# Dynamical Manipulation of Surface Plasmon Polaritons
## 3 Dynamical Focusing of SPP
Simultaneously controlling the polarization and the wavelength of incident light can enable us to manipulate the SPP focus more flexibly. The wavelength determines the positions of the SPP focuses and the polarization plays the on/off role [64], for the SPP lens in Figure 3e. The SPP lens consists of horizontal nanoslits and vertical nanoslits which can be correspondingly excited by vertically polarized and horizontally polarized light, because the polarization component parallel to the nanoslits cannot effectively give rise to SPP. In the design, four imaginary SPP source points are placed in different positions and thedifferent color circles represent the equiphase lines. Vertical nanoslits are placed at the intersections of equiphase lines for 632 nm and 670 nm incident light, denoted by the black dots, while horizontal nanoslits are placed at the intersections of equiphase lines for 710 nm and 750 nm incident light. Thus, for incident light with a particular wavelength and polarization, the SPP generated by the horizontal or vertical nanoslits are in phase and will interfere constructively at the corresponding positions of the imaginary source point. As shown in Figure 4a, a semicircular SPP lens is illuminated by the vortex incident beam with helical wavefront, and the position of SPP focus will be determined by topological charge \(l\) of the vortex beam [83]. The spiral phase carried by the vortex beam can be transferred to the excited SPP. Thus, the phase of SPP can be expressed as \(\varphi_{sp}=(\sigma_{\pm}+l)\theta\), \(0\leq\theta\leq\pi\). Just like the focusing of SPP excited by circularly polarized light in Figure 3a, the SPP focuses generated by vortex beams also experience transverse shifts. For a vortex beam with a larger topological charge, the spiral phase is larger and the displacement will also be larger. Figure 4a shows the experimentally measured SPP distributions for vortex incident beams with different topological charges. The markers \(l=1\), 2, 3, 4, 5 represent the different topological charges and a white line is drawn along the \(y\)-axis to show the displacements of the SPP focuses. It can be clearly seen that the transverse shift of SPP focus grows  
Figure 3: (**a**) Polarization-controlled focusing of SPP with semicircular slits [58]; (**b**) Spin-selected SPP focusing with vertically arranged nanoslits [46]; (**c**) Enlarging the spin-dependent transverse shift of SPP focus by introducing additional spiral phase [62]; (**d**) Multiple-wavelength focusing of SPP with a nonperiodic nanoslit coupler [81]; (**e**)Switchable SPP focusing by changing either the wavelength or polarization of incident light [64]. Reproduced with permissions from: [58], APS, 2008, [46], OSA, 2015, [62], OSA, 2019, [81], ACS, 2011, [64], ACS, 2015.  
with the increase of the topological charge. The interval between the SPP focuses generated by two neighboring topological charges is about 120 nm for 633 nm incident light. This feature can be utilized to discriminate the topological charge of incident light by measuring the displacement of SPP focus. From the above analyses, it can be concluded that the phase of excitation light can greatly influence the distribution of SPP. Thus, controlling the incident light with a spatial light modulator (SLM) can actively modulate the focusing of SPP [36], as shown in Figure 4b. The required phase to focus SPP at a pre-chosen position is obtained with an optimization loop and is then projected onto the metallic nanohole array through lenses \(L_{1}\) and \(L_{\text{obj}}\). The distribution of SPP is imaged on to the camera through lenses \(L_{\text{obj}}\) and \(L_{2}\). Experimental results show that SPP can be focused at target positions (center or corner) without mechanical motion. Amplitude modulation of excitation light with a SLM can also implement dynamical SPP focusing [37]. Fresnel-zone type binary amplitude images are projected onto a metallic grating.