1. Introduction

Localised surface plasmons (LSP) are collective oscillations of free electrons in metal nano-and microstructures of specific shapes and dimensions (antennas) coupled to the electromagnetic field. Their characteristic feature is the subwavelength confinement of the electromagnetic field, utilized in near field imaging [1,2] and ultracompact nanolasers [3]. Further, a strong modification of the field magnitude with respect to the vacuum state, reflected in the photonic local density of states, can be used to control the rate of optical processes, which is exploited e.g. in tip enhanced Raman spectroscopy [4], single molecule fluorescence [5], improving the efficiency of solar cells [6], or enhancing the photoluminescence of quantum dots [7,8]. Another applications, such as sensing [9] or labeling [10], are found in biology, environmental sciences, or human medicine. Antennas of a crescent shape possess several advantageous properties. They can be prepared by electron beam lithography (EBL) [11], but also conveniently manufactured using nanosphere template lithography, whereby a thin gold layer is deposited at an oblique angle on polymer nanospheres [12,13], opening thus the way to the cheap mass production. Close to their sharp tips hot spots of enhanced electric field and electromagnetic local density of states are formed, allowing to enhance the optical processes [14]. In addition, similar to split-ring resonators, crescent geometry supports circular-current plasmon modes, which interact with the magnetic component of the field and are a prerequisite for metamaterials with a negative refraction index [13]. Having only one lateral mirror plane, the crescent antennas allow for a directional response. Recently, they were also used to enhance the performance of the solar cells [14,15].

Properties of LSP are extensively studied by numerous experimental methods. Far-field spectroscopic methods such as absorption spectroscopy [16,17], dark-field microscopy [18–21], or time-resolved two-photon photoemission [22] provide the energy and lifetime [21,22] of LSP. Several imaging techniques exist to reveal the spatial distribution of plasmon near fields. Scanning near field optical microscopy enables the optical mapping of near fields of LSP [23] and surface plasmon polaritons [24], but the spatial resolution is limited to about 50 nm. Scanning transmission electron microscopy (STEM) applied simultaneously with electron energy-loss spectroscopy (EELS) facilitates the excitation and detection of particular plasmonic modes in antennas [25–27]. The electron beam induces the oscillations of free electrons inside antennas. Importantly, the electromagnetic field induced by these oscillations acts back on the impinging electrons, changing both their energy and momentum. By analysing the spectral dependence of the energy loss suffered by electrons, one can deduce the characteristic energies of the various plasmonic modes of antennas. Furthermore, by extracting the energy loss spectral maps, one can observe the spatial distribution of the excitation efficiency of the plasmonic modes. EELS has been successfully applied to map LSP modes in nanospheres [28], nanorods [29], bow-tie antennas [30], split-ring resonators [31], and complex plasmonic assemblies [32], to study the hybridization of plasmons in nanoparticle dimers [33] or the symmetry breaking induced by the substrate [34], to reveal universal dispersion relations [35], etc.

The interpretation of the EELS maps of LSP modes is not straightforward. Despite original attempts to relate EELS to the photonic local density of states (LDOS) [25], pronounced differences between both plasmonic mode characteristics were demonstrated [26]; in particular, EELS was shown to be rather insensitive to the hot spots [26] between the particle dimers. Only since very recently, complex methodologies mutually relating EELS and photonic LDOS, that are based on the modal decomposition of involved quantities, have been developed [36,37]. Thus, it is preferable to accompany EELS measurements by the theory-based interpretation. The simplistic antenna geometries allow for the analytic solution [38,39], but for more complex ones numerical methods specially developed for this purpose should be used [40,41].

2. Methods

2.1. Gold antennas preparation

Gold crescent antennas of height 20 nm and various lateral dimensions were prepared using focused-ion-beam lithography. The silicon nitride membranes with areas of 500 × 500 μm² and thickness of 40 nm were used as the substrate. First, a 20nm-thick Au layer was deposited by ion beam sputtering on the substrate. After that, the antennas were fabricated by focused 30 keV Ga⁺ ion beam (FIB) milling of the gold film in a dual beam system Tescan Lyra. Each antenna was located in the middle of a 1 × 1μm² metal-free square. To verify that plasmonic structures do not significantly interact with the surrounding metallic frames, spectra of equivalent plasmonic antennas embedded in the metal-free squares of different sizes were compared first. Annular dark-field (ADF) STEM images of the samples are shown in Fig. 1. Here, a micro-grain structure of the antennas is clearly visible.

 

Fig. 1 Left: ADF-STEM images of six gold plasmonic antennas involved in this study. The inset in panel A3 displays characteristic spots of electron beam impingement (tips, inner edge, and outer edge of the antenna). The inset in panel A6 shows the lateral antenna dimensions used in the text (length L, width W, and thickness T). Right: The points represent the energies of two dipolar plasmon resonances – D_L mode (horizontal axis) and D_T mode (vertical axis). Experimental (full circles) and numerical (hatched diamonds) values are compared. Different colors correspond to particular structures (red: A1, green: A2, blue: A3, yellow: A4, brown: A5, gray: A6), the dashed lines connect the experimental and numerical results for a particular structure to guide the eye. The theoretical values of the mode energies already reflect the influence of the substrate.

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2.2. Electron energy loss spectroscopy

EELS measurements were carried out using a FEI Titan 80–300 environmental (scanning) transmission electron microscope operated at 300 kV in scanning, monochromated mode. The instrument was equipped with a Gatan Tridiem 866 spectrometer. A 50 μm C3 aperture, camera length of 38 mm, and a spectrometer entrance aperture of 2.5 mm and 0.01 eV per channel dispersion were used for the data acquisition. This corresponds to a convergence semi-angle of 9.2 mrad and a collection semi-angle of 20.7 mrad. The spatial and energy resolution (defined by the full-width-half-maximum of the zero-loss peak), are 0.3 nm and 0.2 eV, respectively. The structure dimensions considered in the calculations were extracted from ADF-STEM images of the samples. The plasmon excitation maps were obtained by extracting the spectrum image in energy slices with 0.1 eV intervals.

2.3. Simulations

To obtain insight into the physical origin of the observed peaks, the EELS response was simulated using the boundary element method (BEM) following Refs [40,41]. To this end we used a free software MNPBEM toolbox [42] together with an in-house developed extension for EELS. The model structure was formed by two discs: from the basic disc of the radius r_B another disc of the radius r_S, displaced by a distance c from the first one, was subtracted. The edges were subsequently rounded with a radius of 5 nm. The height of both discs was set to the value h = 20 nm following the value set for the lithographic process. The other parameters of the antenna geometry were chosen in the way so that the model structures comply with the ADF-STEM images (Fig. 1). For example, the structure A1, the spectra of which are presented in Fig. 2(a), was modelled using r_B = 56 nm, r_S = 55 nm, c = 36 nm. A triangular mesh approximating the surface of the resulting structure was created by a Delaunay triangulation algorithm using COMSOL Multiphysics software. A typical mesh consisted of about 3000 boundary elements and provided accuracy in peak positions of about 10 meV (determined by a comparison with a mesh with about 10000 elements). In most calculations the substrate was not included, as it increases the number of boundary elements considerably and has only a quantitative influence on the results (red shift of the peaks by about 0.2 – 0.3 eV). The substrate (modeled as a finite-size particle attached to the bottom of the gold antenna) was included in some calculations for the accurate determination of the plasmon resonance energies. The dielectric function of gold was taken from Ref. [43], for silicon nitride an infrared value at 1 eV of 3.9 + 0 j was used [44] neglecting the dispersion. Apart from neglecting the substrate, the calculation accuracy is limited by the uncertainties and irregularities of the antenna shape. Remarkably, the variation of the antenna height by 1 nm (5 %) shifts the resonant peak energy by up to 20 meV. Further, sputtered gold forming the antennas is porous and composed of grains. Hence, its dielectric function can deviate from the bulk case used in the simulations [45], which contributes to the simulation error. In total, we estimate the accuracy of the calculated peak positions of 0.1 – 0.15 eV.

 

Fig. 2 (a) Left: Measured energy-dependent loss spectra for the structure A1 (L = 120nm, T = 60nm, W = 86nm) and the electron beam impinging close to the tips (spots T1 and T2, light blue and red line), outer edge (spot OE, dark blue line), and inner edge (spot IE, green line) of the antenna. The inset schematically shows the electron beam positions (the same colors as in the main graph). Right: Energy loss spectra calculated with MNPBEM (colors correspond to the same spots as in the left panel). Solid and dashed lines are related to the antenna on substrate and the free-standing antenna, respectively. (b) Left: Measured EEL spectra for the larger structure A4 (L = 248nm, T = 86nm, W = 187nm) and the electron beam impinging close to the tips (spots T1 and T2; red and light blue line), outer edge (spot OE; dark blue line) and inner edge (spot IE; green line) of the antenna. Right: Energy loss spectra calculated with MNPBEM for a free-standing antenna (dashed lines) and subsequently modified using convolution with a Gaussian function of 0.15 eV FWHM (solid lines). Colors correspond to the same spots as in the left panel.

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3. Plasmon mode mapping

In total six gold crescent-like antennas of various sizes manifesting qualitatively similar plasmonic properties were studied. Annular dark-field (ADF) STEM images of the samples are shown in Fig. 1. The lateral dimensions of the antennas, schematically depicted in Fig. 1, are summarized in Table 3, the height was kept at 20 nm. The antennas can be divided into two subgroups according to their dimensions. In the following, first the smaller antennas (A1, A2) will be discussed thoroughly, and then the distinct features of the larger antennas (A3, A4, A5, A6) briefly described.

Table 1. Lateral dimensions of six antennas involved in the study determined using ADF-STEM images: length L (longitudinal tip – tip distance), thickness T (transverse outer-edge – inner-edge distance, and width W (transverse outer-edge – tip distance). The energies of their plasmon modes D_L (longitudinal dipolar), D_T (transverse dipolar), Q (quadrupolar), and MA (multimodal) as obtained from the EEL spectra.

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Broad range EEL spectra were acquired for the electron beam focused to specific spots close to the antennas (see Fig. 2) as follows: the tips of the crescent (T1, T2), the center of the inner edge (IE), and the center of the outer edge (OE). The distance between the beam and the antenna boundary was set to several nm to assure a strong response while avoiding the penetration of the electron beam into the metal and thus related losses. The electron trajectories are schematically depicted in the inset of Fig. 2(a). With the corresponding colors, the energy loss spectra for a particular smaller structure (A1) are shown in Fig. 2(a). The characteristic EEL spectrum of smaller antennas is composed of three peaks, denoted as D_L, D_T, and MA with increasing energy. It will be shown that the D_L peak corresponds to a longitudinal dipolar mode (the electron oscillations between the tips T1 and T2 along the axial antenna direction. The D_T peak corresponds to a transverse dipolar mode related to electron oscillations between the inner edge of the antenna and its tips forming a dipole moment perpendicular to the longitudinal one, while the MA peak corresponds to several high-order plasmonic modes and its position is related to the onset of interband absorption in gold rather than the geometry of the nanostructure. The D_L peak dominates the spectrum obtained for the excitation spots T1,2 (further T1,2 spectrum), while it is missing or weak in IE and OE spectra. This is not surprising, the odd symmetry of the mode with respect to the mirror plane of the crescent prevents its coupling to the electron beam with the trajectory involved in the mirror plane. The weak non-zero signal is attributed to a non-ideal shape of the crescent and/or to the electron beam positioned slightly out of the mirror plane. The D_T peak is most pronounced in the OE spectrum. It is also present in the T1,2 spectrum as a shoulder of the stronger D_L mode. It is weak in the IE spectrum which can be explained by a similar argument as for the D_L mode in the IE and OE spectra. Although there is no longitudinal mirror plane, the IE spot is close to the center of mass of the structure and the electric field of the D_T mode is rather uniformly distributed along the longitudinal plane containing the spot IE. Thus, the coupling of the mode whose field has the quasi-odd symmetry with respect to that plane to the electron beam the field of which possesses the even symmetry is weak. The MA peak is present in all spectra. The IE spectrum is most suitable for studying its properties due to the absence of the D_L and D_T peaks.

The calculated EEL spectra for the structure A1 and the relevant electron beam spots are shown in the right panel of Fig. 2(a) (both for the antenna on the substrate and free-standing antenna). As in the experiment, we identify three peaks in the spectra. Their energies of 1.3(3), 1.8(1) and 2.3 eV (or 1.5(8), 2.0(8), and 2.4 eV neglecting the substrate) are in a reasonable agreement with the experimental values of 1.3, 1.7, and 2.4 eV, respectively. Similarly, the relative intensities of the modes for each electron beam spot correspond rather well to the experiment. The D_L peak is pronounced at the T1,2 spots and is also weakly excited when moving the beam slightly off the mirror plane (not shown in Fig. 2). The D_T peak is the strongest at the OE spot. In the theoretical IE spectrum it is rather weak, yet stronger than in the experimental IE spectrum – a signature that the model structure does not fully reflect the quasi-odd longitudinal symmetry discussed in the previous paragraph. The MA peak is visible at both the IE and OE spots. Both the D_T and MA peaks are visible or at least perceived in the theoretical T1,2 spectra. The FWHM of the peaks is generally lower than in the experiment, which is attributed to the finite energy spread of the electron beam and the resolution of the spectrometer. Right panel of Fig. 1 compares the experimental and calculated energies of the lowest two plasmon resonances (D_L, D_T) for all six studied antennas. The calculation of the theoretical values of the antenna mode energies took into account the influence of the substrate. Based on the noise of the measured spectra and the spectral width of the peaks we estimate the experimental uncertainty of the peak energies of about 0.1 eV. Considering the theoretical error of peak energies of about 0.15 eV, the agreement of the theory and the experiment is satisfying. The calculated values are systematically overestimated by about 0.1 eV, which can be attributed e.g. to the difference between the actual dielectric function of gold and the bulk dielectric function used in the simulations.

In order to obtain insight into the nature of the modes, the spatial distribution of the loss intensity was studied. Figure 3 displays measured and calculated maps of the loss intensity over the antenna A1 at the loss energy corresponding to the D_L, D_T, and MA peaks. The calculated values are shown only for the electron beam spots in the antenna surroundings. Further, the calculated spatial distribution of the electric and magnetic fields inside the antenna (in its mid-height) is shown. For them, we chose a specific electron beam spot at which the selected peaks dominate (the T1,2 spots for the longitudinal dipolar mode D_L, the OE spot for the transverse dipolar mode D_T, and the IE and OE spots for the multimodal peak MA). We note that both fields are complex quantities. As their real and imaginary parts exhibit a similar spatial distribution, we show for clarity only the dominant components, i.e., the imaginary part of the electric field intensity and the real part of the magnetic field.

 

Fig. 3 Top: D_L mode of the A1 antenna (a–d). Measured (a) and calculated (b) spatial distribution of the loss intensity. Electric (c) and magnetic (d) field induced in the antenna by the electron beam passing nearby the left tip [violet spot in (c)]. The violet arrow in (d) shows the direction of the induced current. Middle: D_T mode of the A1 antenna (eh). Measured (e) and calculated (f) spatial distribution of the loss intensity. Electric (g) and magnetic (h) field induced in the antenna by the electron beam passing nearby the outer edge [violet spot in (g)]. The violet arrow in (h) show the direction of the induced current. Bottom: MA mode of the A1 antenna (i–l). Measured (i) and calculated (j) spatial distribution of the loss intensity. Magnetic field induced in the antenna by the electron beam passing nearby the outer edge (k, violet spot) and inner edge (l, violet spot). The white spot in left bottom corner of the experimental EEL maps (a,e,i) corresponds to a missing data due to a failed measurement. The color scale unit of panels (a,e,i) is count.

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The loss intensity related to the D_L mode exhibits two maxima located around the tips of the antenna and a minimum along the transverse central plane of the crescent (i.e., a nodal plane coinciding with the transverse mirror plane in the model crescent). The electric and magnetic field distributions associated with the D_L mode result from a charge separation and a current flowing in the longitudinal direction [violet arrow in Fig. 3(d)], confirming our assignment of this spectral feature to the longitudinal dipolar mode. Note that the field distribution nearly possesses a mirror plane symmetry, although the excitation is highly non-symmetric. This symmetric field distribution is preserved as the electron beam scans the antenna surrounding. This is a rather strong evidence that only a single plasmon mode dominates the response at the corresponding energy. Similar features are found in the loss intensity and electromagnetic field distribution associated with the D_T peak, but the dipole is oriented along the transverse axis and the loss intensity distribution possesses three maxima [Figs. 3(e) and 3(f)]. Remarkably different behavior is observed in the case of the MA peak [Figs. 3(i)–3(l)]. The loss intensity shows only weak spatial selectivity and is almost homogeneously distributed along the circumference of the crescent. The electromagnetic field distribution is strongly sensitive to the position of the electron beam. To demonstrate this sensitivity, the response of the crescent for the electron beam impinging nearby its inner and outer edge was compared. The magnetic field distribution, shown in Figs. 3(k) and 3(l), corresponds to the excitation current of the electron beam rather than to the current generated by specific plasmonic oscillations. On account of these findings, we conclude that the MA peak is formed by several overlapping plasmon modes. Indeed, at the energies above 2.4 eV the interband transitions contribute substantially to the dielectric function, leading to the broadening of the individual plasmon modes. Further, the energy separation between the modes usually decreases with the increasing order of the modes, as was recently demonstrated in silver nanodisks [35] and also qualitatively follows from the concave (down-bending) character of the surface-plasmon-polariton dispersion curve. It is thus plausible to assume that at higher energies the plasmon modes become unresolvable.

Figure 2(b) shows the measured and calculated EEL spectra for one of the larger antennas (A4). In comparison with the small antenna A1 [Fig. 2(a)], the D_L and D_T peaks are red-shifted and a new peak emerges between the D_T and MA peaks. This new feature is denoted as Q to reflect its prevailing quadrupolar character (note that due to low symmetry of antennas the mode is not purely quadrupolar, but has also dipolar and higher-order components). The calculated spectra again reasonably reproduce the measured ones as long as the substrate is considered (not shown). As the calculated peaks are sharper, the additional Q peak splits into a weak Q₁ peak and a stronger Q₂ peak. It is reasonable to assume that the broadening of spectral peaks arises from the finite resolution of the monochromator and spectrometer. To include this broadening in the calculated data they were convoluted with a Gaussian function. The best agreement with the experiment was obtained for a FWHM of 0.15 eV [shown by solid lines in the right panel of Fig. 2(b)], which is a plausible value for our experimental setup. The measured and calculated maps of the loss intensity are shown in Fig. 4. The D_L, D_T, and MA peaks are similar to those in A1 antenna. The calculated maps of the loss intensity display 4 and 5 maxima for the Q₁ and Q₂ peaks, respectively. The experimental maps are in reasonable agreement with the calculations. In measurements, the Q₂ peak is not fully resolved from its adjacent peaks Q₁ and MA. In particular, a strong loss intensity at the IE spot in Fig. 4(g), not present in the calculated data in Fig. 4(h), belongs to the MA peak. Similarly, a bulky maximum at the OE spot is observed in Fig. 4(g) instead of three separate predicted in Fig. 4(h) because of the contribution of the Q₁ peak. We therefore show in Fig. 4(k) a linear combination of calculated maps of loss intensity of the three peaks (Q₁, Q₂, and MA with relative weights of 0.2, 1, and 0.5, respectively), which agrees well with the measured map of loss intensity of Q₂ peak.

 

Fig. 4 D_L mode of the A4 antenna: Measured (a) and calculated (b) spatial distribution of the loss intensity. D_T mode of the A4 antenna: Measured (c) and calculated (d) spatial distribution of the loss intensity. Q₁ mode of the A4 antenna: Measured (e) and calculated (f) spatial distribution of the loss intensity. Q₂ mode of the A4 antenna: Measured (g) and calculated (h) spatial distribution of the loss intensity. MA mode of the A4 antenna: Measured (g) and calculated (h) spatial distribution of the loss intensity. (k) A sum of calculated loss intensities of modes Q₁, Q₂, and MA with relative weights of 0.2, 1, and 0.5, respectively.

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4. Characteristic properties of plasmonic resonances in crescents

So far the plasmonic modes supported by crescent-shaped antennas have been identified and understood. Next the plasmonic properties which are characteristic for this specific shape and make it attractive for applications will be discussed. In particular, it will be shown that the crescent antennas (i) support two non-degenerate dipolar plasmon resonances (ii) which are both concentrated at the sharp antenna tips where a large field enhancement is possible, (iii) are independently tunable in a wide range of energies by selecting a proper crescent dimensions, and (iv) are compatible with the infrared telecommunication technologies.

One of the prominent features of low-symmetry antennas, including crescents, is that they support two dipolar plasmon resonances at different energies, while for high-symmetry antennas (e.g. discs) the modes are degenerate. Several applications indeed profit from the possibility to use plasmonic antennas for a simultaneous control of optical processes in two different spectral regions. For example, in the plasmon fluorescence enhancement the high energy resonance can be tuned to the energy of the exciting light to enhance the absorption while the low energy resonance is tuned to the energy of the emitter and enhances its radiative decay rate [5,46]. A similar setup was proposed to enhance the efficiency of solar cells by capturing the transmitted subbandgap photons, upconverting them and reflecting back to the active region of the solar cell [47]. In the following the properties of the dipolar resonances will be studied theoretically. In particular we address the evolution of two dipolar modes as the antenna geometry transforms from a disc to a crescent and the possibility to adjust the energies of the plasmon resonances by setting an antenna geometry.

For the transition from the disc to crescent antenna geometry, the antenna was again modelled by mutual subtraction of two displaced discs. From the basic disc (r_B = 55 nm), the intersection with the detracting disc (r_S = 50 nm) was removed. The center-to-center distance between the discs was varied from 105 nm to 25nm so that the full basic disc is smoothly converted to a thin crescent of a thickness of 30 nm. The evolution of the EEL spectra with the changing crescent geometry is shown in Fig. 5 for the relevant electron beam spots (T1,2, IE, OE), at a distance of 5 nm from an antenna boundary. Even as small perturbation as removing a wedge of a thickness of 20 nm is already sufficient for the appearance of two well-distinguished peaks belonging to the longitudinal (D_L) and transverse (D_T) plasmon modes. As the crescent gets thinner, the former peak red shifts rapidly from 2.1 eV to 1.5 eV while the shift of the latter peak is not monotonous and not so prominent (between 2.05 eV and 2.15 eV). Interestingly, the intensity of the transverse loss peak for the inner edge excitation is strongly suppressed for a certain range of crescent thicknesses. This is caused by a quasisymmetric distribution of the mode polarization with respect to the position IE of the excitation beam (as for the longitudinal mode at the mirror plane of symmetry). It should be noted that this effect is manifested in our experimental spectra as a low intensity of the D_T mode at the IE beam spot. The multimodal MA peak at 2.4 eV is not well visible in the simulated energy loss spectra and does not exhibit any pronounced shift. A similar symmetry reduction (from cylindric to three-fold rotation symmetry) has been recently studied by Schmidt et al [48].

 

Fig. 5 The simulated energy loss spectra for crescents of various thicknesses T (inner-edge to outer-edge transverse dimension). The bottom spectrum corresponds to a full disc with a radius r_B = 55 nm (degenerate modes) and for each other spectrum the thickness is consecutively reduced by 10 nm down to 30 nm for the topmost spectrum. The peaks corresponding to the longitudinal and transverse dipolar modes are denoted D_L and D_T, respectively. Different line colors correspond to the electron beam spots T1,2 (red), OE (blue), and IE (green). The solid and dashed lines are alternated only to improve the clarity of the figure.

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Figure 6 shows the maps of the energy loss intensity for the dipolar mode in the disc-shaped antenna and the sum of the longitudinal and transverse dipolar modes in the crescent-shaped antenna. The enhancement of the loss intensity in the vicinity of the sharp features (i.e., tips) of the latter antenna is clearly observed and attributed to the corresponding enhancement of local electric field.

 

Fig. 6 The map of the simulated energy loss intensity for (a) a disc-shaped antenna (c = 105 nm, T = 110 nm) for a peak energy of the dipolar mode (2.07 eV) and (b) a crescent antenna rather close to the disc shape (c = 75 nm, T = 80 nm), summed up for both D_L and D_T dipolar modes (1.94 eV and 2.14 eV, respectively). Antennas are indicated by light gray color. For both antennas, the values r_B = 55 nm and r_S = 50 nm were used.

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Next, the dependence of the mode energies on the particular antenna shape is explored. Left panel of Fig. 7 shows the energies of the three distinct spectral features (D_L, D_T, and MA) as functions of “effective k” of the antenna. This quantity is defined as that one inversely proportional to the characteristic lateral dimension of the antenna (equal to r_B of the antenna except for the LAR scaling where it is equal to r_B of the antenna before the scaling), with the unit value corresponding to the reference crescent with r_B = 55 nm, r_S = 50 nm, c = 45 nm. In k-scaling both lateral dimensions (longitudinal and transverse) are scaled by the same factor (to which the value of k is inversely proportional). The energies of all the modes increase with k and converge to an asymptotic value of about 2.4 eV, which corresponds to the onset of the interband absorption in gold. For the k-interval from 0.25 to 2 and the antennas with h = 30 nm the energy of the D_L mode varies between 0.79 and 1.99 eV and the energy of the D_T mode varies between 1.36 and 2.32 eV (black and red thick solid lines in the left panel of 7). When the height of the antennas is increased, the energies of the plasmonic modes increase as a result of the weakened coupling between the lower and upper antenna boundary. The k-dependences of the antennas with h = 15 nm and 40 nm are shown in Fig. 7(left) by the dashed lines. The energy interval for this height range and k = 1 is 1.48 – 1.77 eV for the D_L mode and 2.00 – 2.21 eV for the D_T mode. The common feature of both k-scaling and varying the height is preserving the lateral shape of the antennas so the energies of different modes shift in the same direction by similar magnitudes. A mutual shift of the energies is possible by changing the thickness of the antenna (as shown in Fig. 6) or by scaling the longitudinal and transverse dimensions by factors F and 1/F, respectively, so that the lateral area is preserved. We define the lateral aspect ratio LAR = F² (higher than one when the longitudinal tip-to-tip distance is increased) and show the k-dependences for LAR = 0.67 and 1.5 in Fig. 7(left) by the dotted lines.

 

Fig. 7 Left: Simulated energies of the modes D_L (black symbols), D_T (red symbols), and MA (green symbols) as functions of “effective k”, defined as inversely proportional to the characteristic lateral dimension of an antenna. The thick solid lines and squares correspond to the reference crescent-shaped antenna (r_B = 55 nm, r_S = 50 nm, c = 45 nm, h = 30 nm). The dashed lines correspond to the antennas with a height of 15 nm (down-pointing triangle) and 40 nm (up-pointing triangle). The dotted lines correspond to the antennas with modified lateral aspect ratios (LAR, see text for details) of 0.67 (left-pointing triangle) and 1.50 (right-pointing triangle). Right: Energies of the two plasmonic dipolar modes (D_L, D_T) in gold crescent antennas of various dimensions plotted as the D_T−D_L energy difference vs. the energy of the D_L mode. The simulated data are displayed by squares. The lines serving as guides for the eye connect the points corresponding to LAR scaling (blue lines) and k scaling for the antenna heights 15 nm (black line), 20 nm (green line), 30 nm (yellow line), and 40 nm (brown line). For comparison, the experimental data are displayed by large red circles.

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By combining the above mentioned scalings, independent and wide-range tuning of the plasmonic mode energies is possible. Right panel of Fig. 7 shows the energies of the D_L and D_T modes so that the horizontal axis corresponds to the energy of the D_L mode and the vertical axis corresponds to the energy difference between the D_T and D_L mode. The results of simulations (squares) show the possibility of the independent tuning of the energy of the D_L mode in the range of 0.8 −2.0 eV and the D_T−D_L energy difference in the range of 0.2 – 0.7 eV. Note that the LAR-scaling (represented by the blue lines) allows to change the energy difference with only minor changes in the energy of the D_L mode. Our experimental results [large red circles in Fig. 7(right)] cover the D_L mode energy range of 0.7 – 1.5 eV for the D_T−D_L energy difference around 0.45 eV. Notably, the larger structures exhibit the D_L resonance between 0.80 and 0.95 eV, covering the infrared telecommunication wavelengths of 1.3 and 1.55 μm (0.95 and 0.80 eV).

Conclusion

We have studied the plasmonic modes in gold crescent-shaped plasmonic antennas using electron energy loss spectroscopy, determined their energies and mapped the spatial distribution of their excitation efficiency. From boundary element simulations we have assigned the observed peaks to particular plasmon resonances and obtained additional attributes such as field distributions. We have demonstrated the existence of two dipolar modes with the mutually perpendicular polarization in all studied structures, as well as the presence of a multimodal assembly at the energy corresponding to the onset of interband absorption in gold. In large structures, two additional modes of a prevailing quadrupolar character have been resolved. In extended calculations, we have demonstrated the broad-range tunability of the energies of plasmon resonances by scaling the dimensions of the antennas, and the compatibility with the infrared telecommunication technology.