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This paper presents a method of calculating the elements of the generalized matrix representation of the macroscopic constitutive relations for a three-dimensional (3-D) array of nonmagnetic inclusions with arbitrary shape. The derivation is based on the quasi-static Lorentz theory and the inclusions are represented by electric and magnetic dipole moments. The 6 6 constitutive relation matrix is expressed in terms of the interaction matrix and the polarizability matrix, which can be numerically calculated using the sum and the difference of opposing plane wave excitations. Numerical examples are given for split ring resonators and a chiral medium consisting of an array of helices to illustrate the usefulness of the formula and to verify the consistency constraint and reciprocity relations for a bianisotropic medium.

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Abstract. Recently, there has been increasing interest in the use of spaceborne synthetic aperture radar (SAR) for measuring forest biomass. However, it is noted that conventional SAR using Cband or higher frequencies cannot penetrate into foliage, and therefore the biomass measurements require longer wavelengths, typically P-band (500 MHz). It is also known that the ionosphere is highly dispersive, causing group delay and broadening of pulses. The variance of the refractive index fluctuations due to turbulence is approximately proportional to f '4. In addition, the Faraday rotation due to the geomagnetic field in the ionosphere becomes significant. This paper presents an analysis with numerical examples of the following effects in the frequency range from 100 MHz to 2 GHz in order to show the frequency dependence and the effects of total electron content (TEC) of the ionosphere. First, the ionospheric turbulence can reduce the coherent length below the equivalent aperture size, and the azimuthal resolution becomes greater than D/2, where D is the antenna aperture size. Second, the ionospheric dispersion causes a shift of the imagery due to the group velocity. Third, the dispersion also creates broadening of the pulse. In addition, multiple scattering due to ionospheric turbulence gives rise to pulse broadening. Fourth, we consider the Faraday rotation effect and show that the ellipficity change is negligible, but the orientation angle changes significantly at P-band. Numerical examples are shown using typical ionospheric parameters, turbulence spectrum, and TEC values.

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