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An issue concerning the use of “Double NeGative” (DNG) metamaterials

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Dear All,

I have an issue concerning the use of “Double NeGative” (DNG) metamaterials. The issue regards either the electromagnetic scattering of plane waves from DNG metamaterial cylinders or the evaluation of the reflection coefficient for waveguides partially filled with metamaterials.

I firstly considered an indefinite (along the z axis), homogeneous cylinder having radius = 4lambda in the case of normally incident plane wave with TM polarization at f = 300MHz (see Fig. 1 in attached files). The cylinder is filled up with a DNG metamaterial having eps_r= -2.2, while mu_r<0 changes from case to case. An indefinite cylinder has been obtained with periodic boundary conditions.
The result from FEKO is compared with a cylindrical wave expansion (see “Normal Incidence Plane Wave Scattering by Conducting Circular Cylinder: TMzPolarization” – Advanced Engineering Electromagnetic, Constantine A. Balanis).
FEKO and the cylindrical wave expansion agree for mu_r =-1 (see Fig. 2) and for mu_r = -1.2 (see Fig. 3), while they disagree for mu_r= -1.3 and mu_r = -1.5 (see Fig. 4 and Fig. 5).
Please, find attached the related .cfx file and relative figures.
 

In the second case, I considered an X-band rectangular waveguide structure (see Fig.6) partially filled with a DNG metamaterial, now with epr_r = -2 and mu_r<0 changing from case to case, and terminated with a short circuit. The result from FEKO has been compared with waveguide theory. While for mu_r from -1 to  -1.2 the reflection coefficient is ok, for mu_r = -1.5 (or in general lower than mu_r=-1.3) the phases of the numerical and analytical reflection coefficients differ: the numerical phase is -79.7° while the analytical one is -105.1°.
Again, the .cfx file is attached.

Thank you very much for any help.

Fig. 1 - cilindro vista alto.JPG

Fig. 2 - cfr_metacyl_DNG_epsr_22_mur_1_.jpg

Fig. 3 - cfr_metacyl_DNG_epsr_22_mur_12_.jpg

Fig. 4 - cfr_metacyl_DNG_epsr_22_mur_13_.jpg

Fig. 5 - cfr_metacyl_DNG_epsr_22_mur_15_.jpg

Fig. 6 - WG_rect.JPG

A_Case1a_metacylinder_DNG_epsr2.2_mur1.cfx A_Case1b_metacylinder_DNG_epsr2.2_mur1.2.cfx A_Case1c_metacylinder_DNG_epsr2.2_mur1.3.cfx A_Case1d_metacylinder_DNG_eps_2.2_mu_1.5.cfx B_Case1a_Rectangular_Waveguide_ partially_filled_memetamaterial_DNG_epsr2_mur1_.cfx B_Case1b_Rectangular_Waveguide_ partially_filled_memetamaterial_DNG_epsr2_mur1.3_.cfx B_Case1c_Rectangular_Waveguide_ partially_filled_memetamaterial_DNG_epsr2_mur12_.cfx B_Case1d_Rectangular_Waveguide_ partially_filled_memetamaterial_DNG_epsr2_mur1.5_.cfx

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