one of the extremities of different metallic structures when changing different parameters of the system. Calculations were performed by using the BEM. Incident electric field polarization is chosen to be parallel to the rod axis. Vacuum is assumed as the embedding material. a) Material: Near field enhancement in the surroundings of three different 5 nm radius spheres made of Coper, Gold and Silver. Smaller damping factors give rise to sharper resonances and higher values for the maximum field enhancement. b) Size effect: Modification of the volume of the system V, keeping the distance between the surface and the observation point constant. The field enhancement on the surroundings of three silver spheres of different radii (r = 5, 10, 15 nm) is calculated. The near field enhancement increases with the volume, saturating for large volumes as V approaches the apparent volume Vd. c) Lightning rod effect: Modification of the length keeping the volume and the distance to the observation point of the system constant, so that V/Vd ≈ 1, for different rod radii r. Sharper structures give rise to higher values of the field enhancement due to the lighting rod effect. d) Coupling: System composed of a rod and a sphere, for different separation distances (d) between the rod and the sphere. The near field in this latter case is evaluated at the center of the gap. Smaller separation distances produce a stronger coupling and a higher field enhancement.

Size effect: The near field enhancement achieved through the excitation of localized surface plasmons decays with the cube of the distance from the surface of the object. In Eq. 3 this decay is accounted by the apparent volume Vd. The maximum field enhancement will occur right at the surface of the object where VVd. When fixing the distance between the surface of the object and evaluation point, higher volumes will give rise to field enhancement values closer to the maximum achievable values, since V/Vd will asymptotically approach unity as the volume of the object is increased. In general, we can conclude that, structures with larger volumes, will allow higher field enhancements in their vicinities.

Fig. 1(b), analyzes this effect. We calculate the near-field spectra in the proximity of silver spheres of different volumes 1 nm outside their surface. For spherical particles, V = (4/3)πa3 and Vd = (4/3)π(a + b)3, where a is the radius of the sphere and b the separation between the surface of the sphere and the observation point. Finally, V/Vd = (a/(a + b))3. Keeping b unmodified, the maximum field enhancement will increase as a becomes larger. It will ultimately saturate, since V/Vd will tend to unity for large values of a.

Lightning rod effect: The field enhancement obtained by increasing the volume of the structure can still be enhanced through further localization of the near-field response with the use of sharper geometries. The reason behind this relies on the lightning rod effect. Large variations of the surface curvature produce a large potential gradient in very reduced areas. Therefore, large field values are produced at sharp structures.

The static polarizability α0=4πε0VLj contains the lightning rod effect in terms of the depolarization factor Lj in the denominator. As the shape of the object gets sharper, which for the prolate spheroid happens when the major axis a is much larger than the minor axis b = c, the static polarizability increases accordingly. As the spheroid becomes more elongated along the j direction, Lj approaches zero. For a prolate ellipsoid the depolarization factor for the major axis La can be expressed as [19

19. Y. Kornyushin, “Plasma oscillations in porous samples,” Sci. Sinter. 36, 43–50 (2004). [CrossRef]

]
La=b2c2a2b2+a2c2+b2c2.
(4)

When written in this form, it is helpful to connect the depolarization factor with a well-defined measure of the sharpness of a surface, i.e. its curvature. For a surface with principal radii of curvature ρ1 and ρ2 at a point, we can define the mean curvature as H=12(1ρ1+1ρ2) and the Gaussian, or total, curvature as K=1ρ1ρ2. We can now express the depolarization La (Eq. 4) in terms of the Gaussian curvature Ka,b,c at the endpoints of the ellipsoid in the direction of the coordinate axes
La=a2/Kaa2/Ka+b2/Kb+c2/Kc.12b2Ka.
(5)
since for an elongated ellipsoid (b=c)Ka=(ab2)2Kb,c. Consequently, we can express the enhancement from the lightning rod effect as being directly proportional to the Gaussian curvature.

We illustrate this effect in Fig. 1(c), by calculating the near field spectra of three structures with different sharpness. To avoid the interplay of any apparent size effects, we elongate a sphere and transform it into a thinner rod while maintaining the total volume and the distance to the observation point constant. In this way, we ensure that the V/Vd ≈ 1. We can observe in the near-field spectra of Fig. 1(c) how the enhancement increases as the radius of the structure decreases and therefore the Gaussian curvature increases. A complementary way of exploiting this effect on an antenna is to use of sharp antenna terminations instead of rounded endings.

Coupling: Coupling of the electromagnetic response of a nanostructure to adjacent metallic systems is known to produce field localization and correspondingly enhancement of the near-field at the region in-between the structures [2

2. H. Xu, E. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of Single hemoglobin molecules by surface enhanced raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999). [CrossRef]

, 9

9. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]

, 20

20. H. Xu, E. J. Bjerneld, J. Aizpurua, P. Apell, L. Gunnarsson, S. Petronis, B. Kasemo, C. Larsson, F. Hook, and M. Kall, “Interparticle coupling effects in surface-enhanced Raman scattering,” Proc. SPIE 4258, 35–42 (2001). [CrossRef]

22

22. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003). [CrossRef] [PubMed]

]. We illustrate this effect in Fig. 1(d) by calculating the near field spectra of a coupled system composed by a 62 nm long silver rod with 9 nm radius silver sphere. We calculate the near-field at the center of the gap between the rod and the sphere for different separation distances d (d = 6 nm, 4 nm and 2 nm). An increase of the near-field maximum can be observed as the separation distance becomes smaller. This effect is connected with the appearance of a coupled bonding plasmon that belongs to the whole system arising from the symmetric coupling of the dipolar plasmons of each nanostructure.

Due to the in-phase excitation of the rod and the sphere, considering them as equipotential surfaces, the potential drop due to the external field is concentrated at the gap. The field enhancement increases proportionally with the inverse of the separation distance [20

20. H. Xu, E. J. Bjerneld, J. Aizpurua, P. Apell, L. Gunnarsson, S. Petronis, B. Kasemo, C. Larsson, F. Hook, and M. Kall, “Interparticle coupling effects in surface-enhanced Raman scattering,” Proc. SPIE 4258, 35–42 (2001). [CrossRef]

]. Fig. 1(d) corroborates this assumption. Taking the peak near-field enhancement for the largest separation distance as a reference (NFo = 80 for do = 6 nm), the NF for the other gap sizes should scale as
NFmax(d)=NFod/do.
(6)

According to Eq. 6, for d = 4 nm and d = 2 nm, the corresponding peak field enhancements should take values of 120 and 240 respectively. These values are in excellent agreement with the maximum field enhancement values calculated by solving Maxwell’s equations numerically using the BEM (121 and 250).

Typically, by means of coupling, the field enhancement can be increased about an order of magnitude with respect to that of the isolated systems. Interestingly, in this particular example of a rod coupled to a small sphere, the spectral response of the coupled system does not red shift when the particles are approached as could be expected. Being the sphere much smaller than the rod, the rod dominates the spectral behavior of the system making the expected red shift due to the coupling between the structures negligible. This particular detail could be specially valuable for spectroscopic applications such as SERS and SEIRA. Carefully designing the rod one could engineer its resonances to match the absorption frequencies of the molecules under study [23

23. J Aizpurua, F. J. Garcá de Abajo, and G. W. Bryant, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8, 631 (2008). [CrossRef] [PubMed]

] and in a second step gain an extra order of magnitude of field enhancement by coupling it to a small sphere without modifying the resonance frequency of the coupled system.

Some optimization strategies based on a combination of some or all of these effects have been applied recently to obtain large field enhancements. We can cite among others [24

24. A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11, 1201 (2011). [CrossRef] [PubMed]

27

27. T. Feichtner, O. Selig, M. Kiunke, and B. Hecht, “Evolutionary optimization of optical antennas,” Phys. Rev. Lett. 109, 127701 (2012). [CrossRef] [PubMed]

] the case of bowtie antennas [28

28. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. Moerner, “Gap-dependent optical coupling of single ”bowtie” nanoantennas resonant in the visible,” Nano Lett. 4, 957–961 (2004). [CrossRef]

], where a combination of interparticle coupling and sharp ends produce large enhancements in the plasmonic antenna gap, or the case of the plasmonic lens [11

11. K. Li, M. Stockman, and D. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003). [CrossRef] [PubMed]

] where three particles of different size are brought together combining effects of size, coupling and sharpness of the structures to produce huge field enhancements. All these studies suggest the use of discrete structures to obtain the enhancing effect. In this contribution, we propose the use of a continuous structure based on a metallic cone where we will induce size, coupling and lightning rod effects with the help of concave and covex deformations of the surfaces at the metallic apex of a cone. We call this structure the indented nanocone.

3. Indented nanocone

We introduce in this section a novel nanostructure that merges simultaneously all the concepts described above. We will consider that the structure is made of silver, using dielectric data from the literature to characterize its optical response [29

29. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 43704379 (1972). [CrossRef]

].

A big metallic cone, when polarized along its main axis, provides a large volume that will ensure maximum field enhancement values in the vicinities of the structure. Complementarily, the sharp the cone apex allows to localize very efficiently the induced surface charge density [30

30. J. Aizpurua, S. P. Apell, and R. Berndt, “Role of the tip shape in light emission from the scanning tunneling microscope,” Phys. Rev. B 62, 2065–2073 (2000). [CrossRef]

]. Figure 2(a) shows the optical extinction cross section of a 300 nm height silver cone of aperture angle of 30° and radius of curvature at the apex of 10 nm. Incident polarization is indicated at the inset of Fig. 2(a). Figure 2(b) shows the corresponding NF spectrum calculated 1 nm below the cone apex. We observe that the highest NF enhancement for such a structure occurs at λ = 985 nm. The surface charge density associated with this localized plasmon mode and the near-field map at the cone apex are shown in Fig. 2(c) and Fig. 2(d) respectively. Field enhancements of around 40 times the field amplitude of the incoming electric field can be obtained in the proximity of this finite conical structure.

Fig. 2 Optical response of a 300 nm height, 10 nm radius and 30° aperture angle silver nanocone a) Extinction cross section in arbitrary units with incident light as displayed in the inset. b) Near-field amplitude enhancement spectra of the silver cone calculated 1 nm bellow the cone apex. c) Surface charge density profile of a cross section of the cone for λ = 985 nm. Blue and red areas indicate regions where the surface charge density is negative and positive respectively. The charge density distribution presents azimuthal symmetry. d) Near-field enhancement distribution of the cone for normal incident light of λ = 985 nm polarized along the cone axis. The optical response of the cone is mainly characterized by a strong localization at the cone apex giving rise to a maximum field enhancement of ∼ 40.

The optical properties of metallic concave and convex geometries offer the possibility to control the symmetry of the surface charge density of the lowest order plasmonic modes [31

31. F. J. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56, 15873–15884 (1997). [CrossRef]

, 32

32. J. Aizpurua, A. Howie, and F. J. Garcá de Abajo, “Valence-electron energy loss near edges, truncated slabs, and junctions,” Phys. Rev. B 60, 11149–11162 (1999). [CrossRef]

]. Figure. 3(a) and Fig. 3(b) show the surface charge density profile for the lowest energy mode of a convex and a concave perfect metallic surface respectively. A concave surface (Fig. 3(a)) presents a symmetric profile for the surface charge density, piling up charge at the edge. On the complementary convex surface, instead, sum-rules ensure that the lowest energy mode will present an anti-symmetric surface charge density profile [31

31. F. J. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56, 15873–15884 (1997). [CrossRef]

, 33

33. S. P. Apell, P. M. Echenique, and R. H. Ritchie, “Sum rules for surface plasmon frequencies,” Ultramicroscopy 65, 53–60 (1996). [CrossRef]

]. As a consequence, a node of the charge is produced at the convex area [34

34. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008). [CrossRef] [PubMed]

], as shown in Fig. 3(b). The combination of a concave and a convex surface thus produces inevitably a change of the sign of the surface charge density at one type of surface with respect to the other. It is possible to create in this way areas where the surface charge density is forced to change sign within the same continuous structure. Consequently, a combination of concave and convex surfaces permits to exploit in the same closed geometry both the aspect of localization, caused by the presence of the sharp edges, as well as the aspect of coupling, happening between facing surfaces with induced surface charge density distributions of opposite sign.

Fig. 3 Surface charge density (σ) plots, in arbitrary units, for the lowest energy modes of a a) convex and b) concave perfect metallic surface. The lowest energy mode for the convex surface presents a symmetric charge density distribution. On a concave structure instead, the surface charge density mode is antisymmetric, presenting a node at the concavity. For an elaborate discussion about these simulations see Ref. [31]. A combination of both kinds of surfaces allows to localize the surface charge density in sharp regions as well as to couple the charges with opposite sign excited at both sides of the concave surface.

A combination of concave and convex surfaces in the same continuous structure can be realized in an indented nanocone structure as the one depicted in Fig. 4(a). Illuminated by light polarized along the cone axis, this geometry allows for a combination of the different near field maximization factors introduced above: a large volume, localization of the charge density at the edges and coupling of plasmonic modes in close proximity.

Fig. 4 Cross section of the geometry of the indented nanocone. a) The combination of the four field enhancement ingredients (a large volume, the localization of the charge density at the edges and the coupling), permits the creation of a field enhancement of ∼ 800 at the tip apex (see Fig. 5) b) Geometrical details of the proposed structure. The upper arrow indicates the rotational symmetry axis of the geometry.

We show in Fig. 5(a) the optical extinction cross section of a silver indented nanocone. The far-field spectrum of the indented nanocone shows strong similarities with that corresponding to the smooth cone presented in the inset of Fig. 5(a). However, a new mode emerging at the near infrared (IR) range of the spectrum appears as a predominant feature. This new mode is very intense and narrow and it seems natural to assign its emergence to the presence of the geometrical features of the indented nanocone. To confirm the nature of this new intense peak, we calculate the surface charge density at the lowest resonant energy (λ = 1061 nm) as show in Fig. 5(c). As expected, the surface charge density is piled up on the convex zones of the geometry (indented nanoconical arms and central tip). Therefore, the local fields show maximum value and localization in these areas. In the concave area, a zero in the surface charge density is induced, forcing the charge density to change sign and effectively acting as a source of coupling and polarization of the system as explained above.

Fig. 5 Optical response of the indented nanocone depicted in Fig. 4. a) Extinction cross section in arbitrary units for the incident polarization displayed in the inset. b) Near-field enhancement spectra of the silver indented nanocone calculated 1 nm below the cone apex. c) Cross section of the surface charge density profile of the indented nanocone for λ = 1061 nm (in arbitrary units) d) Near-field enhancement distribution of the system for normal incident light at λ = 1061 nm polarized along the cone axis. The proposed structure, allows for the combination of the field enhancement ingredients introduced in Fig. 1, giving rise to field enhancement factors of ∼ 800 in amplitude.

Interestingly, the new spectral feature presents the typical lineshape of a Fano-like interference effect [35

35. B. Lukýanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Mater. 9, 707–715 (2010). [CrossRef]

]. As previously mentioned, the concave surface imposes a change of sign of the surface charge density, somewhat decoupling the response of the central tip from the response of the overall object. As a consequence of this forced variation of the sign of the charge, the rest of the smaller convex central tip becomes uniformly charged and its response mimics the response of an electric monopole [36

36. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Optics Expr. 15, 8550–8565 (2007). [CrossRef]

]. If we were to isolate the central tip from the overall object, this monopolar resonance would be unexcitable (dark). It is, in fact, the concave geometry that allows for the excitation of this mode by imposing a zero in the surface charge density at the convex area. In this sense, the combination of a convex and concave surface presents a new strategy, complementary to symmetry breaking [35

35. B. Lukýanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Mater. 9, 707–715 (2010). [CrossRef]

, 37

37. S. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 39273934 (2011). [CrossRef] [PubMed]

, 38

38. F. Neubrech, A. García-Etxarri, D. Weber, J Bochterle, H. Shen, M. Lamy, De La Chapelle, G. W. Bryant, J. Aizpurua, and A. Pucci, “Defect-induced activation of symmetry forbidden infrared resonances in individual metallic nanorods,” Appl. Phys. Lett. 96, 213111 (2010). [CrossRef]

], for the activation of dark modes in nanoscale optical systems. The prominent Fano-like resonance arises from the spectral interference of this previously dark monopolar mode of the central tip and the broader bright mode of the entire cone.

The resulting near-field map for the resonant wavelength (λ = 1061 nm) is shown in Fig. 5(d). A maximum field-enhancement of ∼ 800 in amplitude is achieved for realistic parameters of the arm length and their respective curvatures (see Fig. 4(b) for geometrical details).

The reason for this huge enhancement does not rely on the sharp curvature of the central tip of the indented nanocone, as one intuitively could think on a first approach. Calculations of the field enhancement for the small central tip of the indented nanocone (same curvature) only reach enhancements of the order of one order of magnitude in amplitude. It is the combination of all the ingredients mentioned in this work what makes this structure a unique continuous structure providing such enhancement. In that sense, the role of the convex part of the indented nanocone is crucial for two different reasons. First, it allows for a geometrical localization of the surface charge density, and second, it activates the interference between the the dipolar and the monopolar modes. This gives rise to a spectral region where the surface charge densities of the two resonances interfere constructively boosting the near field response of the system. In conclusion, the concave surface allows for a synergistic combination of all the ingredients for the field enhancement through the activation of a Fano-like interference effect involving a localized mode at the tip apex and a broader mode extended to the whole structure.

Fig. 6 Optical response of the silver indented nanocone for different central tip lengths h. a) Extinction cross section in arbitrary units. The lineshape of the Fano-like interference can be tailored by modifying the central tip length. b) Near-field enhancement spectra calculated 1 nm below the cone apex. The maximum field enhancement occurs for h = 70 nm.

It is possible to go further in the enhancing strategy by providing an additional external coupling to this structure. To this end, we locate an indented nanocone facing a perfect metallic surface acting as a mirror for different separation distances. The image charges on the perfect metal mimic the presence of an additional indented nanocone facing the original structure on a bowtie configuration. Fig. 7(a) shows the NF spectra 0.5 nm below the nanocone tip for 4 different separation distances (d = 4, 3, 2, 1 nm). The extra coupling results in a field enhancement of ∼ 1600 for a separation distance of 1 nm. The near field distribution of the coupled system on resonance (λ = 1212 nm) is shown in Fig. 7(b) for a separation distance of 1 nm, showing a very strong concentration of the fields at the gap between the indented nanocone and the metallic surface.

Fig. 7 Indented nanocone coupled to a perfect metallic surface. a) Near-field amplitude spectra for different separation distances d = (4, 3, 2, 1 nm). b) Near field map for a separation distance of 1 nm at λ = 1212 nm. The extra coupling results in a maximum field enhancement of ∼ 1600 in amplitude.

4. Conclusion

In summary, we have identified the key electromagnetic effects that can be used to optimize the near-field enhancement of a metallic nanostructure and applied them to design a continuous nanoantenna where the field enhancement reaches about the largest values reported in the literature. Further modifications of this concept may lead to even larger factors. To obtain these enhancing factors appropriate values for the dielectric response and damping of the metals have been used as well as realistic parameters for the cone lengths, curvatures and indentations. This structure, or different variations of the same concepts, could be very beneficial in photonic applications based on field enhancement such as surface enhanced spectroscopy and light harvesting for photovoltaics.

Acknowledgments

A.G.E. thanks Ashwin C. Atre for assistance preparing Fig.6 and Fig.7. This work was supported by the Etortek-2011 project nanoiker of the Department of Industry of the Basque Government, project FIS2010-19609-C02-01 of the Spanish Ministry of Science and Innovation and the Swedish Foundation for Strategic Research through the project RMA08 Functional Electromagnetic Metamaterials.

References and links

1.

L. Novotny and N. Van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011). [CrossRef]

2.

H. Xu, E. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of Single hemoglobin molecules by surface enhanced raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999). [CrossRef]

3.

F. Neubrech, A. Pucci, T. Cornelius, S. Karim, A. Garcia-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101, 2–5 (2008). [CrossRef]

4.

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Höök, D. S. Sutherland, and M. Käll, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335 (2005). [CrossRef] [PubMed]

5.

A. Dmitriev, C. Hägglund, S. Chen, H. Fredriksson, T. Pakizeh, M. Käll, and D. S. Sutherland, “Enhanced nanoplasmonic optical sensors with reduced substrate effect,” Nano Lett. 8, 3893 (2008). [CrossRef] [PubMed]

6.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mat. 9, 205–213 (2010). [CrossRef]

7.

A. C. Atre, A. García-Etxarri, H. Alaeian, and J. A. Dionne, “Toward high-efficiency solar upconversion with plasmonic nanostructures,” J. Opt. 14, 024008 (2012). [CrossRef]

8.

Z. Liu, W. Hou, P. Pavaskar, M. Aykol, and S. B. Cronin, “Plasmon resonant enhancement of carbon monoxide catalysis,” Nano Lett. 11, 1111–1116 (2011). [CrossRef] [PubMed]

9.

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]

10.

P. Nordlander and C. Oubre, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004). [CrossRef]

11.

K. Li, M. Stockman, and D. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003). [CrossRef] [PubMed]

12.

M. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004). [CrossRef] [PubMed]

13.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A Plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 34473452, (2009). [CrossRef] [PubMed]

14.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photon. 4, 83–91 (2010). [CrossRef]

15.

F. J. García, De Abajo, and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002). [CrossRef]

16.

F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180–5183 (1998). [CrossRef]

17.

C. F. Bohren and D. R. Huffman, “Absorption and Scattering of Light by Small Particles” (Wiley, New York, 1983).

18.

E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory study of surface enhancement factors for Ag, Au, Cu, Li, Na, AI, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987). [CrossRef]

19.

Y. Kornyushin, “Plasma oscillations in porous samples,” Sci. Sinter. 36, 43–50 (2004). [CrossRef]

20.

H. Xu, E. J. Bjerneld, J. Aizpurua, P. Apell, L. Gunnarsson, S. Petronis, B. Kasemo, C. Larsson, F. Hook, and M. Kall, “Interparticle coupling effects in surface-enhanced Raman scattering,” Proc. SPIE 4258, 35–42 (2001). [CrossRef]

21.

I. Romero, J. Aizpurua, G. W. Bryant, F. J. García, and De Abajo, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–99 (2006). [CrossRef] [PubMed]

22.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003). [CrossRef] [PubMed]

23.

J Aizpurua, F. J. Garcá de Abajo, and G. W. Bryant, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8, 631 (2008). [CrossRef] [PubMed]

24.

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11, 1201 (2011). [CrossRef] [PubMed]

25.

T. J. Seok, A. Jamshidi, M. Kim, S. Dhuey, A. Lakhani, H. Choo, P. J. Schuck, S. Cabrini, A. M. Schwartzberg, J. Bokor, E. Yablonovitch, and M. C. Wu, “Radiation engineering of optical antennas for maximum field enhancement,” Nano Lett. 11, 2606 (2011). [CrossRef] [PubMed]

26.

C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012). [CrossRef] [PubMed]

27.

T. Feichtner, O. Selig, M. Kiunke, and B. Hecht, “Evolutionary optimization of optical antennas,” Phys. Rev. Lett. 109, 127701 (2012). [CrossRef] [PubMed]

28.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. Moerner, “Gap-dependent optical coupling of single ”bowtie” nanoantennas resonant in the visible,” Nano Lett. 4, 957–961 (2004). [CrossRef]

29.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 43704379 (1972). [CrossRef]

30.

J. Aizpurua, S. P. Apell, and R. Berndt, “Role of the tip shape in light emission from the scanning tunneling microscope,” Phys. Rev. B 62, 2065–2073 (2000). [CrossRef]

31.

F. J. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56, 15873–15884 (1997). [CrossRef]

32.

J. Aizpurua, A. Howie, and F. J. Garcá de Abajo, “Valence-electron energy loss near edges, truncated slabs, and junctions,” Phys. Rev. B 60, 11149–11162 (1999). [CrossRef]

33.

S. P. Apell, P. M. Echenique, and R. H. Ritchie, “Sum rules for surface plasmon frequencies,” Ultramicroscopy 65, 53–60 (1996). [CrossRef]

34.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008). [CrossRef] [PubMed]

35.

B. Lukýanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Mater. 9, 707–715 (2010). [CrossRef]

36.

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Optics Expr. 15, 8550–8565 (2007). [CrossRef]

37.

S. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 39273934 (2011). [CrossRef] [PubMed]

38.

F. Neubrech, A. García-Etxarri, D. Weber, J Bochterle, H. Shen, M. Lamy, De La Chapelle, G. W. Bryant, J. Aizpurua, and A. Pucci, “Defect-induced activation of symmetry forbidden infrared resonances in individual metallic nanorods,” Appl. Phys. Lett. 96, 213111 (2010). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(300.6340) Spectroscopy : Spectroscopy, infrared
(250.5403) Optoelectronics : Plasmonics
(240.6695) Optics at surfaces : Surface-enhanced Raman scattering

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 31, 2012
Revised Manuscript: October 5, 2012
Manuscript Accepted: October 6, 2012
Published: October 22, 2012

Virtual Issues
Vol. 7, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Aitzol García-Etxarri, Peter Apell, Mikael Käll, and Javier Aizpurua, "A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone," Opt. Express 20, 25201-25212 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25201


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References

  1. L. Novotny and N. Van Hulst, “Antennas for light,” Nature Photon.5, 83–90 (2011). [CrossRef]
  2. H. Xu, E. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of Single hemoglobin molecules by surface enhanced raman scattering,” Phys. Rev. Lett.83, 4357–4360 (1999). [CrossRef]
  3. F. Neubrech, A. Pucci, T. Cornelius, S. Karim, A. Garcia-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett.101, 2–5 (2008). [CrossRef]
  4. T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Höök, D. S. Sutherland, and M. Käll, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett.5, 2335 (2005). [CrossRef] [PubMed]
  5. A. Dmitriev, C. Hägglund, S. Chen, H. Fredriksson, T. Pakizeh, M. Käll, and D. S. Sutherland, “Enhanced nanoplasmonic optical sensors with reduced substrate effect,” Nano Lett.8, 3893 (2008). [CrossRef] [PubMed]
  6. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mat.9, 205–213 (2010). [CrossRef]
  7. A. C. Atre, A. García-Etxarri, H. Alaeian, and J. A. Dionne, “Toward high-efficiency solar upconversion with plasmonic nanostructures,” J. Opt.14, 024008 (2012). [CrossRef]
  8. Z. Liu, W. Hou, P. Pavaskar, M. Aykol, and S. B. Cronin, “Plasmon resonant enhancement of carbon monoxide catalysis,” Nano Lett.11, 1111–1116 (2011). [CrossRef] [PubMed]
  9. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E62, 4318–4324 (2000). [CrossRef]
  10. P. Nordlander and C. Oubre, “Plasmon hybridization in nanoparticle dimers,” Nano Lett.4, 899–903 (2004). [CrossRef]
  11. K. Li, M. Stockman, and D. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett.91, 227402 (2003). [CrossRef] [PubMed]
  12. M. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93, 137404 (2004). [CrossRef] [PubMed]
  13. S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A Plasmonic dimple lens for nanoscale focusing of light,” Nano Lett.9, 34473452, (2009). [CrossRef] [PubMed]
  14. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photon.4, 83–91 (2010). [CrossRef]
  15. F. J. García, De Abajo, and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B65, 115418 (2002). [CrossRef]
  16. F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett.80, 5180–5183 (1998). [CrossRef]
  17. C. F. Bohren and D. R. Huffman, “Absorption and Scattering of Light by Small Particles” (Wiley, New York, 1983).
  18. E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory study of surface enhancement factors for Ag, Au, Cu, Li, Na, AI, Ga, In, Zn, and Cd,” J. Phys. Chem.91, 634–643 (1987). [CrossRef]
  19. Y. Kornyushin, “Plasma oscillations in porous samples,” Sci. Sinter.36, 43–50 (2004). [CrossRef]
  20. H. Xu, E. J. Bjerneld, J. Aizpurua, P. Apell, L. Gunnarsson, S. Petronis, B. Kasemo, C. Larsson, F. Hook, and M. Kall, “Interparticle coupling effects in surface-enhanced Raman scattering,” Proc. SPIE4258, 35–42 (2001). [CrossRef]
  21. I. Romero, J. Aizpurua, G. W. Bryant, F. J. García, and De Abajo, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express14, 9988–99 (2006). [CrossRef] [PubMed]
  22. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302, 419 (2003). [CrossRef] [PubMed]
  23. J Aizpurua, F. J. Garcá de Abajo, and G. W. Bryant, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8, 631 (2008). [CrossRef] [PubMed]
  24. A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett.11, 1201 (2011). [CrossRef] [PubMed]
  25. T. J. Seok, A. Jamshidi, M. Kim, S. Dhuey, A. Lakhani, H. Choo, P. J. Schuck, S. Cabrini, A. M. Schwartzberg, J. Bokor, E. Yablonovitch, and M. C. Wu, “Radiation engineering of optical antennas for maximum field enhancement,” Nano Lett.11, 2606 (2011). [CrossRef] [PubMed]
  26. C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett.12, 2037–2044 (2012). [CrossRef] [PubMed]
  27. T. Feichtner, O. Selig, M. Kiunke, and B. Hecht, “Evolutionary optimization of optical antennas,” Phys. Rev. Lett.109, 127701 (2012). [CrossRef] [PubMed]
  28. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. Moerner, “Gap-dependent optical coupling of single ”bowtie” nanoantennas resonant in the visible,” Nano Lett.4, 957–961 (2004). [CrossRef]
  29. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 43704379 (1972). [CrossRef]
  30. J. Aizpurua, S. P. Apell, and R. Berndt, “Role of the tip shape in light emission from the scanning tunneling microscope,” Phys. Rev. B62, 2065–2073 (2000). [CrossRef]
  31. F. J. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B56, 15873–15884 (1997). [CrossRef]
  32. J. Aizpurua, A. Howie, and F. J. Garcá de Abajo, “Valence-electron energy loss near edges, truncated slabs, and junctions,” Phys. Rev. B60, 11149–11162 (1999). [CrossRef]
  33. S. P. Apell, P. M. Echenique, and R. H. Ritchie, “Sum rules for surface plasmon frequencies,” Ultramicroscopy65, 53–60 (1996). [CrossRef]
  34. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008). [CrossRef] [PubMed]
  35. B. Lukýanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Mater.9, 707–715 (2010). [CrossRef]
  36. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Optics Expr.15, 8550–8565 (2007). [CrossRef]
  37. S. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett.11, 39273934 (2011). [CrossRef] [PubMed]
  38. F. Neubrech, A. García-Etxarri, D. Weber, J Bochterle, H. Shen, M. Lamy, De La Chapelle, G. W. Bryant, J. Aizpurua, and A. Pucci, “Defect-induced activation of symmetry forbidden infrared resonances in individual metallic nanorods,” Appl. Phys. Lett.96, 213111 (2010). [CrossRef]

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