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FORTH - Modelling Issues addressed

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Presentation on theme: "FORTH - Modelling Issues addressed"— Presentation transcript:

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 resonance
k 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 rotation
g 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)


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