1. Introduction

Scanning near-field optical microscopy (SNOM) enables observation with a spatial resolution beyond the diffraction limit [1–4]. A tapered optical probe with metallic cladding and an aperture of ~10 nm enables the successful detection of the optical near field around target objects to be measured. However, intrinsic transmission loss is inevitable because the tapered nanosized core is much smaller than the wavelength of light, in addition to the difficulty of nanofabrication. Moreover, in a dielectric waveguide, the fundamental mode, HE₁₁ with no cutoff yields high throughput but poor confinement in a very thin core. Several optical probes, such as single- to triple-tapered structures, have been proposed to enhance the transmission and brightness of an optical spot [4–6]. Instead of a regular circular aperture, a bowtie-shaped aperture was also proposed for enhanced transmission, and it achieved a one-order magnitude improvement in transmission compared with the probes with a regular aperture [7]. In addition, extraordinary optical transmission due to waveguide resonance in a tapered probe with a metallic nano-hole provided more than 100 times higher transmission than conventional SNOM probes [8]. However, the power transmission, given as the ratio of output to total input light power through a probe, still remain large, 10⁻⁵–10⁻² for a 10–160-nm aperture, because the transmission significantly declines in a relatively long tapered region.

Another approach is a metal-dielectric-metal (MDM) structure that incorporates the surface plasmon and the antenna concept [9–13]. Seamless transition between dielectric slab waveguides and nanosize MDM plasmonic waveguides has been achieved with high power-coupling efficiency of 70%–90% [9,10], and ~70% power transmission is obtained in a plasmon gap waveguide with a combination of tapered dielectric core and metal cladding [11]. These results indicate superior transmission efficiency compared with conventional waveguides, wherein no plasmons are excited. Although a plasmonic waveguide would offer an advantage for a nanosized probe, it needs high precision fabrication techniques for both metal and dielectric materials. Also, relatively-large absorption in metallic coat or cladding has a risk of heat damage to high-input light power [8].

Recently, Jamid and Almeida proposed a slot-waveguide structure to efficiently confine light power into a very thin core of width typically less than 100 nm [14,15]. In spite of this nanosized core, transverse magnetic (TM) mode light can propagate with low loss along the waveguide axis because of its high-index-contrast structure [16–18]. Moreover, several studies have demonstrated very high power coupling efficiencies of 60%–90% between the slot and normal slab waveguides [19–21]. These results suggest the possibility of resolving the abovementioned issues of large intrinsic transmission loss and low coupling efficiency in the conventional tapered probes used in SNOM. Thus far, several slot-waveguide structures have been reported: photonic nanowire circuits, couplers, amplifiers, and sensors [22–26], which include optical field measurements in a slot waveguide using SNOM [27]. However, to the best of our knowledge, there has been no study on the application of slot waveguides to the optical probe tips of scanning near-field microscopes. The major concern of this study is to provide the possible application of a simple dielectric waveguide without a metal nanostructure.

In the present study, we propose a probe tip comprising a dielectric slot waveguide, and evaluate the transmission efficiency and lateral resolution of the probe tip in both illumination and collection modes using a finite-difference time-domain (FDTD) simulation [28]. For simplicity, we construct two two-dimensional models with slot-waveguide and conventional slab-waveguide structures and compare their characteristics.

2. Optical spots output of waveguide probes

First, we focus on the optical spot output of the slot-waveguide probe tip. Two probe tip models of (a) a slot waveguide with a high-index-contrast structure and (b) a normal slab waveguide for reference are compared in Fig. 1. Here, we also analyze the tapered tip cut off along the dotted red lines with taper angle θ_T, as shown in Fig. 1(a), to compare the validity of the tapered shape generally used in conventional metallic probes. The geometric size of thewaveguides is 2 μm (length) × 1.25 μm (width). We suppose a Si–S_iO₂–Si slot waveguide sandwiched by SiO₂ claddings and their geometrical parameters, i.e., the width of the slot core (d_L), the side core (d_H), and the cladding (d_CL) are 50, 200, and 400 nm, respectively, similar to the typical size of the tips of scanning near-field microscopes. The refractive indices for the low-index (n_L) and high-index (n_H) layer regions are 1.46 and 3.48, respectively. The normal slab waveguide comprises a 50-nm Si core sandwiched by 600-nm SiO₂ claddings. The probes are surrounded by free space or an index-matching fluid with a refractive index of n_SU = 1 or 1.46, respectively. These parameters are summarized in Table 1. Because of the low-loss window for the two materials, the light wavelength is assumed to be 1550 nm and the source width is roughly comparable to the diffraction limit. The source thickness is zero. Moreover, the y- or x-polarized light with a Gaussian profile is launched to the top face of the waveguide, as shown in Figs. 1(a) and 1(b), because the TM and transverse electric (TE) modes can effectively confine the light within the center core regions in the slot and normalslab waveguides. As easily predicted in the normal slab waveguide with a high refractive-index difference, the mode field distribution of the TM mode has a dip at x = 0, which reduces the power confinement.

 

Fig. 1 Optical probe models comprising (a) slot waveguide and (b) normal slab waveguide. A tapered shape with taper angle θ_T in (a) is also analyzed. The x- and y-polarized Gaussian light beams are injected from the light source and propagate along the z axis in (a) and (b), respectively.

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Table 1. Parameters used in the simulation.

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Figures 2(a), 2(b), and 2(c) show the contour maps of the electric field components E_x in the flat-faced slot waveguide with θ_T = 90° and the tapered slot waveguide with θ_T = 45°, and E_y in the normal slab waveguides, respectively. Here, E_x,y is normalized by the peak amplitude of the input light at z = −L and n_SU = 1. In Figs. 2(a) and 2(b), E_x is observed to be well confined in the slot core region, whereas in Fig. 2(c), E_y is observed to spread throughout the waveguide. Although the waveguide length, L, is restricted because of the computing time in our simulation, the light field shown in Fig. 2(b) is supposed to spread more widely for a larger L because of the very small V-value of ~0.3 for the slab waveguide. Regarding the field distribution around the bottom end of the tip, both E_x and E_y are rapidly spread against the distance z because of the scattering effect; however, in Figs. 2(a) and 2(b), an optical spot of 50–200 nm in diameter with an amplitude of 0.5–1.0 is observed within ~100 nm from the bottom surface. Though the optical spot observed in the tapered slot waveguide looks slightly smaller than that in the flat-faced slot waveguide, they spread in almost the same power distribution, as described below. This result indicates the effective illumination by an optical spot with a few tens of nanometers width in the near-field area.

 

Fig. 2 Contour maps of (a) E_x in the flat-faced slot waveguide with θ_T = 90°, (b) E_x in the tapered slot waveguide with θ_T = 45°, and (c) E_y in the normal slab waveguide. E_x,y is the normalized by peak amplitude of the input field. Waveguides are surrounded in free space (n_SU = 1), and white lines indicate their shapes and boundaries between the core and the cladding.

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Next, we examine the power distribution along the x axis to estimate the conversion efficiency for a nanosized optical spot. Figure 3 shows the normalized power distribution defined as S_z(x,z)/S_z(0, −L), where S_z(x,z) is the axial component of the time-averaged Pointing vector at (x,z), and the denominator corresponds to the output of the light source.Figures 3(a)–3(d), 3(e)–3(h), and 3(i)–3(l) are the power distributions obtained at four different positions through the flat-faced slot, tapered slot, and normal slab waveguides, respectively. It is obvious that high power confinement within a center core is kept in the slot waveguides and nanosized optical spots are generated at the near field region of z ≤ 10 nm, as shown in Figs. 3(a)–3(c) and 3(e)–3(g). In contrast, the optical power widely disperses both inside and outside the normal slab waveguide because of low confinement in the core region. These results agree well with the contour maps of the electric field components shown in Fig. 2. To clarify the results, we introduce two parameters: the optical spot size δx_FWHM(z) given as the full width at half maximum (FWHM) of the power distribution curve and the confinement power ratio, $\Gamma (z)=\frac{{\displaystyle \int {}_{spotsizearea{S}_Z(x,z)dx}}}{{\displaystyle \int {}_{sourcearea{S}_Z(x,-L)dx}}}$, where the numerator and denominator are integrated over the optical spot within δx_FWHM(z) and the light source, respectively. Light power density in an optical spot width is written as Γ(z)/δx_FWHM(z).

 

Fig. 3 Normalized light power distribution S_z(x,z)/S_z(0, −L) along the x axis at different locations z in (a)–(d) flat-faced slot waveguides with θ_T = 90°, (e)–(h) tapered slot waveguides with θ_T = 45°, and (i)–(l) normal slab waveguides. δx_FWHM indicates the full width at half maximum (FWHM) of the power distribution.

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Figures 4(a) and 4(b) show δx_FWHM(z) and Γ(z)/δx_FWHM(z) inside and outside the three kinds of waveguides. In the flat-faced and tapered slot waveguides, δx_FWHM(z) is almost constant at 50 nm, corresponding to the width of the slot core, and significantly increases outside the waveguide because of diffraction, e.g., δx_FWHM(z) = 61, 72, and 247 nm for the flat-faced slot waveguide and δx_FWHM(z) = 57, 75, and 322 nm at z = 5, 10, and 50 nm, respectively. The spreading due to the diffraction effect is almost the same in the near field region for these slot waveguides. In the normal slab waveguide, a similar increasing tendency of δx_FWHM(z) is observed in Fig. 4(a), but δx_FWHM(z) begins to spread within the waveguide and its width exceeds 300 nm at the end surface. In Fig. 4(b), the power density Γ(z)/δx_FWHM(z) for the normal slab waveguide tends to moderately decrease both inside and outside of the waveguide, by contrast with the slot waveguides whose curves rapidly decline near the end face. We note that the power density of the optical spot out of the slot waveguides is still completely larger than that out of the normal slab waveguide over the near field region. We also see a large difference of Γ(z)/δx_FWHM(z) between the flat-faced and tapered slot waveguides inside the waveguides, because Γ(z) contains both downward-traveling and upward-reflecting light fields in our simulation, and a smaller reflection at the end surface of the tapered waveguidemay cause a smaller loss due to interference between the two light fields. The slight variability of symbols in Fig. 4(b) inside the waveguide regions occurs because of the same interference effect that depends on position z. The normalized power Γ(z) at z = 5, 10, 50 nm is calculated to be 0.18, 0.18, and 0.31 for the flat-faced slot waveguide and 0.16, 0.17, and 0.40 for the tapered slot waveguide, respectively. These results indicate that 50–250-nm-wide optical spots with high power transmission efficiency of 20%–30% are successfully obtained in the near field region for z ≤ 50 nm. Moreover, a very high power coupling ratio of greater than ~30% between the slot and normal waveguides or the optical fiber has been reported [17,24]. We believe that the transmission efficiency presented here is higher than the typical range of 10⁻⁵–10⁻², which is obtained for conventional metallic-coated taper probes.

 

Fig. 4 (a) FWHM of light power distribution, δx_FWHM, and (b) light power density confined in the δx_FWHM area, Γ(z)/δx_FWHM, as a function of z. Symbols indicate the calculated data for the three types of waveguides, and dotted lines are fitting curves.

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3. Optical probe operated in illumination and collection modes

Next, we analyze an optical probe operated in both illumination and correction modes. Figure 5 shows the schematic of the probe system with a slot waveguide and a nanosized target object. The geometric configuration of the slot waveguide is identical to that shown in Fig. 1(a), except for the photo detector (PD) embedded in the top part of the waveguide. Since there is no remarkable difference in optical spots and transmission properties between flat-faced and tapered slot waveguides, hereafter we evaluate only the flat-faced slot waveguide. For simplicity, we assume that the 50-nm-wide PD can monitor the light power propagating upward through the waveguide without absorption and scattering over the light source area. A target object made of Au with a box shape (width w_TG = 50–200 nm, height h_TG = 50 nm) is set on a stage of SiO₂ and scanned along the x axis. The target distance d_TG between the bottom surface of the waveguide and the top surface of the object is 10 nm. According to the abovementioned result, an optical spot with δx_FWHM(z) = 72 nm and Γ(z) = 0.18 illuminates the surface of the object. Here, we suppose two cases: the optical system is surrounded by free space or an index-matching fluid. Contour maps of the normalized field component, E_x, in the case of n_SU = 1 and n_SU = n_L = 1.46, are shown in Figs. 6(a) and 6(b), respectively. A 100-nm- wide target object is fixed at x = 0. Similar to Fig. 2(a), the light power is well confined within a slot core area, and a small optical spot effectively illuminates the target object. Optical near-field components can be observed to obviously appear in the immediate vicinity of the target object shown in Figs. 6(a) and 6(b). Magnified images of Figs. 6(a) and 6(b) around the target are shown in Figs. 7(a) and 7(d), respectively. Figures 7(b) and 7(c) indicate contour maps when the target position x_TG is shifted to 50 nm and 125 nm in the case of n_SU = 1.46, respectively. The maps in Figs. 7(e) and 7(f) are similar in the case of n_SU = 1. In Figs. 7(a), 7(b), 7(d), and 7(e), light components reflected and widely scatterd at the target object can be observed to propagate upward in the center and side cores of the slot waveguides, even when the target object is in a slightly off-centered position. We also see that the internal reflectioncomponent is obviously caused at the end surface of the waveguide in Fig. 7(f) under the index unmatching case of n_SU = 1; on the other hand, in Fig. 7(c) similar reflection does not appear, which can significantly improve the contrast of an object image, as discussed below.

 

Fig. 5 Optical probe system to observe a target object. The light source and photodetector are embedded in the top part of the slot waveguide. The refractive index of the surrounding area n_SU is assumed to be 1 or 1.46. Light power is monitored with scanning target.

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Fig. 6 Contour maps of E_x in the slot waveguide and around the target object under the surrounding conditions of (a) free space (n_SU = 1) and (b) an index matching fluid (n_SU = 1.46). Here, d_TG = 10 nm, w_TG = 100 nm, and h_TG = 50 nm.

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Fig. 7 Contour maps of E_x around the output region of the slot core under the conditions of (a)–(c) n_SU = 1.46 and (d)–(f) n_SU = 1. Displacement x_TG of the target objects are 0 nm in (a) and (d), 50 nm in (b) and (e), and 125 nm in (c) and (f). White lines indicate the boundaries, and w_TG, h_TG, and d_TG are 100, 50, and 10 nm, respectively.

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Figure 8 shows the received power of PD normalized by the input power as a function of the target object position x_TG and the object width w_TG. All curves indicate obvious peaks at x_TG = 0, and larger received power is obtained for larger values of w_TG. This is because the reflected and scattered light components at the target object increase with the target size within this range. Although the received power contains a background component of ~0.05, the FWHM of the curve peaks coincide well with the target widths of 50, 100, and 200 nm under the condition of index matching, i.e., n_SU = 1.46. For the case without index matching, the skirt part of the curve for w_TG = 100 nm tends to heave for z > 150 nm. From the curves in Fig. 8, the contrast, described as the ratio of the peak power of the normalized received power to the power of the background, are roughly estimated to be 6.3, 2.7, and 1.5 for the cases of w_TG = 200, 100, and 50 nm, respectively, under the condition of n_SU = 1.46. For the case of w_TG = 100 nm and n_SU = 1, the contrast decays to be 1.5. This large degradation is mainly because of the internal reflection at the bottom surface of the waveguide in the case without index matching. Since a small internal reflection at the bottom surface of the side cores remains even when n_SU = 1.46, the abovementioned background component stems and decays the contrast as the received power decreases. This is one of the intrinsic issues for an optical probe incorporating both a light source and photodetector. To suppress the background noise, for example, the slot core with a smaller refractive index, such as air gap, may be effective in a free space environment, and moreover, other detection techniques such as lock-in detection and the dithering of a probe tip would be required to reduce this noise.

 

Fig. 8 Normalized received power at PD as a function of the position of the target object. The optical probe is surrounded in free space (n_SU = 1.0) or an index matching fluid (n_SU = 1.46). Symbols indicate the calculated data for target objects with three different widths w_TG, and dotted lines are fitting curves.

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Finally, we focus on the spatial resolution of our probe for the observation of two closely-aligned target objects, as shown in the inset of Fig. 9. Here, a pair of target objects of Au with a box shape (width w_TG = 30, 50, or 80 nm, height h_TG = 50 nm) is arranged with gap δw_GAPand scanned along the x axis. Moreover, d_TG = 10 nm and n_SU = 1.46. The normalized received power of PD is plotted in Fig. 9 as a function of position x_TG of the midpoint between the two objects. We can see obvious double peaks when δw_gap = w_TG = 50 and 80 nm, and the peak positions coincide well with the center of the object. For the smaller gap condition of δw_gap = w_TG = 30 nm, however, the central dip is absent and the gap is not resolved. This is because an optical spot of ~70 nm in width illuminates the target objects in this model, and the 30-nm gap is buried by broad illumination. As a result, the spatial resolution as the resolvable gap distance is ~50 nm, equal to the center core diameter d_L in our model. This result implies that a smaller d_L of the slot waveguide makes it possible to provide higher resolution; however, in our simulation for d_L = 30 nm and target objects with δw_gap = w_TG = 30 nm, we cannot observe the separated peaks because the received light power is too small to obtain sufficient contrast. Given that a minimum optical spot size or spatial resolution is found in the 20–300 nm range [3–6], our result provides a fully comparable spatial resolution with conventional optical probes where no plasmons are excited.

 

Fig. 9 Normalized received power at PD as a function of the displacement x_TG of the central position between two target objects (Au). The top figure shows the configuration of the slot waveguide and a pair of target objects. Symbols indicate calculated data for different δw_GAP and w_TG, and solid lines are fitting curves. Here, h_TG = 50 nm, d_GAP = 10 nm, and n_SU = 1.46.

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4. Conclusion

In this study, we have presented an optical probe design with slot-waveguide structure. Using numerical FDTD simulation, we demonstrated that an optical spot of 50–250 nm in width is obtained with a transmission efficiency of ~20%, and a spatial resolution of ~50 nm, which corresponds to the slot core width in our model; this is achieved by a probe equipped with both illumination and collection modes. Although some conditions vary, the transmission efficiency presented here is improved compared with that of conventional metallic tapered tip structures. A simple layered structure without a metallic coating is advantageous for easy fabrication and tolerance to the heat-induced damage due to high-input light power, but may have some issues, such as enhancement of the contrast, which will be undertaken in our future study.