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The electromagnetic properties of materials are defined from the two following constitutive parameters: permittivity, e, and permeability, µ; e indicates how the medium reacts when an electric field is applied (field E of the electromagnetic wave), whereas µ indicates how the material behaves further to a magnetic excitation (field H of the electromagnetic wave). A correct writing of Maxwell's equations allows one to consider the electric conductivity of the medium trough an overall expression of permittivity. To take into account the losses that occur in any material, permittivity and permeability need both to be expressed by complex values: e =e '-je ", m =m '-jm ''. Provided that the inhomogeneities of the material are small compared to the wavelength, the electromagnetic response of heterogeneous materials can be represented by a mean permittivity and a mean permeability then termed as effective permittivity and permeability. At last in the case of media endowed with anisotropic electromagnetic properties, permittivity and permeability should be represented by tensors.
To measure the permittivity and permeability of a given material, a sample is placed on the path of a traveling electromagnetic wave, either in free space or inside a propagation structure, i.e. transmission line or waveguide. One can also put this sample at an antinode of the electric or magnetic field of a stationary wave, for example inside a resonator cavity. Reflection and transmission coefficients of the experimental device are directly related to electromagnetic properties of the material of concern; they are measured using a network analyzer. Then, the sample permittivity and permeability are determined from these coefficients and from the electromagnetic analysis of the discontinuities created within the material. To select a characterization method, one should consider: i) the exploited frequency range, ii) the physical properties of the material of concern: is it magnetic or not, low-loss or lossy, isotropic or anisotropic, homogeneous or heterogeneous, dispersive or not? and iii) the shape and nature of the available samples, i.e. plate or thin films, liquid or solid, elastomer or granular. One among the expertise domains of our laboratory in the field of material characterization is the implementation of methods for broad-band measurement of anisotropic magnetic materials (induced field anisotropy). Two specific test structures cells have been developed to characterize the permeability tensor of magnetized materials over a wide frequency range :
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