1. Introduction

Optical fiber nano-probe plays a key role in nanotechnologies, such as scanning near-field optical microscopy (SNOM), nano-lithography and optical tweezer [1–3]. The performance of nano-probe mainly depends on its cone angle and tip diameter, thus the fabrication of probes with different geometrical features attracts remarkable attentions. As is well known, parabolic nano-probe offers higher light throughput than common linear coned probes in the applications of SNOM, due to its short transitional taper of delivering light to the cutoff region [4,5]. Because of the nonlinear probe shape, the fabrication of parabolic probe is a challenging work. Commonly, it is prepared though the heating-pulling method [1,6], namely, a local area of fiber is heated and then pulled, with the deformation and fracture of heated part, a tapered probe with sharp tip is formed. Through the controlling of process parameters such as heating temperature and pulling force, the probe with a parabolic transition region could be obtained accordingly. However, the particular heating and positioning devices often lead to the high-cost, and moreover, the complex experimental factors demand delicate operations during fabrication, which limit the extending of this method. In addition to this, grinding is another effective approach [7–9], where the rotating fiber's endface is exposed to a rotating grinding plate. Under the milling of the plate, the redundant material will be removed, leaving the expectant probe shape finally. The formation of parabolic shape is determined by the gradual variation of the intersection angle between fiber and plate. Although possible to fabricate probes with different shapes, grinding is a method entirely based on mechanical machining with inevitable vibrations, thus, the grand probe often has a rough surface and asymmetric curvature, and furthermore the necessity of clamping and positioning will exacerbate the complexity of the process.

In terms of cost and simplicity, the chemical etching is a fruitful approach to make the nano-probe [10–13], but as far as we know, the controllable fabrication is just limited to the linear instead of parabolic probes. Here we propose an accessible dynamic etching method, which is shown to be a highly effective approach in the fabrication of parabolic nano-probe.

2. Fabrication process of the parabolic probe

In our method, a number of cleaved Ge-B co-doped optical fibers (PSF-GeB-125, Yangtze, Co., Ltd.) are immersed into the buffered hydrofluoric (BHF) acid which is composed of the 40% (wt) ammonium fluoride (NH₄F) solution, the 50% (wt) hydrofluoric (HF) acid and the de-ionized water, with the volume ratio of N: 1: 1 respectively. For safety, the etchant must be covered with a protection layer (isooctane). Compared to the selective etching, a plastic burette is introduced as a key element in the scheme due to its resistance to fluorine ion and the capability of flow control. During etching, the temperature is fixed to 25 °C with the accurate regulation of a heating plate, and the 40% (wt) NH₄F solution is injected in the burette, dropping into the etchant at certain infusion ratios with the regulation of a valve. The sketch of this method is presented in Fig. 1(a) .

 

Fig. 1 Overview of dynamic selective etching. (a) Sketch of etching process. (b) Variation of N to time. SEM micrographs of probe shapes for different etching times: (c) After 60 min static etching. (d) After additional dynamic etching for 30 min. (d) After a final static etching for 10 min. Scale bar: 2 μm.

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Firstly, we immerse three fibers into the etchant of N = 1.2 for a 60 minutes static etching, and then take away one probe. After that, we infuse the NH₄F solution at the rate of 1droplet per 30 seconds for 15 minutes, and the rate of 1 droplet per 2 seconds for 15 minutes subsequently. Moving away another probe, we keep a static etching for 10 minutes, and get the last fiber probe. The variation trend of N to time is plotted in Fig. 1(b). The scanning electron microscopy (SEM) images of the probes corresponding to different etching stages are given Figs. 1(c)-1(e).

The probe in Fig. 1(c) is of a linear cone of 120°, corresponding to the static etching of 60 minutes with N = 1.2. Then, the 120° probe is etched through the dynamic etching, namely, infusion of NH₄F solution at a lower rate of 1 droplet per 30 seconds for 15 minutes (about 3 ml in total), following a rate of 1 droplet per 2 seconds for 15 minutes (about 25ml in total), as can be observed in Fig. 2(d) , an additional quasi-parabolic cone is formed with the reduction of linear cone shape. After that, we statically etch the linear and nonlinear combined probe for 10 minutes with the etchant in previous step, consequently, a linear cone with a 7 μm-wide end is added to the parabola-like cone, and the etching of ready-made part goes further, leaving just a minor linear part left around the tip whose diameter is about 0.1μm, as illustrated in Fig. 1(e).

 

Fig. 2 Derivation from unetched fiber to parabolic probe: (a)-(e) Schematic diagrams of the gradual evolution to parabolic probe. (f)-(k) SEM images of probe shapes corresponding with (a)-(e) respectively.

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In Fig. 1(d), the probe shape appears as an embryonic form of parabolic probe, but its short probe height may hinder the applications to grooved samples, and that the excess of linear cone section will make the shape far away from a parabola. While for an absolute parabolic probe, the tip diameter is beyond nanoscale, which may prohibit the potential of resolution to sub-wavelength. Hence, the cone shape of Fig. 1(e) is the closest to the anticipant parabolic probe, as it could be divided into three sections. The first part is similar to a conventional linear probe, thus provide the advantage of ultra-sharp tip dimension, reaching a sub-wavelength resolution readily. The second part is the parabolic section, the very probe structure that we emphasize here. Since for a parabola, the cone shape far from the apex can be considered as a line segment, for simplicity, we regard the part apart from the apex as another linear section composing the third part.

3. Probe formation mechanism

When dipped into the etchant, the doped core and the pure silica cladding will react with the BHF respectively, generating different reactants. The difference in the solubility of the reactants will result in the distinction of etching rate between the core and cladding, which is a key factor to the probe formation [14]. That is to say, as the cladding is etched back longitudinally, the core begins to protrude from the fiber end, and is then exposed to the etchant axially and radially, thus, it is subjected to the transversal and longitudinal etching, evolving into the cone shape eventually.

It has been proved that the cone angle is significantly influenced by the concentration variation of components in the etchant, namely, θ eventually depends on the value of N [12,14]. For a given N, a corresponding θ is confirmed, if N is varied, θ will be varied accordingly. At the original stage, the unetched fiber is of a flat endface, as presented in Fig. 2(a). If it is dipped into an etchant of N₁, after etching for t₁ minutes, a single cone angle of θ₁ (in fact, the flat endface can be considered as θ₀ = 180°, but we neglect it for simplicity) will be formed, as shown in Fig. 2(b). When N₁ is changed to a value of N₂, during a proper time of t₂, though suffering the continuous etching, the part of θ₁ still remains and a new cone angle of θ₂ begins to protrude from the core, resulting in a double cone with θ₂ < θ₁, as presented in Fig. 2(c). In the similar manner, altering N₂ to a value of N₃, after t₃ minutes etching, a coned entity of θ₃ (θ₃ < θ₂ < θ₁) is generated, leading to a triply coned endface, as given in Fig. 2(d).

Seeing from Figs. 2(a)-2(d), we could get some trends about the cone angle: the newly formed cone angle in each step is smaller than the former, namely, θ₃ < θ₂ < θ₁, with the probe curvature becoming smoother and smoother due to the increased number of coned sections. Based on the similar process, through the controlling of volume ratio N and etching time t, it's quite possible to get the probe of i coned parts (i = 4, 5, ...), with θ_i < θ_i-1 < ... < θ₁, since i becomes large enough, the probe shape will be close to a smooth curvature with the cone angle gradually and monotonously decreasing from the apex to the other end, as presented in Fig. 2(e), which is able to satisfy the characteristics of parabola. The explanation is verified by the SEM micrographs of probes fabricated by multi-step etching mentioned above. As is shown in Figs. 2(f)-2(j), the probe shapes derive from an unetched fiber to a parabolic probe with the increase of cone angles. Hence, in one word, the principle of our etching process is attributed to the proper variation of N relative to the time t.

As aforementioned, gradual transition and monotonous decrease of probe shape are of great importance to the formation of parabolic probe. While in terms of the used optical fiber, we investigated the relationship between cone angle θ and N at the temperature of 25 °C. As indicated in Fig. 3 , θ monotonously decreases from 120° to 30° with the increase of N from 1.2 to 4, just complying with the cone angle variation tendency of parabola. Consequently, both continuous transition and monotonous decrease of θ can be achieved by the consecutive increase of N, which is readily fulfilled through the infusion of NH₄F solution. Since the volume of one droplet is quite small relative to the etchant, N can be considered to increase gradually as time going, giving the possibility to control the final probe shape as long as the infusion ratio can be adjusted properly.

 

Fig. 3 Relationship between N and cone angle θ.

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In terms of the variation of N to time, as has been presented in Fig. 1(b), we divide it into three stages. The first stage, 0-60 minutes with N = 1.2, is defined as the original static etching. The second stage represents the time interval from 60 to 90 minutes, when N is gradually changed to 1.5 from 60 to 75 minutes and then radically altered to 4 from 75 to 90 minutes through the regulation of infusion ratio. This stage exhibits the core idea of our method, and is named as the dynamic etching. Finally, a static etching from 90 to 100 minutes is performed, and could be denoted as the final static etching.

Undoubtedly, the dynamic etching stage plays a chief role in the formation of parabolic probe shape. As is indicated in Fig. 3, θ declines sharply with the enhancement of N in the range of 1.2 to 1.5, and then gradually falls down, verging to be convergent. On the contrary, for a parabola, θ declines slowly near the apex while drops suddenly close to the infinite end. Consequently, infusion ratio should be low enough to keep the gentle transition of cone shape in the pre-stage of dynamic etching, and then with a high rate in the post-stage, leading to the sharp decline of cone angle. Hence, in the dynamic stage, the rate is set at a low value of 1 droplet per 30 seconds at first, and then varied to a quite higher value of 1 droplet per 2 seconds, which gives the very variation trend of N, resulting in the parabolic shape.

As has been illustrated in Fig. 2, the parabolic probe is engendered step by step with a new section added to the former cone. However, it must be emphasized that etching urges not only the formation of new part, but the reduction of ready-formed portion due to its entire exposure to the etchant. Thus, the probe curvature will retract as time going, which may account for the gradual disappearance of linear part.

4. Evaluations of the optical properties

In the heating and pulling process, the diameters of the cladding and core decrease in the same proportion, leading to the coverage of the core [4–6], while the probe here is of an exposed core protruding from the cladding, just as Fig. 1(e) shows. Hence, it follows that an investigation on the optical properties of our parabolic probe would be especially worthwhile. In this paper, we will make comparisons of parabolic nano-probe to several linear probes (30°, 60°, 90°, 120°), through the simulation of light transmission efficiency in SNOM and the experiment on endface light distribution of bare tip.

4.1 Simulation of transmission efficiency

In applications of SNOM, the bare nano-probe is usually coated with an aluminum layer, as is the parabolic nano-probe. According to the etching principle and SEM images, the cone region is just generated from the core, so the model can be regarded as one length of silica with the same refractive indice n = 1.5 as the fiber core, without the deviation of refractive indices between the core and cladding. The 2-dimensional geometrical model of parabolic probe is given in Fig. 4 .

 

Fig. 4 Geometrical model of the parabolic probe coated with an aluminum layer in SNOM.

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There are in total three sections of probe structure excluding the 0.1 μm thick (T = 0.1 μm) aluminum (conductivity σ = 3.03e7 S/m) layer for the probe. Defining the radial direction as the X axis, the longitudinal direction as the Y axis and the center of aperture as the original point, we construct a coordinate to give an explicit description of the model. For the first linear cone, the cone angle is set as 120°, the cone height h₁ = 0.15 μm and the aperture diameter D_a = 0.1 μm. The nonlinear curvature is regarded as a parabola tangent to the 120° cone at the intersection, thus can be easily analyzed through the expression of y = 0.93 x² + 0.14 (unit: μm). In the second linear section, which is tangent to the parabolic shape, the cone angle is set as 30°, and the diameter of cone end (input port) D_c is set to 7 μm. The light source, an in plane wave with the amplitude E_z = 1 v/m and the wavelength λ = 0.633 μm, is perpendicularly loaded on the end of probe. Apart from parabolic probe, the models of linear probes of 30°, 60°, 90° and 120° with the same aperture diameter of 0.1 μm and input port diameter of 7 μm are also established. Having been generated in previous SNOM simulations [15,16], the geometrical models of linear probes are not presented here. Then the simulation is conducted by the finite element method with the commercial software COMSOL Multiphysics 3.5.

Keeping constant the other parameters except for the input wavelength, we calculated the transmission efficiencies which are defined as the ratio of output power flows to input power flows (poynting vector). The variation of transmission efficiencies to different wavelengths for the 30°, 60°, 90°, 120° and parabolic probe is plotted in Fig. 5 .

 

Fig. 5 Transmission efficiencies of the 30°, 60°, 90°, 120° and parabolic probes at different wavelengths.

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Although there are some fluctuations of efficiencies at different wavelengths and cone angles, it is reasonable to draw a conclusion on the whole that the efficiencies decrease with the increase of wavelength for every probe, because a longer wavelength is of a larger cutoff diameter, thus giving a long exponential attenuation region below the cutoff diameter [17]. Moreover, there is an incremental trend on efficiency from the 30° to the parabolic probe. This is probably attributed to the influence of cone length on exponential attenuation length, for a large cone angle, there is a shortened attenuation length, thus leading to a higher throughput [17]. In the comparison between the 120° and parabolic probe, we note that the difference in efficiencies is less apparent, with a minor superiority of parabolic probe over the 120° probe. In fact, the crucial distinction of these probe are not the tip region, but the section guiding light waves to cutoff region, hence, the tiny increment may due to the particular delivering function of light waves for parabolic region, as this smooth transitional curvature is readily to reduce the reflections of light waves at the dielectric-metal boundary [4]. However, generally speaking, both of these two probes perform on throughput with a high order relative to others. While the parabolic probe offers the superiority of a prolonged probe height to the linear 120° probe, which is necessary for observation on samples of deep grooves, thus the parabolic probe not only inherits the ability of the 120° probe with high transmission efficiency, but expands the application field in SNOM.

4.2 Experimental characterization of the probes

To investigate the endface light distributions, we construct a system similar to the conventional light spot detection setup, the sketch is shown in Fig. 6 .

 

Fig. 6 Set-up for observation on light patterns of nano-probes.

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Light from a laser diode at the wavelength of 650 nm (1mw) is couple to the cleaved fiber end through the port of an FC optical fiber adapter, while the other end with nano-probe is exposed to a microscope system (the combination of magnification lenses, CCD and computer) with the positioning of a 3-dimensional (3D) translation stage. Consequently, observer is able to get the magnified images of light spots, and the images of the 30°, 60°, 90°, 120° and parabolic probes in axial view and side view are all shown in Fig. 7 .

 

Fig. 7 Axial view of light distributions where is of the highest intensity: (a) The 30° probe, (b) 60° probe, (c) 90° probe, (d) 120° probe, (e) parabolic probe and (f) the gray scale images of the dashed lines for different probes. Side view of light distributions of central cross-section for different probes: (g) The 30° probe, (h) 60° probe, (i) 90° probe, (j) 120° probe, (k) parabolic probe and (l) the gray scale images of the dashed lines for different probes.

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In perspective of axial view, we focus on the plane where is of the highest intensity for the 30°, 60°, 90°, 120° and parabolic probe, as can be seen from Figs. 7(a)-7(e) respectively, there is a bright light spot in the center. In order to get accurate comparisons of light intensities between parabolic probe and others, we extract the gray-scale maps of arbitrary central cross-section (the dashed line) for all the probes. As indicated in Fig. 7(f), parabolic probe exhibits the highest intensity with the approximation of the 30° and 90° probes, while the 60° probe operates the lowest, about 1/3 of the parabolic probe. That is to say, the parabolic and 30°, 90° probes perform on intensity at a high level in axial direction.

In order to investigate the light beam propagation characteristics, we focus on the central cross section of each probe in side view, the images are given as Figs. 7(g)-7(k). Other than the situation of axial view, the light patterns for every probe are significantly distinctive. As plotted in Fig. 7(l), the gray scale intensity images of the cross-section at the dashed lines indicate that parabolic probe exhibits the highest intensity (close to the 60° probe), while the 120° probe is of the lowest (about 1/3 of the parabolic one). Hence, in the radial direction, both the parabolic and 60° probes are of high intensities.

As mentioned above, the 30° and 90° probes are of favorable light intensity performance axially but unsatisfactory radially, and the 60° probe makes desirable work radially but operates poorly axially. Only the parabolic probe behaves well both axially and radially, implying its capability of tight 3D focusing of light, which may offer the potential applications in particle trapping, photo-reduction and second harmonic excitation [3,18–21].

5. Conclusions

We successfully propose a simple etching process to fabricate the parabolic optical fiber nano-probe. The formation of parabolic shape is explained and could be controlled by the variation of etching composition ratio. This approach is not only confined in parabolic probe, but reveals the potential to fabricate the probes of particular shapes as long as the cone angle can be varied properly through the regulation of infusion ratio.

Our theoretical and experimental investigations show that optical properties of parabolic optical fiber nano-probes are superior to the linear probes with different cone angles. The as-fabricated parabolic probe exhibits a high transmission efficiency in SNOM and the strongest light intensity both axially and radially for the 3D focusing of light, which will offer a wide applications for SNOM, optical trapping, photo-reduction and second harmonic excitations.