The effective permittivity of the two-dimensional multilayered periodic structures which consist of the rectangular dielectric cylinders is examined numerically. The original periodic structure is replaced with a simple structure such as the dielectric slab. By using the reflectance of the periodic structure obtained by the FDTD method, the effective permittivity of the dielectric slab, which has the same reflectance as that of the periodic structure, is obtained by using the transcendental equation. In order to reduce the procedure to obtain the reflectance from the multilayered periodic structures, the reflectance from one-layered structure is used. The range of the application and validity of this procedure is examined.

We calculated the shielding characteristic of a three-dimensional array of strip conductors by using the electric field integral equation method and its expansion to an array structure. From reflection coefficients, the effective permittivity of the array is calculated. The effective permittivity becomes negative in the frequency range above resonance, in which the electromagnetic waves travel through the material in an evanescent mode and the transmission coefficient becomes very small.

This paper proposes a method for estimating the complex permittivity of a small quantity of a sample such as a biological membrane. The feature of this method is that a material with an unknown complex permittivity is mixed with a material with a known complex permittivity in a number of volume ratios. The unknown complex permittivity is estimated by measuring the effective permittivity of the mixtures and by using the mixing formula, which is applied to the composite material. The validity of this estimation method is evaluated using a phospholipid, which is the primary constituent of a biological membrane, in the frequency range from 0.8 GHz to 6 GHz. We confirm that the measured effective permittivity of the phospholipid mixtures, which comprise the phospholipid and Ringer's solution in a number of volume ratios, corresponds to that of the Lichtenecker formula. Additionally, by preparing a number of samples with varying volume ratios the estimation error can be decreased. This estimation method is considered to be effective in the measurement of the complex permittivity for a biological membrane.

New strip arrangements for high Q or high effective permittivity are proposed for artificial dielectric resonators in a waveguide. The quality factor and the effective permittivity are discussed by changing strip arrangement composing the artificial dielectric. Concentrating strips from both sides to the middle in the waveguide leads to increase of unloaded Q. The value becomes high to several thousands by decreasing dielectric loss of the material. Interdigital strip arrangement makes the effective permittivity very high. A resonator of the strip arrangement has effective permittivity over 800 and unloaded Q over 1000. Moreover the resonator exhibits a good spurious characteristic with no unnecessary resonant mode throughout several harmonics range.

We study the electromagnetic wave propagation in three-dimensional (3-D) dense random discrete media containing dielectric spheroidal scatterers. We employ a Monte Carlo method in conjunction with the Method of Moments to solve the volume integral equation for the electric field. We calculate the effective permittivity of the random medium through a coherent-field approach and compare our results with a classical mixing formula. A parametric study on the dependence of the effective permittivity on particle elongation and fractional volume is included.