OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 3186–3198
« Show journal navigation

Local plasmon resonances of metal-in-metal core-shells

Matthew Arnold, Martin Blaber, and Mike Ford  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 3186-3198 (2014)
http://dx.doi.org/10.1364/OE.22.003186


View Full Text Article

Acrobat PDF (2211 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate the tunability and strength of the localized surface plasmons of binary metal-in-metal core-shells. Ellipsoids are used as an analytical model to show how the fill factor continuously tunes a hybridized mode between those of the constituents, suggesting the use of metal combinations with widely differing plasma frequencies for broad tunability. A quasistatic eigenmode method is used separate geometric and material parameters to facilitate prediction of hybridized dipole modes in arbitrary shapes. A modified ellipsoid model is found to adequately describe the symmetric dipole-dipole resonance of well-rounded cuboids.

© 2014 Optical Society of America

1. Introduction

Plasmon resonances are associated with electromagnetic enhancement, which is useful in a variety of applications. Design of these resonances, via changes to geometry and materials, is subject to some important constraints. Resonance requires negative permittivity as typically achieved below the plasma frequency of a metal. These materials damp resonances due to frequency-dependent absorption loss [1

1. M. D. Arnold and M. G. Blaber, “Optical performance and metallic absorption in nanoplasmonic systems,” Opt. Express 17(5), 3835–3847 (2009). [CrossRef] [PubMed]

]. Unfortunately materials with the lowest losses are free-electron-like and tend to be chemically reactive, leaving only a small number of practical choices [2

2. M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22(14), 143201 (2010). [CrossRef] [PubMed]

]. There is some prospect of diversifying options through metallic compounds [3

3. M. G. Blaber, M. D. Arnold, and M. J. Ford, “Optical properties of intermetallic compounds from first principles calculations: a search for the ideal plasmonic material,” J. Phys. Condens. Matter 21(14), 144211 (2009). [CrossRef] [PubMed]

] but this has yet to be verified experimentally. As an alternative, here we explore the use of negative permittivity materials in discrete core-shell geometries.

Binary metal core-shell particles have been previously synthesized, targeting a wide variety of applications that can benefit from manipulating chemical, magnetic, and optical properties, including combinations of many different metals [4

4. M. B. Cortie and A. M. McDonagh, “Synthesis and optical properties of hybrid and alloy plasmonic nanoparticles,” Chem. Rev. 111(6), 3713–3735 (2011). [CrossRef] [PubMed]

]. The optical properties of Au-Ag systems [5

5. L. Feng, G. Gao, P. Huang, K. Wang, X. Wang, T. Luo, and C. Zhang, “Optical properties and catalytic activity of bimetallic gold-silver nanoparticles,” Nano Biomed. Eng. 2, 258–267 (2010).

] have been a particular focus, due to ease of fabrication, stability and strong optical resonances.

The mode positions of spherical Ag-in-Au core-shells have been described as being continuously varying [6

6. P. Mulvaney, M. Giersig, and A. Henglein, “Electrochemistry of multilayer colloids - preparation and absorption-spectrum of gold-coated silver particles,” J. Phys. Chem. 97(27), 7061–7064 (1993). [CrossRef]

] or lying close to the sphere mode of the dominant constituent [7

7. M. Moskovits, I. Srnova-Sloufova, and B. Vlckova, “Bimetallic Ag-Au nanoparticles: Extracting meaningful optical constants from the surface-plasmon extinction spectrum,” J. Chem. Phys. 116(23), 10435–10446 (2002). [CrossRef]

]. Mode sharpness for Ag-in-Au and Au-in-Ag have been measured [8

8. X. Wang, Z. Y. Zhang, and G. V. Hartland, “Electronic dephasing in bimetallic gold-silver nanoparticles examined by single particle spectroscopy,” J. Phys. Chem. B 109(43), 20324–20330 (2005). [CrossRef] [PubMed]

] showing reasonable agreement with theory [9

9. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

]. Field enhancement for both combinations have also been considered [10

10. D. J. Wu, X. D. Xu, and X. J. Liu, “Electric field enhancement in bimetallic gold and silver nanoshells,” Solid State Commun. 148(3-4), 163–167 (2008). [CrossRef]

] with enhancement increasing significantly as shell thickness increases. Interesting results have also been obtained for Au-in-Ag multishells with dielectric cores [11

11. C. E. Román-Velázquez, C. Noguez, and J. Z. Zhang, “Theoretical study of surface plasmon resonances in hollow gold-silver double-shell nanostructures,” J. Phys. Chem. A 113(16), 4068–4074 (2009). [CrossRef] [PubMed]

], including a broad but strong resonance in the interband region of Au.

Other rounded geometries have been investigated, including cylinders [12

12. J. Zhu, “Surface plasmon resonance from bimetallic interface in Au-Ag core-shell structure nanowires,” Nanoscale Res. Lett. 4(9), 977–981 (2009). [CrossRef] [PubMed]

] and rods [13

13. R. Jiang, H. Chen, L. Shao, Q. Li, and J. Wang, “Unraveling the evolution and nature of the plasmons in (Au Core)-(Ag Shell) nanorods,” Adv. Mater. 24(35), OP200–OP207 (2012). [CrossRef] [PubMed]

] – they offer similar tunability to Ag + Au spherical shells. Some investigations of non-spherical shells have been performed, including tuning of stars [14

14. L. Raguin, C. Hafner, and P. Leuchtmann, “Boundary integral equation method for the analysis of tunable light scattering properties of plasmonic core-shell nanoparticles,” J. Comput. Theor. Nanosci. 8(8), 1590–1599 (2011). [CrossRef]

] and cuboids [15

15. G. Park, C. Lee, D. Seo, and H. Song, “Full-color tuning of surface plasmon resonance by compositional variation of Au@Ag core-shell nanocubes with sulfides,” Langmuir 28(24), 9003–9009 (2012). [CrossRef] [PubMed]

], and some experimental evidence suggests that nearly-spherical irregular shapes have modes that are essentially determined by the fill-factor [16

16. L. Chuntonov, M. Bar-Sadan, L. Houben, and G. Haran, “Correlating electron tomography and plasmon spectroscopy of single noble metal core-shell nanoparticles,” Nano Lett. 12(1), 145–150 (2012). [CrossRef] [PubMed]

].

Only a few investigations have attempted to systematically investigate bimetallic systems. A homogenization approach has been applied to estimate the effective permittivity of dual-Drude spherical core-shells [17

17. U. K. Chettiar and N. Engheta, “Internal homogenization: Effective permittivity of a coated sphere,” Opt. Express 20(21), 22976–22986 (2012). [CrossRef] [PubMed]

], however this omitted some modes of the system. A general eigenmode approach has been used for investigating the complicated behaviour of externally-coupled nanorods [18

18. Y. Gu, J. Li, O. J. F. Martin, and Q. H. Gong, “Controlling plasmonic resonances in binary metallic nanostructures,” J. Appl. Phys. 107(11), 114313 (2010). [CrossRef]

]. In this article we also use an eigenmode framework, but emphasize using the fill-factor to tune the resonance in arbitrary core-shell particles.

While it is possible to calculate fully-retarded results, to clarify the physics we focus on small particles where electrostatic limits are reasonable approximations. In this regime absorption dominates over scattering and the position of the resonance depends only on geometric ratios, not absolute size. However, the particles cannot be too small because electron-confinement leads to additional size-dependent damping. This effect damps resonances of thin shells on dielectric cores [19

19. M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009). [CrossRef]

], but it is not clear how metal-metal boundaries would be affected. Here we omit these size effects to concentrate on the more fundamental relationship between resonance, permittivity and shape. We develop a dipole model for the behavior of binary core-shells, which we verify using a combination of a known analytical expression for confocal ellipsoids and the boundary element method [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

, 21

21. I. D. Mayergoyz, D. R. Fredkin, and Z. Y. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]

] which is suitable for arbitrary shapes.

We first manipulate analytical expressions for ellipsoid modes to understand the fundamentals of binary core-shells (Sec. 2), show how to generalize the problem by separation into geometric and material factors (Sec. 3), and investigate the modes of spheres (Sec. 4), ellipsoids (Sec. 5), and cuboids (Sec. 6) to test how the ellipsoid model responds to shape perturbation.

2. Ellipsoid core-shell theory

Equation (2) determines the relationship between geometry and permittivity, and the metal permittivity pairs relate this to the excitation frequency. The physical bounds 0f1 dictate the limits of the regions of resonant permittivities, and since there are two modes each bound results in two bounds on permittivity. The resulting limits are summarized in Table 1

Table 1. Limiting cases for confocal core-shell resonances

table-icon
View This Table
. The strength of the resonance can be determined by considering Eq. (3). The polarizability falls to zero on two of the bounds in Table 1. Further, each material contributes to damping of the resonance through the imaginary part of the permittivity, however these contributions are modulated by the environment. On two of the bounds only one material contributes to damping through its imaginary permittivity.

The combinations of resonant permittivities can be further elaborated by plotting the bounds from Table 1 in core & shell permittivity space; the specific result for spheres (L = 1/3) is shown in Fig. 1
Fig. 1 Optimum fill factor for spherical core-shells (cyan f = 0, magenta f = 1) predicted by Eq. (2) as a function of the core and shell permittivities. Symmetric modes are labelled + + , all others are antisymmetric. Labels CSzd are bounds listed in Table 1. The black lines are K-Al core-shell (solid), and Al-K core-shell (dotted). The black dots are those predicted by Eq. (2) when f = 0, 1/4, 1/2, 3/4, 1.
. There are five resonant regions, which can be accessed through different combinations of materials. Dielectrics have relatively constant permittivityε>1. Metals typically have highly dispersive permittivityε: at low frequencies (where metals are conductors) ε<<0, but at higher frequencies ε~0 (characteristic of plasma). The lower right region of Fig. 1 corresponds to a metal sphere embedded in a dielectric shell and is therefore of limited interest here. The upper left region contains metal shells with dielectric cores as previously studied (would be represented horizontal lines on Fig. 1). In addition, the middle-left region contains combinations that would be best described as conductor shell, plasma core. Conversely, the lower-center region contains plasma shell, conductor core.

Notably, materials with substantially different plasma frequencies trace lines with high or low slope on Fig. 1, and have maximum overlap with the interesting regions where one material is in the conducting regime and the other is near the plasma frequency. In general, the combination with the higher plasma frequency in the shell (low-slope, upper-left Fig. 1) has a charge-symmetric resonance which avoids the zero-strength resonance limits indicated in Table 1, and allows the widest frequency range. This resonance runs from the sphere limit of the core (thin shell “C”) to the sphere limit of the shell (thick shell “S”). There is also a high frequency mode that is anti-symmetric. The opposite combination of low-plasma frequency in the shell (high-slope, lower right in Fig. 1) has two modes that are both anti-symmetric, and are affected by shielding effects near “z” and “d”.

3. Eigenmode method

We now turn our attention to the more general problem of core-shell resonances of arbitrary shapes. The electrostatic response can be written as a generic matrix equation
α=X[γΩ]1E
(4)
In this article the measured quantityαis polarizability, which is important in a number of experimental for example the optical absorption is proportional to the imaginary part. Other measurable quantities can be substituted [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

] but we will not consider them here. The row-vector detection (e.g. dipole) operator Xmeasures an induced field (e.g. surface charge), which is related to material permittivities by the diagonal factorγ, geometric interaction matrix Ω, and the column vector excitation field E (e.g. normal electric field). In this work E is consistent with plane-wave excitation typically used in optical spectroscopy. In principle all of these quantities could be calculated using any electrostatic solution method, but we have found it convenient to use a surface integral approach [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

, 21

21. I. D. Mayergoyz, D. R. Fredkin, and Z. Y. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]

]. In that case X is simply the dipole-moment operator written in terms of surface charge, Ω is the surface charge interaction term, and E is the normal component of the electric excitation at the surface [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

]. Our implementation has been verified against Eq. (1) for spherical and confocal ellipsoid shells, and it was tested for solid cuboids elsewhere [26

26. M. B. Cortie, F. G. Liu, M. D. Arnold, and Y. Niidome, “Multimode resonances in silver nanocuboids,” Langmuir 28(24), 9103–9112 (2012). [CrossRef] [PubMed]

] using both literature values for modes and absorption spectra from the discrete dipole method.

Eigenmode decomposition of Eq. (4) is a useful tool for understanding how modes of the system contribute to observed behavior such as absorption. In unary metal systems the material factor γ is spatially invariant which enables trivial separation of the inversion (for example in multilayered spherical shells [24

24. C. E. Román-Velázquez and C. Noguez, “Designing the plasmonic response of shell nanoparticles: Spectral representation,” J. Chem. Phys. 134(4), 044116 (2011). [CrossRef] [PubMed]

]), however in binary metal systems this is not true. Instead, it is helpful to partition the matrix equation to highlight the different interfaces between materials, each with an associated value of the material factor which we define as
γI=12εc+εsεcεsγO=12εs+εbεsεb
(5)
There are at least two potential approaches to decomposition of modes: one is to write the problem in terms of modes of the system of interfaces [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

], the other is to use interaction of interface modes. We adopt the latter approach here as we find it easier to reconcile with the hybridization approach adopted for unary metal shells [22

22. E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004). [CrossRef] [PubMed]

, 27

27. D. W. Brandl and P. Nordlander, “Plasmon modes of curvilinear metallic core/shell particles,” J. Chem. Phys. 126(14), 144708 (2007). [CrossRef] [PubMed]

]. The advantage of this technique is that it allows us to separate geometric factors from material factors, and to determine results in terms of single interfaces that are easier to calculate. We first determine the eigenvalues Γand eigenvectors Qof each interface separately (I = inner, O = outer), for example:
QIΓI=ΩIQI.
(6)
It can be shown that the eigenvalues should be real, but that the eigenvectors are not necessarily orthogonal [28

28. O. Y. Feng and M. Isaacson, “Surface-plasmon excitation of objects with arbitrary shape and dielectric-constant,” Philos. Mag. B 60, 481–492 (1989).

]. The modes of Eq. (6) can be used as a new basis for the coupled system,
Q=[QIQo],
(7)
implying projection of the sourceEQ1E, the interaction ΩQ1ΩQ, and the detection operator XXQ. The material factor γis unchanged from Eq. (5).

The utility of the decomposition outlined in Eqs. (6) and (7) is that it represents the interaction in terms of separate interface modes, which depend only on geometry and are independent of material. The diagonal blocks of the new Ωare the uncoupled eigenvalues Γwhich are directly connected to depolarization factors often used to conveniently represent the effect of geometry. The off-diagonal blocks of the new Ω represent interface mode coupling which is also geometry dependent, and is sensitive to the overall separation between interfaces. We can gain further insight if we consider coupling between sole modes on each of the interfaces. This approach has been used previously to derive an implicit expression for the resonant permittivity of spheroidal shells [29

29. I. D. Mayergoyz and Z. Zhang, “Numerical analysis of plasmon resonances in metallic nanoshells,” IEEE Trans. Magn. 43(4), 1689–1692 (2007). [CrossRef]

]: here we additionally develop explicit expressions for the mode strengths and in later sections explore the implications of metallic cores and other shapes (cuboids). This dipole-dipole hybridization approach is particularly useful because it is the most fundamental interaction in core-shell systems and dominates many experimental observations. Consideration of Eqs. (4)(7) shows that singly hybridized modes are given by:
α=CII(γOΩOO)+COIΩOI+CIOΩIO+COO(γIΩII)(γOΩOO)(γIΩII)ΩOIΩIO
(8)
where the terms in Eq. (7) for coupling of modes to external fields are given by expressions such as
CIO=XIEO.
(9)
It should be noted that the individual cross terms in Eq. (8) are sensitive to the details of the mode representation, so only combinations such as COIΩOI+CIOΩIO and ΩOIΩIOare comparable between different methods. The first expression represents the accumulated effect of external coupling in through one surface and out through the other (affecting the strength of absorption of coupled modes), and the second expression represents the combined interaction between inner and outer surfaces (affecting the spectral position of coupled modes). It is worth noting that that this eigenmode method could also be applied to externally coupled binary systems [18

18. Y. Gu, J. Li, O. J. F. Martin, and Q. H. Gong, “Controlling plasmonic resonances in binary metallic nanostructures,” J. Appl. Phys. 107(11), 114313 (2010). [CrossRef]

] (i.e. separate particles), but we only investigate internally coupled particles (i.e. core-shells) in this article.

Equation (8) has complex poles that can be used to analyze mode position and absorption strength in the limit of low material losses inγ. Mode position is determined by the characteristic equation in the denominator, and absorption strength is given by the residue which can be approximated via the real part of the numerator divided by the imaginary part of the denominator. In general the mode parameters cannot be determined analytically, however the known analytical result for ellipsoids, Eq. (1), yields the following terms:
CII=fVCOO=V
(10)
COIΩOI+CIOΩIO=fV(12Ls)
(11)
ΩI=1/2LcΩO=1/2LsΩOIΩIO=fLs(1Ls)
(12)
Equations (10)(12) agree with our numerical method and indicate the fundamental scaling of physical interactions with respect to the fill factor. We now test this approach as a semi-analytic framework for understanding general core-shell resonances, starting with spheres and then progressing from spheroids to cuboids.

4. Sphere resonances

To illustrate a combination of real materials with suitably different plasma frequencies, combinations of K (low plasma frequency 3.9eV) and Al (high plasma frequency 15eV) have been overlaid on Fig. 1. Although it might be argued that K is difficult to work with, we use it as an example to demonstrate the exceptional tuning range that is possible with widely differing plasma frequencies, and to clearly distinguish resonances. We interpolated the dielectric function of these materials from published experimental Tables [30

30. J. H. Weaver and H. P. R. Frederikse, “Optical properties of selected elements,” in CRC Handbook (CRC, 2001).

]. The maximum resonance is also plotted in terms of frequency below in Fig. 2
Fig. 2 Absorption maxima of (a) K-Al and (b) Al-K spherical core-shells in free-space. The colored spectra are Eq. (1), at fill factors equally spaced from f = 0 (cyan) to f = 1 (magenta), the dots are the corresponding discrete peaks from Eqs. (2) and (3), and the heavy black line is the path of peaks predicted by Eq. (3). Labels CSzd are bounds listed in Table 1, and the paths are the same as those in Fig. 1.
, together with the electric field in Fig. 3
Fig. 3 Resonant electric dipole fields of (a) K-Al and (b) Al-K core-shells. The fields are calculated at resonance on surfaces, and all are directed normal to the surfaces and parallel to the direction of the excitation field. This is the maximum field on most surfaces except for inside the K-Al shell. The external surface (black), inner and outer shell surfaces (dotted), and core fields are shown. These are consistent with equivalent surface charges, which are symmetric in (a) and antisymmetric in (b). The anti-symmetry is stronger in the lower frequency mode.
. Figure 2 confirms that Eq. (3) is accurate for these materials because it closely matches individual spectral for discrete fill-factors that were calculated using Eq. (1). We verified that these spectra are consistent with the limiting cases of solid spheres (see Table 1), and agree with the numerical method [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

, 21

21. I. D. Mayergoyz, D. R. Fredkin, and Z. Y. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]

] that we use later. K has exceptionally low loss and the combined K-Al resonance is blue-shifted relative to the main resonance of K-only shells, so this combination achieves stronger resonances than most single-metal shells (except Na). As noted above, the combination with K on the inside results in the broadest resonance.

Figure 3 shows the resonant dipole fields on various surfaces - these fields were verified using full vector spherical harmonics [23

23. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).

]. Figure 3(a) confirms that in this case absorption is dominated by the core at low frequency (strong electric field), and the shell at high frequency (outer and largest volume). Note the similarity between the external field and the absorption.

5. Spheroid resonances

Ellipsoidal core-shells offer further tuning possibilities, which has been previously demonstrated for dielectric cores [31

31. H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006). [CrossRef] [PubMed]

], and here we show how our theory applies to some spheroids with metal cores. Specifically, we compare the resonances of K-Al and Al-K core-shells where the outer boundary is the prolate spheroid with aspect ratio of 2 and the excitation is perpendicular to the axis of rotation. Discrete spectra were calculated using a numerical method (boundary elements [20

20. F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

, 21

21. I. D. Mayergoyz, D. R. Fredkin, and Z. Y. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]

]). Figure 4
Fig. 4 Resonances of prolate spheroid core-shells, outer aspect ratio 2 with confocal core, excited perpendicular to the rotation axis. The colored lines were calculated at fill factors f = 0, ¼, ½, ¾, 1 as indicated by the overlaid sketches. These are the full numerical results and have been verified against Eq. (1). The resonance predicted by earlier equations is overlaid in black, using depolarization fixed to that of the outer. The black dots are the discrete maxima predicted by Eqs. (2) and (3) using the same fill-factors as the colored lines. The black line is the path of the maxima predicted by Eq. (3). (a) is K in Al, (b) is Al in K.
shows the confocal result (which was verified against Eq. (1)), and Fig. 5
Fig. 5 Resonances of prolate spheroid core-shells of aspect ratio 2 excited perpendicular to the rotation axis, at various fill factors. The colored lines are full numerical results for the sequence f = 0, 1/4, 1/2, 3/4, 1, as indicated by the overlaid sketches. The black dots are the corresponding peaks predicted by Eqs. (2) and (3). The black line is the path of the peaks predicted by Eq. (3). (a) is K in Al, (b) is Al in K.
shows the result when the core has the same shape as the outer surface. In both cases the predicted maximum has been overlaid assuming that the core depolarization factor is equal to the outer (Eqs. (2) and (3)).

4.1 Confocal spheroids

There is relatively good agreement for the results presented here because the confocal core does not change depolarization much compared to the shell. This means that the confocal core can be adequately approximated by assuming that the depolarization of the core is fixed to the outer, as demonstrated by the good agreement between exact and model results (Fig. 4). In general, for other orientations and shapes, mismatch between confocal and fixed depolarization is quite substantial, especially near f = 0, however modes are not uniformly affected. Confocal resonances that are spectrally distant from the deviating resonance of the core-shell interface (the “d”-bound in Table 1) are less affected: these include prolate parallel and oblate perpendicular K in Al, and oblate parallel low frequency Al in K.

4.2 Self-similar spheroids

When the core is the same shape as the outer surface, correct prediction of uncoupled dipoles is simplified due to fixed core, but there is some mode splitting because the dipole fields of the core and shell are no longer confocal. However, in the prolate perpendicular case shown in Fig. 5, the deviation is minimal due to the nearly confocal core.

Sensitivity to mode mixing is dependent on shape and polarization, in a similar way to the sensitivity of confocal modes to core deviation, with the exception of improvement in the high-frequency Al-in-K. This mode (which lies between “C” and “d” resonances) is dominated by the core, so it is insensitive to mode-mixing and its prediction is significantly improved by fixing the core. In contrast, low frequency Al-in-K prolate parallel (Fig. 6(b)
Fig. 6 Resonance maps in dual permittivity space (imaginary permittivities fixed at 0.1), for self-similar spheroid core-shells with fill factor f = 0.5, aspect ratio 2 and 0.5, and polarization perpendicular and parallel to the axis of revolution: (a) prolate perpendicular (b) prolate parallel (c) oblate perpendicular (d) oblate parallel. Bright colors indicate resonance, blue lines are the dipole-dipole prediction, solid black line is K-in-Al and dashed black line is Al-in-K.
) and oblate perpendicular (Fig. 6(c)) show particularly strong mixing due to proximity of a multipole mode. The maps presented in Fig. 6 assist predictions about the likely accuracy of the dipole-dipole model for other material combinations. Dipole-dipole resonances that have both spatial and spectral overlap with multipoles are likely to be affected by splitting. The maps indicate that there is also strong mixing for zero-zero core-shell permittivity for prolate perpendicular / oblate modes.

In summary, the model works well for spheroids when the core depolarization does not change much with fill factor or the core shape is nearly confocal. In other cases, agreement varies depending on remoteness from the confocal core-shell interface resonance or same-shape multipole modes.

6. Cuboid resonances

Cuboids are known to exhibit multiple modes, making them a useful test-case for the ideas presented in this article. Previously we have found that for relatively rounded (unary) cuboids the dipole dominates, with the quadrupole and face modes appearing only weakly [26

26. M. B. Cortie, F. G. Liu, M. D. Arnold, and Y. Niidome, “Multimode resonances in silver nanocuboids,” Langmuir 28(24), 9103–9112 (2012). [CrossRef] [PubMed]

]. We will compare how the internal and external coupling parameters of a cuboid vary with fill-factor compared to ellipsoids (Fig. 7
Fig. 7 Resonance parameters of cuboids with roundness exponent p = 0.5. Internal interaction parameters are in (a) and external coupling strengths are in (b). Blue and green are the core and shell respectively, red is the core-shell coupling product, and cyan is the special cross-coupling term given by Eq. (11). Markers are the numerical result; the lines are a generalization of the ellipsoid model where the relevant parameters of the outer shape have been substituted.
), and test how well a dipole-dipole hybridization model can predict absorption in a K-Al system (Fig. 8
Fig. 8 Resonances of cuboids with roundness exponent p = 0.5. The analytic ellipsoid model with numerical coupling factors is overlaid in black. (a) is K in Al, (b) is Al in K.
).

First looking at the coupling parameters, we generalize the ellipsoid model by substituting relevant parameters from the outer cuboid (i.e. using the numerical cuboid value of L, and replacing V with COO). Figure 7 shows that there is very good agreement except for minor deviation in the cross-coupling terms. This is perhaps to be expected because the near-field of the dipole of a cuboid is unlikely to scale confocally. Despite this minor error, we now use the model dipole-dipole parameters as inputs to the ellipsoidal maximum model for comparison with numerical resonance results (Fig. 8). Multimode splitting is clearly evident, which notably spreads the low energy anti-symmetric Al-in-K resonances in Fig. 8(b). However, there is reasonable agreement with the symmetric K-in-Al resonance in Fig. 8(a).

Further evidence for the effect of mode-mixing is presented in Fig. 9
Fig. 9 Resonance map in dual permittivity space (imaginary permittivities fixed at 0.1), for moderately rounded cuboid core-shell with fill-factor f = 0.5 and roundness p = 0.5. Bright colors indicate resonance, blue lines are the dipole-dipole prediction, solid black line is K-in-Al and dashed black line is Al-in-K.
, which shows that the region with the shell more negative (i.e. K-in-Al) is least affected. In general we would expect the accuracy of the ellipsoidal model to decline further as the cuboid sharpens (p→0) and higher order modes become dominant: further calculations show that in fact the conclusions drawn from Fig. 8 also apply to p = 0.2 and p = 0.1 (which is a relatively hard-edged cuboid), as the differences observed are only moderately enhanced.

7. Conclusion

In conclusion we have shown how to predict the ideal limit of resonances of bimetallic ellipsoidal core-shells, and used this to investigate some of the possibilities of this geometry. In particular we found that some resonances of shapes that are nearly ellipsoidal can be reliably approximated by an ellipsoid model parameterized via the fill-factor: these resonances include spheres (exact), prolate spheroids excited perpendicular to the rotation axis, and well-rounded cuboids. We found that operating near the plasma frequency of the core enables continuous tuning over a range that is not accessible if the core is dielectric. The permittivities and charge symmetry of this mode mean that damping is surprisingly weak and thus resonance strength is maintained relatively well. Ideally the materials should be both free-electron-like and have very different plasma frequencies to allow a wide tuning range. Achieving this type of combination will require some care, but the general idea of using plasma regime of a metal to tune resonances allows additional choice, and other multi-metal geometries should be investigated further.

Acknowledgments

We acknowledge useful conversations with Michael Cortie, and use of the UTS high performance computer.

References and links

1.

M. D. Arnold and M. G. Blaber, “Optical performance and metallic absorption in nanoplasmonic systems,” Opt. Express 17(5), 3835–3847 (2009). [CrossRef] [PubMed]

2.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22(14), 143201 (2010). [CrossRef] [PubMed]

3.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Optical properties of intermetallic compounds from first principles calculations: a search for the ideal plasmonic material,” J. Phys. Condens. Matter 21(14), 144211 (2009). [CrossRef] [PubMed]

4.

M. B. Cortie and A. M. McDonagh, “Synthesis and optical properties of hybrid and alloy plasmonic nanoparticles,” Chem. Rev. 111(6), 3713–3735 (2011). [CrossRef] [PubMed]

5.

L. Feng, G. Gao, P. Huang, K. Wang, X. Wang, T. Luo, and C. Zhang, “Optical properties and catalytic activity of bimetallic gold-silver nanoparticles,” Nano Biomed. Eng. 2, 258–267 (2010).

6.

P. Mulvaney, M. Giersig, and A. Henglein, “Electrochemistry of multilayer colloids - preparation and absorption-spectrum of gold-coated silver particles,” J. Phys. Chem. 97(27), 7061–7064 (1993). [CrossRef]

7.

M. Moskovits, I. Srnova-Sloufova, and B. Vlckova, “Bimetallic Ag-Au nanoparticles: Extracting meaningful optical constants from the surface-plasmon extinction spectrum,” J. Chem. Phys. 116(23), 10435–10446 (2002). [CrossRef]

8.

X. Wang, Z. Y. Zhang, and G. V. Hartland, “Electronic dephasing in bimetallic gold-silver nanoparticles examined by single particle spectroscopy,” J. Phys. Chem. B 109(43), 20324–20330 (2005). [CrossRef] [PubMed]

9.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

10.

D. J. Wu, X. D. Xu, and X. J. Liu, “Electric field enhancement in bimetallic gold and silver nanoshells,” Solid State Commun. 148(3-4), 163–167 (2008). [CrossRef]

11.

C. E. Román-Velázquez, C. Noguez, and J. Z. Zhang, “Theoretical study of surface plasmon resonances in hollow gold-silver double-shell nanostructures,” J. Phys. Chem. A 113(16), 4068–4074 (2009). [CrossRef] [PubMed]

12.

J. Zhu, “Surface plasmon resonance from bimetallic interface in Au-Ag core-shell structure nanowires,” Nanoscale Res. Lett. 4(9), 977–981 (2009). [CrossRef] [PubMed]

13.

R. Jiang, H. Chen, L. Shao, Q. Li, and J. Wang, “Unraveling the evolution and nature of the plasmons in (Au Core)-(Ag Shell) nanorods,” Adv. Mater. 24(35), OP200–OP207 (2012). [CrossRef] [PubMed]

14.

L. Raguin, C. Hafner, and P. Leuchtmann, “Boundary integral equation method for the analysis of tunable light scattering properties of plasmonic core-shell nanoparticles,” J. Comput. Theor. Nanosci. 8(8), 1590–1599 (2011). [CrossRef]

15.

G. Park, C. Lee, D. Seo, and H. Song, “Full-color tuning of surface plasmon resonance by compositional variation of Au@Ag core-shell nanocubes with sulfides,” Langmuir 28(24), 9003–9009 (2012). [CrossRef] [PubMed]

16.

L. Chuntonov, M. Bar-Sadan, L. Houben, and G. Haran, “Correlating electron tomography and plasmon spectroscopy of single noble metal core-shell nanoparticles,” Nano Lett. 12(1), 145–150 (2012). [CrossRef] [PubMed]

17.

U. K. Chettiar and N. Engheta, “Internal homogenization: Effective permittivity of a coated sphere,” Opt. Express 20(21), 22976–22986 (2012). [CrossRef] [PubMed]

18.

Y. Gu, J. Li, O. J. F. Martin, and Q. H. Gong, “Controlling plasmonic resonances in binary metallic nanostructures,” J. Appl. Phys. 107(11), 114313 (2010). [CrossRef]

19.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009). [CrossRef]

20.

F. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]

21.

I. D. Mayergoyz, D. R. Fredkin, and Z. Y. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]

22.

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004). [CrossRef] [PubMed]

23.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).

24.

C. E. Román-Velázquez and C. Noguez, “Designing the plasmonic response of shell nanoparticles: Spectral representation,” J. Chem. Phys. 134(4), 044116 (2011). [CrossRef] [PubMed]

25.

M. D. Arnold, M. G. Blaber, M. J. Ford, and N. Harris, “Universal scaling of local plasmons in chains of metal spheres,” Opt. Express 18(7), 7528–7542 (2010). [CrossRef] [PubMed]

26.

M. B. Cortie, F. G. Liu, M. D. Arnold, and Y. Niidome, “Multimode resonances in silver nanocuboids,” Langmuir 28(24), 9103–9112 (2012). [CrossRef] [PubMed]

27.

D. W. Brandl and P. Nordlander, “Plasmon modes of curvilinear metallic core/shell particles,” J. Chem. Phys. 126(14), 144708 (2007). [CrossRef] [PubMed]

28.

O. Y. Feng and M. Isaacson, “Surface-plasmon excitation of objects with arbitrary shape and dielectric-constant,” Philos. Mag. B 60, 481–492 (1989).

29.

I. D. Mayergoyz and Z. Zhang, “Numerical analysis of plasmon resonances in metallic nanoshells,” IEEE Trans. Magn. 43(4), 1689–1692 (2007). [CrossRef]

30.

J. H. Weaver and H. P. R. Frederikse, “Optical properties of selected elements,” in CRC Handbook (CRC, 2001).

31.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics

ToC Category:
Plasmonics

History
Original Manuscript: September 6, 2013
Revised Manuscript: December 17, 2013
Manuscript Accepted: December 18, 2013
Published: February 4, 2014

Citation
Matthew Arnold, Martin Blaber, and Mike Ford, "Local plasmon resonances of metal-in-metal core-shells," Opt. Express 22, 3186-3198 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-3186


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. D. Arnold, M. G. Blaber, “Optical performance and metallic absorption in nanoplasmonic systems,” Opt. Express 17(5), 3835–3847 (2009). [CrossRef] [PubMed]
  2. M. G. Blaber, M. D. Arnold, M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22(14), 143201 (2010). [CrossRef] [PubMed]
  3. M. G. Blaber, M. D. Arnold, M. J. Ford, “Optical properties of intermetallic compounds from first principles calculations: a search for the ideal plasmonic material,” J. Phys. Condens. Matter 21(14), 144211 (2009). [CrossRef] [PubMed]
  4. M. B. Cortie, A. M. McDonagh, “Synthesis and optical properties of hybrid and alloy plasmonic nanoparticles,” Chem. Rev. 111(6), 3713–3735 (2011). [CrossRef] [PubMed]
  5. L. Feng, G. Gao, P. Huang, K. Wang, X. Wang, T. Luo, C. Zhang, “Optical properties and catalytic activity of bimetallic gold-silver nanoparticles,” Nano Biomed. Eng. 2, 258–267 (2010).
  6. P. Mulvaney, M. Giersig, A. Henglein, “Electrochemistry of multilayer colloids - preparation and absorption-spectrum of gold-coated silver particles,” J. Phys. Chem. 97(27), 7061–7064 (1993). [CrossRef]
  7. M. Moskovits, I. Srnova-Sloufova, B. Vlckova, “Bimetallic Ag-Au nanoparticles: Extracting meaningful optical constants from the surface-plasmon extinction spectrum,” J. Chem. Phys. 116(23), 10435–10446 (2002). [CrossRef]
  8. X. Wang, Z. Y. Zhang, G. V. Hartland, “Electronic dephasing in bimetallic gold-silver nanoparticles examined by single particle spectroscopy,” J. Phys. Chem. B 109(43), 20324–20330 (2005). [CrossRef] [PubMed]
  9. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  10. D. J. Wu, X. D. Xu, X. J. Liu, “Electric field enhancement in bimetallic gold and silver nanoshells,” Solid State Commun. 148(3-4), 163–167 (2008). [CrossRef]
  11. C. E. Román-Velázquez, C. Noguez, J. Z. Zhang, “Theoretical study of surface plasmon resonances in hollow gold-silver double-shell nanostructures,” J. Phys. Chem. A 113(16), 4068–4074 (2009). [CrossRef] [PubMed]
  12. J. Zhu, “Surface plasmon resonance from bimetallic interface in Au-Ag core-shell structure nanowires,” Nanoscale Res. Lett. 4(9), 977–981 (2009). [CrossRef] [PubMed]
  13. R. Jiang, H. Chen, L. Shao, Q. Li, J. Wang, “Unraveling the evolution and nature of the plasmons in (Au Core)-(Ag Shell) nanorods,” Adv. Mater. 24(35), OP200–OP207 (2012). [CrossRef] [PubMed]
  14. L. Raguin, C. Hafner, P. Leuchtmann, “Boundary integral equation method for the analysis of tunable light scattering properties of plasmonic core-shell nanoparticles,” J. Comput. Theor. Nanosci. 8(8), 1590–1599 (2011). [CrossRef]
  15. G. Park, C. Lee, D. Seo, H. Song, “Full-color tuning of surface plasmon resonance by compositional variation of Au@Ag core-shell nanocubes with sulfides,” Langmuir 28(24), 9003–9009 (2012). [CrossRef] [PubMed]
  16. L. Chuntonov, M. Bar-Sadan, L. Houben, G. Haran, “Correlating electron tomography and plasmon spectroscopy of single noble metal core-shell nanoparticles,” Nano Lett. 12(1), 145–150 (2012). [CrossRef] [PubMed]
  17. U. K. Chettiar, N. Engheta, “Internal homogenization: Effective permittivity of a coated sphere,” Opt. Express 20(21), 22976–22986 (2012). [CrossRef] [PubMed]
  18. Y. Gu, J. Li, O. J. F. Martin, Q. H. Gong, “Controlling plasmonic resonances in binary metallic nanostructures,” J. Appl. Phys. 107(11), 114313 (2010). [CrossRef]
  19. M. G. Blaber, M. D. Arnold, M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009). [CrossRef]
  20. F. García de Abajo, J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56(24), 15873–15884 (1997). [CrossRef]
  21. I. D. Mayergoyz, D. R. Fredkin, Z. Y. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]
  22. E. Prodan, P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004). [CrossRef] [PubMed]
  23. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).
  24. C. E. Román-Velázquez, C. Noguez, “Designing the plasmonic response of shell nanoparticles: Spectral representation,” J. Chem. Phys. 134(4), 044116 (2011). [CrossRef] [PubMed]
  25. M. D. Arnold, M. G. Blaber, M. J. Ford, N. Harris, “Universal scaling of local plasmons in chains of metal spheres,” Opt. Express 18(7), 7528–7542 (2010). [CrossRef] [PubMed]
  26. M. B. Cortie, F. G. Liu, M. D. Arnold, Y. Niidome, “Multimode resonances in silver nanocuboids,” Langmuir 28(24), 9103–9112 (2012). [CrossRef] [PubMed]
  27. D. W. Brandl, P. Nordlander, “Plasmon modes of curvilinear metallic core/shell particles,” J. Chem. Phys. 126(14), 144708 (2007). [CrossRef] [PubMed]
  28. O. Y. Feng, M. Isaacson, “Surface-plasmon excitation of objects with arbitrary shape and dielectric-constant,” Philos. Mag. B 60, 481–492 (1989).
  29. I. D. Mayergoyz, Z. Zhang, “Numerical analysis of plasmon resonances in metallic nanoshells,” IEEE Trans. Magn. 43(4), 1689–1692 (2007). [CrossRef]
  30. J. H. Weaver and H. P. R. Frederikse, “Optical properties of selected elements,” in CRC Handbook (CRC, 2001).
  31. H. Wang, D. W. Brandl, F. Le, P. Nordlander, N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited