Broadside - Coupled Split Ring Resonator (BC-SRR) Metamaterial-Like Slow-Wave Structure. Sabahattin C. Yurt

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1 Department of Electrical & Computer Engineering MURI Teleconference Broadside - Coupled Split Ring Resonator (BC-SRR) Metamaterial-Like Slow-Wave Structure Sabahattin C. Yurt cyurt@unm.edu Sarita Prasad Kostyantyn Ilyenko Mikhail Fuks Edl Schamiloglu September 5, 2014

2 1 DESIGN CONSIDERATIONS 2 HFSS RESULTS - DISPERSION RELATION AND FIELD CHARACTERISTICS 3 3D MAGIC SIMULATION RESULTS 4 CONCLUSION & FUTURE WORK 5 REFERENCES 2/15

3 1 DESIGN CONSIDERATIONS All Metallic Structure Eliminate electric breakdown Avoid dielectric charging Cerenkov Radiation Non- Bianisotropic Backward wave propagation Opposite direction of vectors S and k No dependence of D on H No dependence of B on E Broadside Coupled SRRs Metamaterial Double Negative Property Below cut-off propagation Smaller structures (Transverse dimensions of the structure to be much smaller than a wavelength) Negative epsilon, mu and refractive index 3/15

4 1 DESIGN CONSIDERATIONS Edge Coupled Split Ring Resonator (EC-SRR) t Broadside Coupled Split Ring Resonator (BC-SRR) t ε ε It has bianisotropic property due to asyetry of the inner and outer rings D = ε E + ξ H B = μ H + ϛ E It has non-bianisotropic property due to broadside coupling of rings and charge distribution does not result in a net electric dipole. No magnetoelectric coupling 4/15

5 1 DESIGN CONSIDERATIONS Anti-syetric Broadside Coupled Double Split-ring Metamaterial-like Design 1 st Model 2 nd Model r WGout r WGin r out r in l h d α r WGout r WGin r out r in l h d α deg deg Period much less than the operational wavelength Mounted inside a regular cylindrical waveguide μ Split Rings, ε Waveguide 5/15

6 1 DESIGN CONSIDERATIONS Power Dependence on Number of Split Rings Maximum power is obtained with 18 elements 6/15

7 2 HFSS RESULTS - DISPERSION RELATION Light Beam Very low group velocities Operating frequency 1.1 GHz f cte21 = ρ mnc 2πa a = 0.04 m 5.3 GHz Evanescent Mode 7/15

8 2 HFSS RESULTS - FIELD CHARACTERISTICS H-Field (X-Y Plane) E-Field (X-Y Plane) E-Field (z-x Plane) These results show the TE-like mode syetry and that almost all of the energy is concentrated in the region between the split ring and the output waveguide thereby favoring the extraction of the RF field with a coaxial waveguide 8/15

9 3 3D MAGIC SIMULATION RESULTS Simulation Parameters Cathode Radius 1.75 cm Anode Radius 4 cm Number of Rings 18 Applied Voltage 500 kv Voltage Rise-time 1 ns Magnetic Field 2 T 9/15

10 3 3D MAGIC SIMULATION RESULTS Output Power Efficiency = 12 % FFT of the RF signal TE-like mode (Evanescent mode in the waveguide) 10/15

11 3 3D MAGIC SIMULATION RESULTS RF Mode measured at the output port of the coaxial waveguide To propagate the TE -like mode at 1.1 GHz, it would require a cylindrical waveguide 13.3 cm in radius. This design provides 3 times reduction in size. a = 4 cm 11/15

12 3 3D MAGIC SIMULATION RESULTS Plot of Particle momentum Pz along the axial length of the SWS The evanescent wave leads to the formation of electron traps that exhibit resonant particle distribution similar to that of a virtual cathode. Space Charge Limited Current > Beam Current 12/15

13 3 3D MAGIC SIMULATION RESULTS RF Field Between Two Rings (600 kv/cm) 13/15

14 4 CONCLUSION & FUTURE WORK Double split rings in waveguide are produce negative mu and epsilon, backward wave and can be used as a slow-wave structure for Cerenkov microwave sources. All metallic structures are able to eliminate electrical charging effect. The grounded split rings generate a TE-like RF mode at a frequency of 1.1 GHz which is evanescent in the waveguide. The TE-like mode gets transformed into a hybrid mode due to reflections from the non-uniformities introduced by the SRR structure. This, in turn, provides the Ez component for interaction with the electron beam. The generated evanescent wave gets reflected from the up and down ends of the waveguide therefore provides feedback for RF generation. This, in turn, leads to electron traps that exhibit similar particle momentum distribution to that of a virtual cathode oscillator. The coaxial power extraction allows for an effective RF mode extracting. Transmission line model is still being studied. Experiments are being planned. 14/15

15 5 REFERENCES 1. Shapiro, M.A., S. Trendafilov, Y. Urzhumov et al., Active Negative-Index Metamaterial Powered by an Electron Beam, Phys. Rev. B, vol. 86, (2012). 2. Steshenko, S. and F. Capolino, Single Dipole Approximation for Modeling Collections of Nanoscatterers, Ch. 8, in Capolino, F., Ed., Theory and Phenomena of Metamaterials, CRC Press, Boca Raton, FL, Ricardo Marque s et al, Metamaterials with Negative Parameters, Chapter 2 page Zhang, K. and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2 nd Ed., Springer Press, Berlin-Heidelberg, Germany, Yaniv Y., A. Niv et al., Excitation of a Single Hollow Waveguide Mode using Inhomogeneous Anisotropic Sub-Wavelength Structures, Optics Express, vol. 15, (2007). 6. Oleg M. and J.A. Harrington, Dielectric-Lined Cylindrical Metallic THz Waveguides: Mode Structure and Dispersion, Optics Express, vol. 18, (2010). 15/15