Toroidal Response of Asymmetric Metasurfaces with Multiple High Q-Factor Resonances Samuel Gomez Mentor: Sirak M. Mekonen Searles Applied & Materials Physics Laboratory Howard University June 20, 2018

Introduction/Background: Metamaterials Metamaterials have shown great capability when it comes to manipulating electromagnetic waves Composed of unit cells in periodic patterns, which are smaller than the wavelength of the waves they are influencing Each individual structure composing the material is a “metamolecule”

Recent Progress Possibilities for negative indexes of refraction Beam-forming applications have been explored through use of gradient metasurfaces Metasurfaces make possible a high quality factor, which would be useful for sensing and slow-light devices, as well as precise measurement of small resonance shifts Additionally, with regards to beam control, non-uniform metasurfaces have a greater degree of freedom THz waves, which are studied through the use of metamaterials, offer a higher spatial resolution, as well as a nonionizing effect

Graphene capabilities in metamaterial/THz wave research Graphene is a very intriguing material, as its properties can be modified in order to produce certain results in research Its fermi level can me modified through an applied gate voltage By putting sheets of graphene in contact with metasurfaces, we can tune the resonance frequency of the composite By stacking sheets of the them, you can modify the optical conductivity of the graphene Graphene has optical transparency, high electron mobility, and it is flexible Has plasmons (collective oscillations of charge carriers) Interestingly, at plasmon resonance, THz optical conductivity of patterned graphene becomes independent of frequency

Split Ring Resonators (SRR) Split rings resonators are composed of various geometries, and it is through these that you can tune responses to THz waves Ramdass, Adrian, et al. “Using a Split Ring Resonator to Harvest RF Energy from a PCB Transmission Line.” YouTube, YouTube, 19 Apr. 2016, www.youtube.com/watch?v=qVH7E6wMnAE.

Base Structures for each experiment Zheng, Xiaobo. “Tuning the Terahertz Trapped Modes of Conductively Couple Fano-Resonators in Reflectional and Rotational Symmetry.” Optical Materials Express, vol. 8, no. 1, 1 Jan. 2018, pp. 105–118. Chen, Xu, and Wenhui Fan. "Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance." Optics letters 42.10 (2017): 2034-2037ianyu Xiang, Tao Lei, Sen Hu, Jiao Chen, Xiaojun Huang, and Helin Yang A toroidal dipole is an electromagnetic occurrence that has been observed through experiments using metamaterials. It is produced by currents flowing on the surface of a torus shape along its meridians. Here, an array of magnetic dipoles are arranged in the “head-to-tail configuration along a torus”.

Group Comparisons (experiments) Group Name Simulation Package Method Substrate Metal Conductivity Permittivity SAMPL HFSS Finite Element Method Gallium Arsenide Aluminum α = 3.8 * 107 S/m. ε = 12.9 + i0.12 Opt. Mat. Exp. CST Microwave Studio Finite Difference Time Domain Gold α = 4.1 * 107 S/m. Chen et al 1 Finite Integration Method F4B Copper α = 5.96 * 107 S/m. ε = 2.65 [1] Chen, Xu, and Wenhui Fan. "Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance." Optics letters 42.10 (2017): 2034-2037ianyu Xiang, Tao Lei, Sen Hu, Jiao Chen, Xiaojun Huang, and Helin Yang

Methodology for SAMPL One of the main differences in design was the different gap lengths (g1,g2). Chen et al used the same gap spacing for each gap, also for Opt. Mat. Exp. Chen et al also used much larger dimensions for their design, in the millimeter range. The periodicity of SAMPL designs was 6 microns less than that of the Opt. Mat. Exp. Structure. All experiments varied the distances between the gaps and the centers of the material. SAMPL symmetric design

Symmetries + = + = + = + = Rotational and Reflectional preserved + = + = Rotational and Reflectional preserved Reflectional preserved + = + = No symmetry Reflectional preserved

How it works

Case 1 Case 2 Case 3

Chen et al vs. Optical Materials Express The structure used by Chen et al is comparable to the rotational geometry from Opt. Mat. Exp, however its dimensions are larger (mm). Closer and sharper peaks on the transmission graph than the rotationally symmetric design. X direction polarized wave (parallel to gaps) Only rotational symmetry + = Chen, Xu, and Wenhui Fan. "Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance." Optics letters 42.10 (2017): 2034-2037ianyu Xiang, Tao Lei, Sen Hu, Jiao Chen, Xiaojun Huang, and Helin Yang

Summary of program Worked more on analysis and comparison of data from SAMPL structures and other groups’ data Analyzed significance of symmetry and different forms in exciting various electromagnetic occurrences Learned how to work with THz spectroscopy on the HASSP Became familiar with finite element method through running numerical simulations Worked with programs such as LaTeX, Igor, HFSS

Acknowledgements Financial support from the REU Site in Physics at Howard University NSF Award PHY 1659224 is gratefully acknowledged