1. Introduction

Plasmonic devices utilizing surface plasmon polaritons (SPP) as optical information carrier offer opportunities for interfacing with high-speed photonic components and small-size electronic circuits [1, 2]. The unique properties of SPP, such as high localization and remarkable field enhancement at metal/dielectric interface, are exploited to enable the light manipulation on subwavelength scales [3, 4]. To achieve the similar functionalities of traditional electrical circuits on plasmonic chips, including guiding, switching and multiplexing, effective modulations of SPP with the help of nanostructures or tailored excitation optical beams are required. In most of the reported research work, beams with amplitude modulation are used as the light sources. In this paper, we propose a versatile method for SPP manipulation by incident phase modulations where a specific phase-activated optical vortex (OV) beam is demonstrated as an example. With the help of FDTD simulation and theoretical analysis, we realize in-plane focusing and efficient coupling of SPP into multiple subwavelength dielectric-loaded surface plasmon polariton waveguides (DLSPPWs) by sequentially shifting the phase of illuminated OV beam. Although various methods for focusing SPP on a metal surface have been reported [5–10] and comprehensively reviewed in [11] recently, there is no much work related to the dynamic tuning of the plasmonic focal spot. By inclining the incident Gaussian beam with appropriate angle, Ref [10] reported the coupling of SPP into three metallic stripe waveguides and realized the multiplexer functionality. In comparison with such manually-controlled optical-path-different system, our method offers a flexible and alternative way for focusing and multiplexing SPP and it shows dynamic and reconfigurable advantages in terms of illumination.

An OV beam is well known for its phase singularity and nonuniform wavefront. Mathematically, the electric field of OV beam can be described as [12]

2. Dynamic manipulation of SPP with OV beam

We use the FullWAVE module of the commercial RSOFT software [15] to implement FDTD simulations of SPP focusing and multiplexing. A schematic is illustrated in Figs. 1(a) and 1(b). An OV beam polarized along the x direction and focused by an objective lens illuminates the arc-shaped slit perforated through the 200-nm-thick silver film from the substrate side. At 633 nm wavelength in free-space, dielectric constant of silver is ε_m = −15.89 + 1.078i. The propagation constant of SPP along the Ag/air interface is k_spp = (1.033 + 0.00234i)k₀, resulting in the SPP wavelength of 613 nm and propagation length of 21.5 μm. For an OV beam with topological charge l, the SPP emitted from the two ends of the 72° arc slit has a total phase difference of . A conventional Gaussian beam can be seen as a special case of l = 0, thereby the initial SPP excited along the arc are in-phase and will constructively be interfered in the centre, resulting in a bright focal spot in the central point. However, for an OV beam carrying a nonuniform wavefront $\exp \left(il\theta \right)$, this nonzero phase difference alters the SPP interference pattern and produces an angular displacement of the focal spot. Figure 1(c) gives a typical phase map of the OV beam of l = 20. The phase distribution is divided into 20 parts in the azimuthal direction, and linearly increases from 0 and 2π in each part anticlockwise. For positive topological charges, since SPP generated in the upper part of the slit has a phase delay relative to that of the lower part and a shorter optical path is required to compensate such phase difference, the diffraction angle of the focal spot is positive to ensure the constructive interference condition and vice versa. Figure 1(d) shows FDTD simulation result of the SPP focus for l = 20, where the radius and width of the arc-shaped slit are 6 μm and 240 nm respectively. A bright focal spot is formed at the 5.67 μm distance away from centre of the slit with a diffraction angle about 19.7°. The full width at half maximum (FWHM) along and across the focal spot are 1.6 μm and 0.424 μm, respectively.

 

Fig. 1 Schematic configuration of SPP phase modulation with OV beam which is focused by the objective lens onto the subwavelength slit: (a) top view and (b) side view. (c) Typical phase map of OV beam of topological charge l = 20. (d) Normalized |E_total|² distribution of focused SPP generated by x-polarized OV beam of l = 20 taken from 100 nm above the silver surface. The radius, width and opening angle of the arc are 6 μm, 240 nm and 72° respectively. White arrow indicates center of the focus.

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If the OV phase mask is coded with different topological charges, either positive or negative, diffraction angle of the focal spot can dynamically be tuned in a wide range. The larger the topological charge, the greater the diffraction angle. We have sequentially shifted the focal spot away from the centre by using different topological charges ranging from −40 to 40. For instance, the diffraction angle for l = −20 and l = 40 is −19.7°and 41.2° respectively, as shown in Figs. 2(a) and 2(c). It is also seen that the shape of the focal spot does not show apparent degradation when varying the topological charges. Further investigation indicates that the diffraction angle is approximately proportional to the topological charge at fixed geometrical parameters. For R = 6 μm as an example, the diffraction angle increases 1.028 degree when the topological charge is increased by 1, corresponding to 107 nm shift of the focal spot in the lateral direction. Moreover, it is worthy to emphasis that the phase difference and sequent deflection of the focal spot in our paper and reference [10] originate from two different mechanisms: the former comes from the intrinsic helical phase of optical vortex beam, while the latter roots in the inclining of incident Gaussian beam. Using the same wavelength (532 nm), arc angle (120°), arc radius (5 μm), slit width (175 nm) and similar total phase differences (8.67π corresponding to charge 13 and 8.974π corresponding to 16° incident angle), it is calculated that the diffraction angle of the focal spot is 10.95° and 11.3° in our case and reference [10], respectively. Hence, our simulation and theoretical work can indirectly be verified by the experiment.

 

Fig. 2 Normalized |E_z|² distribution generated by OV beam of (a) (b) l = −20 and (c) (d) l = 40. The displayed area is 10μm × 12μm. (a) (c) are FDTD simulation results, and (b) (d) are the results from theoretical model. White arrow indicates center of the focus. (e) Dependence of diffraction angle of the focal spot on the topological charges for R = 6 μm.

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This phenomenon can be interpreted by Huygens-Fresnel principle. The longitudinal plasmonic field near the focal point is attributed to the superposition of the initial SPP which are excited along the arc, and it can be expressed as

3. Multiplexing SPP into DLSPPWs

Next, we couple the focused SPP into dielectric waveguide arrays fabricated on the silver film. The detailed arrangement is shown in the inset of Fig. 3(d) . The DLSPPWs have attracted increased interests of optics community because of their relatively low bend and propagation loss, compatibility with different thermal-optical, electrical-optical and nonlinear Kerr materials for the development of active plasmonic components [17]. The dielectric medium is assumed to be PMMA with thickness 250 nm and refractive index 1.49, which can easily be spin-coated onto the silver film in the experiment. The centre-to-centre seperation between adjacent waveguides is 1.3 μm. By using the OV beams with discrete topological charges of −20, 1, 20 and 40, the optical energy near the focal spot are efficiently coupled into the second to the fifth waveguide channels from the bottom as shown in Figs. 3(a) to 3(d) respectively, despite of the PMMA stripe as narrow as 250 nm. The 250-nm-thickness PMMA film only sustains TM₀ mode whose effective index is 1.587, and the FWHM across the focal spot is as small as 302 nm. The biggest difference between positive- and negative-charge optical vortex beams is that they possess opposite chirality, anticlockwise for positive charges and clockwise for negative charges. It is flexible to dynamically adjust the coupling channel using optical vortex beams with appropriate charge values and signs.

 

Fig. 3 The multiplexing of SPP into dielectric-loaded surface plasmon waveguides with 1.3 μm center-to-center separation using OV beams of topological charges (a) l = −20, (b) l = 1, (c) l = 20 and (d) l = 40. The displayed area is 12μm × 12μm. The detailed arrangement is shown in the inset of Fig. 3(d). Blue colour is the PMMA and light gray is the Ag surface. The thickness and width of the PMMA stripe are both 250 nm.

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4. Unidirectional excitation and focus of SPP

Due to rotational symmetry of the setup, the OV beam emanates from the objective lens and converges toward the geometric focus. Therefore, SPP can unidirectionally be excited and then focused with properly chosen slit width and focal angle of incident OV beam [18]. The ratio of optical energy of SPP propagating to the two opposite directions of the slit is strongly dependent on the two parameters of a fixed thickness Ag film. The result is depicted in Fig. 4(a) in logarithmic scale. The upper limit of the incident angle is 42°, which is determined by the numerical aperture (NA = 1) of the objective lens. Obviously, there are two regions where the SPP are efficiently and unidirectionally excited. Especially when the slit width is around 400 nm, there are a wide range of feasible incident angles from 9.5° to 37°, where the ratio of optical energy of the two opposite propagating SPP is over 100. Absolute value of the electric field intensity in the left side of the slit also possesses a peak in this range which is not shown here. Figure 4(b) gives an example of unidirectional excitation and focus of SPP. In comparison with the result in Fig. 1(d), it is obviously seen in Fig. 4(b) that the SPP propagating to the rightward direction are efficiently blocked, and almost all of SPP propagate and are focused in the left side of the slit. As a result, the focusing efficiency of SPP can further be improved and the possible background noise caused by the random scattering from the adjacent plasmonic components will be reduced.

 

Fig. 4 (a) The dependence of the ratio of optical energy in the two opposite directions on the slit width and incident angle (in logarithm scale). (b) An example of unidirectional excitation and focus of SPP by OV beam of l = 20. The slit width is 400 nm, and the incident angle is 20°. White arrow indicates center of the focus.

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5. Conclusions

In conclusion, we numerically demonstrated a versatile method for phase modulation of SPP with topological-charge-related OV beam. In combination with an arc-shaped slit, the generated SPP are tightly focused into subwavelength spot in lateral direction, and the diffraction angle of the focal spot can dynamically be shifted by sequentially changing the topological charge of OV beam. We also investigated the coupling and multiplexing of the focused SPP into subwavelength DLSPPWs as well as the capability of unidirectional excitation of SPP. This method offers an alternative way to the existing manually-controlled optical-path-different system, but with dynamic and reconfigurable advantages. In addition to the fundamental functionality proposed here, the concept of phase modulation of SPP with structured optical beams will also enable prospective applications in optical manipulation and super-resolution imaging, such as standing-wave surface plasmon resonance fluorescence microscopy [19] which can rely on the shift of interference pattern of counter propagating SPP excited by OV beam with variant topological charge. These underlying studies are very likely lead to new exciting and exploratory applications of plasmonics.