1. 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

2. 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”

3. 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

4. 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

5. 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,

6. 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 (2017): ianyu 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”.

7. 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 = 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 (2017): ianyu Xiang, Tao Lei, Sen Hu, Jiao Chen, Xiaojun Huang, and Helin Yang

8. 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

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

10. How it works

11. Case 1
Case 2
Case 3

12. 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 (2017): ianyu Xiang, Tao Lei, Sen Hu, Jiao Chen, Xiaojun Huang, and Helin Yang

13. 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

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