Assignment 3 Solution12 November 2012

The real part of the permittivity near the operating frequency (indicated by a vertical line at 8.55 GHz) for the ten cloak unit cell designs.

8.0 8.2 8.4 8.6 8.8 9.0f@GHzD3.20

3.25

3.30

3.35

3.40

3.45

3.50

3.55

3.60Re@eD

The real part of the permeability near the operating frequency (indicated by a vertical line at 8.55 GHz) for the ten cloak unit cell designs.

8.2 8.4 8.6 8.8 9.0f@GHzD

-0.4

-0.2

0.0

0.2

0.4Re@mD

The real part of the permittivity vs cloak radial coordinate for the ten unit cell designs, blue disks. The theoretical material specification is shown by the green line.

0 10 20 30 40 50r @mmD0

1

2

3

4Re@eD

The real part of the permeability vs cloak radial coordinate for the ten unit cell designs, blue disks. The theoretical material specification is shown by the green line.

10 20 30 40 50r @mmD

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30Re@mD

The real part of the averaged permittivity vs. frequency for the ten unit cell designs, in the neighborhood of the resonances.

17 18 19 20 21 22 23f@GHzD

-40

-20

0

20

40

Re@eD

The real (blue) and imaginary part (red) of the averaged permittivity vs. frequency for cylinder 1 unit cell design. The extracted and averaged permittivity is shown by solid disks and the Lorentzian fit curve is shown by a solid line.

21.4 21.6 21.8 22.0 22.2f@GHzD

-100

-80

-60

-40

-20

20

40

e

The Lorentzian fit parameters:f0 = 21.6308, δ = 0.0486217, εs = 1.69179, ε∞ = 1.47543

The real part of the averaged permeability vs. frequency for the ten unit cell designs, in the neighborhood of the resonances.

6.5 7.0 7.5 8.0f@GHzD

-40

-20

0

20

40

Re@mD

The real (blue) and imaginary part (red) of the averaged permeability vs. frequency for cylinder 1 unit cell design. The extracted and averaged permeability is shown by solid disks and the Lorentzian fit curve is shown by a solid line.

7.1 7.2 7.3 7.4 7.5 7.6f@GHzD

-80

-60

-40

-20

20

40

m

The Lorentzian fit parameters:f0 = 7.29677, δ = 0.0194013, µs = 1.26199, µ∞ = 1.02927