Plasmonic focusing of infrared SNOM tip patterned with asymmetric structures

Qinbai Qian; Haochi Yu; Peng Gou; Jie Xu; Zhenghua An

doi:10.1364/OE.23.012923

1. Introduction

Since the initial innovation [1, 2], scanning near-field optical microscope (SNOM) has been used in an increasing number of application fields including material, device and biological science. This technology could reach a much more microscopic perspective beyond the so called diffraction limit than the traditional optical microscope. Indeed, the inspiring spatial resolution is achieved by exploring the sample near field with a tapered probe whose performance directly affects the resolution of SNOM. Previous researches have revealed that the near-field intensity at the tip apex as well as the tip sharpness will affect the resolution to a great extent [3–5]. Therefore, for scattering-type version of SNOM (s-SNOM), an external high power laser or thermal source is usually required to excite longitudinal local near-field enhancement between the tip and the sample surface [6–10]. However, with strong external illumination, much weaker intrinsic sample information such as the thermal near-field [11] may be buried in the large background signal. The necessity of using intense lasers brings limitations to real applications and is also likely to damage samples particularly biological objects. In that case, a tip with the ability of high efficient near-field enhancement will do a great favor to relieve high-power-density requirement and even be available for passive s-SNOM [12, 13]. Exactly, due to the evanescent nature, the versatile surface plasmon polaritons (SPPs) are deft at the manipulation of light propagation and localization on sub-wavelength scale [14, 15]. What we can imagine is, extremely intense local fields will be excited at the tip apex if SPPs are launched and propagate toward the very tip.

Considering the tip shapes, one of the simplest methods to generate SPPs is grating coupling. Based on this, series of simulated and experimental investigations have been done in which the tip surface is patterned with grating of bumps [16, 17], grooves [18–20] or slits [21]. Most of these works are carried out on condition of external illumination utilizing lateral incident mode or tapered hollow metal waveguide mode. While in the area of infrared research, which contains fairly abundant light-matter interaction information such as molecular vibrations and electron-phonon interactions, some novel and creative studies, for instance the passive s-SNOM for thermal excited near-field explorations [12, 13], require the relief of most of the unwanted far-field excitation to the sample. Thus better choices may be patterned full metal tips which should be efficient in near-field excitation and probing under normal incident mode (infrared radiates from the sample). For that kind of tips, there is still dearth of descriptions about the grating performance in light scattering, especially about tips patterned with dielectric gratings which are also capable in SPPs generation [15].

In this paper, we focus on bump-shaped gratings and give intelligible explanations about their competences in light energy concentration. We survey the field enhancement effects of SPPs excited by linearly polarized light in cases of different patterned bumps including symmetric/asymmetric structures and metal/dielectric materials. Asymmetric structures generalized as bump size asymmetry (BSA) (insert picture in Fig. 1(c)) and bump position asymmetry (BPA) (insert picture in Fig. 1(d)) show much greater ability in longitudinal field enhancement than symmetric ones. We propose one simple charge distribution function to well interpret this. Then, we reveal the great difference of tip-enhanced mechanism between tips patterned with metal and dielectric bumps. For metal bumps, only one peak related to SPP standing wave resonance appears. While for dielectric bumps, two significant resonance peaks could be observed in the spectra of field enhancement if the dielectric material and bump size are well chosen. We find that these two peaks are related to SPP standing wave resonance and geometric local surface wave resonance respectively. What’s more, Fano resonances can be observed when changing the spacing between the tip apex and the nearest bump, which may improve the spectroscopic sensitivity and hence extend the applications of s-SNOMs by utilizing the Fano-tip platform. Finally, on account of our desired working frequency which is located in the intermediate infrared range, the matching grating period should be large enough and hence the real tip tapering profile should not be ignored. Our results show that it is still applicable to adopt grating coupling to generate SPPs if each interval between two neighboring bumps is carefully adjusted according to the tapering curvature.

Fig. 1 (a) Sketch of full-metal tip patterned with symmetric metal bumps, the cone angle is set at $30^{\circ}$ . The electric energy density distributions of (b) the symmetrically patterned metal tip ( $h = 800 n m$ ) (c) the BSA metal tip ( $h_{L} = 800 n m$ ; $h_{R} = 400 n m$ ) and (d) the BPA tip ( $h_{L} = 800 n m$ ; $p_{0, R} = 1.5 p$ ), shown with the same color scale. (e) Sketch of charge distribution (un-strict) of the symmetrically patterned metal tip. The $| E_{Z} / E_{i} |$ frequency spectrums of (f) the BSA and (g) the BPA tips, $| E_{Z} |$ is the longitudinal electric intensity at the tip apex and $| E_{i} |$ is the electric intensity of the incident light.

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2. Full-metal tip with metallic bumps

Our simulation works are carried out with the three-dimensional finite difference time domain (FDTD) method under ‘open (add space)’ boundary conditions. The structure of the full metal tip patterned with symmetric and uniformly-spaced bumps is sketched in Fig. 1(a). The cross profile of each bump is a circle whose half is buried into the tip. The bump height and the spacing between the tip apex and the nearest bump are expressed as $h$ and $p_{0}$ respectively [Fig. 1(e)]. The incident light whose wave vector orients along the direction (z) paralleling the cone axis is linearly polarized (along y direction) plane wave with its E-field amplitude defined as a unit of value. Therefore, the SPPs waves excited by such bump grating would travel upward or downward along the tip surface. It should be noted that, by irradiation of our desired incident intermediate infrared light, typical metals, such as gold and silver, behave approximately as perfect conductors (PEC) because of the large negative real and positive imaginary parts of the metal permittivity [15]. Hence, the metal parts of tips in our simulations are replaced by PEC for convenience of calculations.

Generally, elaborately designed grating periods for SPPs excitation should meet the phase-matching condition [15] written as:

β = k_{0} \cdot \cos θ \pm n \cdot \frac{2 π}{p}

where

β

is the propagating constant of SPP,

k_{0}

is the incident electromagnetic wave vector,

θ

is the included angle between the incident light direction and the tip slope and it happens to be half of the cone angle according to the geometrical relationship,

p

is the corrugation period (spacing between two neighboring rings), and

n

is a positive integer (

n

= 1,2,3…).

In the right part of Eq. (1), sign ‘ + ’ represents the SPPs propagating upward, and sign ‘-’ for the downward ones. It is clear that only the downward SPPs could contribute to the local near-field enhancement at the tip apex, thus the applicable grating period $p$ can be derived from Eq. (1) as following:

p = n \cdot {(\frac{1}{λ_{s p}} + \frac{\cos θ}{λ_{0}})}^{- 1}

where

λ_{0}

is the wavelength of the incident light, and

λ_{s p}

is the wavelength of SPP which can be estimated by:

λ_{s p} = λ_{0} \cdot {(\frac{ε_{d} + ε_{m}}{ε_{d} \cdot ε_{m}})}^{1 / 2}

where

ε_{m}

and

ε_{d}

are the dielectric constant of metal and surrounding dielectric, respectively. As for our PEC tip,

| ε_{m} | \to \infty

, so

β \approx k_{0}

and

λ_{s p} \approx λ_{0}

in the PEC/air interface. The grating period

p

can be further simplified as:

p \approx n \cdot \frac{λ_{0}}{1 + \cos θ}

When $n = 1$ , we get the smallest applicable value of $p$ . Note that the Eq. (4) is not strictly but approximately correct because of the finite number of bumps allowed to extend along the short tip sloping side. Despite this, Eq. (4) still provides certain reference significance for choosing the values of $p$ to obtain resonant responses of specific frequencies.

For the symmetrically patterned tip, the periodic bumps induce the surface electromagnetic field to change like a standing wave over time whose antinodes happen to be the bumps and greatly enhanced the field intensity in the vicinity of bumps. Unfortunately, the field intensity at the tip apex which we are mostly concerned about is not enhanced as much as the bump vicinity due to the geometric symmetry. Furthermore, rarely longitudinal component, which contribute the most to the tip-sample interaction, is contained in the field intensity at the apex. Therefore, breaking the symmetry seems to be a pleasurable method to give rise to longitudinal field component at the apex [16, 17, 22]. The simplest method would be to place the symmetrically patterned tip at an oblique angle but the experimental facility should be readjusted correspondingly which we are not going to discuss, and the following is mainly confined to the tip pattern asymmetry method (BSA and BPA).

In our simulations, both the BSA tips and BPA tips are patterned with two bump groups distributing on the tip surface of both sides. The bump size ( $h$ ) and the bump position ( $p_{0}$ ) of the either group may be different from the corresponding ones of the other group. We interpret the competence of asymmetrically patterned tips in remarkable longitudinal field enhancement from the perspective of charge accumulation. The charge oscillation aroused by either bump group at the tip apex can be approximately expressed by a time-depended cosine function:

q = A \cdot \cos (ω t - φ) = A (h) \cdot \cos (\frac{2 π c}{λ_{0}} \cdot t - φ)

or:

q = A \cdot e^{- i (ω \cdot t - φ)}

where

A

is the amplitude depended on the bump size,

φ

is the phase delay concerned with the bump position, and

c

is the speed of light in the vacuum. The longitudinal electric field intensity should be proportional to the absolute value of the total amount of charge of both sides, namely:

| E_{z} | \propto | \sum q | = | q_{L} + q_{R} | = | A_{L} \cdot e^{- i (ω \cdot t - φ_{L})} + A_{R} \cdot e^{- i (ω \cdot t - φ_{R} - π)} |

| E_{z} | \propto \sqrt{A_{L}^{2} + A_{R}^{2} - 2 A_{L} A_{R} \cdot \cos (φ_{R} - φ_{L})}

where the subscripts ‘L’ and ‘R’ indicate the left and the right side of the tip apex (similarly hereinafter), and the phase difference

π

comes from the opposite traveling directions of the two SPP waves projected in the horizontal plane. Obviously, both the BSA (

h_{L} \neq h_{R} \to A_{L} \neq A_{R}

) and BPA (

p_{0, L} \neq p_{0, R} \to φ_{L} \neq φ_{R}

) tips could lead to nonzero

| \sum q |

and hence stimulate the longitudinal local near-field enhancement. For the symmetrically patterned tip, the bump size and the bump position of both sides are correspondingly equivalent. Therefore the complete offset of charge leads to extremely weak longitudinal field intensity at the tip apex [Fig. 1(e)].

In Figs. 1 and 2, the grating period $p$ of all the tips are set at $7.63 μ m$ , the values of $p_{0}$ are preliminarily assumed to equal $p$ except the one of the right bump group of the BPA tip [Fig. 1(d)]. The cone angle is chosen at $30^{\circ}$ and the total simulation domain is about $27 \times 27 \times 43 μ m^{3}$ . The minimum grid size is set to $20 n m$ , which is smaller than both the associated wavelength ( $15 μ m$ ) and also the needlepoint radius ( $100 n m$ ). The simulation frequency range is 15-25THz and the attenuation degree of field energy is set to −80dB. In fact, due to the restriction of the computer competence, our simulation settings are chosen as tradeoffs between the computational cost and the simulation reliability. For example, a sharper cone angle or a smaller needlepoint radius can lead to a higher enhancement, but that would need denser grid and hence increases the computational cost. While on the other hand, blunter tips require larger simulation domains which also add to the computational burden.

Fig. 2 The electric energy density distributions in the x-y plane close to the tip apex of (a) the symmetrically patterned metal tip ( $h = 800 n m$ ), (b) the BSA metal tip ( $h_{L} = 800 n m$ ; $h_{R} = 0 n m$ ) and (c) the BPA tip ( $h = 800 n m$ ; $p_{0, R} = 1.5 p$ ). (d) - (f) Magnifications of the central zone of the upper row pictures. FWHM of the (g) BSA tip and (h) BPA tip, the value of $λ_{0}$ is chosen at $15 μ m$ .

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The electric energy density distributions (y-z plane, at 20THz) of the symmetrically patterned tip ( $h = 800 n m$ ), the BSA tip ( $h_{L} = 800 n m$ ; $h_{R} = 400 n m$ ) and the BPA tip ( $h = 800 n m$ ; $p_{0. R} = 1.5 p$ ) are respectively shown in Figs. 1(b)-1(d) with the same color scale. It can be seen that the asymmetrically patterned tips show better performances in realizing the electric energy ‘hot spot’. The frequency spectrums of $| E_{Z} / E_{i} |$ (the subscribe ‘ $i$ ’ means the incident light and the E-field probe is put in the lowest point of the tip apex, similarly hereinafter) of the BSA tips (the left bump heights are locked at $800 n m$ but the right ones sweep from $0 n m$ to $800 n m$ ) and the BPA tips (the spacing between the right first bump and the tip apex $p_{0, R}$ increases from $p$ to double $p$ and the left side keeps unchanged, the bump height is $800 n m$ ) are shown in Figs. 1(f) and 1(g) (the colors represent the field intensity ratios between $| E_{Z} |$ at the tip apex and $| E_{i} |$ ). It is clear that all these asymmetrically patterned tips have single-peak resonances (near 20 THz or $15 μ m$ in wavelength) whose positions slightly vary from each other because of their minor shape variances. For the BSA tip, the brightest electric energy ‘hot spot’ obtained when the bump height difference between both sides attain its maximum ( $Δ h = h_{L} - h_{R} = 800 n m$ ); and for the BPA tip, the largest local near-field enhancement happens when the value of $p_{0, R} / p$ is about 1.5.

In addition to the field enhancement, to investigate the lateral resolution which is the another main characteristic of a SNOM tip, we evaluate the full width at half maximum (FWHM) of the ‘hot spot’ from the electric energy density distribution on the x-y plane close to the tip apex (at 20THz). Figures 2(a)-2(c) show the side-by-side comparisons of the ‘hot spot’ among the symmetrically patterned tip ( $h = 800 n m$ ), the BSA tip ( $h_{L} = 800 n m$ ; $h_{R} = 0 n m$ ) and the BPA tip ( $h = 800 n m$ ; $p_{0, R} = 1.5 p$ ), and Figs. 2(d)-2(f) are the corresponding magnifications of the central zones of the upper row pictures (notice the difference in the color scales). Clearly, the symmetric tip fails to get a ‘hot spot’ but a relative ‘dark spot’ at the tip apex. For the asymmetric tips, FWHMs along the x and y directions are shown in Fig. 2(g) (BSA tips) and Fig. 2(h) (BPA tips) (the meanings of the horizontal axises are respectively the same with the vertical ones of Figs. 1(f) and 1(g)). Roughly, the asymmetrically patterned tip has the ability to achieve a fairly high resolution approximating 3.5 percent of the incident wavelength. As for the BSA tip, it reveals that a larger bump height difference ( $Δ h$ ) leads to a higher resolution (or smaller FWHM), which has the similar trend of its performance in field enhancement. And for the BPA tip, the lateral resolution seems not to change remarkably. Moreover, one may notice that, within tolerance, the FWHM along y is normally larger than the one along x in BSA tip, while the case of the BPA tip is just the opposite. We deduce that such difference is due to the symmetrical component of structure since the BSA tip can loosely be regarded as the superposition of a symmetric tip with bump height of $h_{R}$ and another BSA tip only one side of which has bumps with height of ( $h_{L} - h_{R}$ ). And for the symmetrical component, because of the polarization of the incident light (along y direction), two ‘hot spots’ would appear on both sides of the tip apex (refer to Figs. 2(a) and 2(d)), and hence worse the resolution along y direction.

In the next section, we will consider replacing the PEC bump with dielectric material and studying their differences in tip-enhanced mechanism.

3. BSA tip with dielectric bumps

Based on the discussion above, to focus on the influence of the bump material and avoid introducing too much variables, we choose the BSA tip with $h_{R} = 0 n m$ for the following research. One notices that, except metal gratings, dielectric surface-relief gratings on a flat metallic surface are also capable in the SPPs transmission [23]. It is demonstrated by us that dielectric bumps patterned on the tip surface not only have the similar ability in the SPPs transmission, but also bring in some other optical phenomena such as Fano effect which is rarely combined with SNOM tips. Our findings provide a unique method to utilize the Fano effect and may potentially widen the availability of traditional SNOMs.

The structure of our designed dielectric bump tip as sketched in Fig. 3(b) is composed of dielectric half tori (green colored) and PEC groove tip (gray colored). The dielectric material we choose for simulation is loss free glass with permittivity of 4.82. The grating period is chosen at $7.12 μ m$ which is fit for the desired incident wavelength $λ_{0} (12.5 μ m - 27 μ m)$ avoiding the higher order reflections. The simulation domain and the minimum grid size are set at about $32 \times 32 \times 52 μ m$ and $20 n m$ . The attenuation degree of field energy is set to −80dB. From the spectra of the longitudinal field enhancement at the tip apex [Fig. 3(a)], it is clear that two significant resonance peaks gradually emerge meanwhile redshift albeit to a different degree by increasing the bump size $h$ from $980 n m$ to $1780 n m$ (the value of $p_{0}$ is kept at $p$ ). What’s more, a dip may appear in the position of the long-wavelength peak when we sweep the value of $p_{0}$ , in purpose of studying its influence on the field enhancement, from $p$ to double $p$ [Fig. 4(a)]. To investigate the natures of the resonance peaks and also the dip, we check their corresponding distributions of electric field and propose an equivalent dimer model especially for the dip.

Fig. 3 (a) The $| E_{Z} / E_{i} |$ frequency spectrums of the dielectric BSA ( $h_{R} = 0 n m$ ) tips with different bump heights. (b) The structure of the dielectric BSA tip (shown as separated parts), composed of dielectric half tori (green colored) and PEC groove tip (gray colored). The electric field distribution (shown as the $E_{y z}$ vector fields, the electric field polarization direction of incident light parallels to the y axis) corresponding to (d) mode 1 and (e) mode 2 marked in Figs. 3(a) and 3(c) the electric field distribution (the same observation way) of the full-metal BSA tip ( $h_{L} = 1780 n m$ ; $h_{R} = 0 n m$ ) at its resonance frequency.

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Fig. 4 (a) The $| E_{Z} / E_{i} |$ frequency spectrums of the dielectric BSA ( $h_{R} = 0 n m$ ) tips with different value of $p_{0}$ .The distributions of electric fields (shown as the $E_{y z}$ vector fields, the electric field polarization direction of the incident light parallels to the y axis) corresponding to (b) position A, (c) position B and (d) position C of line ‘ $p_{0} = 2 p$ ’ shown in Fig. 4(a), the arrows represent the charge oscillation directions.

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For the two resonance peaks (choose line ‘ $h = 1780 n m$ ’ in Fig. 3(a) as an example), we connect the long-wavelength resonance peak (mode 1) with the groove geometric resonance due to the field bouncing between both sides of an individual groove [Fig. 3(d)], while the short-wavelength resonance peak (mode 2) whose electric field distribution pattern [Fig. 3(e)] is similar to the one of the PEC bump tip [Fig. 3(c)] is actually caused by the standing waves of SPPs propagating between neighbor grooves. Further conclusion can be made from Fig. 3(a) that the long-wavelength resonance peak is more sensitive to the bump size $h$ than the short-wavelength one. In general, such two resonance modes of the dielectric bump tip are brought about by the patterned groove grating whose property can be found in previous literatures such as [24–27].

The electric field distributions of the Fano dip and its adjacent two peaks (position B, A and C of the ‘ $p_{0} = 2 p$ ’ curve in Fig. 4(a)) are shown in Figs. 4(c), 4(b) and 4(d), respectively. Obviously, in positions near the Fano dip, the field distribution of part ②, which oscillates like a quadrupole, is a dark plasmon mode and hence cannot be directly excited by the incident light but can be excited by the bright mode of part ① which actually plays the role of a diploe source. While, the bright mode (B) of part ① can be directly excited via the path way: $| I 〉 \to | B 〉$ by the incident light (I) whose wavelength (about $24 μ m$ at the Fano resonance frequency of position B in Fig. 4(a)) is twice the length of part ① ( $L_{p a r t 1} = p_{0} - p \approx 12 μ m$ ). Moreover, the bright mode (B) of par ① can also be excited via another pathway [28]: $| I 〉 \to | B 〉 \to | D 〉 \to | B 〉$ when frequencies of incident light (I) are resonant with both dark (D) and bright (B) modes. At the Fano resonance frequency, these two pathways destructively interfere with each other resulting in the canceling of the polarization of the bright mode and hence the charge oscillation of part ① is greatly depressed. In other word, the Fano effect appearing in our dielectric bump tip can be understood as destructive interference between the dark and bright plasmon modes supported by different parts of the tip surface. Similar Fano resonance can be found in the system composed of a long and a short nanorod [29], indicating that our equivalent dimer system is reasonable.

In brief, our simulation work demonstrates the possibility of utilizing the Fano effect with SNOM tips, on which little study has been carried before. Promisingly, new intercrossed applications may be found between scanning and sensing.

4. Grating coupling for non-ideal cone tips

The non-patterned full metal tip can be fabricated by electrochemical corrosion [30]. While the tapering parts of these tips may not be perfect ideal cones but non-ideal ones with bending surfaces. Roughly, such non-ideal cone tips can be divided into two main types: the inward cone type and the outward cone type [Fig. 5(a)]. Normally, the length of the tip tapering part is hundreds of times longer than the grating period for visible or near-infrared light illumination. In that case, the generatrix curvature has very little impact on the grating patterning with finite number of bumps. However, due to our desired mid-infrared incident light, the long matching grating period would lead to a large grating region within which the generatrix curvature could not be ignored. The following we shall investigate the grating coupling for such non-ideal cone tips using BSA tips ( $h_{R} = 0 n m$ ) as examples.

Fig. 5 (a) Profile section views of the inward cone tip (the darkest profile), the outward cone tip (the lightest profile) and the ideal cone tip (the moderate profile). (b) The $| E_{Z} / E_{i} |$ frequency spectrums of the ideal cone tips (dash lines) and the inward/outward cone tip (solid lines). The electric energy density distributions (shown with the same color scale) of (c) the inward cone tip, (d) the ideal cone tip and (e) the outward cone tip.

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It is certain that the phase-matching condition mentioned above must be amended to be fit for non-ideal cone tips. Notice that the generatrix curvature of general metal tip obtained from electrochemistry erosion is not too big, to keep things simple, we replace the curving generatrix with segments of straight line. In our 3-D simulations, both the inward and outward cone generatrices are composed of 5 straight-line segments. The length of each straight-line segment and the included angle between the straight-line segment and the cone axis are set as $p_{i}$ and $θ_{i}$ (i = 1,2,3,4,5). Four asymmetric PEC bumps are placed at each junction. The relationship of two contiguous straight-line segments is described as $θ_{i + 1} = θ_{i} + Δ θ$ , where $Δ θ$ with a positive/negative value leads to an outward/inward cone tip.

To make comparisons, the bottom diameter and the height of the inward/outward cone tip are respectively the same as the ones of the standard ideal cone tip [Fig. 5(a)]. The simulation settings are the same with the ones in Part 2 in our article. Results show that the grating coupling method for SPPs generation is still valid if the period satisfies the following relation equation:

p_{i + 1} (1 + \cos θ_{i + 1}) = p_{i} (1 + \cos θ_{i}) = n \cdot λ_{0}

In Fig. 5, we set ( $θ_{1} = {7.5}^{\circ}$ ; $Δ θ = {3.75}^{\circ}$ ) for the outward cone tip, ( $θ_{1} = {22.5}^{\circ}$ ; $Δ θ = - {3.75}^{\circ}$ ) for the inward cone tip and $θ = 15^{\circ}$ for the standard ideal cone tip. From the $| E_{Z} / E_{i} |$ spectral responses ( $| E_{Z} |$ is the longitudinal electric field intensity at the tip apex), it is clear that the inward/outward cone tip has performances similar to the standard ideal cone tip in longitudinal field enhancement. Impressively, the inward cone tip has the highest resonance peak value but the outward cone tip has the lowest. The electric energy density distributions of the inward/outward and the standard ideal cone tips (Figs. 5(c), 5(e) and 5(d) with the same color scale) also show that the brightest electric energy ‘hot spot’ is generated by the inward cone tip. As we mentioned above, for the ideal cone tip, a sharper cone angle could lead to higher longitudinal field enhancement. To clarify whether the bending surface will influence the tip enhancement, two more ideal cone tips with $θ = {7.5}^{\circ}$ and $θ = {22.5}^{\circ}$ are also simulated (their heights are the same with the standard ideal cone tip with $θ = 15^{\circ}$ ). As we can see from Fig. 5(b), the tip with inward surface with $θ_{1} = {22.5}^{\circ}$ ; $Δ θ = - {3.75}^{\circ}$ (outward surface with $θ_{1} = {7.5}^{\circ}$ ; $Δ θ = {3.75}^{\circ}$ ) exhibits even larger (smaller) enhancement than the standard tip, i.e., with $θ = {7.5}^{\circ}$ ( $θ = {22.5}^{\circ}$ ).Therefore, we can conclude that the tip surface profile also plays an important role on the performance in the longitudinal field enhancement.

Without losing generality, our results here show that one can also pattern non-ideal cones with unequal-interval bumps according to the surface curvature to generate SPPs for the purpose of tip enhancement.

5. Conclusions

The main purpose of our work is to find efficient methods in realizing the local near-field enhancement at the apex with a scattering type full metal tip whose working wavelength is in the mid-infrared band. Asymmetrically patterned tips show great competences in focusing incident light energy into nano ‘hot spot’. For the metal bump patterned tip, its performance in enhancing the longitudinal local near-field could be interpreted with a time-depended charge distribution function. Normally, both the bump size asymmetry and bump position asymmetry would influence the longitudinal field intensity at the tip apex. For the dielectric bump patterned tip, the mechanism of local field enhancement may be much more complex due to its torus and groove structure. With appropriate dielectric material and well-designed structure parameters, one could observe two significant resonance peaks correspondingly relate to the groove geometric resonance mode and the SPPs standing wave resonance mode in the frequency spectrum of longitudinal field enhancement ( $| E_{Z} / E_{i} |$ ) at the tip apex. And due to the interaction between the grating and the tip apex, a Fano dip may happen in the position of the groove geometric resonance peak when changing the spacing between the tip apex and the nearest groove. Considering the practical situation in which the tapering parts of the tips before being patterned may not be perfect ideal cones but non-ideal ones with bending surface, our simulation results show that it is still possible to use the grating coupling method to realize the local near-field enhancement while the intervals between neighboring bumps should be designed according to the surface bending curvature.

Our work provides a fundamental guideline to the tip optimization in near-field infrared microscope applications. Despite of the small number of bumps and their simple geometry in this study, future simulation and experimental work can involve a large tip design freedom with more bumps/trenches structures and/or pattern shapes with great complexity. For instance, tips with spiral bumps with omnidirectional asymmetry could be expectable in realizing efficient near-field field enhancement with tailored spectroscopic property and improved insensitivity to the polarization of incident light. Experimentally, the proposed tip structures can be fabricated via electrochemical etching with subsequent focused ion beam (FIB) etching/deposition which has been proven to be versatile in tip decoration.

Acknowledgments

This work is financially supported in part by the National Natural Science Foundation of China (Nos. 11427807/11174057).

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Plasmonic focusing of infrared SNOM tip patterned with asymmetric structures

Abstract

1. Introduction

2. Full-metal tip with metallic bumps

3. BSA tip with dielectric bumps

4. Grating coupling for non-ideal cone tips

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Equations (9)

Optics Express