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Additional Information for
High-Directivity Emissions with Flexible Beam Numbers and Beam
Directions Using Gradient-Refractive-Index Fractal Metamaterial
By He-Xiu Xu*, Guang-Ming Wang, Zui Tao, and Tie Jun Cui*
Prof. Tie Jun Cui, He-Xiu Xu, Zui Tao
State Key Laboratory of Millimeter Waves, Department of Radio Engineering
Southeast University, Nanjing 210096, China
E-mail: tjcui@seu.edu.cn
He-Xiu Xu, Prof. Guang-Ming Wang
Missile institute, Air Force Engineering University, Xi’an 710051, China
E-mail: hxxuellen@gmail.com
This Additional Information includes Figs. S1-S7.
SI Figures
The effective permittivity as a function of px and py shown in Fig. S1 is retrieved from the Sparameters calculated through CST Microwave Studio. In all cases, the residual geometrical
parameters of the FR structure are kept constant. As is shown, the electric resonant frequency
continuously shifts upwards as px and py increase simultaneously. Moreover, the frequency
shift seems to be saturated when px and py reach 9mm, indicating that the gap capacitance can
be negligible. In this scenario, the capacitance formed between close neighbouring sections of
the FR itself plays a dominant role in determining the electric resonance. Moreover, the
variance of the resonant intensity is also the same as that of the resonant frequency, further
confirming that the capacitor contributing the resonance contains two parts, namely the interring capacitor and the capacitor formed between close neighbouring sections of the FR itself.
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Fig. S1. The real part of retrieved effective permittivity as a function of px and py.
Fig. S2. Retrieved effective material parameters of the core layer. The lattice constant of
element is px×py×pz=5×5×3mm3, and the geometrical parameters are d1=4.54 mm, d2=0.24
mm and d3=0.7 mm when scale=0.6.
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Fig. S3. Retrieved effective material parameters of the coat layer. The lattice constant of the
element is px×py×pz=5×5×6 mm3, and the geometrical parameters are d1=4.54 mm, d2=0.24
mm and d3=0.7 mm when scale=0.6.
Fig. S4. Simulated gain of the proposed highly-directive emission system as a function of S at
5.5 GHz.
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Fig. S5. Snapshots of Ey components on the upper surface of the lens aperture. (a) Without the
GRIN lens. (b) With the GRIN lens.
Fig. S6. Measurement setup for the free-space near-field mapping system.
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Fig. S7. Simulated and measured far-field patterns for (a)-(c) single-beam and (d)-(f) fourbeam highly-directive emission system.
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