Bernhard Michel

Single scattering by red blood cells

A highly diluted suspension of red blood cells (hematocrit 0.01) was illuminated with an Ar or a dye laser in the wavelength range of 458-660 nm. The extinction and the angle-resolved intensity of scattered light were measured and compared with the predictions of Mie theory, the Rayleigh-Gans approximation, and the anomalous diffraction approximation. Furthermore, empirical phase functions were fitted to the measurements. The measurements were in satisfactory agreement with the predictions of Mie theory. However, better agreement was found with the anomalous diffraction model. In the Rayleigh-Gans approximation, only small-angle scattering is described appropriately. The scattering phase function of erythrocytes may be represented by the Gegenbauer kernel phase function.

MAXWELL GARNETT AND BRUGGEMAN FORMALISMS FOR A PARTICULATE COMPOSITE WITH BIANISOTROPIC HOST MEDIUM

We present here the application of Maxwell Garnett and Bruggeman formalisms to homogenize very general bianisotropic-in-bianisotropic particulate composites, assuming the inclusion particles to be ellipsoidal.

Incremental and differential Maxwell Garnett formalisms for bi-anisotropic composites

Abstract We present, compare and contextualize two approaches to the homogenization of bi-anisotropic-in-bi-anisotropic particulate composite medias: (i) the incremental Maxwell Garnett (IMG) formalism, in which the composite medium is built incrementally by adding the inclusions in N discrete steps to the host medium; and (ii) the differential Maxwell Garnett (DMG) formalism, which is obtained from the IMG in the limit N →∞ . Both formalisms are applicable to arbitrary inclusion concentration and are well-suited for computational purposes. Either of the two formalisms may be used as an alternative to the well-known Bruggeman formalism. Numerical results for the homogenization of a uniaxial dielectric composite medium and of a chiroferrite are presented.

The role of anisotropy in the Maxwell Garnett and Bruggeman formalisms for uniaxial particulate composite media

A particulate composite medium in which the host and the spherical inclusions are made of uniaxial dielectric - magnetic media with parallel crystallographic axes is considered. The polarizability dyadics of a single inclusion are obtained, showing in detail the significant role played therein by the degree of anisotropy of the host medium. The derived expressions are used to set up the Maxwell Garnett and the Bruggeman formalisms for homogenization of the particulate composite medium. Numerical results are presented to show that the degree of anisotropy of the homogenized composite medium (HCM) is a non-trivial function of the degrees of anisotropy of the constituent media. Shifts in axial and transverse Frohlich resonances are also predicted.

Bruggeman formalism for two models of uniaxial composite media : Dielectric properties

Abstract The Bruggeman formalism is rigorously implemented on two models for homogenizing a composite medium—wherein identical, parallel, isotropic dielectric, cylindrical inclusions of electrically small cross-section are randomly dispersed in a homogeneous, isotropic dielectric host medium. The inclusion medium is supposed to be dispersed in the homogenized composite medium (HCM) as cylindrical particles in both models. However, the host medium is dispersed as cylindrical particles in the first model and as spherical particles in the second. Numerical results show that the Wiener bounds are complied with by both models, although they yield different estimates of the anisotropic dielectric properties of the HCM. Both models also exhibit percolation. Benchmarking against careful experiments appears to be necessary to evaluate the adequacy of either model. The described models may eventually find use for on-line inspection and control of manufacturing processes for aligned fibrous composite media.

Homogenization of similarly oriented, metallic, ellipsoidal inclusions using the Bruggeman formalism

Abstract The effective relative permittivity dyadic of a composite material made by randomly embedding parallel, ellipsoidal, isotropic, metallic inclusions in an homogeneous, isotropic, dielectric host material is computed using the Bruggeman formalism with exact depolarization dyadics. Numerical calculations carried out for iron inclusions at 670 nm free-space wavelength indicate that the inclusion volume fraction at the percolation threshold is direction-dependent, being lower in those directions that the ellipsoids have longer extents. When the longest principal semi-axis of an ellipsoidal inclusion exceeds a certain relative size – about three to five times as large as the other two principal semi-axes – the Bruggeman estimate of the effective permittivity along this direction does not indicate a percolation threshold, becoming merely a simple weighting of the permittivities of the two materials in relation to their volume fractions.

On the application of the strong property fluctuation theory for homogenizing chiral-in-chiral composites

The bilocal approximation is used along with the strong property fluctuation theory (SPFT) to homogenize (i.e. estimate the effective constitutive properties of) a chiral-in-chiral composite. Important properties of the covariance function of the spatial distribution of the two materials are deduced and interpreted with respect to the homogenization results. Comparison is made with the Maxwell Garnett and the Bruggeman approaches. The correlation length is an additional parameter that distinguishes the SPFT in the bilocal approximation from the Bruggeman approach (as well as from the Maxwell Garnett approach). The SPFT in the bilocal approximation turns out to be a size-dependent extension of the Bruggeman approach, the two homogenization procedures yielding almost the same results at very long wavelengths but not at shorter wavelengths.

CORRECTION TO ''MAXWELL GARNETT AND BRUGGEMAN FORMALISMS FOR A PARTICULATE COMPOSITE WITH BIANISOTROPIC HOST MEDIUM''

In this paper, a new design technique has been proposed for microwave nonhomogeneous media filters. The main attraction of this kind of filter is in its use for matching purposes. These components, in fact, can be used to realize a wide frequency hand matching. Via the new expression of the reflection coefficient, very fast design formulas have been carried out, which can be successfully used either for analysis or synthesis purposes. In the first case, as shown in Table 1, the CPU time used for computing the reflection coefficient Ž . strongly drops down using the new closed-form 12 instead Ž . of the other one 4 . In the second case, as shown in Table 2, physical parameters of the filter can be straightforwardly computed.

The covariance function, bilocal approximation and homogenization of chiral-in-chiral composite materials

In continuation of an earlier paper on the application of the bilocal approximation (BA) within the framework of the strong property fluctuation theory (SPFT), an important restriction on the covariance function is lifted and the consequences numerically examined.