LETTER pubs.acs.org/NanoLett
On Chip Plasmonic Monopole Nano-Antennas and Circuits Ronen Adato, Ahmet A Yanik, and Hatice Altug* Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 St. Mary’s Street, Boston, Massachusetts 02215, United States
bS Supporting Information ABSTRACT: Analogues of many radio frequency (RF) antenna designs such as the half-wave dipole and Yagi-Uda have been successfully adapted to the optical frequency regime, opening the door for important advances in biosensing, photodetection, and emitter control. Examples of monopole antennas, however, are conspicuously rare given the element’s extensive use in RF applications. Monopole antennas are attractive as they represent an easy to engineer, compact geometry and are well isolated from interference due the ground plane. Typically, however, the need to orient the antenna element perpendicular to a semiinfinite ground plane requires a three-dimensional structure and is incompatible with chip-based fabrication techniques. We propose and demonstrate here for the first time that monopole antenna elements can be fashioned out of single element nanoparticles fabricated in conventional planar geometries by using a small nanorod as a wire reflector. The structure offers a compact geometry and the reflector element provides a measure of isolation analogous to the RF counterpart. This isolation persists in the conductive coupling regime, allowing multiple monopoles to be combined into a single nanoparticle, yet still operate independently. This contrasts with several previous studies that observed dramatic variations in the spectral response of conductively coupled particles. We are able to account for these effects by modeling the system using circuit equations from standard RF antenna theory. Our model accurately describes this behavior as well as the detailed resonance tuning of the structure. As a specific practical application, the monopole resonances are precisely tuned to desired protein absorption bands, thereby enhancing their spectroscopic signatures. Furthermore, the accurate modeling of conductive coupling and demonstrated electronic isolation should be of general interest to the design of complex plasmonic circuits incorporating multiple antennas and other current carrying elements. KEYWORDS: Plasmonics, nanoparticles, coupling, SEIRA, antennas, nanocircuits
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ptical and infrared antennas based on the resonances of noble metal nanoparticles enable the efficient conversion of propagating far-field radiation to highly localized and enhanced electromagnetic fields confined to subwavelength volumes.13 As this capability is not present in traditional optical elements limited by diffraction such as lenses and mirrors, they open the door for a number of exciting new applications. These include surface enhanced spectroscopies,412 ultracompact, highspeed photodetectors,13,14 and enhanced nonlinear processes.1517 In these applications, a variety of particle geometries have been used in order to achieve the desired antenna functionality. These include spherical nanoparticles,18 rod,19,20 and bowtie21 shapes. These particles all function essentially as half- or full-wave dipole antennas, supporting resonances characterized by charges driven to opposite ends of the structure or concentrated in a small feed gap by the incident electric field. The quarter wave monopole antenna is another common radio frequency (RF) structure,22 though analogous nanoparticle implementations are far less common. The one notable example is the incorporation of a rod-shaped nanoparticle onto the tip of a metal clad tapered fiber used as a near-field microscopy (NSOM) probe.23,24 In RF engineering practice, the monopole antenna has a number of attractive features. It is a compact element and intuitive r 2011 American Chemical Society
to engineer. Furthermore, the conducting ground plane acts to isolate the antenna element from those beneath it, simplifying the design of complex structures where the antenna is integrated with a number of other circuit elements. As a result, monopole antennas are commonly observed in everyday devices such as cell phones and radio towers. Despite its widespread adoption at radio frequencies, the need for a semi-infinite ground plane poses problems for implementing monopole antennas at optical frequencies. This is due primarily to the fact that most nanoparticle substrates, especially lithographically patterned ones, are essentially two-dimensional. An exact analogy with the RF structure would require a three-dimensional (3D) structure. This occurred naturally in refs 23 and 24, where a metal-coated fiber surface acted as a ground plane, and also can be obtained in some more exotic fabrication methods25 but is typically not compatible with standard fabrication schemes. In this work, we show that quarter wave monopole antenna elements can in fact be fashioned out of single element nanoparticles in conventional planar geometries. We accomplish this Received: July 24, 2011 Revised: November 3, 2011 Published: November 28, 2011 5219
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Nano Letters by using a long bar oriented perpendicular to our antenna element as a nanoreflector. This planar antenna element along with the single nanoscale wire reflector on which it relies represents a significant departure from the typical RF design and previous implementations at optical frequencies. As such we analyze in detail the properties of isolated elements as well as its impedance characteristics relevant to its electrical connection to other plasmonic circuitry. The enabling functionality of the reflector is demonstrated in that it allows for compact device fabrication and acts in a manner similar to a ground plane to isolate the antenna. This is demonstrated by designing a double monopole structure capable of supporting two broadly tunable resonances associated with the different elements. Uniquely, we observe that the reflector element not only provides the expected near-field isolation, but also offers a measure of electrical isolation when the antennas are conductively coupled. This unexpected effect is accounted for by considering current flow in between the excited antenna arms and the reflector within the framework of circuit theory. In doing so we develop a model that accurately predicts the behavior of our coupled antenna system over a wide range of frequencies and geometrical parameters. Finally, we leverage the ability to accurately engineer our monopole resonances by demonstrating surface-enhanced infrared absorption spectroscopy (SEIRA) on adsorbed protein monolayers. In this application, the precise tuning of the plasmonic antenna resonances to the target vibrational modes is critical for maximizing signal enhancement. Although we focus here on the use of the reflector in engineering the monopole antenna device, the approach of using a long nanorod as a general reflector element could be useful to a number of applications where conceptual three-dimensional structures incorporating mirror planes could be made more practical by planarization. The ability to isolate nanophotonic antenna elements as well as accurately model their conductive coupling could prove useful in implementing progressively more complex circuits incorporating multiple antennas and other current carrying elements.26,27 A monopole antenna can be viewed as a compacted dipole antenna, where half of the antenna is formed by an image, rather than a physical structure. This picture is illustrated in Figure 1a,b, which plots the idealized current distributions for a dipole and monopole antenna respectively. The distributions are sinusoidal modes with the full length of the dipole supporting an integral number of oscillation periods.28,29 For the monopole, however, the image formed by the ground plane implies that the physical structure need only support a half period of the given current oscillation. As a result, the resonance wavelengths of the dipole antenna are given roughly by the linear scaling law20,2831 2 λm ¼ ð1Þ nbg LDip þ C m while the monopole follows eq 1 but with LDip f 2LMono, LDip and LMono being the physical lengths of the wires. In the equation, nbg is the background refractive index, C is a constant,32 and m is the mode number. At optical frequencies, thin, rectangular cross sectional, rod-shaped nanoparticles are used to achieve functionality similar to that of the dipole antenna. An important distinction between an RF antenna and its nanoparticle analogue, however, is that the former is generally coupled to a transmission line and a load or generator, while a nanoparticle is simply isolated on a substrate. Although an RF antenna may support any of the modes in Figure 1a,b, based on the resulted
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Figure 1. Monopole antenna resonances. (a) Idealized current distributions for a thin wire dipolar antenna. The first three resonant modes, m = 1, 2, 3, which correspond to lengths L = λ/2, λ, and 3λ/2, respectively, are shown. (b) The same as (a) here for a monopole positioned next to a perfect ground plane. The ground plane is illustrated as the shaded vertical gray bar with the portions of the current/physical structure formed by images plotted as dashed lines. (c) FDTD-simulated extinction cross sections for a rectangular cross section nanorod (blue inset, curve) and a planarized monopole antenna (red inset, curve). (d) FDTD-simulated current density (x-component) and instantaneous electric field amplitude (|E|, V/m) on resonance for the rod antenna (blue curve in panel b). Panels f and g are the same for the monopole antenna (red curve in panel b). For the current density plots (d,f), |Jx| is evaluated along the line z = 45, y = 95 nm, which corresponds to 5 nm in from the top and left faces of the rod. The E-field in (e,g) is taken in the xy plane at z = 0 (cut through the center).
charge distributions we can see that for a solid rod-shaped particle, only the odd ordered modes can couple to normally incident plane wave radiation. By the same arguments, the even ordered modes are associated with cut particles, that is, those having a small gap at their center. The discrepancy can then be reconciled by noting that a solid particle is equivalent to a shortcircuited antenna, while a cut particle is just an open circuited one. The odd (even) ordered modes can then be assigned as short (open) circuit resonances.33 A second important distinction between RF antennas and their plasmonic counterparts is that the latter are typically confined to planar geometries, especially in any chip-based implementation. This is of special significance to the design of a monopole antenna where the requirement of a semi-infinite ground plane implies a 3D structure, preventing the straightforward scaling of the antenna to smaller sizes. While in RF engineering the ground plane often occurs quite naturally, often being the physical ground, this is generally not the case in most lithographically fabricated structures. This difficulty can be circumvented, however, by applying another concept from RF design, the use of thin wire reflectors to mimic a ground plane.22 While in RF designs this may be done to reduce cost, wind resistance, or simplify numerical simulations, here we use a single nanorod as a reflector in order to realize a 5220
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Figure 2. Composite double monopole antenna. (a) Schematic of the structure. The two monopoles are combined such that their reflectors overlap completely. (b) FDTD simulated extinction cross sections of the composite (structure A, black curve), and the two constituent monopoles (structures B and C, red and blue curves, respectively). The far-field resonances of the composite are indicated in the figure as AI and AII for the short and long wavelength ones. For the constituent monopoles, BI and CI indicate the positions of the first order resonances for each B and C, which are comparable with AI and AII, respectively. (c) Near-field amplitude of EX variation with wavelength. As shown in the inset, the field is measured at the end-faces of the x-aligned rod elements. Due to the different spatial positions of the AI and AII modes, the E-field for the composite structure is monitored at the two locations shown in the inset. These are represented by the black solid (spatial position associated with AI) and dashed (spatial position associated with AII) curves. (df) Near-field (|E|) spatial patterns for the indicated structure and mode. Each field is plotted at the indicated far-field resonance frequency, and all are taken at cuts z = 0, through the center of the structure. Panels d ansd e are for the composite, while panels f and g are for B and C, respectively.
monopole element within the constraints of the standard planar geometries. At the mid-infrared wavelengths examined, gold (Au) is an excellent conductor, hence a thin nanorod effectively enforces the boundary condition Etan = 0 at its surface, just as a mirror or ground plane does. The desired effect is demonstrated with the finite difference time domain (FDTD) simulations34 of the extinction cross sections for the two particle geometries shown in Figure 1c. Both particles have rectangular cross sections with thickness (t = 0.1) widths (w = 0.2 μm) and lengths (LDip = LMono = 0.9 μm), as are typical of EBL fabricated structures. The structures are simulated as isolated particles embedded in a homogeneous dielectric background with a refractive index of n = 2.55 (representative of a silicon (Si) substrate35). The m = 1 resonance for the rod is observable as the strong extiction peak (blue curve) around 6.5 μm, while the resonance peak for the monopole antenna is strongly red shifted to a wavelength of ∼10 μm (red curve). The red shift is not quite as large as would be expected given eq 1 and Figure 1a,b, which would imply a doubling of the resonance wavelength to ∼13 um. We attribute the smaller observed red shift to (i) differences in the amount of E-field reflected by the reflector rod and an infinite ground plane and (ii) a loading effect due to the electrical connection between the reflector and the excited antenna arm. Effect (ii) will be examined in the next section within the framework of circuit theory and will be shown to account for the majority of the resonant behavior of the proposed structure. The identification of the resonance as the m = 1 mode of a monopole antenna is shown in Figure 1dg that examines the FDTD calculated current density and electric near field profiles for the two structures. The current density (x-directed) for the nanorod is shown in Figure 1d and matches well with the functional form expected for the idealized distribution for the m = 1 mode.36 In contrast, for the monopole particle the x-component of the current density in Figure 1e takes the form of a half-period cosine, as expected from
Figure 1b. The near-field spatial profile plotted in Figure 1g now shows strong enhancement only at the one end of the particle with a relatively uniform distribution around the rest except for some increase in amplitude near the sharp corners due to the lightning rod effect. This confirms the behavior of the particle as a monopole antenna and the functionality of the perpendicular rod as a nanoscale wire reflector element in its effective mimicking of a ground plane. The demonstrated monopole antenna element offers a number of attractive features that could prove useful in designing plasmonic nanoparticles or collections of them. As mentioned previously, the elements are compact and isolated from interfering fields of neighboring circuitry (or particles in this case). We demonstrate these concepts by leveraging the monopole antenna functionality to engineer a compact, multiband antenna comprised of two such elements, shown in Figure 2a. Ideally, the two elements should tune independently from one another, according to eq 1, providing a means with which to implement two broadly tunable resonances. A significant concern, however, in linking multiple elements in this manner is that they are conductively coupled. Previous studies of contacting nanoparticles including coupled nanorods,37,38 rodring pairs,39 and split ring resonators (SRRs)40 have typically observed a complete redistribution of surface charges and currents, resulting in dramatic changes in the spectral response. In contrast, in bringing the two monopole antennas into contact, however, no such abrupt changes are observed in the FDTD simulations as shown in Figure 2bg. Both the far-field extinction cross section and the near-field spectral behavior of the composite structure are well replicated by the constituent monopoles at their respective operational frequencies. The composite structure is comprised of monopole antennas with lengths LMono = LI = 0.6 μm and LMono = LII = 0.2 μm. The extinction cross sections of the constituent monopoles shown in Figure 2b (blue and red curves) well replicate the two 5221
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Nano Letters modes (indicated as AI and AII) observed in the composite. To further demonstrate the effect in the near-field, the spectral dependence of the EX field component is monitored at a position 5 nm off of the end face of the nanorods in Figure 2c. For the composite, EX is measured at each end as shown in the inset due to the differing spatial positions of the modes. On the LI side EX shows a large peak at AI which lines up well with the curve due to structure B (see black solid and red solid curve) but little to no amplitude variation near AII. A similar effect is observed for the field monitored on the other end of the composite with the variation due to the II-monopole (see black dashed and solid blue curves). Finally, we find the near-field spatial profiles, plotted at the resonance frequencies in Figure 2f,g, also closely resemble those of the composite shown in Figure 2d,e. The reflector arm thus isolates the two monopole antennas, allowing them to operate independently, despite their being combined in a single particle. We note additionally, that completely removing the reflector along with any conductive contact between the two particles (i.e., such that they are two rods aligned end to end, spaced by 200 nm) results in a dramatic blue shifting of the resonances and significant redistribution of the current density as expected based on the discussion outlined in Figure 1 (see Supporting Information Figure S1). The experimental demonstration of the ability to integrate multiple monopole antennas on planar surfaces is presented in Figure 3. The particles were fabricated by a standard EBL and liftoff procedure on silicon (Si) substrates. The nominal dimensions of the particles are the same as in the FDTD simulations, all having rectangular cross sections with w = 0.2 μm and t = 0.1 μm, the latter corresponding to the thickness of gold (Au) evaporated on top of a thin (5 nm) titanium adhesion layer. As can be seen in the scanning electron microscope (SEM) images in Figure 3c,d, the particles are arranged at random positions (but fixed orientations) to eliminate any effects due to array periodicity such that the single particle response can be measured.11,30 The particles are arranged in 100 100 μm2 arrays (i.e., one array per different geometry), each of which contains N = (33)2 particles (particle density is that of a 3 3 μm periodic array). The far-field extinction spectra are measured using a Fourier-transform infrared (FTIR) spectrometer and IR microscope (Bruker IFS 66/s and Hyperion 1000; NA = 0.4 objective) in transmission mode.41 The spectra comparing the monopole and rod antennas in Figure 3a show the same dramatic red-shifting behavior for the monopole antennas as was previously examined numerically. Additionally, the realization of the composite structure formed from constituent monopole elements, as proposed, is demonstrated in Figure 3b. As with the numerical simulations, the resonance wavelengths of the constituent monopoles (CI and BI) agree extremely well with the two modes of the composite structure (AI and AII). That the two monopoles operate independently is indicative of their isolation not only in terms of near-field coupling, but also conductive coupling. In contrast to several previous experiments, this last feature is quite surprising and it is not clear how the isolation of electronic currents is maintained between the conductively coupled monopoles. This effect can be understood by considering current flow between the various structural elements that form the antenna. These are identified as the two monopoles, denoted MI and MII, and the two ends of the reflector arm, MR (these are always identical), as illustrated in Figure 4a. Given that the coupling between components is conductive, characterized by freely flowing current, it is natural to model their interactions by
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Figure 3. Experimental realization of the planar monopole and composite antennas. (a,b) Experimental extinction cross sections, determined from transmission measurements. (a) Comparison of a nanorod (blue curve) and planar monopole antenna (red curve) with LDip = LMono = 0.9 μm as in Figure 1c. (b) Extinction spectra for a composite double monopole antenna (structure A, black curve) and particles corresponding to the two constituent monopole elements (structures B and C, red and blue curves). The structures are the same as in Figure 2b. The resonances are indicated as in Figure 2b. (c,d) Representative scanning electron microscope (SEM) images of fabricated nanorod (c) and composite double monopole (d) structures. In both, the white scale bare is 2 μm long.
treating them as linked in an electrical circuit. In general, each element can be assigned a complex input impedance, Zin which gives the ratio of voltage to current at its terminals and therefore represents its properties from the viewpoint of the rest of the circuit (for the structure here, Zin is calculated from standard antenna theory, see Supporting Information). Considering current flow between the elements, a circuit comprised of the 5222
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Figure 4. Conductive coupling between antenna modeled via circuit theory. (a) Illustration of the model and definitions of quantities of interest. The antenna is composed of four monopoles (MI, MII, and two identical MR elements) with lengths LI, LII and LR/2 as shown, which are defined as in Figures 1 and 2. Each presents an input impedance (Zin) at the terminals of the four-way crossing. For light polarized in the x-direction, only the modes of the I and II arms are excited. (b) Equivalent circuit for MI excitation, with the rest of the elements (MII and the two MR) acting as a load. The load input impedance, ZL is computed from the parallel combination of the three elements as shown. The equivalent circuit for MII excitation is identical, but with ZI and ZII interchanged. (c) Input impedance (Zin = Rin + jXin) characteristics of a monopole antenna (length, L = 0.6 μm) calculated via the analytical induced emf method. (d,e) Variation of the input reactance of the various components as well as the combined load reactance when the monopole antennas are not equal in length, as indicated above each, the parameters are LI = 0.7 μm and LII = 0.3 μm. MI excitation is considered in (d), while MI is shown in (e). (f) Component reactance for the special case of LI = LII. In (df), the black arrow indicates the resonance wavelength which corresponds to the condition XI = XL or XII = XL (black and red or blue curve crossings) depending on whether MI or MII excitation is considered.
individual elements’ Zin’s can be drawn. This is illustrated for the composite structure in Figure 4b. The total impedance, ZTot, can then be determined using standard circuit theory equations with the resonance frequencies determined by the zero crossings of its imaginary part (XTot = 0).26,31,33 The dependence of the properties of an antenna element on its geometry and frequency are thus captured in its input impedance parameter. The input impedance of a monopole antenna can be evaluated analytically using the induced emf method of classical antenna theory (for details see Supporting Information). The results of such calculations are shown in Figure 4c for a LMono = 0.6 μm monopole antenna with a cylindrical cross section, 0.025 μm in diameter. The real part corresponds to the input resistance, Rin, which determines the power dissipated by the antenna as radiation (i.e., PRad = 1/2|I|2Rin). The imaginary part corresponds to the input reactance (Xin) and determines the energy stored in the antenna’s reactive near-field with positive (negative) values indicating an inductive (capacitive) character. In Figure 4c, the first order, m = 1, resonance corresponds to the first (in terms of lowest frequency) zero crossing, at around λ/nbg = 4LMono. On the other hand, the m = 2 resonance at around λ/nbg = 2LMono is characterized by extremely large values of Rin and Xin. Similar trends follow for the even and odd higher order resonances. In modeling the composite monopole structure as shown in Figure 4a,b, the input impedances of the two monopoles, ZI and ZII are calculated analytically as described in the previous paragraph. Additionally, the two reflectors are of the same geometry as the monopoles and therefore should support similar modes. Although they are not directly excited by incident radiation, their input impedance, ZR, is also calculated as that of a monopole. As
shown in Figure 4a, the four elements are linked at a four way junction. When light is incident on the structure (polarized in the x-direction), both MI and MII are excited, setting up current flow and a voltage drop across the element. Since the components are linear, superposition can be used to consider each excitation separately. For each, there will be three unexcited elements acting as a load on the antenna. The load impedance (ZL) is the parallel combination of their three input impedances, as shown in Figure 4b. The resonance frequency of the structure for MI excitation is then that at which the load reactance cancels out that of the excited monopole element,that is, XI = XL. The standard impedance combination formulas can be used to determine the load impedance and therefore the corresponding resonance frequency AI (see Supporting Information). The resonances of MII are computed analogously but with ZI and ZII interchanged. The calculations model the antenna as cylindrical in cross section with a radius of 0.025 μm. The background refractive index is taken to be 2.55 as in the FDTD calculations. All other parameters are taken as the nominal values for the fabricated structures; there are no fitting parameters used. The important feature of the load impedance is that it consists of the parallel combination of the two ZR elements and ZII (ZI) for MI (MII) excitation. As a result, the load impedance at a given wavelength will be largely determined by whichever element has the smallest impedance values. Physically this is due to the preferential flow of current down the path of least resistance. It is this feature that is responsible for the observed electrical isolation of the two monopoles in the composite. The mechanism can be understood by considering the input impedances of 5223
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Figure 5. Tuning of the composite monopole and loading effects. (ac) Effects of varying the reflector length. (a) Experimental data, Mode-I and Mode-II correspond to the red and blue data points, respectively. The monopole lengths, LX, are indicated. (b) Same as (a), but calculated from the circuit relations. (c) Simplified illustration of the loading effects. Red and blue dashed lines are the reactance of AI and AII while the green curves plot the reactance of the two reflectors in parallel (its negative is plotted so that the resonance corresponds to the crossing between the red (blue) and green curves for Mode I (Mode-II). Solid, dashed, and dotted green curves correspond to lengths of LR = 1.2, 1.6, and 2.0 μm. (df) Effects of varying the relative lengths of the two monopoles. (d) Experimental data, the dotted black vertical line corresponds to LI = LII = 0.5 μm. The dashed black line is obtained from a linear fit. (e) Same as (d), but for the circuit calculation. (f) Simplified reactance plot, similar to (c). Here, increasing LI/decreasing LII shifts the red and blue curves along the corresponding arrows.
the excited elements as well as the load as in Figure 4df. Panels d and e are representative of the numerically and experimentally examined composite structure (LI = 0.7, LII = 0.3 μm). The excitation of MI is considered in panel d. The excited element reactance, XI is plotted (red curve) along with the negative of the reactance for the other elements as well as the total load, XL (black curve). The resonance wavelength corresponds to the crossing point between the black and red curves, indicated by the arrow. Most importantly, over the majority of the spectrum (wavelengths >6 μm), the load impedance is essentially identical to that of the two MR elements (compare green and black curves). This is a result of the asymmetry in the structure; because the MII monopole is smaller than MI, its reactance takes on large (capacitive) values at the wavelengths where XI is moderate. Because of the parallel nature of the circuit, the majority of the current thus flows through the reflector elements and the effect of MII on the resonance wavelength is negligible. An analogous effect is observed in Figure 4 (e) for MII. The load impedance is again clearly determined by the reflector elements near the resonance (black arrow, crossing between blue and black curves). The main exception is when LI = LII. In this symmetric case, the two monopoles are degenerate and therefore their reactance takes on moderate values and cross zero at the same wavelengths. As shown in Figure 4 f, the load impedance is now determined almost entirely by the other monopole near resonance. This implies that for the symmetric structure the flow of current is predominantly from MI to MII with the resonances being independent of the reflector. The intuition gained in this model is important in allowing us to control the structural resonances in a predictable manner, as demonstrated in Figure 5. For example, an immediate consequence of the discussion in the previous paragraph is that we
should expect the resonance wavelengths of both modes to vary strongly with the reflector length, except when LI = LII. This is because when LI 6¼ LII the load reactance is XL ≈ XR/2 and the resonances are determined by XI = XR/2 and XII = XR/2 for AI and AII, respectively. For the symmetric case, however, XL ≈ XII and the matching condition, XI = XL is then XI = XII = XI, which is satisfied at XI = 0. This is confirmed experimentally in Figure 5a where the resonance wavelengths of the two modes can be seen to red shift monotonically with increasing reflector length when the two monopoles are unequal in length. The single mode supported by the symmetric geometry (black markers), however, does not vary. The corresponding circuit calculations in Figure 5b replicate these trends extremely accurately. Examination of the reactance plot in Figure 5c allows one to trace the origin of the red shift to the shifting of the reflector reactance to progressively larger wavelengths (along the green arrow). Additionally, the effects of varying the relative lengths of the two monopoles are examined in Figure 5df. The total length of the structure is held constant at 1 μm (as in Figures 2 and 3) such that the interaction between the two monopoles is the only factor changed. Increasing LI therefore decreases LII. The resonant wavelength of the two modes can be expected to shift in opposite directions. In the simplest approximation, the linear scaling law of eq 1 could be used with LDip f 2LI and LDip f 2LII for AI and AII, respectively. This corresponds to the black dashed line in the figure, where the nbg and C values were obtained by a linear fit to experimental data from a sample of nanorod (dipole) antennas of varying length. Comparing the experimental data (markers) with the dashed line, we can see that the general trend is reasonable, although clear deviations can be observed. In particular, while AI does red shift linear as LI is increased, it does so at a reduced rate in comparison with the linear approximation (solid red markers 5224
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Nano Letters vs dashed black line in Figure 5d). Additionally, AII blue shifts at a progressively smaller rate as LII is reduced. These features are captured very well by the circuit calculations shown in Figure 5e. Again, examining the reactance plots in Figure 5f allows us to elucidate the reasons for the observed effects. The reactance associated with AI, XI crosses the load reactance (green curve) at a roughly linear region as it shifts to higher wavelengths (red arrow) resulting in the roughly linear, but reduced slope, variation of AI. On the other hand, comparing the blue and green curves in the figure, whose crossing determines AII, we can identify the rapidly increasing, inductive reactance of the load near its m = 2 resonance to be responsible for the nonlinear variation of AII as LII is reduced. This description of the antenna characteristics and coupling in terms of an electrical circuit thus gives an intuitive picture of the characteristic behavior of the structure and allows for its resonances to be tailored in a predictable manner. The tunable nature of the proposed monopole antenna elements is critical for its use in practical applications. In the mid-infrared, for example, resonances of plasmonic antennas can be used to strongly enhance the absorption associated with the vibrational modes of chemical bonds via surface enhanced infrared absorption spectroscopy (SEIRA). The technique allows one to obtain bond specific spectral fingerprints of extremely small quantities of molecules, down to single monolayers, in contrast with standard infrared absorption spectroscopy measurements that typically require relatively long path lengths. In order to maximize signal enhancements, plasmonic resonance must spectrally overlap with the vibrational mode of interest. As a demonstration of this effect as well as the strong near-field enhancement associated with the monopole resonances, we used them to enhance the characteristic Amide-I and II bands of bound protein monolayer. The protein amide bands are associated with the bonds present in the protein backbone (Amide-I, CdO stretch; Amide-II, CN stretch, NH wag combination). While they are common to all proteins, here we focus on protein A/G and its binding to an antibody, immunoglobulin G (IgG). This protein combination is of special importance to immune reaction sensors and virus detection. In a typical plasmonic sensor, protein A/G is adsorbed to the gold surface, and then used to bind and orient the antibodies.42,43 In the demonstration here, we follow a similar procedure to bind the two proteins to the surface of our gold nanoparticles. Details are given in the Supporting Information. The nanoparticle substrates and measurement setup are similar to those discussed previously. We note that, however, in these experiments we use a calcium fluoride (CaF2) substrate as its lower refractive index results in greater field overlap with the adsorbed protein layer, increasing our sensitivity. Additionally, measurements are taken here in a reflectance geometry. An advantage of this setup is that since the substrate itself reflects very little light (
