Abstract: In this paper gold nanorings (NRs) are applied as particularly well-suited sensing elements for mapping the radially symmetric electric fields in the high numerical aperture focus of cylindrical vector beams. The optical properties of gold nanorings are analyzed by a combination of extinction and single particle dark field spectroscopy as well as confocal photoluminescence (PL) imaging. The results are compared to numerical calculations. The in-plane components in the focus of the cylindrical vector beams are estimated through the PL intensity distributions of the NRs. The optimum overlap between the structure and excitation is visualized by a narrow centre spot in the far-field PL scan.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Manipulating and confining electromagnetic fields with metallic nanostructures is a priority direction in plasmonics . Furthermore focusing to sub-diffraction limits is highly important in a variety of applications, such as surface enhanced Raman spectroscopy (SERS) , biochemical sensing , scanning near-field optical microscopy (SNOM) [4–6], nano-light sources , meta-materials , or nonlinear optics . In most of these applications the interaction of light with metallic nanostructures is used for the excitation of (localized) surface plasmon-polaritons. The excitation of plasmons is accompanied by a resonantly enhanced electromagnetic near-field in the active area of the nanostructures. For particles with different shapes, such as nanorods [10, 11], nanocones , nanodiscs , nano-shells , triangular structures , bowtie nano-antennas , nanorings , symmetry broken rings , and many more the plasmon response has been thoroughly researched.
Over the last two decades, metallic annular nanostructures have been investigated in many experimental as well as theoretical publications. Nanorings (NRs) feature a variety of optical phenomena due to their axial symmetry and their unique electric and magnetic field distribution [19, 20]. Different dipolar and multipolar plasmon resonances may be excited when the ring structures are placed within an external electromagnetic field of a particular polarization . The wavelengths of the plasmon resonances depend on the size, shape and chemical composition of the nanostructure and can be tuned over a wide range in the visible and near-infrared regimes . The simple tuneability of the resonance wavelength opens applications for NRs in various scientific fields ranging from micromagnetics to nanoscaled photonics, biosensing, waveguiding, nanomedicine, and to nano-emitters [23–27].
The most common processes for the fabrication of NR arrays are colloidal lithography [28–30], nanoimprint lithography , chemical synthesis [32, 33], and electron beam lithography (EBL) [34, 35], however there are also more unconventional fabrication techniques such as annealing of gold nanoclusters, stretched imprinting, or printing via carbon nanotube templates [36–38]. Depending on the application and fabrication method, metal rings of various materials, such as Au , Ag , Al , or Co , and chemical composition [41–43], as well as a wide range of sizes from few nanometres  up to several micrometers [23, 44] have been produced over the years.
In recent articles the plasmonic properties of annular nanostructures have been described as an electromagnetic interaction between the nanodisc and the nanohole plasmon resulting in two resonances of bonding and antibonding modes [17, 24, 45, 46]. The surface charge distribution of the bonding mode exhibits the same signs on the inner and outer walls of the ring, leading to a resonance in the near-infrared. The surface plasmon resonance in the visible spectrum can be explained through coupling between the surface charges on the inner and outer walls of the ring (antibonding mode) and is therefore determined by the ring width rather than the ring diameter. An additional out-of-plane resonance is expected in the visible range if the NR is excited by axially oriented field components, which was only rarely discussed in previous references.
In most studies, either non-polarized or linearly polarized light was used as the excitation field [24, 47]. In a theoretical investigation, the properties of NRs were studied in focused Gaussian beams as well as in cylindrically polarized vector beams (CVBs) .
The higher order doughnut-shaped modes of CVBs are polarized purely in the plane transversal to the direction of propagation for parallel (collimated) beams. The laser modes exhibit rotationally symmetric arrangements of the electric field components. The spatially dependent field vectors feature linear polarization at each point within the beam profile, which is oriented parallel to the radial vector for radially polarized beams, and perpendicular to the radial vector for azimuthally polarized beams. When the CVBs are tightly focused, the electric field distribution of the azimuthally polarized beams remains purely transversal, while the radially polarized beams exhibit an additional strong longitudinal component in the direction of propagation. In the plane of propagation, the polarization has been shown to feature elliptical polarization , while the polarization in the transversal plane shows locally changing linear orientations depending on the beam type, numerical aperture of the focusing element, and spatial position [12, 49–53]. By choosing between tightly focused azimuthally or radially polarized CVBs, one can thus switch between an electric field distribution that is oriented exclusively in-plane, or predominantly out-of-plane. These features make them particularly attractive for imaging and spectroscopy of individual nano-objects, being able to distinguish between in-plane vs. out-of-plane excitation without the mode mixing present e.g. in tightly focused linearly polarized beams. A review on using CVBs to determine the 3D orientation of individual nano-objects can be found in . Wherever such CVBs are applied, suitable test structures are required to determine the intensity distribution in the focal plane. The ring-shape of the transversal electrical field components in the focus suggests that ring-shaped nanostructures are particularly well-suited to perform a size-dependent electrical field mapping. The photoluminescence (PL)  intensity distribution of NRs when scanned through the focus of a CVB can be explained by the spatial overlap conditions between the ring and the individual components of the field in the focal spot.
Full information on the electric field and phase distribution in the focal plane is a prerequisite for fully understanding light-matter-interaction in the focus. In previous studies, strong efforts have been made to develop techniques for the mapping of electric vector field or overall intensity distributions in the focal plane of differently polarized and tightly focused laser beams. For example, 1D projections and cross-sections through the electric energy density distribution in the focus can be precisely mapped using the knife-edge technique [56–58]. Mappings of the overall 2D intensity distribution in the focus have been achieved by scanning fluorescently marked polystyrene spheres through the focus in a confocal scanning setup. Here the isotropic emitters do not discern between vectorial field components, but give a clear size mapping of the focus through the overall field intensity . Pioneering publications have shown that single dye molecules in a laser focus act as point-like dipoles. The characteristic patterns of their fluorescence images can be attributed to the dipole orientation of the molecules relative to the local polarization of the electric field . This way, also the presence of longitudinal field components could be verified [51,61]. An alternative approach for mapping longitudinal mode distributions was outlined by looking at surface deformations of photopolymers upon illumination . The dipole mapping technique offers a powerful analytical tool for monitoring transition dipole moments of molecules or quantum dots as well as molecular dynamics or tautomerism processes at the single molecule level [59, 63]. Hence, given a known orientation of the dipoles, one could vice versa deduce the local three-dimensional orientation of the electric field. Similar studies were shown using single metal nanorods as the point-like dipoles and monitoring the gold luminescence or scattered light [11, 64]. Likewise, it has been shown by the authors that the out-of-plane components can be mapped by vertical nanocone structures [12, 51, 65]. Still, preparing single emitters with a known orientation of the dipole remains a challenging task. Also, for mapping the full electrical field distribution in a focus, the dipolar pattern needs to be evaluated at each point of an image scan, with the emitter being optically and rotationally stable for the entire time of the scan .
Thorough mappings of CVB field distributions were also performed in the near-field using tapered fibers, scattering near-field scanning optical microscopy, or photoinduced force microscopy [67–71]. In these cases, the interactions of sharp probe tips with the focus fields are recorded. These methods are technically more demanding than using confocal far-field scanning microscopy, and artefacts can be induced by the influence of the tip shape. By using independent polarization detectors, the three-dimensional local field polarization vectors could be reconstructed [69, 70].
As will be demonstrated in this study, gold NRs open the possibility of mapping the in-plane components of the intensity distribution by measuring the far-field PL in a comparably simple confocal scanning microscope configuration. We discuss the case of light interaction with metallic NRs when their dimension is on the order of the focus diameter. The optical behaviour of gold NRs with variable geometries is investigated under different illumination conditions. The plasmon resonances are determined, and the in-plane electric field distribution in the focus of CVBs is mapped by the PL scan patterns of the NRs. The vectorial nature of the electrical field comes into play as strong PL signal is observed when, and only when, the local electrical field is oriented perpendicular to the gold NR, i.e. resonantly exciting localized plasmons along the width of the NR. Combining the information on the position of the laser focus relative to the center of the nanoring with this information, one does not just obtain information on the presence of the electric field, but also on its field component perpendicular to the ring structure. Plotting the positions of high intensity where the PL signal appears, one could reconstruct the distribution of the radial and azimuthal in-plane field vectors. The out-of-plane field components do not resonantly excite the NR in the present case. The NRs thus enable the experimental determination of the in-plane focus dimensions, which play a crucial role in the interaction with the sample during any kind of optical measurements. A precise knowledge of the focus properties may be imperative for meaningful data interpretation. This technique uses stable gold nanostructures that do not suffer from bleaching with time. A simple test sample containing a variation of gold NRs can be prepared and reused before each new experiment using CVBs to calibrate the scanning table via the defined 2D spacing of the ring structures in an array structure, and probe the quality of the CVB focus. Due to the rotationally symmetric structures, any beam asymmetry would lead to systematic deviations in the PL scan images. If the beam is not tightly focused, this will be apparent from the focus size evaluation. Clearly the geometry of the sample first needs to be independently validated by other means, such as scanning electron or atomic force microscopy. The general concept of using the resonant overlap of specific electric field components with suitably shaped gold nanostructures could be expanded to different higher order laser beams by adapting the nanostructure shape to mimic the field distribution in the focus, or even to nonlinear (second harmonic generation) imaging, as was recently demonstrated by the authors . Conceptually, the local electric field distribution can be reconstructed from the fact that high signal intensity (PL, SHG or otherwise) is observed whenever the local electric field vector coincides with a resonant feature of the plasmonic gold nanostructure [52, 72, 73]. Since the distance between the centers of the focus and of the nanostructure are known at each scan position, the distance of the respective electric field vector from the focus center can be reconstructed. If other, non-resonant vector components were simultaneously present, they would lead to additional signal at different focus positions. Thus the in-plane electric field distribution may be reconstructed from the observed scanning images.
Any imperfections in the nanofabrication could lead to intensity variations of the PL patterns. For this reason, a redundancy in the nanostructures, i.e. preparing arrays of nominally identical structures, is helpful, since variations from pattern to pattern may be attributed to nanoscale variations in the structures, whereas systematically occurring features point towards the CVB as the source. The relative alignment of the focus and nanostructure can be evaluated with high precision from the centrosymmetric patterns forming an array structure. If instead of the radially symmetric nanostructures single isotropic gold particles were used, the vectorial information would be lost in the present technique.
An elegant method for reconstructing the full amplitude and phase information of the electrical vector field based on the scanning of a simple gold nanosphere was recently demonstrated in . Here the scattering signal interfering with the reflected light was recorded as a back focal plane image for each position. By suitable post-processing, integrating over different angular ranges, the respective squared electric field components and relative phases in the focal plane could be mapped with high precision. In comparison, the approach presented here does not reach the same level of precision and does not access the vertical field components. However, it provides a simple straight-forward practical test of CVBs that does not require any post-processing beyond reading out the PL images.
Arrays of gold NRs in square lattices are fabricated on a glass substrate coated with a homogeneous film of indium tin oxide (ITO) to avoid charge accumulation effects during EBL. In this work two different schemes for the fabrication of gold NR arrays are introduced, see Figs. 1(a) and (b).
In the first case, a gold layer is deposited by thermal evaporation directly on ITO/glass without any adhesion layer and spin-coated with a hydrogen silsesquioxane (HSQ) negative resist layer. The HSQ is pattered into NR arrays by EBL (Philips XL 30 SEM, 30 kV accelerating voltage) with periodicity p, various ring centre diameters d and average widths w, see Fig. 1(c). The thickness of the gold layer determines the height h of the structures. After a development process (in tetramethylammonium hydroxide solution) cross-linked HSQ acts as an etch mask for the gold. In a subsequent Ar ion milling process (Roth & Rau Unilab) both layers are dry-etched until the etch mask and uncovered Au layer are simultaneously removed. During the ion milling process the angle of incidence of the ion beam is tilted by 30° with respect to the surface normal, and the sample is continuously rotated, which allows us to obtain homogenous smooth nanostructures with vertical sidewalls . The processing steps are shown schematically in Fig. 1(a).
In the second case, ITO/glass is spin-coated with a polymethyl methacrylate (PMMA) positive resist layer. The NR arrays are defined in the PMMA layer by EBL. After the development process (in methyl isobutyl ketone:isopropanol mixture), oxygen plasma cleaning is applied to the sample in order to remove potential residues within the patterned shapes. The gold layer is deposited by thermal evaporation, while the gold thickness is chosen according to the desired height h of the nanostructures. The PMMA layer is fully removed by a lift-off process that yields a periodic array of well-defined gold NRs on the substrate. The processing steps are shown schematically in Fig. 1(b).
Using these fabrication processes, gold NR arrays with variable geometries from high and narrow rings (mostly by means of scheme 1(a)) to low and wide rings (mostly by means of scheme 1(b)) can be achieved. In all cases the glass substrate is coated with a layer of ITO with a thickness of 50 nm, and the periodicity of the NRs p is fixed at 2 µm. Rings with diameters d from 250 to 850 nm, heights h of 50 nm, and average widths w of 50 nm are produced using both fabrication processes and show no obvious differences of their optical properties. The results shown in this paper mostly refer to rings fabricated by means of scheme 1(b).
Dark field scattering spectra of NRs are measured by using an inverted dark field microscope (Nikon Eclipse Ti-U). The sample with gold NR arrays is illuminated with a non-polarized white light source (halogen lamp) at large angles from above through a dark-field condenser (NA 0.80-0.95). The collection angle of the 100x objective (NA 0.33) is smaller than that of the dark-field condenser. The directly transmitted light is blocked and the scattered signal is spatially filtered by a pinhole in the image plane, such that signal from a sample area of about 2 µm in diameter is detected by the spectrometer (Ocean Optics QE 65000). Scattering spectra of single nanostructures are obtained by dividing the background-corrected scattering signal by the background-corrected lamp spectrum.
In the visible spectral range, both in-plane and out-of-plane collective oscillations of the electrons can be excited in the rings. The plasmonic modes are selectively addressed and spectrally identified by performing extinction measurements in transmission mode using long working distance objectives. Illumination with a white light source takes place through a weakly focusing 20x objective (NA 0.28), while a second objective (50x, NA 0.42) is used for detection. Spatial filtering by a 200 µm diameter fiber ensures that signal from a sample area (array) of about 15 µm in diameter is collected by the spectrometer (Ocean Optics QE 65000). The NRs are pointing towards the detection side. Two parallel oriented linear polarizers are inserted in the illumination and detection paths and rotated by 90° for measurement with either transverse electric (TE) or transverse magnetic (TM) polarization. Owing to the long working distance, the sample can be gradually tilted from normal incidence up to about 60° relative to the incident beam. That way, TE polarized light can be employed to excite only the mode(s) in the sample plane, while TM polarized light gives a superposition of the in-plane (base) mode and the out-of-plane (axial) mode, with changing weights for an increasing tilt angle. The spectra show the logarithm of the background-corrected lamp spectrum divided by the background-corrected transmitted signal (absorbance).
To analyze the behaviour of the plasmon modes in differently polarized electromagnetic fields the experimental dark field and extinction spectra of gold NRs are compared with simulations. The plasmon modes of the NRs in the visible arise mainly from the excitation of the ring cross section (width and height). The closed ring does not have a finite lateral aspect ratio, therefore the cross section-related NR resonances can be approximated by modelling an infinite nanorod with the width and height chosen to match the cross section of the fabricated NRs. The gold rod with slightly rounded edges is modelled with COMSOL Multiphysics. The refractive index nAu of gold is taken from Johnson and Christy , and the refractive index nITO of ITO from the Refractive Index Database . As the excitation source electromagnetic fields with two perpendicular polarizations across the rod, corresponding to the base mode and axial mode (as indicated in the inset of Fig. 2(e), and frequencies over the visible and near-infrared range (480 nm to 800 nm) are used. The intensity scattered from the nanostructure is integrated in the far-field for each frequency.
The PL properties of gold NRs are investigated in a home-built inverted confocal microscope. Higher order doughnut-shaped laser modes (HeNe laser, λ = 632.8 nm) are obtained by passing a linearly polarized Gaussian laser beam through a mode converter. The converter consists of four half-wave plates arranged in four quadrants similar to , with subsequent filtering by a pin-hole to remove higher spatial frequencies [11,59], see also Appendix A. The sample is illuminated from below using an index-matched oil immersion objective (NA 1.25). The gold nanostructures are positioned in the upper half-space in air. The electric field distribution in the focal plane of the AP laser mode is oriented purely transversal (Exy(AP) perpendicular to the optical axis), while the electric field distribution of the RP laser mode contains longitudinal (Ez(RP) along the optical axis) and transversal (Exy(RP)) components that result in a Gaussian-like total intensity distribution, see Appendix A, Fig. 5. In this paper, the PL images are obtained by raster scanning of NR arrays through the diffraction limited focus of an either RP or AP beam. The position-dependent PL intensity signal generated in the focus is collected from below, i.e. from the illumination side, and detected in the far-field by a single-photon counting avalanche photodiode (APD), while the elastically scattered laser light is cut off by an optical long pass filter. The general working principle is e.g. illustrated in . This way, purely the luminescence created at the location of the gold nanostructures by resonant interaction with the electrical field of the CVBs is collected, while the background at positions without any overlap with gold structures remains dark. Compared to e.g. evaluating scattering images as in Ref [11,74], where the signal intensity is determined by interference between the laser light reflected from the interface and the scattered light, these images may be more straightforward to interpret.
3. Results and discussion
Periodic arrays of gold NRs are fabricated using EBL and characterized by scanning electron microscopy (SEM). The NRs with an average width of w = 50 nm and various centre diameters are established in a reproducible and well-controlled manner (see Experimental). The variation of the width is estimated to be ± 5 nm. Typical SEM images of NRs with nominal centre diameters d = 250, 450, 650 and 850 nm are shown in Fig. 2(a).
According to published theoretical and experimental results gold NRs exhibit two main optical resonances in the visible to near-infrared region. The plasmon resonance modes can be characterized as the antibonding and bonding modes . In order to find the correlation between the ring shapes and their plasmonic resonance, the NRs were investigated using single particle dark field spectroscopy. Due to the spectral limitation of the spectroscopy setup (maximum wavelength ~900 nm) it was only possible to measure the antibonding mode of the NR plasmon resonance. Identical resonance peaks for NRs with equal ring widths were observed independent of the ring diameter. Measured scattering dark-field spectra of gold NRs with d = 250, 450, 650 and 850 nm are shown in Fig. 2(b). The NR with 250 nm centre diameter was slightly narrower (w = 46 nm) than the rest. The shift of the respective resonance peak (from 618 nm to 606 nm) confirms the ring width dependency of the plasmon antibonding mode. The weak shoulder in the spectra between 400 nm and 500 nm is attributed to interband transitions in gold.
The main peak in the scattering measurement in Fig. 2(b) corresponds to the dipolar resonance of the in-plane (or base) plasmon mode . Additionally, an axial component of the plasmon mode can occur in the visible due to plasmon coupling between the upper and lower surfaces of the NR. To address this mode, the NRs were investigated by means of their angle-dependent extinction spectra. Extinction spectra of gold NRs (d = 450 nm, h = 50 nm, w = 50 nm) that were measured with TE and TM polarization of the incident light, while the sample was tilted from normal incidence up to about 60° relative to the incident beam, are shown in Figs. 2(c) and 2(d), respectively. The spectral weight of the two components of the plasmon mode can be varied by changing the polarization. With the purely in-plane polarized TE polarized light, only the base mode at ~600 nm is excited, see Fig. 2(c), while TM polarized light with both in-plane and out-of-plane electric field components results in a superposition of the base mode and the axial mode (appearing at ~535 nm), with changing weights for an increasing tilt angle, see Fig. 2(d).
To verify the spectral positions of the base and axial plasmon modes, the experimental spectra are compared with Finite Element Method simulations as described in the Experimental section. The simulated spectra of an infinite nanorod with the same cross-section as the NRs under electromagnetic field excitations polarized perpendicular or parallel to the substrate are shown in Fig. 2(e). This separation of the base and axial plasmon modes in a rod is just an approximation, but the simulation supports our interpretation of the plasmon components and helps to understand how the individual components can be excited effectively. The simulated axial plasmon mode is resonant at 535 nm and is 2.25 times weaker than the base plasmon mode, which is resonant at 607 nm. The simulations are in good agreement with the scattering and extinction measurements.
The photoluminescence intensity distributions of gold NRs that are excited by cylindrical vector beams are investigated using an inverted confocal microscope. The results are shown in Fig. 3. Typical examples of NRs with centre diameters from 369 nm to 751 nm, 50 nm width and 50 nm height are shown in Fig. 3(c). The RP and AP laser modes of a He-Ne-laser (632.8 nm) beam are used as the excitation source. More information on higher order laser modes can be found in Appendix A. The electric field distribution in the focus of the RP laser mode consists in a superposition of doughnut-shaped transversal Exy(RP) and strong spot-shaped longitudinal Ez(RP) components. However, according to the measurements and simulation in Fig. 2, the base plasmon mode of the gold NRs resonant at 607 nm is much better matched to the laser wavelength than the axial component. The electric field distribution in the focus of the AP laser mode consists of purely transversal Exy(AP) components parallel to the substrate. The near-resonant excitation of the base cross section of NRs with the transversal component Exy(RP) and Exy(AP) leads to strong PL intensity, whereas the axial mode resonant at 535 nm is not visibly excited with the 632.8 nm laser beam. PL signal is thus efficiently generated when the in-plane electric field in the focus of the laser beam is polarized normal to the ring.
Line cuts through the normalized PL images of NRs excited using AP and RP laser beams, centered individually for clarity, are illustrated in Figs. 3(a) and 3(e), respectively. The far-field PL signal scans of annular nanostructures using the AP laser mode display ring shapes. The diameter of these PL rings increases with that of the NR. The far-field PL signal using the RP laser mode is generated whenever the electric field Exy polarized normal to the ring overlaps with the ring width. The PL signal intensity can be maximized when the focus is centred within the NR, depending on the spatial overlap between the focus and the ring.
For the AP mode, the distance from the ring centre to the maxima of PL intensity RPL,A can be calculated as RPL,A2 = Rr2 + RAPLM2, with Rr the NR radius and RAPLM (using RAPLM = 190 nm from beam simulations, see Appendix A, Fig. 5) the radius of the intensity maximum of the AP laser mode in the focus, in a simple geometrical model, see Appendix B, Fig. 6. The diameter of the ring-shaped PL patterns was experimentally determined for single NRs by fitting the line cuts through the normalized PL with two Gaussian functions, see Fig. 4(a). The diameters of the PL patterns (DPL,A = 2* RPL,A), averaged over up to 9 NRs for each size, are plotted versus the ring centre diameters (d = 2*Rr) in Fig. 4(a). The error bars show the standard deviations of the measurements. It can be observed that the measured PL diameters are systematically smaller than the values from the geometric calculation with RAPLM = 190 nm, shown in Fig. 4(a) as “calculation”. If the corresponding curve DPL,A = (d2 + 4RAPLM2)1/2 is fitted to the measured data using RAPLM as a free parameter instead, the value RAPLM = 152 ± 9 nm is obtained, which clearly underestimates the value expected from the beam simulations. If however instead of the central diameter the inner edge of the NR (at Rr - w/2) is inserted, a value of RAPLM = 191 ± 8 nm can be extracted. These results may indicate either that the strongest signal for the azimuthal case in fact originates from overlap with the inner edge of the NRs, or that the simulation overestimates the real focus size. This discrepancy requires further investigation.
For the radial mode the excitation field Exy(RP) in the focus polarized normal to the ring forms more complex patterns of the PL intensity, consisting in an outer ring and an inner peak or ring. The outer ring is created when the focus is located outside the NR and overlaps with one side of the NR. For the inner structure the focus is located and overlapping with the NR from within the NR. The distance from the ring centre to the outer maxima of PL intensity RPL,R can be calculated as the sum of the ring radius Rr and the radius at the intensity maximum of the transversal doughnut-shaped field of the RP laser mode in the focus RRPLM: RPL,R = Rr + RRPLM, see Appendix B, Fig. 6. The measured average diameters of the PL patterns are evaluated in an analogous manner as for the azimuthal mode. The measured average diameters of the outer PL maximum (DPL,R = 2* RPL,R) versus the ring centre diameters (d = 2*Rr) plotted in Fig. 4(b) are in good accordance with the calculations (using RRPLM = 190 nm from beam simulations). In reverse, the actual in-plane electric field distribution in the focus of the RP beam, i.e. the experimental intensity maximum of the RP laser mode RRPLM, can be determined by fitting the measured values of RPL,R and Rr. Thus RRPLM = 185 nm ± 14 nm is extracted, very well confirming the value of 190 nm assumed from the beam simulations.
The distance from the ring centre to the inner maxima of PL intensity for the beam located within the nanostructure, see Appendix B, Fig. 6, can be calculated as the difference between the ring radius Rr and the radius RRPLM: RPL,Rinside = |Rr - RRPLM|. This ring-shaped pattern can only be observed for the biggest ring with 738 nm diameter. In the case where the NR exactly matches the transversal doughnut-shaped field of the RP laser mode, Rr ≈RRPLM, and thus RPL,Rinside ≈0, the PL signal creates a narrow spot-like pattern in the centre of the intensity scan, thus directly indicating the focus diameter through the spot with the smallest FWHM (full-width-at–half-maximum). By fitting the line cuts through the inner spot- or ring-like PL intensity with Gaussian functions we determined the FWHM of the inner feature FWHMPL,Rinside, which should be equal to: FWHMPL,Rinside = 2*RPL,Rinside + FWHMRPLM, where FWHMRPLM is the FWHM of the doughnut-shaped intensity distribution of the RP laser mode in the focus (see Appendix A). The FWHM of the PL intensity for the beam positioned inside the NR was averaged over 9 single nanostructures for each ring size. The calculation (for RRPLM = 190 nm, FWHMRPLM = 190 nm) and measurements of the FWHM of the inner PL maximum under excitation with an RP mode versus the ring centre diameter are plotted in Fig. 4(c). The error bars show the standard deviation of the measurements.
The far-field PL signal is maximized at the centre of the PL distribution and the FWHM is minimized when the diameter of the gold NRs is matched to the focus size of the RP laser beam. This condition is observed for the smallest rings, which is in good agreement with the simulated focus diameter of 380 nm. In a future study, the range around the expected minimum could be further monitored by means of more closely spaced diameter values. By the independent evaluation of the outer and inner features of the RP PL intensity patterns, two strategies are available for the determination of the radial focus dimensions.
In summary, periodic arrays of gold nanorings with different diameters are created in a reproducible and well-controlled manner and characterized by scanning electron microscopy. Their optical features are investigated in connection to PL signal generation from NRs with different sizes. The localized surface plasmon resonances of NRs in the visible range are dominated by the antibonding mode. In this work, additionally a second cross-sectional plasmonic mode, the axial plasmon mode of the gold NRs, is identified in extinction experiments, and both modes are verified in simulations. The spectral separation of the plasmon modes allows for the dominant excitation of the NR base mode for PL mapping by choosing a suitable excitation wavelength, leading to a selectivity of excitation with in-plane electric field components.
When a NR is scanned through a laser focus, the resulting photoluminescence intensity distribution is governed by the polarization of the incident beam and the overlap conditions between the ring and the individual field components in the focus. The near-resonant in-plane excitation of NRs using the transversal component Exy(RP) of radially or Exy(AP) of azimuthally polarized laser beams leads to strong PL excitation. The PL distributions can be interpreted by geometric considerations. The PL scans of NRs through the focus of an azimuthally polarized laser beam display rings, the diameter of which increases with that of the NR. The PL scans through the focus of a radially polarized laser beam show two concentric rings with a dip at the centre for bigger NRs. The inner ring can be contracted into one narrow spot when the NR dimensions match the in-plane focus size and their centers coincide. This allows for a direct read-out of the focus dimensions simply by looking at the confocal PL scan image of NRs with a size variation. Knowing the focus size and the electric field distribution in the focus is invaluable for the interpretation of nano-optical measurements. To a certain extent one can rely on beam calculations for simulating the expected focus, however under experimental conditions the values may differ considerably from the ideal case. With the strategies presented in this work the in-plane components of the electric field distribution in the focus of CVBs can be determined by means of the PL response of NRs, thus no longer having to rely on focus simulations only.
Appendix A Formation of higher order laser modes
Higher order doughnut-shaped laser modes are obtained by passing a linearly polarized Gaussian laser beam through a mode converter (four-quadrant half-wave plates oriented at 45° to each other). Rotating these plates by 90°, either a radially polarized (RP) or an azimuthally polarized (AP) cylindrical vector beam (CVB) is generated. In Fig. 5(a) the formation of RP and AP doughnut modes is described schematically . After the half-wave plates, the beams still contain higher spatial frequencies due to the non-continuous junctions between the wave plates. Therefore, a pin-hole is added in the beam path for spatial filtering after the mode converter to obtain the beam profiles as in Fig. 5(a) [11, 59]. While the electric field distribution in the focal plane of the AP laser mode is purely transversal (Exy(AP) perpendicular to the optical axis), the electric field distribution of the RP laser mode in the focus contains a longitudinal (Ez(RP) along the optical axis) and a transversal (Exy(RP)) component that result in a Gaussian-like total intensity distribution. Fig. 5(b) shows the calculated intensity profiles of RP and AP laser modes for a HeNe laser (632.8 nm wavelength) in the focus of a high numerical aperture (NA = 1.25) objective. The calculations are based on the angular spectrum representation of focal vector beams [79, 80]. They were performed following the method outlined in Refs [53, 68, 81], using the program “PMCalc” by M. Sackrow, a modified version of the program “Focused Fields” developed by M. A. Lieb and A. J. Meixner. The same glass-air interface as in the experiments was taken into account. The full-width-at-half-maximum (FWHM) of the longitudinal field intensity distribution of a focused RP beam amounts to about 235 nm. The diameter at the intensity maximum for the transversal doughnut-shaped field of either RP or AP beams at 632.8 nm wavelength amounts to 380 nm (corresponding to the radii of the intensity maxima of the AP and RP laser modes in the focus RAPLM = RRPLM = 190 nm in the manuscript). The FWHM of the doughnut-shaped intensity distribution is 190 nm.
Appendix B Photoluminescence imaging of gold nanorings
By illumination of gold nanorings (NRs) with RP and AP CVBs different photoluminescence (PL) scan patterns are obtained depending on the ring diameters and polarization of the excitation source. The PL patterns can be explained by the respective spatial overlap between the gold ring and the individual electric field components in the focal spot. Using an either AP or RP HeNe laser beam, in the present case the in-plane plasmon mode of the NRs is excited more effectively. The PL signal is generated when the electric field Exy polarized normal to the ring overlaps with the ring width. In order to explain the non-uniform PL scan images of gold NRs, the generation of the PL signal is schematically illustrated in Fig. 6. Here the signal formation for the PL mappings using the AP laser mode, see Figs. 6(a) and 6(b), and RP laser mode, see Figs. 6(c) and (d), are discussed by the example of the largest gold NRs with a centre diameter of 751 nm, see Figs. 6(a) and 6(c), and the smallest gold NRs with a centre diameter of 369 nm, see Figs 6(b) and 6(d). The arrows indicate the orientation of the electric field Exy in the focus. The black arrows do not contribute to PL signal generation, while the yellow arrows illustrate the part of the excitation field in the focus which contributes to PL signal generation when the laser beam is centered in the mapping position marked by a red dot.
For the azimuthal mode the distance from the ring centre to the maxima of PL intensity RPL,A, red arrow in Fig. 6(a), can be simply calculated as the hypotenuse of a right-angled triangle: RPL,A2 = Rr2 + RAPLM2, with Rr the ring radius, black line in Fig. 6(a), and RAPLM the radius of the intensity maximum of the transversal doughnut-shaped field of the AP laser mode, green line in Fig. 6(a). Note that the maxima of PL intensity always appear when the centre of the beam is located outside of the nanostructure, see Figs. 6(a) and 6(b).
For the radial mode the excitation field Exy(RP) in the focus, which is polarized normal to the ring width, forms more complex patterns of PL intensity. The maxima appear when the transversal doughnut-shaped field Exy(RP) centered at the mapping positions marked by a red dot (inside of the structure as well as outside) overlaps with the ring, leading to two maxima per side (two concentric rings). The distance from the ring centre to the maxima of PL intensity outside the ring RPL,R, red arrow in Fig. 6(c), can be calculated as a sum of the ring radius Rr, black line in Fig. 6(c), and the radius at the intensity maximum of the transversal doughnut-shaped field of the RP laser mode RRPLM, green line in Fig. 6(c): RPL,R = Rr + RRPLM. The distance from the ring centre to the maxima of PL intensity for the beam located inside of the nanostructure can be calculated as the difference between the ring radius Rr and the radius RRPLM, see black and green lines in Fig. 6(c): RPL,Rinside = |Rr - RRPLM|. In the case Rr ≈ RRPLM, the ring diameter is matched to the transversal doughnut-shaped field of the RP laser mode, and RPL,Rinside ≈ 0. The PL signal forms a narrow spot-like pattern in the centre of the outer ring pattern, see center sketch Fig. 6(d). For the bigger ring radii with Rr >> RRPLM the spot-like pattern of the PL signal expands to form an inner concentric ring, see Fig. 6(c).
German-Israeli Foundation for Scientific Research and Development (Young Scientists’ Program); Carl Zeiss Stiftung (Nachwuchsförderprogramm 2012); “Kompetenznetz Funktionelle Nanostrukturen” of the Baden-Württemberg Stiftung; Région Champagne-Ardenne (Expertise de Chercheurs Invités); European COST Action MP1302 Nanospectroscopy; Deutsche Forschungsgemeinschaft (DFG); Open Access Publishing Fund of University of Tübingen
Valuable input at the revision stage by Kai Braun as well as support by Deutsche Forschungsgemeinschaft and Open Access Publishing Fund of University of Tübingen is gratefully acknowledged.
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