Effects of asymmetric surface corrugations on fully metal-coated scanning near field optical microscopy tips

: We propose a new configuration for a fully metal coated scanning near field (SNOM) probe based on asymmetric corrugations in the metal coating. The variation in the metal surface induces coupling mechanisms leading to the creation of a localized hot spot under linearly polarized excitation. Field localization is an effect of paramount importance for resolution but cannot be achieved with standard axisymmetric fully metal-coated probes, unless a more cumbersome radially polarized excitation is used. Our simulations show that this promising structure allows one to simplify the mode injection procedures circumventing the need for a radially polarized beam.


Introduction
Scanning near field optical microscopy (SNOM) is an important tool to investigate nanostructures as it can provide information not only on the topography but also on the optical properties of the sample under study with subwavelength resolution beyond the diffraction limit of classical optical microscopy [1][2][3]. This technique relies on the use of near field interactions between the sample and a probe that can be used either to locally excite the sample, whose response is then detected in the far field (illumination mode), or to collect the near field response of the sample broadly irradiated with a far field excitation (collection mode). Alternatively, the probe can be used as both a local illuminator and a local collector in the so-called illumination/collection mode, which makes use of near field interactions for both excitation and detection. The latter configuration, attractive because of its potential applications to non-transparent samples, inherently requires much better throughput than the other two operating modes.
Due to the outstanding key role played by the probe in the interaction with the analyzed sample, independently of the operating mode, such a component has been object of lingering attempts of optimization.
In fact, the first proposed probes, the so-called aperture probes based on metal-coated dielectrics, offer poor performance in terms of both resolution and throughput [2,4,5]. Such probes can be viewed as tapered hollow metal waveguides, along which different modes can propagate [2,6]. As linearly polarized HE 11 modes are usually used for their excitation, the resulting near field distribution is asymmetric, a further shortcoming for this class of probes [7].
Apertureless fully metal-coated SNOM probes represent an interesting alternative because of their high volume manufacturability, the greater manufacturing reproducibility and the easier control over their shape [8]. Typically, they have been excited either by illumination from a focusing lens or in a prism-based total internal reflection configuration [7,9]. In spite of the reported high resolution, the drawback in the use of external illumination lies in a detrimental strong background. To obviate this problem, internal back excitation can be used [7,9,10].
The resolution of fully metal-coated tips is highly sensitive to the polarization state of the input field. The probe input aperture exhibits a pair of orthogonal linearly polarized eigenmodes, followed by a radially polarized one. Both numerical and experimental studies have shown that the excitation of a radially polarized mode results in a localized hot spot in the near field zone of the probe apex with a peak amplitude higher than the one of the linearly polarized modes [7,[11][12][13], a feature of paramount importance for SNOM applications.
Thorough numerical and experimental analyses have been carried out to scrutinize the behaviour of fully metal-coated probes under internal radially polarized excitation [9][10][11][12][14][15][16][17]. The role of surface plasmon-polaritons (SPPs) propagating towards the apex provides an explanation for the nanofocusing properties of fully metal-coated probes [9,14,[18][19][20]. The strong localization achievable with a radially polarized excitation has been justified as the outcome of the energy transfer from the waveguide mode (WGM) to the SPP when their respective wavevectors are matched [14,20]. Later, a more detailed analysis has taken into account not only the role of the outer SPP mode sustained at the air/metal interface, but also the one of the inner SPP mode confined on the inner metal/fiber interface [9]. Similar conclusions about superfocusing were drawn on the grounds of intermodal coupling considerations, taking also into account the interaction between the inner and outer SPPs. The induced surface plasmons excited on the metal surface will converge towards the end of the tip and interfere constructively due to the rotational symmetry of the input polarization and the probe. On the other hand, if a linearly polarized beam is coupled in a purely axisymmetric probe, the surface plasmon excitation will cancel out because of the opposite charges on the opposite sides of the tip [16,17].
However, the injection of radially polarized beams requires a quite cumbersome procedure that is extremely sensitive to misalignments, which would eventually undermine the potential benefits stemming from the use of a radially polarized mode. Hence, it would be desirable to find a way to get superfocusing effects similar to those observed for radial polarization injection by using a more easily excitable linearly polarized mode.
Proper modifications in the originally axisymmetric structure have been shown to induce coupling from one or even both the linearly polarized modes into the radial one.
Previous studies showed that even unintentional asymmetries like single and multiple air spherical bubbles could produce weak coupling from one of the two linearly polarized modes into the radial one [20]. Stronger and more easily predictable coupling can be achieved by the introduction of intentional modifications like unilateral and bilateral slits [21], or a cut stripping off both the metal coating and the core [22]. Localized hot spots, whose characteristics in terms of full width at half maximum (FWHM) and peak values could be optimized by tuning some geometric parameters, were obtained by the injection of a mode with proper linear polarization. An asymmetry in the illumination is behind the field localization in the offset apertured -metal coated dielectric apertureless (OAMDA) structure proposed in [23]; the structure consisted in an atomic force microscopy type cantilevered silicon dioxide tip, where both the cantilever arm and probing tip were coated with silver film. In the cantilever arm, and directly adjacent to the tip base, an aperture was placed. A single lobed localized hot spot was obtained with a proper choice of the tip height, by using incident light polarized linearly in the direction perpendicular to the interface between the base of the tip and the offset aperture.
The rich variety of coupling mechanisms that can be tuned by introducing asymmetries in the fully metal-coated structure offers interesting perspectives for other modified geometries. In this paper, we have considered asymmetric corrugations involving just one half of the outer metal surface.
The influence of axially symmetric periodic corrugations on the performance of aperture tips has been considered in [24,25]. SPPs on the internal metal surface were shown to be enhanced by the introduction of either semicircular grooves or rounded rectangular grooves on the core-metal interface. Higher charge density distribution and therefore improved throughput were obtained by varying geometric parameters of the internal corrugation.
The role of corrugations in apertureless probes has been examined experimentally [26,27], and numerically [28]. In particular, in the experimental studies, linear gratings were written by focused gallium ion beam on an electrochemically etched gold tip. Gratings were prepared on a number of tips with different distances from the tip end. SPPs were excited in these periodic structures by light impinging on the grating at normal incidence with a wavelength close to the grating period. The optimal choice of the distance between the grating and the tip apex was suggested to be a trade off between propagation losses increasing with the distance and the desire for an excitation region well separated from the apex to suppress the direct far field illumination of the apex. In the numerical study, two different cases were investigated: SPP excitation by light incident first on a single groove and then on a grating of grooves with variable period was examined. In both the cases, SPPs were excited giving rise to strong field enhancement at the tip apex, the grating showing greater spectral selectivity than the single groove.
Periodically corrugated metal wires were also proposed for imaging applications in the terahertz regime [29][30][31], and at microwave frequencies [32]. In this spectral range metals resemble a perfect conductor and the negligible penetration of the electromagnetic fields leads to highly delocalized SPPs. However, the dispersion relation of SPPs can be engineered at will by periodically structuring the cylindrical surface with grooves. The geometry-controlled surface waves thus generated were named spoof SPPs because of their mimicking characteristics. Superfocusing in conical structures [29], and field concentration by tapering the inner radius of the grooves in cylindrical structures [29,31], were reported in numerical simulations.
In the following sections, we analyze the effect of semicircular corrugations on the outer metal surface on the performance of a fully metal-coated tip with internal linearly polarized excitation. The corrugations will take on the form of either indentations, that is the metal is carved away from the tip, or bumps, in which case the metal swells. Even if the corrugations will be located on a regular spatial pattern, they cannot be strictly regarded as a periodic grating. In fact, first, the portion of tip considered is small to allow a large number of corrugations to be studied and to examine the influence of a change in the period and, second, the alternation of the two materials determining the corrugation (air and metal) will often wipe out the periodicity.
We will demonstrate that tailoring material combinations and geometric parameters in the corrugations can give rise to localized hot spots for one of the linearly polarized modes. Despite the fabrication of the structures under study appears to be more challenging than the previously proposed configuration based on a cut [22], but not more difficult than the slitbased ones, however it offers a much wider range of parameters that can be varied to improve tip performance than those previously examined. Furthermore, beside proposing a new modified structure to get field localization by injecting a linearly polarized mode, this study casts light on the possible effects of unintentional corrugations. In fact, so far, defects only in the form of air bubbles or small oxide holes in the metal layer or metal spherical grains close to the tip apex have been taken into account [8,33]. Scars in the metal surface and more extended metal protrusions (resulting, for example, from the combination of closely spaced metal grains) have not been examined. Even if only some specific combinations are considered, the results of our simulations can give some indications on how other forms of inhomogeneities can affect tip performance.
Among the different numerical methods used in the past to simulate fully metal coated SNOM probes, ranging from the multiple multipole method [10,17], to the finite integration time domain technique [8,9,11,13,21], or the finite difference time domain method [7,23], we have preferred the finite element method, chosen also in [15,16], because of the ease in handling complicated geometries due to the use of unstructured grids.

Computational model
Our three-dimensional (3D) simulations have been carried out by using a finite element based commercial software (Comsol Multiphysics). The computational process is articulated in two steps. First, a two-dimensional (2D) analysis is run to calculate the eigenmodes at the input port. Then, the first three eigenmodes are propagated through the structure in a 3D analysis. Second order elements with minimum size of about 0.8 nm have been used.
As the simulations are extremely computationally intensive because of the different scales of the metal layer and the dielectrics, only the very end of the tip is examined. As anticipated, this limits the range of parameters we can change (for example, the distance between the corrugations). In the past, simulations involving larger portions have been possible only when the structure was less computationally challenging, as for the case of axially symmetric probes, where one can benefit from the rotational symmetry of the probe to reduce the problem complexity either with the body of revolution finite difference time domain method or even with approximate 2D simulations [7,24]. The introduction of asymmetries prevents us from resorting to these simplifications and imposes the need for a full 3D analysis as done for the asymmetric fully metal coated probes in [8,21,22].
The structure of the standard fully metal-coated axisymmetric probe and that of the corrugated probe are sketched in Fig. 1(a) and 1(b), respectively. In both the cases, the probe consists of a silica core (n = 1.5) surrounded by an aluminium coating (n = 0.645 + 5.029i at the operating wavelength λ = 532 nm). The inner silica cone radius is 225 nm, while the metallic hollow cone outer radius is 275 nm. Both cones are rounded: the radius of curvature of the inner cone is 10 nm, the one of the outer cone is 20 nm. The apex angle for both of them is 30°. The overall modelling domain is a 1.6 m cylinder with radius 1 m. The five sections of rings with an opening angle (the angular section covered by the corrugation) of 160° are formed by joining a truncated toroid of 20 nm radius with two hemispheres having the same radius. They have a z-spacing amounting to 150 nm (where z is the direction along which the probe axis lies), with the first bottom one centred at 150 nm from the input port. As anticipated, the corrugations can be either indentations or bumps, that is the rings are filled either with air or metal. For the sake of simplicity, the different configurations under study will be indicated with the following shorthand notation: each of the rings will be named after the initial of the filling material, starting from the bottom; for example, a configuration with three lower metal rings and two upper air rings will be labelled as mmmaa. The radius of the toroid was chosen to create an effective perturbation in the original structure without causing a radical change such as complete metal perforation. The five corrugations were equally spaced in the section of the probe where both the inner core and the metal coating are present. In Fig. 2, the first three eigenmodes, i.e. the two lowest order linearly polarized modes (H and V) and the radially polarized one (R), are reported together with the corresponding near field distributions obtained in a transverse plane located at 10 nm from the tip apex in the case of a fully axisymmetric probe.
The near field plots, representing the square of the norm of the electric field, are taken over a square area 600 nm by 600 nm centred at the origin of the coordinate system and are normalized to the maximum value of the electric field intensity distribution for the radial polarization in order to emphasize the relative field strengths. The same plane will be considered also in the following sections for the modified structures. The field distributions will be normalized to the R peak value of the standard axisymmetric probe. Strong localization is observed for the R mode due to the constructive interference of the surface waves along the taper, with an ultrasmall hot spot resulting from the combination of two weaker two-lobed transversely polarized patterns and a stronger single spot z-component. The FWHM of the intensity of the electric field was calculated to be 38 nm. Note that this does not represent the ultimate resolution achievable with fully metal coated probes, because, as shown in [11], the size of the hot spot is influenced by the final rounding in the metal coating that, in our simulations, was chosen to be 20 nm in radius just for convenience and can be decreased at will. Its value is necessary only as a reference for comparison. On the other hand, destructive interference of surface waves at the tip apex gives rise to two-lobed distributions for the H and V modes, polarized mainly along the x and y axis respectively and extended over an area whose shape is not well defined and whose average size is approximately 400 nm (where the size is measured as the distance over which the field is more than or equal to half of its peak value). The peak value of such distributions is about 50 times smaller than the peak of the R spot.

Parametric analysis of the corrugated probe
The asymmetric corrugations studied in this paper are expected to create field localization for the H mode as they determine an asymmetry along x. In the subsequent paragraphs, parametric studies about the suggested configuration are carried out to assess the impact of variations in the sequence of materials, that is of indentations and bumps, and the influence of some geometric parameters like the opening angle of the rings. The effects of the replacement of air with oxide will be investigated as well.

Change in material sequence
The normalized near field distributions for the structure in Fig. 1(b) are reported for the configuration amama (Fig. 3). As expected, field localization is achieved not only under R excitation, as in the axisymmetric probe, but also for the H one, while the V distribution does maintain an almost two-lobed distribution.
Of course, the possibility to get a single-lobed intensity distribution by the injection of a linearly polarized mode is not sufficient alone for SNOM applications. Characteristics like the size of the spot as well as its peak value compared to the one obtained with the injection of a radially polarized mode in an axisymmetric fully metal-coated probe are of primary importance for a thorough and careful comparison of different probe configurations. For this purpose, a systematic analysis of these features for all the possible permutations of air indentations and metal bumps for the same structure was carried out.
First of all, in order to check whether shrinkage in the near field distribution takes place for the H mode injection in the corrugated asymmetric structure, we calculated the FWHM [ Fig. 4(a)]. With the exception of only one configuration, the size of the near field distribution undergoes a dramatic reduction in all of the cases and, for most of the structures, a real ultrasmall spot with a FWHM comparable to that observed for the R mode excitation in the axisymmetric probe is created. Fig. 3. Normalized near field intensity distributions in a plane located at 10 nm from the apex of the structure in Fig. 1(b) and amama material combination. As also the peak value of the obtained spot plays a key role for SNOM applications, we calculated its ratio with respect to the peak value obtained for the axisymmetric probe under radially polarized excitation [ Fig. 4(b)]. The H peak value generally increases compared to the case of the standard axisymmetric probe. However, only few material combinations give rise to values comparable or, in two cases, even much superior to the radial peak for the axisymmetric probe. Moreover, it can be observed that the presence of the sequence air/metal/air in the upper three rings brings about higher peak values, with the best results given by the amama configuration.
As the field localization in the modified structure occurs only for the R and H modes, it is important for the H mode to be significantly higher than the V distribution. The latter one keeps on having a substantially two-lobed broader distribution for all the material combinations. Therefore, too strong peak values could determine degradation in resolution in case of misalignments. Figure 4(c) reports the ratio of the H peak value to the V peak value for the different structures. Also in this case, the best results are reached when an air/metal/air alternation is present in the upper corrugations, with values that should enable a clear prevalence of the H distribution over the V one.
The contrast of the H field distribution was also examined to characterize the strength of the peak value with respect to the background [ Fig. 4(d)]. Contrasts even above 100 can be achieved for some configurations.
An overall analysis of the previous graphs suggests the use of configurations with the air/metal/air combination in the upper three semirings to optimize performances in terms of peak size and strength, with the best results obtained for the amama structure. Another conclusion that can be drawn from a global analysis of the previous graphs is that, if a certain material combination is effective in achieving field localization for the H distribution, generally the complementary one is not.
All the shown data can be interpreted in the light of the interplay of mode coupling mechanisms and interaction of the external SPP with the outer surface roughness. In fact, as pointed out previously, in an axisymmetric probe under linearly polarized excitation the SPPs on the opposite sides have opposite polarities and thus their contributions cancel out at the apex. The presence of the corrugation locally tunes the coupling of the inner and outer SPPs and the characteristics of the outer SPP on one side of the tip. These mechanisms can modify the properties of the SPPs on one side of the tip in such a way that the electric fields associated with SPPs on the opposite sides of the probe do not have opposite phases any longer. Some configurations can result in a net prevalence of the SPP on one of the two sides and thus in field localization. Moreover, the asymmetry can also introduce a coupling from one of the linearly polarized modes into the radial one. This means first that, in some cases, even unintentional corrugations stemming from defects could have a beneficial effect on the tip behaviour. Second, intentional corrugations can be introduced on purpose to get a localized hot spot with a linearly polarized excitation, which can be obtained in an easier way than the radial one.

Change in the dielectric material
As a second step, we examined the effect of replacing an air indentation with a metal oxide bump. For the case under study, we chose aluminium oxide filling (with index of refraction n = 1.54). The reason for the analysis of the effects of metal oxide bumps lies in the fact that, especially for some metals like silver, metal oxide layers are likely to be originated. So far, only metal oxide defects in form of holes perforating the metal coating have been examined [8]. Simulations on dielectric-metal-dielectric probes under internal radially polarized illumination have shown the possibility to tune the intensity collected at the tip apex by changing the permittivity of a thin dielectric nanocladding surrounding a fully metal coated probe [34]. Such a phenomenon had been experimentally verified for a fully metal-coated probe covered by a dielectric layer whose index of refraction was varied [19,20]. Moreover, it has been shown that the coupling between surface modes at the core-conductor interface and the conductor-covering layer interface becomes more efficient when the index of refraction of the core is close to the index of refraction of the covering layer [35,36]. The structure we considered is the same as in the previous paragraph, with air replaced by oxide (denoted by the initial o in our shorthand notation). Also for this series of simulations, we took into account all the possible permutations of metal and oxide for the five semirings. Fig. 5. Normalized near field intensity distributions in a plane located at 10 nm from the apex of the structure in Fig. 1(b) and omomo material combination.  Figure 5 shows the field distributions for the omomo structure. As visible, the desired field localization for the H polarized mode is achieved, while the V polarized mode is not remarkably affected by the asymmetry.
Also for this configuration, we analyzed the characteristics of the H spot originated by the asymmetric corrugation, as the sequence of materials (metal and oxide) changed. First, the FWHM of the H field distributions for all possible permutations were compared [ Fig. 6(a)]. Results are similar to the ones obtained for the air-metal based structure and show the creation of an ultrasmall hot spot for most of the configurations.
The analysis of the peak value of such a spot compared with the one obtained for a fully metal coated axially symmetric probe under radially polarized excitation [ Fig. 6(b)] confirms once again that the alternation of dielectric/metal/dielectric in the upper three semirings provides better results, but also points out that the substitution of air with metal oxide gives rise to stronger peak values. Also the ratio between the peaks of the H and V distributions improves with respect to the previous air-metal based structure [ Fig. 6(c)]. Similar considerations hold for the contrast of the H hot spot [ Fig. 6(d)].
An overall analysis of the previous graphs confirms the trend shown in the air-metal corrugations, in that some metal-dielectric alternations give better results especially in terms of peak value of the achieved spot. Besides, when air is replaced by metal oxide, a further enhancement in the collected signal occurs, ensuing from a better coupling between the inner and outer SPPs.

Change in the angle of the corrugation
Finally, we tried to assess the impact of some geometric parameters on the probe performance. As anticipated, the limited computational domain does not allow us to change dramatically many geometric features, such as the distance between the portions of rings. An analysis of the effect of a variation of the opening angle of such corrugations was instead feasible and was carried out by increasing the opening angle from 110° to 160° with a step of 10°. Figure 7 reports the field distributions for the H polarization over the 600 nm by 600 nm output plane as a function of the angle, together with their normalized profiles along the x and y axes. As visible, in all the cases almost symmetric ultrasmall spots with similar sizes are generated. Compared to the cut and slit based tips, the symmetry of the spots is apparently better in all the cases, irrespective of the geometric parameters. However, as the angle increases, the intensity profile shows a more rapid decay.
To get better insight into the characteristics of these distributions, a quantitative analysis of the size and peak value of the H hot spots has been carried out.
Simulations reveal no significant variations in the FWHM for the H hot spots, which oscillates between 40 nm to 43 nm without any regular trend [ Fig. 8(a)].
On the contrary, other figures of merit for the H spot change remarkably as a function of the opening angle. Figure 8(b) reports the ratio of the H spot peak value with respect to the R hot spot for a standard axisymmetric tip. The ratio increases as the angle increases, which means that stronger coupling mechanisms occur with a more extended asymmetry, leading to an improvement in the intensity of the H hot spot. As a counter effect, however, the ratio with respect to the V peak value deteriorates with larger opening angles, as can be observed in Fig. 8(c). This behaviour, which can be probably ascribed to a stronger interaction of the SPP for the V polarized excitation as the asymmetry approaches the x = 0 axis, seems anyway not likely to mar the performance of the probe for higher opening angles. The contrast of the H hot spot increases as the angle increases until saturating for larger angles to an almost constant value, as illustrated in Fig. 8(d).
In conclusion, even smaller asymmetries generate coupling mechanisms which globally improve as the asymmetry involves larger portions of the tip.

Conclusions
The possibility of using asymmetric corrugations in the metal coating of fully metal-coated SNOM tips to induce field localization for one of the two linearly polarized modes was numerically demonstrated. Our 3D simulations on the effects of five equidistant semicircular corrugations introduced in just one half of the tip, in the form of either bumps or grooves, revealed that the linearly polarized mode oriented along the direction of the asymmetry (x in our simulations) can undergo significant spatial shrinkage and increase in intensity for proper choices of material combinations for the corrugations. Namely, by studying the effects of all the possible material permutations of air and metal in the five rings, it was shown that some configurations, especially those involving an air/metal/air alternation in the upper three rings, can give rise to very high quality ultrasmall hot spots for the H linearly polarized mode. The results were explained as the outcome of the interplay of improved coupling mechanisms between the H mode and the R mode and between the inner SPP confined at the silica/metal interface and the outer SPP supported at the metal/air interface. The achievement of field localization for a linearly polarized mode allows circumventing the cumbersome procedure required for the injection of a radially polarized mode.
The structure based on corrugations, even if a bit more challenging from the point of view of fabrication with respect to the cut probe [22], offers a larger number of possibilities to be tailored. In particular, we explored two possible variants, one based on the change in the dielectric and one based on the variation of a geometric parameter, that is the opening angle of the corrugations. In the first case, we replaced air by metal oxide. Simulations showed similar trends for the alternation of metal and dielectrics, with better results achieved for an oxide/metal/oxide combination in the upper three semirings. However, the substitution of air by oxide brings about an advantageous enhancement of the intensity of the H hot spot. Then, the angle of the corrugations was changed for the air-metal based system. This latter series of simulations generally confirmed the tendency of asymmetries involving more extended portions of a tip to give stronger coupling mechanisms and thus better field localization for the linearly polarized mode.
The proposed structure is still open to other routes for improvement. For example, the effects of real periodic corrugations extended over longer tip sections as well as variations in the shape of the corrugation or in the dielectric could be studied. Moreover, corrugations in orthogonal directions could be combined to induce field localization on both the linearly polarized modes. It is noteworthy that, despite posing major complications in the fabrication step compared to the cut tip, the suggested probe still appears easier to be realized than the tips with slits, using, for example, focused ion beam. Indentations have been actually already realized in fully metal probes [27]. Moreover the hot spots achieved for the asymmetrically corrugated probe show better symmetry properties than those of the cut and slit based tips. A last point worth to be highlighted is that our simulations cast light also on the possible effects of corrugations resulting for example from closely spaced metal grains and show that they could induce weak coupling mechanisms beneficial for the overall probe behaviour.
In brief, the proposed structure offers potential benefits for the behaviour of fully metalcoated probes. Experimental investigations based on the selective excitation of linearly and radially polarized modes and on tip-on-tip measurements, as done for the axisymmetric fully metal-coated probe in [13], are necessary to validate the results of our simulations and the reproducibility of this promising tip.