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Design of a plasmonic near-field tip for super-resolution IR-imaging

The concepts of spoof surface plasmon polaritons and adiabatic field compression are employed to design metallic near-field probes that allow guiding and focusing of mid-infrared wavelength electromagnetic radiation and provides subwavelength field confinements and a lateral optical resolution of about 10 nm.


I. INTRODUCTION
In the past decades scattering scanning near-field microscopy (s-SNOM) in the infrared (IR) spectral region has become an established tool for imaging applications including electronic, polymeric and biological nanostructures. After a period of experimental showcases there is now a drive to increase its sensitivity and lateral resolution to a level where single molecule detection and imaging becomes accessable. However, owing to the long wavelength nature of the involved fields these efforts are limited, unless strategies are pursued that exploit the internal resonances of the sample and/or tip to enhance the coupling between the probe and the sample. Huber et al. [1][2][3] have utilized phonon polariton resonances of polar crystalline materials to achieve nonlinear field enhancements with a lateral resolution of 40 nm at IR and THz wavelengths. As a matter of fact, this approach is restricted to materials such as SiC, Si 3 N 4 , SiO 2 or III-V semiconductors (e.g. GaAs, InP) excluding all materials that do not exhibit phononic resonances including biological and soft materials.
In search of increased flexibility of s-SNOM the alternative approach [4] utilize the shape and internal resonances of the probe to excite surface plasmon polaritons (SPPs) that can concentrate the electromagnetic radiation into subwavelength regions [5,6]. Unfortunately these resonances lie outside the chemical fingerprint region which limits the range of applications to optical wavelengths. In order to overcome these limitations, Pendry and coworkers [7,8] suggested the introduction of a periodic arrangement of grooves and holes into the surface of a perfect electric conductor (PEC). This enforces the generation of SPP-like modes, so-called spoof SPP or designer SPP, at any any desired frequency in dependence of the periodicity. So far, this concept of designer SPP has been experimentally demonstrated in the microwave and THz regime [9][10][11][12]. Out of the number of theoretical investiagtions dealing with spoof SPPs [13][14][15][16][17][18][19][20][21][22][23][24] the work in Refs. [15,18] is of most interest for the purpose of the work presented here as it utilizes spoof SPPs for THz microimaging. The authors proposed a periodically furrowed metallic tapered waveguide structure that focuses THz radiation down to the micrometer scale. In this paper we will pick up this strategy and present a novel design of a near-field nanotip which supports surface waves in the mid-IR wavelength domain between 5.7 and 6 µm, containing the dominant lipid and protein absorption bands, and focuses them down to the 10nm-scale. Our strategy is to find the grating parameters of a corrugated PEC wire to support spoof SPP modes in the wavelength range 5.7 -6 µm. This grating is then grafted onto the surface of a lossy gold tip onto which a sharp gold nanoantenna is planted. The field enhancement and confinement properties of this hybrid multiscale structure are analysed by means of finite-element method (FEM) based electromagnetic simulations.

II. METHODS
To find the proper/correct dimensions of corrugations that can confine and guide mid-IR electromagnetic radiation between 5.7 and 6 µm along a gold metal tip we will approach the problem as follows: In the first step, we calculate the dispersion relation of surface waves 3 propagating on an azimuthally corrugated perfect electric conducting (i.e. non-dissipative) wire of outer radius R, surface grating periodicity D, and indentation width and depth a and h, respectively (see. Fig. 1a)). To this end, we have to solve numerically the implicit equation [18]: where k n = k z + n(2π/D) with k z denoting the surface wave vector in z-direction (along the wire axis). 1090, 1660, 1740 and 3300 cm −1 impinges in TM-mode (i.e. p-polarized with E-field parallel to the plane of incidence which coincides with the picture plane) from the bottom of the wire along its vertical axis. For the frequency dependence of the complex dielectric constant of gold, we used the Lorent-Drude model with parameters taken from Ref. [25]. According to the the spoof SPP dispersion curve belonging to our grating (Fig. 2a)), we expect an Since a real s-SNOM experimental setup would not employ a corrugated wire as a probe, we need to replace the metal wire of radius R by a tapered tip that would need to efficiently guide and focus IR radiation as the electromagnetic fields travel along the surface grating towards the tip. This concept of adiabatic field compression is illustrated in Fig. 3a) which shows the spoof SPP dispersion curves for five different corrugated gold wires with the same grating parameters a and D and the same outer radius R as before, but different inner radii, surface. This behaviour is also reflected in Fig. 3b), which shows the simulated field energy density plot for a lossy gold wire at 1660 cm −1 with fixed outer radius and variable inner radius gradually decreasing from 1.41 µm at the bottom to 0.88 µm at the top of the wire.
As the surface waves travel along the wire from bottom to top the gradual decrease of the inner radius is accompanied by a gradual reduction of the group velocity and accordingly an increase in the spatial confinement.

III. RESULTS AND DISCUSSION
In view of our aim of designing a plasmonic assisted IR near-field nanoprobe, we will now consider a rounded gold cone as displayed in Fig. 4a) with dimensions common to most IR scattering-based scanning near-field optical microscopy (IR s-SNOM) probes. In detail, the tip is 25 µm long with an full cone angle of 40 • and a tip curvature radius of 40 nm. It has been shown that tips with an apex diameter of 80 nm can achieve a lateral optical resolution of about the same size [26]. Onto its surface we imprint our previously designed grating with dimensions D = 940 nm, a = 0.5 D, and h = D. In contrast to our previous illustration of adiabatic field compression, here we keep the groove depth fixed and gradually reduce the outer tip radius instead (Fig. 4b)). For this corrugated tip, we expect a higher field confinement but a field extent at the tip apex as big as with the uncorrugated version. In anticipation of this, we also consider a third structure, what we call a corrugated supertip (Fig. 4c)), where we fit a 2.5 µm long sharp apex on top of the corrugated cone. This gold nanoantenna has a base diameter diameter of 300 nm, a full cone angle of 6.65 • , and a curvature radius of 5 nm. Such an acute structure can be fabricated by electron-beam induced deposition and has been utilized to achieve sub-10 nm resolution in the optical regime [6]. Due to the dimensions of our grating, it is not possible to corrugate the nanoantenna as well, so the grating does not stretch all the surface up to the apex.
To determine how these three different structures perform in terms of confinement, we conducted FEM electromagnetic simulations where all tips were illuminated from the base by a p-polarized plane-wave with a frequency of 1660 cm −1 , first at angle of incidence of 0 • (Fig. 5, top row) and then at 75 • (Fig. 5, bottom row) with respect to the tip axis, where the latter configuration has been used in all our previous experimental work [26][27][28][29][30] as well by others [31,32]. The field energy density distribution is normalized by the field energy density of the incident light. At first glance, there is no field enhancement at 0 • incidence, even though we see for the corrugated structures excitation of spoof SPPs that are strongly confined to the grating. By contrast, we observe a field confinement at the tip apex for an angle of incidence of 75 • , which increases as we switch from the uncorrugated tip to the corrugated tip and then to the corrugated supertip.
Before we eloborate on the angular dependence of the field enhancement, we first quantify the field confinement as an assessment for the achievable optical lateral resolution. As a measure we take the lateral field extent around the tip measured as the radial distance at which the field energyr starts to follow a different power law visible as kinks in Fig. 6a).
Expecting the field extent to be comparable to the tip diameter we find the corrugated supertip to exhibit a sharp field distribution with a width of about 10 nm and a field enhancement of up to 3 orders magnitude larger compared to the ordinary tip, which provides a relatively poor lateral resolution of about 80 nm in agreement with the experimental findings mentioned earlier. Its corrugated counterpart provides the same lateral resolution, but about a factor of 2.5 better field enhancement thanks to the grating-induced SPPs. Now, regarding the angular dependence of the field enhancement as depicted in Fig.   6b), the curve belonging to the uncorrugated gold tip features a multiple peaked, sloping distribution with the maximum at 30 • similar to the study in Refs. [33,34]. In agreement with antenna theory [35],

IV. CONCLUSION
By means of mode matching, we designed an experimentally feasible surface grating that excites spoof SPPs in the chemical fingerprint region between 5.7 and 6 µm (i.e. between 1660 and 1755 cm −1 ). We grafted this grating onto the surface of a tapered metal waveguide structure to which we appended a nanoscale antenna with a 5 nm tip radius. FEM electromagnetic simulations revealed extraordinary field enhancement of 2-3 orders higher compared with conventional IR near-field probes. This field enhancement is accompanied by field confinement at the tip apex of the order of 10 nm holding the prospect of a fourfold increase in lateral optical resolution in comparison with conventional metal probes utilized in current s-SNIM apparatus. A goniometric analysis of the field excitation revealed a broad range of angles under which extraordinary field enhancement can be achieved. Thus, implementation of the nanoprobe presented here into existing near-field IR microscopy apparatus should be possible with minor or no modifications. With such a plasmon-assisted mid-IR nanoscopy probe available the label-free imaging of single protein or lipid molecules within biological tissue is possible. Adapting the grating to the appropiate wavelength, such a probe can be also deployed to detect small fluctuations in the free carrier concentration of highly doped seminconductor nanostructures.
V. ACKNOWLEDGEMENT