Broadband spin Hall effect of light in single nanoapertures

OPEN Light: Science & Applications (2017) 6, e16276; doi:10.1038/lsa.2016.276 Official journal of the CIOMP 2047-7538/17 www.nature.com/lsa ORIGINAL ARTICLE Broadband spin Hall effect of light in single nanoapertures Xian-Gang Luo, Ming-Bo Pu, Xiong Li and Xiao-Liang Ma With properties not previously available, optical metamaterials and metasurfaces have shown their great potential in the precise control of light waves at the nanoscale. However, the use of current metamaterials and metasurfaces is limited by the collective response of the meta-atoms/molecules, which means that a single element cannot provide the functionalities required by most applications. Here, we demonstrate for the first time that a single achiral nanoaperture can be utilized as a meta-macromolecule to achieve giant angular spin Hall effect of light. By controlling the spin-related momenta, we show that these nanoapertures can enable full control of the phase gradient at a deep-subwavelength level, thus forming unique building blocks for optical metasurfaces. As a proof-of-concept demonstration, a miniaturized Bessel-like beam generator and flat lens are designed and experimentally characterized. The results presented here may open a door for the development of meta-macromolecule-based metasurfaces for integrated optical systems and nanophotonics. Light: Science & Applications (2017) 6, e16276; doi:10.1038/lsa.2016.276; published online 16 June 2017 Keywords: geometric phase; metasurface; nanoaperture; spin Hall effect of light INTRODUCTION The past decade has witnessed the rapid development of artificially structured metasurfaces. Owing to the unique electromagnetic responses of the meta-atoms or meta-molecules arranged in the two-dimensional (2D) plane, metasurfaces have enabled many exciting applications, such as imaging below the diffraction limit1–4, controlling light rays beyond Snell’s law5–9, changing polarizations and chirality10–16 and mimicking the physical processes in quantum systems17–21. Compared with traditional bulk optical components, metasurfaces hold great advantages since only one single layer with vanishing thickness is required to achieve complete control of the light fields22–27. Regarding the light–matter interaction in metasurfaces, the role of circularly polarized light (CPL) has drawn special attention in recent years10,28. As indicated in quantum theory, the polarization state of CPL corresponds to the spin angular momentum, which is coupled with the phase gradient of light following a process named optical spin–orbit interaction (OSOI)29–33. The spin-related phase can also be used to generate the angular spin Hall effect of light (SHEL), where a handedness-dependent momentum shift is introduced to the incident CPL17–19. The phase shift originating from the OSOI is often termed geometric phase because of its geometric nature29. Although the first demonstration of such phase at the radio frequency can be dated back to the 1960s34, the realization of functional devices in the optical range has only been accomplished lately. In the polarization gratings29 and q-plates30, linear momentum and angular momentum could be converted to CPL by properly designing the continuous anisotropic structures. Nevertheless, because of the lack of a general design procedure and precise fabrication techniques, it is difficult to realize arbitrary phase modulation with subwavelength resolution35. To overcome this obstacle, discrete or quantized optical antennas were proposed to construct metasurfaces and achieve various optical functionalities6,35–38. These metasurfaces relied on the combination of different elements to create the phase gradient, while each individual element (meta-atom) introduced only a locally constant phase. The finite dimension of the discrete elements, however, may severely limit the accuracy of the phase distribution, as well as the diffraction efficiency. Consequently, it would be much more appealing for both the theoretical understanding and practical application if a single nanostructure can be used to realize an arbitrary phase profile39. Note that, although some pioneering lines of work on the polarization-dependent transmission of light through single holes have been reported11,32, they were not optimized in the framework of the geometric phase. In this paper, we demonstrated that a perfect continuous and dispersion-free phase gradient can be observed in a single catenaryshaped nanoaperture perforated on a thin metallic screen. The phase gradient is attributed to the OSOI in the space-variant anisotropic aperture, which leads to a giant and broadband angular SHEL. We also designed and experimentally characterized a single deformed catenary aperture, as well as a catenary array, to generate various types of phase distribution. The results may open many perspectives regarding the design of optical metasurfaces. State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China Correspondence: XG Luo, Email: Received 17 October 2016; revised 28 December 2016; accepted 3 January 2017; accepted article preview online 6 January 2017 Broadband spin Hall effect of light XG Luo et al 2 MATERIALS AND METHODS We focus on a slim subwavelength aperture perforated on a metallic screen with vanishing thickness. By ‘slim’, we mean that the aperture has a length much larger than the width, while the width is much smaller than the operating wavelength. As shown in Figure 1a, such an aperture could be mathematically treated with two parameters, that is, the inclination angle ζ(x) with respect to the x axis and the width w. Since the early work of Bethe in 194440, it is known that traditional Kirchhoff’s diffraction theory does not fulfill the electromagnetic boundary conditions for small apertures even if the thickness of the screen is decreased to zero. In particular, owing to the polarizationdependent transmission41, the incident fields do not equal the fields at the output side of the aperture and the diffraction (or scattering) phenomena may become completely different from that predicted by Kirchhoff’s theory (Figure 1b). As depicted in Figure 2a, the aperture we used is obtained by connecting two ‘catenary of equal strength’42–44 curves with a vertical shift of Δ:
y1 ¼ Lp lnðjsecðpx=LÞjÞ ð1Þ y2 ¼ Lp lnðjsecðpx=LÞjÞ þ D where Λ is the horizontal length of the catenary. Because the value of Equation (1) is infinite for x = ± Λ/2, the curves should be truncated at the two ends with a value of δx; thus, the span of x is (−0.5Λ+δx, 0.5Λ − δx). Under CPL illumination, the anisotropic transmission would result in a geometric phase for the cross-polarized light, which is twice the inclination angle of the aperture and can be written as Φ = − 2σζ(x)28. Here, σ = ± 1 denotes the left-handed circular polarization (LCP, σ = − 1) and right-handed circular polarization (RCP, σ = 1), (...truncated)