Visualizing the near-field coupling and
interference of bonding and anti-bonding modes
in infrared dimer nanoantennas
Pablo Alonso-González,1,* Pablo Albella,2 Federico Golmar,1,3 Libe Arzubiaga,1
Félix Casanova,1,4 Luis E. Hueso,1,4 Javier Aizpurua,2 and Rainer Hillenbrand1,4,5
1Nanooptics Group, CIC nanoGUNE Consolider, 20018 Donostia – San Sebastián, Spain
2Centro de Física de Materiales (CSIC-UPV/EHU) and Donostia International Physics Center (DIPC), 20018
Donostia-San Sebastián, Spain
3I.N.T.I.–CONICET, Av. Gral. Paz 5445, Ed. 42, B1650JKA, San Martín, Bs As, Argentina
4IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
5r.hillenbrand@nanogune.eu
*palonso@nanogune.eu,
Abstract: We directly visualize and identify the capacitive coupling of
infrared dimer antennas in the near field by employing scattering-type
scanning near-field optical microscopy (s-SNOM). The coupling is
identified by (i) resolving the strongly enhanced nano-localized near fields
in the antenna gap and by (ii) tracing the red shift of the dimer resonance
when compared to the resonance of the single antenna constituents.
Furthermore, by modifying the illumination geometry we break the
symmetry, providing a means to excite both the bonding and the “dark”
anti-bonding modes. By spectrally matching both modes, their interference
yields an enhancement or suppression of the near fields at specific
locations, which could be useful in nanoscale coherent control applications.
©2013 Optical Society of America
OCIS codes: (180.4243) Near-field microscopy; (110.3080) Infrared imaging; (250.5403)
Plasmonics; (260.3910) Metal optics.
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1. Introduction
Light illuminating a metal nanostructure can resonantly excite surface plasmons, which are
collective oscillations of free electrons in the metal that lead to the formation of highly
enhanced nano-localized optical fields at the metal surface, the so-called “hot spots” [1]. The
frequency and intensity of these oscillations are highly sensitive to the nanostructure shape,
size, and environment, offering the possibility to control and manipulate electromagnetic
fields at the nanometer scale [2–4]. In the last years, this function of metal nanostructures has
promoted the development of a large variety of applications including surface-enhanced
Raman scattering (SERS) [5], nanoscale plasmon rulers [6], or novel enhanced photo-
detection and photo-emission mechanisms [7].
A vast range of plasmonic antenna structures showing different functionalities have been
proposed [8–14]. Particularly interesting are those formed by combinations of simple metallic
elements that couple through near-field interaction [15–30] (often referred to as plasmonic
molecules). Due to their coupling behavior, plasmonic molecules show the appearance of
unique hybridized plasmon modes [23, 24, 29, 31, 32], in analogy to the hybridization of
wave functions in molecules. Importantly, the near-field coupling of these modes in a
plasmonic structure promotes the appearance of prominent interfering effects such as
plasmonic Fano resonances [13, 33–38] or electromagnetic induced transparency (EIT) [39–
41], which offer extended possibilities in the design and tuning of the antenna’s optical
response [4].
Although the study of coupling, hybridization and interference of plasmon modes has
become increasingly ubiquitous in the literature during the last years, it has been mainly
conducted by far-field characterization techniques on complex plasmonic structures such as
oligomers [35, 42], “dolmen, Pi” antennas [43] or multilayer nanoshells [44], supported by
near-field calculations. The ability to visualize and, more importantly, to tune these coupling
phenomena in the near field of the plasmonic antennas will facilitate the creation and
development of a variety of novel plasmonic devices, where the optical properties can be
controlled at the nanoscale. One relevant example of a basic plasmonic structure showing
coupling behavior is the dimer antenna, which is formed by two metal nanorods separated by
a nanoscale gap [16, 17, 19, 23–26, 29, 30, 45, 46]. In such a dimer, the strong near-field
interaction across the gap causes hybridization of plasmon modes that in analogy to the
energy levels in a molecule leads to the splitting of modes into a lower-energy bonding mode
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
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and a higher-energy anti-bonding mode. The bonding mode is characterized by a parallel
alignment of the electric dipoles on each nanorod, producing strong field enhancement in the
gap region. The anti-bonding mode is defined by an anti-parallel alignment of the dipoles [23,
47].
Here, we use scattering-type scanning near-field optical microscopy (s-SNOM) to directly
visualize the coupling, hybridization and interference of bonding and anti-bonding modes in
the near field of infrared dimer antennas. The excitation of the anti-bonding mode, which is
symmetry-forbidden for plane wave illumination, is achieved by rotating the antennas relative
to the plane-wave illumination, which introduces retardation and thus symmetry breaking.
The excitation of both the bonding and anti-bonding modes allows us to visualize their
complex interference directly in the near field of the antennas. We observe a net enhancement
or suppression of local fields at specific locations, which can provide a novel strategy for an
active control of the near-field enhancement in an optical antenna.
2. Mapping near-field coupling in dimer antennas
Figure 1(a) illustrates the experimental set-up that we use for mapping the near-field
distribution and topography of infrared dimer antennas. We use a side-illumination s-SNOM
[33, 48, 49] (Neaspec GmbH) where a Si tip, vibrating vertically at frequency Ω, is used to
scatter the antenna fields while recording the topography. Using a parabolic mirror objective,
the antenna is illuminated at an angle of about 50° from the surface normal with the focused
beam of a CO2 laser (λinc = 11.1 μm), which is polarized parallel to the long axis of the antennas (s-polarization). The same objective is used for collecting the backscattered light.
Using a polarizer in front of the detector, we select the horizontally (s-polarized) or vertically
(p-polarized) fields backscattered by the tip. Signal demodulation at higher harmonics nΩ of
the tip oscillation frequency in combination with a pseudo-heterodyne interferometric
detection [50] yields background-free near-field ampitude |En| and phase φn maps. The topography image of a typical dimer antenna studied in this work is shown in Fig.
1(b). It consists of two longitudinally aligned metal nanorods separated by a gap with a
nominal width of 50 nm. The antennas were fabricated on a CaF2 substrate by electron beam lithography and designed to exhibit the fundamental dipolar resonance at a wavelength of
about 11 μm. Figure 1(c) shows the s-SNOM amplitude and phase images when the p-
polarized backscattered field (yielding mainly the out-of-plane near-field component) is
recorded. Note that for better visibility of the antenna phase, we display random phase values
by a grey color scale. A random phase occurs in areas where the amplitude signal is below the
noise level, which essentially is the case on the substrate where the antenna fields are weak.
Each nanorod shows large amplitude signals |E4|p at their extremities that oscillate out of phase for φ4p = 180°. At the antenna gap no field is observed, owing to the absence of out-of-plane near-field components in the gap center [18]. This near-field amplitude and phase
distribution reveals an accumulation of charges of opposite sign at both sides of the gap
region [26], which indicates capacitive coupling between the nanorods. Mapping the s-
polarized backscattered fields (yielding the in-plane field distribution at the gap), we obtain
the amplitude |E4|s and phase φ4s images shown in Fig. 1(d). We observe significant signals at the extremities of the nanorods and an exceptionally intense field |E4|s at the antenna gap. A full width at half maximum (FWHM) of about 50 nm is obtained for this “hot spot”, which
agrees well with the nominal gap width (measured by scanning electron microscopy (SEM)).
This strongly localized and enhanced field at the gap center further indicates a capacitive
coupling between the nanorods and thus, the excitation of a bonding mode in the dimer
antenna [45].
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
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Fig. 1. Experimental set-up and near-field imaging. (a) Illustration of the s-SNOM used for
mapping the near-field distribution and topography of infrared dimers. The Si tip, which
vibrates at the mechanical resonance frequency Ω of the AFM cantilever, is used to scatter the
antenna fields. Using a parabolic mirror objective, the dimer is illuminated with the focused
beam of a CO2 laser (Einc), which is polarized parallel to the long axis of the antennas (s-polarization). The same objective is used to collect the backscattered light (Eff). A polarizer in front of the detector ensures the selection of either s-polarized or p-polarized backscattered
fields. Signal demodulation at higher harmonics nΩ in combination with a pseudo-heterodyne
interferometric detection yields background-free near-field amplitude |En| and phase φn maps [50]. (b) Topography and near-field images of a dimer antenna for (c) p-polarization (|E4|p, φ4p) and (d) s-polarization (|E4|s, φ4s) detection schemes. The imaging wavelength is λinc = 11.1 μm. The dashed white line in the phase images highlight the nanorods contour.
It is well known that the resonance of the bonding mode of a dimer antenna with gap
width g and a total length of 2L + g lies at lower energies than the dipolar mode of one single
nanorod of length L [15, 16, 32], as illustrated in the schematics of Fig. 2.
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
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Fig. 2. Diagram of energy levels as a function of nanorod length L for dimer antennas and
single nanorods. At a fixed illumination wavelength λinc (red dashed line) the lower energy bonding mode in a dimer antenna (red) occurs at a shorter nanorod length L1 than the fundamental.
The measurement of this energy shift would be a clear verification of the capacitive
coupling in a dimer structure. In the following we experimentally demonstrate this energy
shift in the near field of the antennas. To this end we fabricated sets of dimers and single
nanorods of varying length 2L + g, respectively L, and imaged both of them at λinc = 11.1 μm with our s-SNOM. The gap width g is the same for all dimer antennas. Figure 3(a) shows a
schematics of the s-SNOM experiment and Figs. 3(b)-3(d) the topography and near-field
amplitude |E4|s and phase φ4s images of the set of dimer antennas with a nominal gap width g = 50 nm, obtained by recording the s-polarized backscattered field. The length L of the dimers
decreases from the top to the bottom and from the left to the right. Each antenna structure is
separated 10 μm to the others to avoid any near-field coupling among them.

Fig. 3. s-SNOM imaging of dimer antennas. (a) Schematics of the s-SNOM experiment. The
longitudinal axis of the antennas is parallel to the incident polarization. (b) Topography, (c)
near-field amplitude |E4|s and (d) phase φ4s images of dimer antennas taken at λinc = 11.1 μm.
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 1275

Figures 4(a) and 4(b) show higher-resolution amplitude |E4|s and phase φ4s images of some of the individual antennas. For later comparison with the calculated local field at the antenna,
we plot in Fig. 4(c) and 4(d) the square root of the amplitude 4sE and half the phase φ4s/2
measured in the center of the antenna gap (red dots) as a function of nanorod length, since the
antenna enhances both the illumination of the tip as well as the scattering from the tip (double
scattering process) [49]. We observe that with increasing nanorod length L (from the bottom
to the top in Figs. 4(a) and 4(b)) the amplitude signal increases, reaching a maximum at a
length of Lres-dimer = 3.35 μm. With further increasing length, the amplitude decreases, revealing the resonance behavior of the antennas [51]. The phase (Fig. 4(b), 4(d))
continuously increases with increasing L, which further confirms the existence of an antenna
resonance. For comparison we also plot in Fig. 4(c) and 4(d) the square root of the
amplitude 4sE and half the phase φ4s/2 measured on top of the extremities of single nanorods
(blue dots), as indicated by a blue cross in Fig. 4(d). We note that the single nanorod antennas
(images and data published in ref. 49) and the dimer antennas were fabricated on the same
CaF2 substrate within the same e-beam lithography process. All antennas were imaged within one experiment, i.e. with the same tip and the same imaging parameters (same tapping
amplitude and demodulation order). We see that the single nanorod resonance occurs at a
nanorod length Lres-single = 3.7 μm, which is clearly larger than the resonance length Lres-dimer = 3.35 μm of the bonding mode in the dimer antennas. This shift of the resonance length ΔLres = Lres-dimer - Lres-single corresponds to a red-shift of the bonding mode, as illustrated in Fig. 2.

Fig. 4. Verification of near-field coupling in dimer antennas. (a) Near-field amplitude |E4|s and (b) phase φ4s images of dimer antennas with a varying length L. The horizontal white lines separate the images taken individually. (c) Comparison of the normalized near-field
amplitude 4sE in dimer antennas (red dots) and single nanorods (blue dots) as a function of
nanorod length L. (d) Comparison of the near-field phase φ4s/2 in dimer antennas (red dots) and single nanorods (blue dots, data from ref [49].) as a function of nanorod length L. The crosses
in the antenna schematics show the locations were the fields were evaluated: the center of the
gap for the dimers and the nanorod extremity for the single nanorods. Numerical calculations
by FDTD of the in-plane component of the antennas’s near-field amplitude and phase are also
shown in (c) and (d) by red (dimers) and blue (single nanorods) solid lines.
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 1276

In order to confirm this result, we calculated numerically by a finite-difference in time-
domain (FDTD) method the near-field amplitude and phase (solid lines) at the same antenna
locations where the experimental values were measured (marked by crosses in the inset of
Fig. 4(d)). We find an excellent agreement between calculations and experiments,
corroborating the spectral shift and thus the capacitive coupling in the dimer antennas.
3. Interference of bonding and anti-bonding modes in dimer antennas
The coupling across the gap in the dimer antennas opens the possibility to excite a higher-
energy anti-bonding mode, which is characterized by the anti-parallel alignment of electric
dipoles at both sides of the gap. The excitation of this mode is symmetry-forbidden for plane
waves under normal incidence. It is thus generally referred in the literature to as a “dark”
mode. However, it can be excited if the symmetry is broken [22, 23, 29, 52–54]. This can be
achieved, as we show in the following, upon rotation of the sample with respect to the
incident field, which under a side-illumination geometry introduces a phase shift along the
antennas due to retardation.
In Fig. 5 we schematically illustrate the energy splitting into bonding (parallel red arrows)
and anti-bonding (anti-parallel blue arrows) modes in dimer antennas for two different
nanorod lengths, LA and LB.

Fig. 5. Diagram of energy levels as a function of nanorod length L for the bonding and anti-
bonding modes in dimer antennas. At a fixed illumination wavelength λinc (black dashed line) the lower energy bonding mode in a dimer antenna (parallel red arrows) occurs at a shorter
length LA than the higher energy anti-bonding mode (anti-parallel blue arrows) at LB. The graphs display schematic near-field amplitude and phase spectra of the bonding (red) and anti-
bonding (blue) modes.
For longer antennas, the energy levels shift to lower energies. Assuming that both modes
can be excited, this implies that at a fixed energy/(light frequency) (dashed black line) we can
access the bonding mode for short antennas at a nanorod length LA and the anti-bonding mode when the nanorod length is increased to LB. Being in resonance with the bonding mode (at length LA), we expect that this mode dominates the antenna response, as the relatively narrow anti-bonding mode is shifted to significantly higher energies (see schematic spectra to the
left). The situation, however, is different when we are in resonance with the anti-bonding
mode (at length LB). Because the resonance of the bonding mode is relatively large (see schematic spectra to the right), it overlaps with the resonance of the anti-bonding mode. Being
in resonance with the anti-bonding mode at LB, we thus expect the excitation and interference of both bonding and anti-bonding modes. In order to study this situation, we imaged dimer
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 1277

antennas of different length, which were rotated in-plane by 20° degrees in order to break the
symmetry and thus to excite both bonding and anti-bonding modes. A sketch of the
illumination geometry is depicted in Fig. 6(a) (the p-polarized scattered field is detected,
yielding |E3|p and φ3p, which corresponds to the out-of-plane local field component). In Figs. 6(b)-6(d) we show the topography and the experimental near-field amplitude and
phase images of the 20°-rotated dimer antennas for nanorod lengths ranging from L = 2.7 μm
to 4.8 μm. The images were taken at λinc = 11.1 μm. For the shortest dimer antenna (LA = 2.7 μm), we observe a symmetric near-field distribution with strong fields oscillating out of phase
for 180° at the nanorod extremities and across the gap. This near-field pattern is similar to that
obtained for the non-rotated antennas (Fig. 1(c)), indicating that the bonding mode is
dominating the optical response of the antenna at this nanorod length (corresponding to the
schematics at LA in Fig. 5).
-

(b)
(c) (d)
1 µm
L= 4.8 µm
L= 4.4 µm
L= 4.1 µm
L= 3.8 µm
L= 3.6 µm
L= 3.4 µm
L= 3.2 µm
L= 2.7 µm
Max
0 |E3|p 3p LA
LB
Einc
20º
(a)
40º

Fig. 6. s-SNOM imaging of 20°-rotated dimer antennas. (a) Schematics of the s-SNOM
experiment. The dimer antennas are rotated in-plane by 20°. (b) Topography, and (c) near-field
amplitude |E3|p and (d) phase φ3p images of dimer antennas with a varying length L ranging from 2.7 μm to 4.8 μm. The horizontal white lines separate the images taken individually.
With increasing nanorod length L (from the bottom to the top in Figs. 6(b)-6(d)), we
observe an asymmetry in the near-field distribution. At the extremity of the left nanorod we
observe an amplitude maximum at LB = 3.8 μm, while at the extremity of the right nanorod the amplitude is much lower and does not exhibit a clear resonance maximum (Fig. 6(c)).
Simultaneously, the phase on the left and right nanorod develops different with increasing
nanorod length. On the left side of the gap, the phase increases by about 160° (from red to
dark blue in Fig. 6(d)), while on the right side of the gap it increases by about 110° (from light
blue to red in Fig. 6(d)). As a result of this behavior, the phase jump across the gap is slightly
smaller than 180° for the long antennas, L > 3.8 μm (the change from dark red to light red
across the gap corresponds to 120°). We attribute this behavior to the excitation of both
bonding and anti-bonding modes in the dimer (corresponding to the schematics at LB in Fig. 5). Constructive interference on the left nanorod (owing to parallel alignment of the local
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 1278

dipole oscillations of bonding and anti-bonding modes) yields enhancement of the local fields,
while destructive interference on the right nanorod (owing to antiparallel alignment of the
local dipole oscillations of the bonding and anti-bonding modes) yields reduction of the local
fields.

Fig. 7. Interference of modes in rotated dimer antennas. (a) Experimental (|E3|p, φ3p) and calculated out-of-plane near-field amplitude and phase images for a nanorod length LA = 2.7 μm and (b) a nanorod length LB = 3.8 μm. (c) Numerically calculated values of the near-field amplitude and (d) phase of the out-of-plane near-field component at the left/right side of the
gap (red/blue curve). The red and blue crosses mark the positions at 300 nm from the gap on
top of the antennas where the near-field amplitude and phase were extracted from the near-
field images. For comparison the near-field amplitude and phase for non-rotated antennas (grey
curves) evaluated at the same location are also shown.
To corroborate the constructive and destructive interference of bonding and anti-bonding
modes, we performed numerical FDTD calculations of the near-field distribution of the
rotated antennas, according to the illumination geometry depicted in Fig. 6(a) (without the tip
been considered). In the calculations we apply perfectly matched layers as boundary
conditions and assume Gaussian profile for the incident beam. Figures 7(a) and 7(b) show the
calculated out-of-plane near-field amplitude and phase images of the antennas with LA = 2.7 μm and LB = 3.8 μm, exhibiting good agreement with the experimental images (taken from Fig. 6). To understand the asymmetric near-field distribution, we show in Fig. 7(c), 7(d)
amplitude and phase values as a function of the nanorod length L, calculated 300 nm to the
left and to the right of the antenna gap, and 10 nm above the antenna surface (positions
marked by crosses in the inset of Fig. 7(c)). We also show the amplitude and phase for the
non-rotated dimer antennas (grey curves) evaluated at the same positions. To quantitatively
compare the rotated and non-rotated antennas, we multiplied the amplitude of the latter by the
incidence normalization factor cos(20°). For nanorod lengths around LB, the amplitude to the left of the gap (red curve) is increased compared to the non-rotated antenna (grey curve),
while to the right of the gap (blue curve) the amplitude is reduced and exhibits a dip. This
observation substantiates constructive interference between bonding and anti-bonding mode
on the left nanorod, and destructive interference on the right nanorod. At lengths below LA, amplitude and phase on both nanorods match well with that of the non-rotated antenna, as
here the anti-bonding mode is negligibly weak (as schematically shown in Fig. 5). At nanorod
lengths substantially much larger L > LB, the near-field amplitudes on both sides of the gap become nearly equally strong. However, the phase difference between the left and right side
of the gap is significantly reduced to about 120° (see right-hand side of Fig. 7(d)), compared
to the non-rotated antennas where the phase jump across the gap is 180° (grey curves). We
explain this behavior by a phase shift between the bonding and anti-bonding modes while
#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 1279

both modes exhibit similar field magnitudes (see schematics in Fig. 5) This phase shift
between the two modes can be understood by considering that the resonance of the anti-
bonding mode is expected for L > LB. Thus, the phase shift between the anti-bonding mode and the incident field (0º reference) assumes values around 90° for L > LB, (right-hand side schematics in Fig. 5), while the phase shift between the bonding mode and the incident field
approaches nearly 180° (grey curve in Fig. 7(d)).
4. Summary
In summary, we have presented a detailed s-SNOM study of coupling and hybridization of
modes in infrared dimer antennas. In section 2 we verified capacitive near-field coupling and
the consequent excitation of the bonding mode. This has been achieved by visualizing the
enhanced near-field amplitudes inside the antenna gap and by measuring the red-shift of the
resonance in the near-field of the antennas. In section 3 we studied the excitation of the
symmetry-forbidden anti-bonding mode in the dimer antennas. To this end, we introduced a
rotation of 20° in the antenna illumination geometry, which yields retardation along the
antennas and thus a breaking of the system’s symmetry. As a result, the excitation of both
bonding and anti-bonding modes yields a near-field interference, which manifests in the near-
field images as an enhancement and suppression of local fields at specific locations of the
dimers. The coupling and interference of antenna modes as shown here provides a useful
mechanism for nanoscale coherent control applications.
Acknowledgments
We acknowledge support from the European FP7 projects “Nanoantenna” (FP7-HEALTH-
F5-2009-241818-NANOANTENNA), NMP (NMP3-SL-2011-263104- HINTS), and
“SPINTROS” (257654), and the National Projects MAT2009-08398, MAT2009-08494 and
FIS2010-19609-C02-C01 from the Spanish Ministerio de Ciencia e Innovacion. We also
acknowledge the Marie Curie Actions PIRG06-GA-2009-25647, ITAMOSCINOM, as well as
the Basque Government Program PI2011-1 and Etortek-2011 (nanoiker).

#178728 - $15.00 USD Received 25 Oct 2012; revised 22 Dec 2012; accepted 22 Dec 2012; published 11 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 1280