1. Introduction

Metallic nanostructures supporting the surface plasmons demonstrate remarkable capability to realize the light manipulation at nanometer scale [1–7], which have been considered as indispensable building-blocks to construct nano-photonic devices and circuits with the feature size beyond diffraction limitation [8–16]. As a key component of the surface plasmons based devices, plasmonic waveguides have been studied extensively [17–21], including the photon-plasmon coupling [22–24], propagating modes [25–28], group velocity [29–32], interference [33,34], energy loss [35–40] and emission direction [41–43], etc. It has been reported that the crystalline gold and silver nanowires can guide surface plasmons up to tens of micrometers with relative low loss of energy [44,45]. Based on these plasmonic waveguides, some functional elements have been achieved, such as the plasmonic routers/splitters [46–48], logic gates [49,50] and modulators [51,52], etc. For example, plasmonic router/splitter can be realized based on coupled thin nanowires, that is, branched structures [46]. By active control of the phase or polarization state of the incident light, the near field intensity at the branch junction can be modulated by the interference of propagating surface plasmon modes, thus routing the surface plasmons transmission [25,47,49,52]. So far, many studies have been focused on designing these branched nanowire structures to manage the plasmons routing/splitting [46–49,52,53]. However, little is known about the surface plasmons propagation and emission on a thick nanowire. It would be quite interesting when the nanowire becomes a thick one, where the propagating surface plasmons can be separated spatially. With well-defined end facets, it can naturally provide multiple outcoupling channels, which can be coupled with different plasmonic elements simultaneously to construct more complicated plasmonic circuits. Hence, an understanding about the surface plasmons propagation and emission on the thick nanowire is meaningful to the development of waveguide design and plasmonic integrated circuits.

In this paper, we investigated the properties of surface plasmons propagation and emission in a thick nanowire (D ~500 nm). It was found that the thick silver nanowire can provide multiple outcoupling channels and function as a potential nanoscale polarization beam splitter. Firstly, the surface plasmons were launched at one end of the nanowire. By rotating the emitting polarization analyzer, it was revealed that the propagating surface plasmons emission were composed of two parts: one was emitted from the C1 facet of the nanowire end with the polarization θ = 30° (I₁), the other was emitted from the C2 facet with the polarization θ = 150° (I₂). While varying the polarization of incident beam (α), the splitting ratio $I_1^{30°}/I_2^{150°}$ can be tuned. Especially, when the α was an acute angle, splitting ratio was larger than 1, that is, more energy was routed to the C1 facet. While, more energy was routed to C2 if the α was set as an obtuse angle, which made the splitting ratio smaller than 1. This phenomenon can be well understood by the interference between the fundamental plasmon mode and high order modes on each side of the thick nanowire.

2. Experimental section

The crystalline Ag nanowires were synthesized by a typical polyol process with ethylene glycol serving as both solvent and reducing agent and poly(vinylpyrrolidone) as the coordination reagent [54]. The final products were washed two times each with acetone and ethanol to remove the excess reagents and by-products. Then, a drop of diluted suspension of Ag nanowires was placed on indium tin oxide (ITO) glass slide and dried under ambient condition. Here, the conductivity and transparency of ITO substrate were necessary for the following scanning electron microscope (SEM) and optical characterizations. By SEM, nanowires with different lengths and diameters can be found and measured. Then, with the help of coordinates on ITO glass, each characterized nanowire can be specifically identified again under optical microscope. To launch the propagating surface plasmons, 633 nm laser was focused on one end of the nanowire through a 100 × oil immersion objective (N.A. = 1.35). The incident polarization was rotated by a half-wave plate. The emission from the other end of the nanowire was collected through the same objective and recorded by a CCD (DVC-1412AM high-resolution digital camera). By rotating the polarization analyzer in front of the CCD detector, the polarization-dependent light emission from the nanowire end can be obtained. The numerical simulations were performed using commercial numerical simulations based on Finite-Difference Time-Domain (FDTD). In simulations, the dielectric data of silver come from the work of Johnson and Christy, the refractive index of surrounding oil is 1.518.

3. Results and discussion

Figure 1(a) demonstrates the SEM image of an Ag nanowire of length 3.8 μm and diameter 510 nm. The detailed terminal shapes are shown in Fig. 6 (see Appendix). Here, for simplicity, we define the facets of the emission end as C1 and C2. The angles α and θ correspond to the incident polarization and the rotation of emitting polarization analyzer. Both of them are rotated anticlockwise relative to the longitudinal axis. When a 633 nm laser is focused on one end of the nanowire with the polarization parallel to the longitudinal axis, a bright emission spot can be observed at the other end, as shown in Fig. 1(b), which indicates the excellent performance for surface plasmons propagation. Interestingly, we found that the spatial distribution of emission spot on the nanowire end was highly dependent on the rotation of analyzer. As shown in Fig. 1(c), when emitting analyzer is parallel to the longitudinal axis (θ = 0°), the spot is almost centered at the nanowire end. However, rotating the θ to 60°, strong light emission can only be measured from the C1 facet and the emission from C2 is very dim. This phenomenon can also be well revealed by the corresponding line intensity profile across the nanowire end, as shown in right panel of Fig. 1(c). Further rotate the θ to 90°, two clearly resolved spots at the C1 and C2 facets can be observed simultaneously. When the analyzer is tuned to 120°, it is found that the emission is mainly from the C2, while the C1 emission is quenched. These results indicate that two light spots with different polarized orientations are emitted from the nanowire end. One is at the C1 facet with the polarization around θ = 30° (I₁), and the other is at the C2 facet with the polarization around θ = 150° (I₂). Hence, this thick nanowire with well-defined end facets can provide multiple outcoupling channels, and function as a potential nanoscale polarization beam splitter. The emission intensity as a function of the analyzer rotation angle θ is shown in Appendix Fig. 7. From the polar plot, we can know that the splitting ratio ($I_1^{30°}/I_2^{150°}$) under this parallel excitation is about 1.2:1.

 

Fig. 1 Plasmons excitation and emission in a thick wire. (a) SEM image of silver nanowire of length 3.8 μm and diameter 510 nm. The α and θ correspond to the incident polarization and the rotation of emitting analyzer. The facets of emission end are denoted as C1 and C2, respectively. (b) Optical image of the nanowire emission under the excitation of a 633 nm laser. Red arrow indicates that the incident polarization is along the nanowire axis. (c) Left panel: the optical images of surface plasmons emission acquired under different θ degrees, including 0°, 60°, 90° and 120°, respectively. Right panel: the corresponding line intensity profile of nanowire end emission.

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Furthermore, when the incident polarization was tuned to 33°, we can still observe the beam splitting phenomenon during the emitting analyzer rotation, as shown in Fig. 2(a). It is similar to the parallel excitation, when the emitting analyzer is tuned to 60°, the light is mainly from C1, while C2 is quenched, which means that the emission from C2 facet is still polarized at around 150° (nearly perpendicular to the C2 facet). And at θ = 90°, two clearly resolved emission spots can be observed. Further rotate the analyzer to 120°, the emission from C1 is quenched. That means, as the incident polarization is changed, the polarized orientations of the two split emissions maintain to be perpendicular to the respective emitting facets. However, from the polar plot in Fig. 2(b), we notice that the splitting ratio has varied. For this excitation condition (α = 33°), the splitting ratio $I_1^{30°}/I_2^{150°}$ is about 1.44:1, which means that more energy is routed to the C1 facet. Hence, the overall emission polarization rotates to around 10° (the direction of the emission polarization was defined as the angle θ_max, where maximum emission was measured). In contrast, when the incident polarization is rotated to 152°, as shown in Fig. 2(c), it is found that more energy is routed to the C2 facet. From the polar plot in Fig. 2(d), we can know that the splitting ratio $I_1^{30°}/I_2^{150°}$ is about 1:1.37. These results mean that the splitting ratio $I_1^{30°}/I_2^{150°}$ can be tuned by changing the incident polarization. Here, owing to the symmetric geometry of incident end, the excitation configurations at α = 33° and 152° are almost equivalent with each other. The difference between the splitting ratios may be resulted from the asymmetries in the excitation beam and/or the shape of the nanowire emission end.

 

Fig. 2 Plasmons excitation and emission at different incident and emission polarizations. (a) Optical images of propagating plasmons emission at incident polarization α = 33°. The analyzer angles are θ = 60°, 90° and 120° for (i)-(iii), respectively. (b) Emission intensity as a function of analyzer angle θ for the case in (a). (c) Οptical images of propagating plasmons emission at incident polarization α = 152°. The analyzer angles (i)-(iii) are the same as the ones in (a). (d) Emission intensity as a function of analyzer angle θ for the case in (c).

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The emission intensity as a function of the analyzer rotation angle θ under different incident polarizations (α = 0°~170°) were also systematically measured. Part of the data are shown in Fig. 3(a). The correlation between the incident (α) and emission (θ_max) polarization is summarized in Fig. 3(b). It is found that, when the incident polarization α is in the range of 0°~75°, the θ_max is located at around 10°. However, if α is tuned to the regime of 105°~170°, the θ_max drastically jumps to around 160°. This phenomenon corresponds to the reversal of splitting ratio (I₁/I₂) from 1.52 to 0.36, as shown in Fig. 3(c), which means that the brightness of the C2 facet (I₂) exceeds the C1 (I₁) during the rotation of α from 75° to 105°. Interestingly, when the incident polarization is set as 90°, two emission maximums can be obtained at θ = 30° and 150°, respectively. These two maximums just correspond to the emission of I₁ and I₂. And the splitting ratio $I_1^{30°}/I_2^{150°}$ is about 1:1.13. Figure 3(c) summarizes the splitting ratio as a function of incident polarization. It is clear that, when the α is an acute angle, more energy can be routed to the C1 facet, which makes the splitting ratio larger than 1. While, more energy is routed to C2 facet if the α is set as an obtuse angle, which makes the splitting ratio smaller than 1. The schemes of this polarization beam splitting on the thick nanowire with multiple outcoupling channels are shown in the inset of Fig. 3(c).

 

Fig. 3 Polarization beam splitting on thick nanowire. (a) Emission intensity as a function of the analyzer rotation angle θ, for different incident polarizations (α = 30°, 60°, 75°, 90°, 105°, 120°, 150° and 170°, respectively). (b) Correlation between the incident (α) and emission (θ_max) polarization in the thick nanowire surface plasmon waveguide. θ_max is the analyzer angle, where maximal emission is obtained. The dashed line is drawn to guide eyes. (c) The splitting ratio as a function of incident polarization. The insets demonstrate the schemes of beam splitting in this single nanowire.

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To further understand the light splitting mechanism in this single thick silver nanowire, electromagnetic calculations were performed using FDTD method. For simplicity, we simulated a nanowire with the length 3.8 μm, diameter 500 nm and thickness 300 nm to reproduce the experiments. The wire ends are terminated by triangles similar to the shapes shown in Fig. 6. The propagating surface plasmons were launched by focusing 633 nm laser on one end of the nanowire. Figure 4 presents the distribution of near-field intensity around the nanowire surface, under different incident polarizations. For nanowire with radius comparable to the excitation wavelength, three dominant modes can be generated, including the fundamental transverse magnetic mode (TM₀) and higher order doubly degenerate hybrid modes (HE₁ and HE_-1) [25]. The charges of TM₀ mode oscillate along the nanowire axis, and the HE₁ and HE_-1 modes correspond to charge oscillations in the horizontal and vertical plane, respectively [47,52,55]. For parallel excitation (α = 0°), the TM₀ mode and HE_-1 mode can be generated, and the supposition between these two modes results in a spatially dependent interference, that is, “beat.” Hence, the surface plasmon near field distribution along the x-y plane is axis-symmetric, as shown in panel i of Fig. 4(a), and the electric field intensity at the C1 and C2 end facets are also equal with each other, as shown in panel i of Fig. 4(b). For the perpendicular excitation, only the HE₁ mode can be launched and the field is symmetrically distributed on two sides of the nanowire, as shown in panel ii of Fig. 4(a). Hence, the electric field intensity at C1 and C2 end facets are also equal, as shown in panel ii of Fig. 4(b). For 0°<α<90°, the three dominant modes (TM₀, HE_-1 and HE₁) are launched simultaneously and the coherent interference of these modes can form a spiral near-field pattern. As shown in panel iii of Fig. 4(a), a prominent spiral field distribution shape along the x-y plane is obtained under the excitation of α = 45°. For this case, more surface plasmons are just routed to C1 facet, as shown in panel iii of Fig. 4(b), which results in the light splitting ratio (I₁/I₂) larger than 1. Considering the geometry symmetry, when α is set as 135°, more energy will be routed to the C2 facet.

 

Fig. 4 (a) The electric field distribution of propagating surface plasmons on the nanowire surface. The scale bars are all 500 nm. (b) The electric field distribution and direction (black arrows) of propagating surface plasmons on the nanowire end. The scale bars are all 100 nm. Panels (i)-(iii) correspond to the incident polarization of α = 0°, 90° and 45°, respectively.

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The instantaneous electric field directions around the emission end are also shown in Fig. 4(b). Take the parallel excitation as an example, the excited dipoles corresponding to the electric field directions are denoted by white arrows ${\overrightarrow{p}}_1$, ${\overrightarrow{p}}_2$, ${\overrightarrow{p}}_3$ and ${\overrightarrow{p}}_4$, respectively. The emission from C1 facet is contributed by the superposition of ${\overrightarrow{p}}_1$ and ${\overrightarrow{p}}_2$. Hence, the resultant emission polarization will be nearly normal to the C1 facet. On the other hand, the C2 emission is the superposition of ${\overrightarrow{p}}_3$ and ${\overrightarrow{p}}_4$, whose polarization will be nearly perpendicular to the C2 facet. For α = 90° and 45° excitation cases, the emission polarizations are also determined by the suppositions of excited dipoles around the nanowire end, as shown in panel ii and iii of Fig. 4(b). Figure 5 further shows the field distribution under the parallel excitation, when an emitting polarization analyzer is added. Obviously, as the analyzer direction is normal to the C1 facet (θ = 30°), the emission is mainly from the C1 facet. While, the emission is mainly from the C2 facet, when the analyzer direction is normal to the C2 facet (θ = 150°). These results well reproduce the behaviors of multi-channels outcoupling and polarization beam splitting of thick silver nanowire observed in experiments. Through the multiple outcoupling channels, the thick nanowire can be further integrated with other plasmonic elements to construct more complicated plasmonic devices.

 

Fig. 5 The emitting polarization dependent near-field distribution of propagating surface plasmons on the nanowire end. (a) Analyzer is rotated to θ = 30°, (b) θ = 150°. The red arrow indicates that incident polarization is parallel to nanowire axis.

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4. Conclusion

In conclusion, we have shown that a thick silver nanowire with well-defined end facets can function as multiple outcoupling channels and polarization beam splitter. The propagating surface plasmons can be emitted to the free space through the two spatially separated end facets, and the polarizations are all nearly normal to the respective emitting facets. By changing the polarization of incident light, the splitting ratio can be tuned in the range of 1.52~0.36. The numerical simulations demonstrate that polarization beam splitting mechanisms in the thick nanowire are the interference of different propagating surface plasmon modes and superposition of excited dipoles at the wire end. These findings would deep our understanding on the propagating behaviors of surface plasmons, and certainly benefit for development of integrated plasmonic devices.

Appendix

 

Fig. 6 The detailed terminal shape of the characterized silver nanowire.

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Fig. 7 The emission intensity as a function of analyzer rotation angel θ. The incident polarization is parallel to the nanowire axis (α = 0°).

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Funding

National Natural Science Foundation of China (11774245 and 11704266); Fok Ying Tung Education Foundation, China (151010); Beijing Municipal Commission of Education (the General Foundation [KM201810028006] and Scientific Research Base Development Program); Capital Normal University (Training Program of the Major Research Plan and Yanjing Scholar Foundation).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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