Polarization-controlled Plasmonic Structured Illumination

： Structured light in the subwavelength scale is important for a broad range of applications ranging from lithography to imaging. Of particular importance is the ability to dynamically shift the pattern of the fields, which has led to the development of structured illumination microscopy. Further extension of structured illumination to plasmonic systems has enabled imaging beyond diffraction limit. However, structured illumination usually requires complicated optical setups entailing moving mechanical parts. Here a polarization tunable structured plasmonic fields (SPF) is proposed and experimentally demonstrated. The SPF is formed by surface plasmon interference (SPI) generated by a fishbone-shaped metasurface on a thin gold film. Importantly, the SPF can be continuously shifted by merely varying the linear polarization state of an incident beam. The precise control of the fringes of structured illumination and elimination of mechanical control will have great potential in subdiffractional imaging for practical applications.

unidirectional excitation of SPPs 2, 14-16 etc. Interestingly, metasurfaces can be designed to exhibit switchable optical functionalities controlled by the polarization state of the incident light. In particular, the scattering phase of each constituent element of metasurfaces can be made polarization-dependent via two means: resonance induced dynamic phase and orientationcontrolled geometric phase. The former allows for independent and arbitrary phase profiles on each of the two orthogonal linear polarizations 7,[17][18][19][20] . The latter, i.e. geometric phase approach, allows for precise and spin-dependent control of the phase profiles [21][22][23][24] . Polarization-dependent phase utilizing either dynamic or geometric phase designs alone is limited to switching between two states, while combining dynamic and geometric phase can provide extra degrees of freedom for phase modulation, which has led to a number of applications including generation of polarization-independent orbital angular momentum 25 , phase control of arbitrary orthogonal states 26 .
In this paper, we experimentally demonstrate dynamically controllable plasmonic fringe patterns formed by two counter propagating surface plasmon beams. The shift of periodic SPI can be accurately tuned by simply rotating the direction of incident linear polarization. Based on this scheme, a practical application of SIM is proposed and numerically simulated utilizing the polarization-controlled tunable structured SPI. In contrast, the shifts of structured SPI in previous works were tuned by varying the excitation angle 4,6,27 or wavefront of incident light 28 , entailing complicated mechanical device or costly optical components, such as Galvo scanner, digital micromirror device and high NA. objective. Our approach eliminates the need for mechanical moving parts and may provide potential practical applications such as structured illumination microscopy (SIM) [29][30][31] , maskless lithography, 32,33 and optical manipulation 34 . In order to achieve polarization controlled tunable SPI, we employ periodic fishbone grating arrays carved in a thin gold film as shown in Figure 1a. Fishbone grating array has been utilized to realize tunable unidirectional excitation of SPPs by different circularly polarized beams 2, 14 .
Each unit cell contains two orthogonal nanoslits separated in both x and y directions, with their orientations forming an angle j of -π/4 and π/4 respectively with the y axis. Each single anisotropic nano-aperture can be approximately regarded as a local subwavelength dipole antenna, with its orientation perpendicular to the long axis of nano aperture. The SPPs pattern excited from a nano aperture is approximately that of an in-plane point dipole and exhibits an anti-phase radiation pattern (Figure 1c) about the long axis of nano aperture. Under the illumination of a circularly polarized beam with spin s, where s = ±1 represent the right-handed and left-handed polarization states, respectively, each dipole moment acquires a geometric phase s . Therefore, the spin dependent phase of the SPPs excited by each aperture can be obtained by varying the orientation angle of the nano-aperture. When the nanoslits are arranged in an array in the y direction with lattice constant less than the SPP wavelength (Figure 1a), the SPP can only be excited in the +x and -x directions. The SPPs excited by the two columns of apertures can be expressed as: (1) where and are the amplitude of SPPs excited by the two columns of apertures, respectively, with , represents the SPP wave excited along the +x and -x direction, respectively. kspp is the magnitude of SPPs wave vector, which can be expressed as: where ω and c represent the circular frequency and the velocity of light in vacuum, εm and εd are the permittivities of the gold and dielectric, respectively. The intensity of SPPs excited by each pair of columns of apertures can be expressed as: Thus, the sinusoidal fringe formed by SPI can be continuously shifted by rotating the direction of linear polarization.
( ) To demonstrate the polarization-controlled structured illumination described above, we fabricate fishbone grating arrays on a gold film with the following parameters: w=90nm, L=180nm, S=152nm, D=300nm, h=210nm, d=7.3µm and φ=π/4 working at λ=632.8nm. The wavelength of SPPs on the gold/air interface is λ spp =608nm. There is a vertical offset between neighboring columns of apertures to reduce the near-field coupling between adjacent columns of nanoapertures. A relatively thick gold film (h=210nm) is used to block direct transmission of light.
As shown in Figure 2a  KHz for quartz crystal tuning fork. The minimum scan distance of a step is 100 nm.
The gold film with periodic fishbone grating arrays is fabricated on the glass substrate using focused ion beam (FIB) from Carl Zeiss AURIGA crossbeam (FIB-SEM) workstation. The ion source is Gallium (Ga) at 30keV beam energy. For milling the groove patterns, 20 pA beam current was chosen with minimum spot size of 13 nm. Its scanning electron microscope (SEM) images are shown in Figure 3a, b. Figure 3d shows the experimental SPPs intensity distribution under the normal incidence with 30° polariztion, where the standing SPPs wave can be observed. The period of SPI detected is about 300 nm, which agrees well with the simulation. Figure 3f shows the field intensity distribution of SPPs in the same region under the excitations of a laser beam with different polarization angles (30°, 90°and 150°). The dash lines denote the position corresponding to the maximum of a SPI fringe. It is observed that the fringe laterally shifts at a step of about λ spp /6 when the polarization angle is tuned from 30° to 150° at a step of 60°. The quality of measured interference fringe is limited by the scanning step, non-uniform illumination of incident beam and possible sample damages during the near-field scanning process. Via Fourier transform of the intensity distribution, the frequency contents of the interference fringe expressing in Eq. 6. can be expressed as: The first orders provide the information about the periodic SPI patterns. Thereinto, the lateral shift of the sinusoidal fringe tightly links with the phase shift of the +1 order . And it can be more precisely calculated by λ spp ⋅ . Figure 3g, h. show the Fourier transform of the simulated and experimental patterns, respectively. Both results reveal peaks at 0 and ±k spp , which is consistent with Eq. 7. Figure 3i shows the simulated and measured lateral shift of the fringe upon illumination of different linearly polarized beams. The plot shows that the lateral shift of the SPI Moreover, distance between the two patterned areas can be increased by reducing the attenuation of SPP. This may be achieved by using high quality metal films such as the single crystalline Au film 35,36 .  Figure 4g, with the center to center distance of two adjacent fluorescent beads marked in the figure. Two closely located fluorescent beads, with lateral adjacent distance well below the diffraction limit can be distinguished utilizing the proposed structured illumination system.
In conclusion, we have demonstrated that polarization-controlled tunable phase profiles could be realized by utilizing the spin dependent unidirectional excitation of SPPs. The relationship between incident polarization state and phase of SPPs is studied both numerically utilizing FDTD simulation and experimentally using near field scanning. The phase-shifting of periodic SPI can be continuously tuned ranging from 0 to 2π by rotating the direction of incident linear polarization.
Based on this, we evaluated the performance of a plasmonic SIM utilizing the polarizationcontrolled tunable SPI. Owing to the precise phase modulation of SPI without the need for mechanical control, the approach is promising a broad range of applications including superresolution imaging, chemical analysis and maskless lithography.

Supporting Information
Optimization details of the fishbone grating and the reconstruction algorithm of PSIM. (PDF)