Tailor the Angular Dispersion of Metasurfaces Meng Qiu*, Min Jia, Shaojie Ma, and Lei Zhou State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai, 200433, China qium@fudan.edu.cn Abstract – Angular dispersion is widely existed in all kinds of optical systems. Metasurfaces, which has many great optical responses and broad applications, constructed by 2-D lattice of E-M resonators, always have strong angular dispersion. We considering the metasurfaces as a TBM system in solid state physics, and find the key point leading the angular dispersion is coupling strength between nearest resonators. This strength can be understand by a recently developed tight-binding theory and effective model to describe the plasmonic couplings between nanoparticles. By changing the relative position (orientation angles) of resonators, we can control the coupling strength between them, then control the angular dispersion. We did THz experiments of plasmonic metasurfaces to verified our expects. Motivations: II. Mechanism Angular dispersion is widely found in many kinds of metasurfaces [5]. Dispersion of a 2-D lattice: only consider nearest coupling Measurement settings Changing the incident angle of THz light to change kx. Use THz Time-domain spectroscopy and measured the transmission of our sample. Can be change by changing the orientation angle and distance of resonators Wave vector along surface Lattice Constant θ   2t1,2 / f0 (%) 2t1,2 / f0 (%) Problems 2t1,2 / f0 (%) Physical understandings of why we have angular dispersion. No guidelines (so very hard) to control angular dispersion in metasurfaces. Experimental Results The resonance frenquency changes by changing incident angle Questions 2t1,2 / f0 (%) What is the key mechanism causing angular dispersion? How to control the angular dispersion in metasurfaces without changing its basic optical response? I. Background Tight-binding method (TBM) [2] and effective model [3] The angular dispersion changes by changing orientation angle of resonators (different samples) III. Experiments Rewrite Maxwell Equations and Lorents Model to “Schordinger Equation Like” formulism [4] . Samples (Au on silica): different orientation angles gives different coupling strength. By TBM in solid state physics, the frequency splitting of two coupled resonators: Where θ = 0, 15, 30, 45 (deg) Using multiple expansion: Conclusions Couplings between resonators causing angular dispersion. Tailor angular dispersion of metasurfaces by changing orientation angles of resonators. [1] Z. Song, et al., APL 101,18(2012) [2] B. Xi, et al., Phys. Rev. B, 83, 165115 (2011) [3] M. Qiu, et al., Opt. Letters. 40, 2 (2015). [4] A. Raman et al., Phys. Rev. Letters, 104, 65(2010) Electric dipolar interaction Radiation correction Interaction between P and M Magnetic dipolar interaction