Surface plasmon resonance spectroscopy of single bowtie nano-antennas using a differential reflectivity method

We report on the structural and optical properties of individual bowtie nanoantennas both on glass and semiconducting GaAs substrates. The antennas on glass (GaAs) are shown to be of excellent quality and high uniformity reflected by narrow size distributions with standard deviations for the triangle and gap size of = 4.5 nm = 2.6 nm and = 5.4 nm = 3.8 nm, respectively. The corresponding optical properties of individual nanoantennas studied by differential reflection spectroscopy show a strong reduction of the localised surface plasmon polariton resonance linewidth from 0.21 eV to 0.07 eV upon reducing the antenna size from 150 nm to 100 nm. This is attributed to the absence of inhomogeneous broadening as compared to optical measurements on nanoantenna ensembles. The inter-particle coupling of an individual bowtie nanoantenna, which gives rise to strongly localised and enhanced electromagnetic hotspots, is demonstrated using polarization-resolved spectroscopy, yielding a large degree of linear polarization of ρmax ~ 80%. The combination of highly reproducible nanofabrication and fast, non-destructive and non-contaminating optical spectroscopy paves the route towards future semiconductor-based nano-plasmonic circuits, consisting of multiple photonic and plasmonic entities.

Single metal nanoparticles 1 , nanoparticle dimers 2 or even nanoparticle arrays 3 are well known to concentrate visible 4 , infrared 5 and microwave 6 radiation from the far-field into sub-wavelength sized optical volumes whilst simultaneously giving rise to strong electric field enhancements 7,8 on the order of 10 3 − 10 4 . In particular optical antennas 9 such as bowtie nanoantennas have been shown to provide besides extraordinarily high field enhancements 10 , also directionality 11 , broadband spectral responses 12 , local electrical control 13 with potential for tunability 14 , highly efficient electro-optical driving 15 and full polarization control 16 . Amongst others, such systems found already applications in surface enhanced Raman spectroscopy 17 , ultra-high resolution lithography 18 and microscopy 19 , bio-chemical sensing 20,21 , spontaneous emission control 22 and enhancement 23,24 , non-linear optics 25,26 and solar energy conversion 27 .
Chemical synthesis 28 of plasmonic nanostructures is well established and widely-used since sophisticated and expensive equipment is not required to produce large amounts of plasmonic nanoparticles. However, nano-lithography techniques offer much higher flexibility in controlling and deterministically designing the optical properties of plasmonic nanostructures. For example, it is possible to tailor the localised surface plasmon polariton resonance via precise adjustment of size 29,30 and shape 31 , as well as the polarization of the scattered photons via the antenna geometry 16 . Moreover, the exact control of the particle location and density during the lithography process enables to switch on radiative coupling in arrays of nanoparticles 32 and, thus, give rise to multipolar surface plasmon modes 33 and collective surface lattice resonances 34 . This proves crucial to design novel properties such as magnetic polarizability 35 , negative-refractive indices 36 or phase-gradients 37 in metasurfaces 38 .
Scientific RepoRts | 6:23203 | DOI: 10.1038/srep23203 Many spectroscopy techniques for studying single plasmonic nanostructures have been established in recent years 39 . Examples include scanning near-field optical microscopy 40 , attenuated total internal reflection 4 , extinction or transmission experiments 2 and dark field spectroscopy 41 . However, the majority of those methods either demand expensive equipment, require specially designed samples or contaminate their surface. Therefore, a reliable, fast, non-destructive and cheap measurements method with high spatial resolution would be highly attractive for determining the optical properties of the individual plasmonic nanostructures on a future semiconductor-based plasmonic nano-circuit 42,43 .
Here, we present a systematic and comprehensive study of the structural and optical properties of individual, lithographically defined bowtie nanoantennas 12 on glass and semiconducting GaAs substrates using differential reflection spectroscopy. Therefore, we fabricated antennas with sizes 100 nm≤ s 0 ≤ 150 nm, feed-gaps down to 5 nm and tip radii r c = 14 ± 5 nm using electron beam lithography 30 . Scanning electron microscopy yields narrow distributions of triangle size and gap size on glass (GaAs) substrates with standard deviations of σ = . nm 4 5 s glass σ = .
( ) ( ) , respectively, indicating highly uniform and reproducible nanofabrication. The corresponding optical properties of individual bowtie nanoantennas are investigated using high-spatial resolution, differential reflection spectroscopy, demonstrating the linear (inverse cubic) dependence of the surface plasmon resonance energy E res on the triangles size (gap size) 12,30 . Comparison between measurements on single and ensembles of bowtie nanoantennas 30 show clear indications of inhomogeneous broadening 4 , varying between 0.07 eV and 0.21 eV for s 0 = 100 nm and s 0 = 150 nm, respectively. Finally, we study the inter-particle coupling between the two nano-triangles forming the bowtie nanoantenna using polarization-resolved spectroscopy. Those measurements show strongly linearly polarized emission along the main axis of the antenna for the coupled mode with a degree of polarization up to ρ max ~ 80%. Our results are contrasted with studies on semiconductor GaAs substrates and all experiments are shown to be in excellent agreement with numerical simulations 44 .

Results
In Fig. 1(a), we present a selection of scanning electron microscopy images of lithographically defined Au bowtie nanoantennas on a non-conducting glass substrate, consisting of two nominally equilateral nanotriangles, arranged in a tip-to-tip-configuration 12,30 . The top (bottom) row shows bowtie nanoantennas for constant nominal triangle size s 0 = 140 nm (gap size g 0 = 10 nm) and increasing g 0 (s 0 ) between 5 nm (100 nm) and 50 nm (150 nm) from left to right, respectively. The antenna thickness was kept constant at t = 35 nm. The triangles forming the bowtie nanoantenna are of high quality, indicated by their smooth edges and surfaces without observable distortions or fraying. The typical tip radii was found to be r c = 14 ± 5 nm. The highly reproducible fabrication process is further supported by the histograms plotted in Fig. 1(b), representing the number of individual bowtie nanoantennas as a function of triangle size deviation Δ s ≡ s − s 0 and gap size deviation Δ g ≡ g − g 0 in the left and right panel, respectively. Here, s and g denote the experimentally determined triangle and gap size, respectively, as defined in the leftmost images in Fig. 1(a). We extracted s and g from high resolution scanning electron microscopy measurements for ~300 nominally identical bowtie nanoantennas without any pre-selection, with s 0 and g 0 spanning the range given in Fig. 1(a). Both histograms for Δ s and Δ g are well described by a Gaussian distribution = −  Fig. SM1. We conclude that we established a highly reproducible lithography process for bowtie nanoantennas with a fabrication accuracy of ~10 nm, giving rise to reproducibly fabricated nanoantennas with feature sizes down to 10 nm. We note that bowtie nanoantennas with gap sizes g < 10 nm are not reproduced with 100% yield due to the ~10 nm resolution limit of the used electron beam system. Therefore, sub-10 nm gap sizes can only be obtained based on a statistical approach and imaging is impeded in particular on non-conducting substrates due to charging effects. However, we could clearly distinguish antennas with sub-10 nm gaps from clustered antennas in the optical characterisation and comparison with the corresponding simulations, since clustered antennas give rise to spectrally detuned localized surface plasmon polariton resonance.
To study the optical response of individual bowtie nanoantennas, we used a home-built confocal microscope that facilitates measurements of the broadband (Δλ ~ 400 − 1600 nm) reflectivity of a diffraction limited laser spot generated by a white-light super-continuum source as schematically shown in Fig. 2(a). The excitation beam is, if not stated otherwise, linearly polarized along the long axis of the bowtie nanoantenna (defined as y-axis in Fig. 1(a)), reflected from a beamsplitter and focused onto the sample via a microscope objective. The reflected light is collected via the same objective, transmitted through the beamsplitter and guided via an optical fibre to a spectrometer. For more details on the setup and the used optical components we refer to the Methods Section. In order to determine the localised surface plasmon polariton resonance of an individual nanoantenna, we performed two subsequent measurements; first, we measured the reflectivity R on (E) from an individual bowtie nanoantenna as a function of energy E as shown by the red curve in Fig. 2(b). Here, the upper inset depicts a light microscopy image recorded in our setup, which displays the bowtie nanoantennas (s 0 = 140 nm, g 0 = 10 nm) arranged in a periodic array with a lattice constant of a = 1.5 μm and the white light excitation spot focused on one single antenna. In a second step, we recorded a similar reflectivity spectrum R off (E) from a location spatially displaced from the bowtie nanoantenna array as shown by the lower inset in Fig. 2(b) for reference. The corresponding spectrum R off (E) is plotted in blue. From the measurements of R on (E) and R off (E) we calculate the differential reflectivity ΔR/R off ≡ (R on − R off )/R off , which represents a measure for the scattered light from the bowtie nanoantenna 46 . The ΔR/R off -spectra determined from the reflectivity measurements shown in Fig. 2(b) is presented in panel (c). We observe a peak-like response with a resonance maximum γ res at the resonance energy E res , interpreted as the dipolar localised surface plasmon polariton resonance of the investigated bowtie nanoantenna 39 . Furthermore, we can extract from the differential reflectivity spectrum the full width at half maximum Γ res and, thus, gain insights into the related plasmon lifetime T pl via T pl = 2 /Γ res 41 , where  denotes the reduced Planck constant.
In the following, we use our method to systematically study the optical properties of individual bowtie nanoantennas fabricated on both glass and GaAs substrates as a function of s 0 and g 0 . The experimentally obtained ΔR/R off -spectra for g 0 = 10 nm and triangle sizes 100 nm < s 0 < 150 nm in steps of Δs 0 = 10 nm are presented in Fig. 3(a) for bowtie nanoantennas on glass. We observe a systematic shift of the localised surface plasmon polariton resonance from E res = 1.39 eV to higher energies E res = 1.73 eV with decreasing s 0 , attributed to reduced retardation effects of the exciting electromagnetic field and the depolarization field inside the metal particles 47 . The blue-shift in E res is accompanied by a decreasing resonance maximum γ res from γ res = 1.37 to γ res = 0.67, which is due to a reduction of the geometrical scattering cross-section of the antennas with decreasing s 0 . In Fig. 3(b), we present corresponding finite-difference time-domain simulations 44 of the scattering cross-section σ for bowtie nanoantennas on a glass substrate with g 0 = 10 nm, r c = 20 nm and varying triangle size 100 nm < s 0 < 150 nm. We find increasing E res and decreasing γ res with decreasing s 0 , both in excellent qualitative and quantitative agreement with our experimental results. We compare the measured and simulated data for E res as a function of s 0 and g 0 in Fig. 3(c,d), respectively. Blue (black) symbols denote the experimental results for bowtie nanoantennas on a glass (GaAs) substrate, whilst the red symbols represent the simulation results. In general, we observe a comparable linear (cubic) trend for the s 0 -(g 0 -) dependence of bowtie nanoantennas on glass and GaAs with shift-rates for the s 0 -dependence of − (6.8 ± 0.3) meV/nm and − (6.3 ± 0.2) meV/nm, respectively. The global red-shift of the GaAs data of ΔE ~ 0.3 eV is due to the increase in refractive index of Δn ~ 2.0 as compared to glass 30 behaviour observed in the gap size dependence in Fig. 3(d) is due to near-field interaction, describing the coupling of the surface plasmons in the two adjacent triangles by a coupling of effective point dipoles 48 . Simulations of the spatial electromagnetic field distribution for similar bowtie nanoantennas are presented in ref. 30. Additional spectra and the corresponding simulated scattering cross-sections for the g 0 -dependence on glass and the s 0 -and g 0 -dependence on GaAs, respectively, are presented in Fig. SM2. As a consequence, we experimentally studied localised surface plasmon polariton resonances for individual bowtie nanoantennas using differential reflection spectroscopy and obtained excellent agreement with numerical simulations of the scattering cross-sections. This combined experimental-simulation approach enables us to reproducibly design and deterministically control the localised surface plasmon polariton resonance of individual nanoantennas. As demonstrated in the previous section, the localised surface plasmon polariton resonances of bowtie nanoantennas depend strongly on the triangle size s 0 and gap size g 0 . Even though our fabrication process was shown to be highly reproducible, slight variations in s 0 and/or g 0 will still result in non-negligible variations of the localised surface plasmon polariton resonances. Therefore, measurements on ensembles of bowtie nanoantennas as investigates in ref. 30 are expected to show enlarged resonance linewidths Γ res due to size-and shape-induced inhomogeneous broadening 46 . To test this hypothesis, we compare in Fig. 4(a) two typical differential reflectivity spectra  recorded from an individual (N = 1) and an ensemble (N ~ 12) of bowtie nanoantennas on a glass substrate in blue and black, respectively. Here, N denotes the number of bowtie nanoantennas excited simultaneously in the differential reflectivity measurements. The left upper and lower insets in Fig. 4(a) show white light microscopy images of the bowtie array with the excitation spot of the white light super-continuum source and a halogen lamp for single and ensemble antenna spectroscopy, respectively. The differential reflectivity spectra ΔR/R off for single and ensemble antenna measurements exhibit a maximum at comparable E res , attributed to the localised surface plasmon resonance. However, the corresponding resonance linewidth Γ res for the measurement of an individual bowtie nanoantenna is found to be considerably narrower as compared to bowtie nanoantenna ensembles, clearly visible on a normalized differential reflectivity scale as shown in the inset of Fig. 4(a). The larger linewidth for the ensemble measurement is attributed to inhomogeneous broadening.
We systematically investigated this effect by determining Γ = res N 1 of individual bowtie nanoantennas with constant g = 10 ± 3 nm as a function of measured triangle size s. The results of those measurements are plotted as blue symbols in Fig. 4 is attributed to enhanced radiation damping for increasing antenna sizes 49 . Furthermore, we present for comparison differential reflectivity measurements conducted on bowtie nanoantenna ensembles 30 for nominal sizes 100 nm < s 0 < 150 nm with Δs 0 = 10 nm as black symbols in Fig. 4(b). In addition to the linear increase in Γ ∼ res N 12 with increasing s 0 due to enhanced radiation damping, we observe a global offset Γ Γ Γ ∆ = − ∼ = res r es N res N 12 1 for the ensemble measurements attributed to inhomogeneous broadening, which varies between ΔΓ res = 0.07 eV and ΔΓ res = 0.21 eV for s ~ 100 nm and s ~ 150 nm, respectively. We note that the unexpected non-constant offset ΔΓ res for increasing s cannot be explained based on the current experiments and requires further experimental and theoretical investigations, which will be presented elsewhere. Altogether our results demonstrate the impact of small variations in triangle size s and gap size g on the localised surface plasmon polariton resonance of bowtie nanoantennas despite the high fabrication accuracy achievable with state-of-the-art nanotechnology.
Finally, we investigate the inter-particle coupling between the localised surface plasmon polaritons in the individual Au triangles, which form the bowtie nanoantenna 30,48 . Therefore, we performed differential reflectivity measurements on an individual bowtie nanoantenna with s 0 = 140 nm and g 0 = 10 nm as a function of the excitation polarization angle θ. Here, θ is defined as the angle between the electric field vector of the linearly polarized excitation and the long axis of the bowtie nanoantenna, i.e. the y-axis as defined in Fig. 1(a). We show in Fig. 5(a), the differential reflectivity signal ΔR/R off of a single bowtie nanoantenna encoded in colour as a function of energy E and excitation polarization angle θ. We observe two energetically separated resonances at E c = 1.41 eV and E uc = 1.75 eV for θ c = (0°, 180°) and θ uc = (90°, 270°), respectively, which we attribute to the coupled and uncoupled nanotriangle resonances. The E c -resonance appears at significantly lower energy as compared to the resonance of an individual nanotriangle E uc due to near-field coupling between the localised surface plasmon polaritons in the two triangles 48 . This finding is in good agreement with similar studies on bowtie nanoantenna ensembles as a function of gap size 30 , where increased gap sizes lead to a vanishing of the polarization resolved response, due to decreased interparticle coupling. We support this assumption by numerical simulations of the scattering cross-section σ for a bowtie nanoantenna with s 0 = 140 nm and g 0 = 10 nm. We compare in Fig. 5(b) the simulation results for the coupled (θ c = 0°, red dashed curve) and uncoupled mode (θ uc = 90°,red solid curve) with the according ΔR/R off -spectra shown in blue and green, respectively. We obtain excellent qualitative and quantitative agreement between the experimental and theoretical resonance energies = .
. . Furthermore, we determine from the ΔR/R off -spectra of the coupled and uncoupled mode, the degree of linear polarization defined with respect to γ c as ρ = , where γ c and γ uc denote the corresponding differential reflectivity signals at E c and E uc , respectively, as introduced in Fig. 2(c). In Fig. 5(b), we plot ρ as a function of energy E as grey symbols and observe for both the coupled and uncoupled mode clearly linearly polarized emission with ρ c = 80% and ρ uc = − 42%. Moreover, we plot in Fig. 5(c) the integrated ΔR/R off -signal at E c and E uc as a function of excitation polarization angle θ in blue and green, respectively. We observe a clear anti-correlation of the ΔR/R off -signal between the coupled and uncoupled mode, indicating that they scatter light along the long-(θ = 0°) and short-axis (θ = 90°) of the bowtie nanoantenna, respectively. From our findings, we conclude that the strong near-field coupling leads to a considerable red-shift of the localised surface plasmon resonance by ΔE ≡ |E uc − E c | = 340 meV as compared to uncoupled nanotriangles.

Discussion
In summary, we presented a comprehensive study on the structural and optical properties of individual Au bowtie nanoantennas defined by electron beam lithographically on glass and GaAs substrates. The demonstrated highly uniform nanofabrication process in combination with the fast and reliable differential reflection spectroscopy established, paves the way for bowtie nanoantennas on high-refractive index semiconductor substrates 30 as essential building blocks in future optically active semiconductor-plasmonic integrated circuits 43,50 . In particular the integration of antennas with other functional optical components such as for example plasmonic waveguides 51,52 or photonic crystals 52,53 requires along with this high degree of control and repeatability during nanofabrication also a fast, cheap and non-destructive spectroscopy method to independently test the optical response of the individual plasmonic units. Typical semiconductors like gallium arsenide and silicon rule out well-established techniques such as for example 'attenuated total internal reflection' 4 and 'transmission experiments' 2 since both require transparent substrates. Single-particle spectroscopy using a dark field microscope 41 requires immersion oils that contaminate the sample surface and, thus, modifies the optical properties of the plasmonic nanoparticles. In contrast to scanning near-field optical microscopy 40 , which demands expensive equipment and records information in a serial manner, the demonstrated differential reflectivity spectroscopy method offers quick and direct insights into the main optical properties of bowtie nanoantennas and potentially also works at cryogenic temperatures. The latter property becomes important when coupling plasmonic antennas to optically active emitters embedded in the semiconductor substrates 54,55 . In combination with the control over the antenna position 56 and local electric contacts 13 , this enables to engineer the spontaneous emission dynamics in such hybrid semiconductor-plasmonic nanosystems via the well-known Purcell-effect 57 . The enhancement is linked to the resonance linewidth Γ res via the so-called quality factor Q = E res /Γ res and, therefore, nanostructures yielding minimum linewidth are favourable. The obtained Q-factors for the bowtie nanoantennas studied range between 5 and 10 and are in good agreement with studies on chemically synthesized spherical Au nanoparticles 41 . Additional numerical simulations of truncated bowtie nanoantennas are presented in Fig. SM3, indicating a further improvement of Γ res by a factor 1.3 − 1.5× . This is achieved by modifying the triangles of the bowtie nanoantenna to a 'two-wire gap'-like antenna 13,25 , giving rise to a reduction of the antenna volume, whilst simultaneously keeping the resonance energy constant. Further improvement of the Q-factor is expected by using single-crystalline metals due to a reduction of Ohmic losses in the metal as recently demonstrated in refs 58 and 59. Finally, it is well known that Ag instead of Au does not only allow to further increase the surface plasmon polariton energy, but also shows promise of decreased losses since the interband transitions are shifted towards higher energies 46 . In conclusion, we believe that our study provides an important step towards the marriage of semiconductor devices and nano-plasmonic concepts for the realization and optimization of efficient optical on-chip nanocircuits 60 .

Methods
Sample fabrication and layout. Structural characterisation. To determine the geometrical parameters of the fabricated nanoantennas we took scanning electron microscopy images using a Raith E-line system at an electron acceleration voltage of 5 kV and an aperture size of 10 μm. We recorded the pictures by stepping from one antenna to another and conducting a single shot scan in order to avoid charging effects, which occur especially on the glass samples. The obtained images were analysed by hand using the "Carl Zeiss SmartTiff Annotation Editor" (V1.0.1.2). As stated in the main text we extracted s and g from high resolution scanning electron microscopy measurements of ~300 bowtie nanoantennas without any pre-selection. To quantify the tip radius we evaluated 20 "feed-gap tips" of the upper triangle and found a value of r c = 14 ± 5 nm.
Optical spectroscopy. For optical spectroscopy we used either a white-light super-continuum source (Fianium WhiteLase micro) for single particle studies or we collected and collimated the light from a halogen lamp (Philips Fibre Optic Lamp, Type 6423 XHP FO) for ensemble measurements. Both beams were sent through a beamsplitter and an apochromatic high numerical aperture (NA = 0.9) objective to focus the light onto the sample surface. We determined the spot sizes to be µ ∅ = ± . , respectively. The sample were placed on an open-loop piezo stage (Thorlabs NanoMax) in combination with a tiltable stage in order to provide an accurate positioning and an exact alignment of the plane perpendicular to the optical path. The reflected light was collected by the same objective, transmitted through the beamsplitter, a fibre coupler and a multimode optical fibre before it was dispersed and analysed in a 0.5 m imaging spectrometer (Princeton Insturments Acton SP2500i, grating: 300 l/mm). Both excitation and detection channels were equipped with linear polarizers (Thorlabs, LBVIS100-MP2) and λ/2-waveplates (Thorlabs, AHWP10M-980) mounted on computer controlled motorized sample stages (Thorlabs, PRM1/MZ8) to adjust and analyse the polarization. For the measurements on glass (GaAs) we used a 600 nm (800 nm) long pass filters and a Si-CCD -Princeton Instruments Spec-10 (InGaAs linear array -Princeton Instruments, OMA V). When using the super continuum source to investigate the nanoantennas on GaAs, we also installed a 1064 nm notch filter in order to suppress the residual light from the seed laser, which potentially can damage the InGaAs detector. To cover the broad energy range discussed in the main part of this work, we always recorded four spectra of different centre energies, which were merged afterward. The integration time was always set to 1 s.

Simulations.
We simulated the scattering cross-sections of the bowtie nanoantenna using a commercially available finite difference time domain solver (Lumerical Solutions, Inc., FDTD solutions, version: 8.11.387). The design of the simulation cell is based on the Mie scattering tutorial that can be found on the Lumerical homepage 61 . Consequently, we used a three dimensional simulation cell that is terminated by perfectly matched layers. The bowtie was modelled using the extruded N-sided equilateral polygon with rounded corners that is also provided on the Lumerical homepage 62 . To excite the structures we used a total field scattered field (TFSF) source and FDTD scattered field monitor to compute the scattering cross-section. At the centre of the simulation cell, i.e. around the bowtie feed-gap region, we used a mesh size of 2 nm, whereas in the outer regions the value was set to 4 nm. The used simulation file is available in the supplementary material.