1. Resonance properties of metallic ring systems: A rigorous approach
V. Conclusions
A rigorous mode expansion theory under quasi-static limit was developed for metallic ring systems. Then we applied it to several SRR systems and the results were verified by FDTD simulations. Finally the ideas can be extended to other systems, such as cross structure.
Publications:
[1] Zhou & Chui, Phys. Rev. B (2006).
[2] Zhou & Chui, Appl. Phys. Lett (2007).
[3] Xueqin Huang, et. al., Phys. Rev. B (2008).
[4] S. T. Chui, et. al., J. Appl. Phys. 104, (2008).
[5] L. Zhou, et. al., Materials Today 12, no.12, (2009).
Resonance properties of metallic ring systems: A rigorous approach
Xueqin Huang, Yi Zhang, S. T. Chui and Lei Zhou
Phys. Dept., Fudan Univ., Shanghai, People’s Republic of China
Metallic ring-like systems play a crucial role in meta-material research, because they provide negative magnetic permeability through magnetic resonance. However, there still exist some unsolved problems: the inductive/capacitive effects are not completely considered, the calculations done before are for cylinders not rings and so on. So our motivation is to establish a rigorous approach which can calculate inductive/capacitive parameters rigorously and provide the intrinsic properties of ring systems, such as resonance frequencies, induced dipole moments, etc.
I. Basic theory --- mode expansion
As shown in the left, Fourier transform of Ohm’s law gives:
Finally arrive at the eigenvalue equation:
in which
Diagonalize the H matrix gives the resonance frequencies;
Current distribution gives the induced dipole moments.
II. Application single ring[1]
III. Application coplanar double rings[2]
Resonance frequencies are shown:
Analytical results FDTD
Resonance frequencies are shown:
Analytical results FDTD
Relative frequency shift:
Excellent agreement with experiment results:
IV. Application broad-side coupled double rings, rectangular cross-section SRR[3]
Average fields over cross section to get L&C parameters;
Use mode-expansion method to get eigenmodes of broad-side coupled SRR;
FDTD results are coincide with our theoretical ones very well.