1. FORTH - Modelling Issues addressed
Heraklion 18/9/2003
Issues addressed
Development/adaptation of the Finite Difference Time Domain Method for lossy and for dispersive media
Microwave Studio
SRR parametric study
CMM parametric study
(based on the structures constructed at FORTH)

2. Modelling tools: Finite Difference Time Domain (FDTD) method
Implementation for lossy and for frequency dispersive materials, in 2D and 3D
Lossy dielectrics:
(through an equivalent current)

3. Dispersive materials (more equations)

4. Problems  For stability time step must be comparable to 1/pe
Large structures  low frequencies  periods much larger than 1/pe 
Difficult to apply to metallic structures with u.c. size larger than 10 m
Application to “equivalent” smaller structures??
Are equivalent (scalability of the problem)?? ( different)
For relatively thick wires YES…. (structures 3 orders smaller  characteristic frequencies “almost” 3 orders larger and relative relation the same)

5. Microwave Studio (commercial software)
Time Domain Solver & Frequency domain solver & Eigenmode solver
Treats the metals as perfect conductors or as lossy media with im=i/ or as dispersive media
Advantage: Possibility for very thin wires
Disadvantages: No periodic boundary conditions are possible  Difficult to treat large systems
For dispersive media works only for small structures (like FDTD)
Frequency domain solver not complete yet

6. Metamaterial characteristics vs system parameters
SRR parameters
Wires parameters
Based on the experimental systems - with aim to optimise them

7. FORTH GaAs structure (in plane)
Board: GaAs
=12.3, thickness=0.3 mm
Metals: Cu and Ag
At 10 GHz:
Skin depth=0.6 m
At 100 GHz:
Skin depth=0.2 m
Layer of 20x20 unit cells
Unit cell of 0.5 x 0.5 x 0.3 mm
f  30 GHz

8. FORTH PCB structure (in-plane)
Board: PCB
=4.4, thickness=1.5 mm
Metals: Cu and Ag
Thickness=0.03 mm
At 10 GHz:
Skin depth=0.6 m
At 100 GHz:
Skin depth=0.2 m
Layer of 20x20 unit cells
Unit cell of 5 x 3.63 x 5.5 mm
f  10 GHz

9. Dependence of the SRR dip on: Wires width (w) Rings distance (s)
1 SRR unit cell g w s d
Dependence of the SRR dip on:
Wires width (w)
Rings distance (s)
Wires depth (d)
Rings gaps (g)
Orientation relative to E

10. 1 SRR: FIELDS on resonancek E

11. 1 SRR: Influence of wires width (w) and distance (s)g w s d
Reduction of rings width (50%)  reduction of dip freq. (13%)
Reduction of rings distance (70%)  reduction of freq. (25%)
Depth (thickness) of rings does not affect a lot the SRR dip

12. 1 SRR: Influence of gaps width (g)
Smaller gaps  smaller dip-frequency

13. 1 SRR u.c.: Influence of rotationg w s d E k g w s d E k
No considerable change in the magnetic dip Change in the electric response

14. To reduce the magnetic dip frequency (m)?
Thin rings
Rings close together
Small gaps
Large area of the outer ring g w s d E
Qualitative agreement with

15. Electric response ? Wires ? Wires + cut-SRRs ? Wires + closed-SRRs ?
Aim: Isolate and control the electric response

16. SRR: Fields
SRR off-resonance
Closed SRR k E
Cut-SRR

17. GaAs system x 10-2
Cut-SRR
Closed-SRR
Wires + Closed-SRRs: smaller cut-off ('p) than wires + cut-SRRs or wires

18. GaAs system (x 10-2): Influence of the wire width
Increase of width  increase of p
Influence larger than the expected from the logarithm relation

19. Wires + closed-SRRs: Influence of the rings width on 'p
Double rings width
The SRR rings width does not affect the electric response (p’)

20. Changing the metal depth (GaAs system)
Thin (depth =1m)
Thick (depth =20 m)
Increasing the depth  Cut off freq. is increased
The depth of the closed-SRRs does not contribute to the change of p’

21. To increase the cut-off frequency ('p)?
Wide continuous wires
Additional wires
Thick metal

22. Possibility of separate control of 'p and m
Conclusion
Possibility of separate control of 'p and m
To lower the SRR dip frequency without affecting the 'p:
Rings thinn and close together
Gaps small
To lower the 'p without affecting the SRR dip
Wide and thick wires (only the continuous wires)