We propose a new solution for high hot–spot density creation by coupling a particle and a cavity in a structure dubbed a plasmonic enhanced particle–cavity (PEP–C) antenna. In comparison to analogous particle–based dimer antenna structures, the PEP–C allows both a higher maximum field and an order–of–magnitude higher hot–spot density. In addition, the hot–spots of the PEP–C antenna can be precisely controlled, resulting in increased reliability. We elucidate the photonic characteristics of the PEP–C antenna and show tuning and optimization through choice of geometric parameters. These properties make the PEP–C antenna an excellent candidate for plasmonic–based biomolecular sensors.
© 2009 Optical Society of America
Despite much interest in recent years, nanoparticle plasmonic probes have yet to find widespread commercial application as molecular sensors. While recently much attention has been paid to maximizing the local electromagnetic fields surrounding metallic nanoparticles and substrates in the hope of increasing molecular sensitivity [1, 2, 3, 4, 5, 6, 7], increasing the density of locally enhanced regions has been generally neglected, and may be at least as important in achieving sensitive and reliable devices. If a molecule is to be detected using such plasmon–based techniques as surface enhanced Raman spectroscopy (SERS) , surface enhanced fluorescence , local surface plasmon resonance (LSPR) shift , or plasmon resonance energy transfer (PRET) , then the important question may not be solely the strength of the localized field, but the probability that a molecule will occupy a region of enhancement. If a molecule can be thought analogous to a fish in a lake, then the more hooks, the better the chance of a catch.
A major focus of plasmonic antennae recently has been on particle–particle interactions [12, 13, 14, 15] and sharp–tip structures [2, 16, 17]. Such antenna can produce extremely high localized electromagnetic fields (hot–spots), resulting in molecular sensitivities up the level of single molecule detection . However to date, large scale reliable single molecule nanoparticle–based plasmonic detection remains elusive. We suggest two issues have limited progress: i) detection regions are limited to the sparsely (and often randomly) distributed hot– spot regions surrounding antenna and ii) hot–spots are critically dependent on the distance between two points or sharp–tip curvature of a structure, both of which are extremely difficult to control. These issues are intimately tied to fabrication limitations, as even nanometer–sized tolerances can cause large fluctuations in local field intensity, and the most precise fabrication approaches (e.g. electron–beam lithography) are typically not amenable to large–scale fabrication and cannot generate nanogap features less than 3nm.
Increasing the density of hot–spots has the potential to achieve both increased sensitivity, because more regions are available to detect molecules, and reliability, since the tolerance of a particular hot–spot becomes less critical for device functionality. However, increasing hot–spot density requires a paradigm shift in the plasmonic architectures that have been proposed. In this article, we propose that the plasmonic coupling between a plasmonic nanoparticle and a plasmonic mirror in a structure, which we call a plasmon enhanced particle–cavity (PEP–C), can provide significant increases in both hot–spot intensity and density. In addition, precise control of hot–spot geometry in the PEP–C antenna allows reproducible nanoarchitectures for high device reliability. We note that flat mirror and sandwich structures have been studied recently and shown to be powerful SERS substrates [19, 20, 21]; however these studies do not consider complementary geometries (the positive curvature of the particle and the negative curvature of the cavity) between a particle and cavity as studied here.
We illustrate the PEP–C antenna in Fig. 1. The structure can be defined geometrically by a particle of radius r, a spacer layer (which may be a dielectric) of thickness d, and an offset h of the particle–cavity centerline from the surface. In this study both the particle and the surface are considered to be gold, but in general either could be replaced with any plasmonic material. Because both cavities and nanoparticles can be made to self–assemble into arrays [22, 23], the PEP–C can be fabricated into large–areas entirely with “bottom–up” techniques and integrated into microfluidic chips, as illustrated in Fig. 1(b)–(c).
The basic unit of the PEP–C antenna consists of a truncated spherical void in a metallic surface, a spacer layer (which may be a dielectric), and a spherical nanoparticle. The geometry can be described mathematically using the particle radius r, spacer thickness d, and height of the nanoparticle–cavity centerline from the surface h. To create a physically relevant model, the sharp edge of the truncated spherical void is rounded with a 2nm radius of curvature, and we find that this parameter is not critical to the resonant modes and magnitude of local field enhancement.
We consider both the surface and the nanoparticle to be gold, with complex permittivity ε given by an analytical model  of the experimental data  for bulk gold, and with relative permeability μ= 1.
We consider both the surface and the nanoparticle to be gold, with complex permittivity ε given by an extention of the Drude model :
where ε ∞ = 1.53, λp = 145, γp = 17000, A 1 = 0.94, ϕ 1 = - π/4, λ 1 = 468, γ 1 = 2300, A 2 = 1.36, ϕ 2 = - π/4, A 2 = 331, and γ 2 = 940 to fit the experimental data for bulk gold . The relative permeability of gold is assumed to be μ = 1.
The PEP–C structure is assumed to be present in free–space (ε = μ = 1), and for generality the dielectric spacer layer is also assumed to have the properties of free–space. We define a linearly polarized plane wave incident on the structure at angle θ.
The complexity of the PEP–C geometry requires numerical solution, as no known analytic techniques are available. We developed a three–dimensional model using the commercial finite element software COMSOL. The software numerically solves over the domain of interest the time–harmonic Maxwell equations, which reduce to the Helmholtz equation . Scattering boundary conditions were used to eliminate nonphysical reflections at the domain boundaries. An adaptive mesh was used, and the mesh was refined until further refinements in element number or size of the domain did not cause changes in the result, verifying a converged model. We also verified our model in the limiting case of a single isolated sphere against the analytic Mie theory .
For the results presented below, we compute the surface–average local field enhancement as follows:
where S is the surface of the sphere, and herein the incident electric field is assumed to be |E 0| = 0. Since we are motivated by surface enhanced spectroscopies, where molecular interaction occurs in the near field and molecules may attached on any region of the nanoparticle surface, the surface average electric field is the most relevant measure of plasmon resonance.
3. Results and Discussion
The local electromagnetic fields surrounding the PEP–C antenna are significantly different from those in particle–particle or sharp–tip antennae, where high local fields derive from the gap between the closest points of two particles or at sharp tips. Because of the complimentary positive and negative curvature of the particle and cavity, respectively, in the PEP–C structure the plasmonic interaction occurs over a physically extended region, as shown in Fig. 2. The gold surfaces of the particle and cavity act as plasmonic mirrors, trapping the light in the curved nanogap region between them. The result is that the hot–spot extends through nearly the entire nanogap, causing the computed surface–average local field enhancement (|E|SA = 40) to be an order of magnitude larger than for gold particle dimers . Since the hot–spot regions are known to determine both LSPR shifts  and the enhancement factor for surface–enhanced spectroscopies such as SERS, the significant increase in hot–spot density should correspond to an increase in molecular sensitivity.
It is important to consider, does an increase in hot–spot density require a concomitant reduction in the maximum local intensity achievable? Ultimately, the total electromagnetic energy distributed throughout hot–spots must be limited by conservation of the incident energy. However, it is clear from Fig. 2 that this regime has not yet been reached: the maximum local electric field amplitude |E|max = 120, corresponding to a SERS electromagnetic enhancement of |E|4 max > 2×108 (achieved for λ = 700nm, r = 20nm, d = 2nm, h = θ = 0), is a 5–fold increase in SERS enhancement compared to a particle dimer with the same particle radius and gap distance at resonance. Thus, the PEP–C is clearly a more efficient antennae, as it can simultaneously attain both a higher maximum field and higher hot–spot density than a particle dimer.
We next consider the tunability of the PEP–C; namely, can the resonances be tuned by varying the geometric parameters? And which parameters are critical for achieving high field enhancement? Tunability is an essential characteristic of any plasmonic architecture designed for molecular detection: firstly, since tuning resonance to the “biological window” is necessary to prevent cellular damage, and secondly, because tuning to the vicinity of specific molecular resonances can create large increases in both SERS  and LSPR–shift  signals.
As the radius of the particle–cavity system is increased, while keeping a fixed spacer distance, the primary plasmon resonance peak is redshifted significantly (Fig. 3(a)). Unlike the redshift observed in isolated nanoparticles, the shift is quite sensitive to particle size, and does not significantly broaden as it is redshifted. Thus, the particle–cavity size presents a simple way to tune the plasmon resonance of the PEP–C into the near infrared (NIR) without a large loss in enhancement or the sharpness of the plasmon peak. The sharpness of the plasmon peak is critical for detecting a LSPR shift upon molecular binding .
The primary plasmon peak resonance is dipole–like, with opposite sides of the nanoparticle coupled to the corresponding sides of the cavity, as shown in Fig. 2. However, it is clear in Fig. 3(a) that as the PEP–C increases in size, multiple peaks emerge as the result of multipole resonance modes. We show schematically in Fig. 3(c) the dipole, tripole, and quadrapole resonant modes which cause the primary, secondary, and tertiary peaks, respectively. It is notable that these resonances exist for a relatively small PEP–C size; for example, such resonances would not be seen in an isolated nanoparticle of similar radius. The PEP–C structure thus allows the possibility of tuning to multiple resonances for multiplexed sensing while keeping the structure size small—keeping particle (and hot–spot) density high.
Each resonance peak can be further tuned by varying the thickness of the spacer layer d, as shown in Fig. 3(b). Decreasing the spacer causes a redshift in plasmon resonance and significant increase in local field enhancement, analogous to the effect shown in nanoparticle dimer systems . As with nanoparticle dimer and other nanogap systems, the magnitude of the local field enhancement, and hence the effectiveness of the device, depends strongly on controlling the spacer thickness. However, in the PEP–C structure, this spacer layer can be precisely controlled (e.g. by growth of an oxide layer). Furthermore, since the nanogap is not between two points, but two surfaces, there is greater tolerance in the PEP–C structure. As a result, we expect that the reliability of PEP–C antennae should be significantly higher than other plasmonic nanogap structures.
Each resonance is also affected by the location of the height of the particle–cavity centerline from the surface, with a redshift occurring as the centerline is lowered beneath the surface, as shown in Fig. 4(b). For the limiting case of the particle–cavity centerline above the surface with a distance h > r the cavity vanishes, resulting in a particle above a flat surface. In this case the particle and surface are only weakly coupled, and the plasmon resonance is dominated by the particle resonance, which for gold is between 500 – 600nm for small particles. The plasmon peak indeed approaches this value for h = 3r/4 in Fig. 4(b). As the particle–centerline is lowered beneath the surface, increased coupling between the particle and cavity causes a redshift in the plasmon peak and significant increase in the local field enhancement. However, the surface begins to prevent effective transfer of light into the coupled mode. In the limiting case, light would be completely reflected for a particle–cavity far below the surface. Hence, the optimal enhancement occurs for the centerline of the particle–cavity near the plane of the surface, in the regime 0 < h < -3r/4.
Finally, we investigated the effect of varying the angle of incidence, as shown in Fig. 4(c). We find that the local field enhancement systematically decreases as the incident angle is brought away from the normal. Because of its symmetry, the resonance of the spherical nanoparticle should have little dependence on the angle of incidence, but for the truncated cavity this is not the case. Indeed, it has been shown both experimentally and computationally that the strongest resonances of truncated spherical nanocavities occur for normal incidence . We note that normal incidence remains the optimal condition for PEP–C structures with h ≠ 0 as well.
We have introduced and optimized the PEP–C structure as a tunable plasmonic antenna. Because of its complementary geometry, PEP–C can achieve both higher maximum local field (|E|max = 120) and an order of magnitude higher hot–spot density (|E|SA = 40) than comparable particle dimer structures. Furthermore, precise control of hot–spot geometry in the PEP–C antenna allows for high device reliability. We have elucidated the multipole resonances of PEP–C, shown plasmon band tuning across the visible and near–infrared spectrum, and shown optimization of the structure through choice of geometric parameters. We believe PEP–C antennae can provide a significant step toward label–free sensitive and selective plasmonic sensors.
This work was funded by a NSF graduate research fellowship and DARPA support for SERS science and technology fundamentals.
References and links
1. D. K. Gramotnev, M. W. Vogel, and M. I. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys. 104, 034311 (2008). [CrossRef]
2. T. H. Taminiau, F. B. Segerink, R. J. Moerland, L. (K.) Kuipers, and N. F. Van Hulst, “Near–field driving of a optical monopole antenna,” J. Opt. A 9, S315–S321 (2007). [CrossRef]
3. V. Giannini and J. A. Sánchez-Gil, “Excitation and emission enhancement of single molecule fluorescence through multiple surface–plasmon resonances on metal trimer nanoantennas,” Opt. Lett. 33, 899–901 (2008). [CrossRef] [PubMed]
4. S. Chen, L. Han, A. Schülzgen, H. Li, L. Li, J. V. Moloney, and N. Peyghambarian, “Local electric field enhancement and polarization effects in a surface–enhanced Raman scattering fiber sensor with chessboard nanostructure,” Opt. Express 16, 13016–13023 (2008). [CrossRef] [PubMed]
7. L. Guerrini, J. V. Garcia-Ramos, C. Domingo, and S. Sanchez-Cortes, “Building highly selective hot spots in Ag nanoparticles using bifunctional viologens: application to the SERS detection of PAHs,” J. Phys. Chem. C 112, 7527–7530 (2008). [CrossRef]
8. K. Kneipp, M. Moskovits, and H. Kneipp (Eds.), Surface–Enhanced Raman Scattering: Physics and Applications (Springer, Germany, 2006). [CrossRef]
9. E. Fort and S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D. 41, 013001 (2008). [CrossRef]
10. K. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem. 58, 267–297 (2006). [CrossRef]
11. G. L. Liu, Y.-T. Long, Y. Choi, T. Kang, and L. P. Lee, “Quantized plasmon quenching dips nanospectroscopy via plasmon resonance energy transfer.” Nat. Methods 4, 1015–1017 (2007). [CrossRef] [PubMed]
13. Y. Lu, G. L. Liu, and L. P. Lee, “High–density silver nanoparticle film with temperature–controllable interparticle spacing for a tunable surface enhanced Raman scattering substrate,” Nano. Lett. 5, 5–9 (2005). [CrossRef] [PubMed]
14. I. Romero, J. Aizpurua, G. W. Bryant, and F. J. García de Abajo, “Plasmons in nearly touching metallic nanopar–ticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006). [CrossRef] [PubMed]
15. A. L. Lereu, G. Sanchez-Mosteiro, P. Ghenuche, R. Quidant, and N. F. Van Hulst, “Individual gold dimers investigated by far– and near–field imaging,” J. Microsc. 229, 254–258 (2008). [CrossRef] [PubMed]
16. H. G. Frey, F. Keilmann, A. Kriele, and R. Guckenberger, “Enhancing the resolution of scanning near–field optical microscopy by a metal tip grown on an aperture probe,” App. Phys. Lett. 81, 5030–5032 (2002). [CrossRef]
17. J. Merlein et al., “Nanomechanical control of an optical antenna,” Nature Photon. 2, 230–233 (2008). [CrossRef]
19. J. K. Daniels and G. Chumanov, “Nanoparticle–mirror sandwich substrates for surface–enhanced Raman scattering,” J. Phys. Chem. B 109, 17936–17942 (2005). [CrossRef]
21. C. J. Orendorff, A. Gole, T. K. Sau, and C. J. Murphy, “Surface–enhanced Raman spectroscopy of self–assembled monolayers: sandwich architecture and nanoparticle shape dependence,” Anal. Chem. 77, 3261–3266 (2009). [CrossRef]
22. V. Santhanam, J. Liu., R. Agarwal, and R. P. Andres, “Self-assembly of uniform monolayer arrays of nanoparticles,” Langmuir 19, 7881 (2003). [CrossRef]
23. Y. K. Hwang et al., “Palladium and gold nanoparticle array films formed by using self–assembly of block copolymer,” J. Nanosci. and Nanotechnol. 6, 1850 (2006). [CrossRef]
25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
26. J. D. Jackson, Classical Electrodynamics, 3rd Ed. (John Wiley & Sons, USA, 1999).
27. M. Born and E. Wolf, Principles of Optics, 4th Ed. (Permagon Press, Scotland, 1970).
29. A. J. Haes, S. Zou, G. C. Schatz, and R. P. Van Duyne, “Nanoscale optical biosensor: short range distance dependence of the localized surface plasmon resonance of noble metal nanoparticles,” J. Phys. Chem. B 108, 6961–6968 (2004). [CrossRef]
30. A. D. McFarland, M. A. Young, J. A. Dieringer, and R. P. Van Duyne, “Wavelength–scanned surface–enhanced Raman excitation spectroscopy,” J. Phys. Chem. B 109, 11279–11285 (2005). [CrossRef]
31. A. J. Haes, S. Zou, J. Zhao, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy near molecular resonances,” J. Am. Chem. Soc. 128, 10905–10914 (2006). [CrossRef] [PubMed]
32. Cole et al., “Understanding plasmons in nanoscale voids,” Nano. Lett. 7, 2094–2100 (2007). [CrossRef]