Ari Sihvola

The complex dielectric constant of snow at microwave frequencies

The complex dielectric constant of snow has been measured at microwave frequencies. New and old snow at different stages of metamorphosis have been studied. The results indicate that the complex dielectric constant is practically independent of the structure of snow. For dry snow, the dielectric constant is determined by the density. For wet snow, the imaginary part and the increase of the real part due to liquid water have the same volumetric wetness dependence. The frequency dependence of the complex dielectric constant of wet snow is the same as that of water. A nomograph for determining the density and wetness of wet snow from its dielectric constant is given. A snow sensor for field measurement of the dielectric constant has been developed. It can be used for determining the density and the wetness of snow by a single measurement.

Perfect Electromagnetic Conductor

In differential-form representation, the Maxwell equations are represented by simple differential relations between the electromagnetic two-forms and source three-forms while the electromagnetic medium is defined through a constitutive relation between the two-forms. The simplest of such relations expresses the electromagnetic two-forms as scalar multiples of one another. Because of its strange properties, the corresponding medium has been considered as nonphysical. In this study such a medium is interpreted in terms of the classical Gibbsian vectors as a bi-isotropic medium with infinite values for its four medium parameters. It is shown that the medium is a generalization of both PEC (perfect electric conductor) and PMC (perfect magnetic conductor) media, with similar properties. This is why the medium is labeled as PEMC (perfect electromagnetic conductor). Defining a certain class of duality transformations, PEMC medium can be transformed to PEC or PMC media. As an application, plane-wave reflection from a planar interface of air and PEMC medium is studied. It is shown that, in general, the reflected wave has a cross-polarized component, which is a manifestly nonreciprocal effect. This is in contrast to PEC and PMC limiting cases, for which there is no cross-polarized component.

Effective permittivity of mixtures: numerical validation by the FDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional (2-D) dielectric mixture is calculated by FDTD simulations of such a sample in a TEM waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits. Calculated permittivity distribution is also compared with theoretical mixture models. No model seems to be able to predict the simulated behavior over the whole range of volume fraction.

Mixing Rules with Complex Dielectric Coefficients

This article discusses the determination of effective dielectric properties of hetereogeneous materials, in particular media with lossy constituents that have complex permittivity parameters. Several different accepted mixing rules are presented and the effects of the structure and internal geometry of the mixture on the effective permittivity are illustrated. Special attention is paid to phenomena that the mixing process causes in the character of the macroscopic dielectric response of the mixture when the losses of one or several of the components are high or when there is a strong dielectric contrast between the component permittivities.

Backward-wave regime and negative refraction in chiral composites

Possibilities to realize a negative refraction in chiral composites in dual-phase mixtures of chiral and dipole particles are studied. It is shown that because of a strong resonant interaction between chiral particles (helices) and dipoles, there is a stop band in the frequency area where the backward-wave regime is expected. The negative refraction can occur near the resonant frequency of chiral particles. Resonant chiral composites may offer a root to realization of negative-refraction effect and superlenses in the optical region.

Analysis of a three-dimensional dielectric mixture with finite difference method

The present paper reports the results of a numerical analysis of electric fields in random dielectric materials. The effective permittivity of a three-dimensional (3D) dielectric mixture is calculated by the finite difference method. The results show the distribution of the effective permittivity of a mixture with different random inclusion positionings. New empirical mixing models are created as least squares approximations to fit the collection of numerical results. The calculated permittivity distribution is also compared with theoretical mixture models, showing that in case of clustered inclusions, the Bruggeman model is quite reasonable. On the other hand, if the inclusions in the mixture are separate, the results are closer to the Maxwell-Garnett model.

Realization of the PEMC boundary

Perfect electromagnetic conductor (PEMC) is a nonreciprocal generalization of both the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC). Because PEMC does not allow electromagnetic energy to enter, it can serve as boundary material. Possibilities for the realization of a PEMC boundary are studied in terms of a layer of certain nonreciprocal materials resting on a PEC plane. It is shown that the parameters of a bi-isotropic or a gyrotropically anisotropic medium can be chosen so that the interface of the layer acts as a PEMC boundary to normally incident waves. After a modification of medium parameters, the same is shown to be asymptotically valid for arbitrary plane waves. A structure for the realization of such a boundary is suggested.

Transformation method for problems involving perfect electromagnetic conductor (PEMC) structures

Perfect electric conductor (PEC) and perfect magnetic conductor (PMC) can be generalized to perfect electromagnetic conductor (PEMC), a medium where certain linear combinations of electromagnetic fields are required to vanish. In differential-form representation, the corresponding medium is characterized as the simplest possible medium. It is defined through a scalar admittance parameter, whose zero and infinite limits yield the PMC and PEC media, respectively. In this paper a duality transformation is found that has the property of transforming PEMC to PEC and an isotropic medium to itself. Thus, problems involving PEMC objects in air can be transformed to problems with PEC objects in air which can be solved through traditional techniques and then transformed back. Several simple examples are treated to demonstrate the principle. PEMC has the potential of having similar applications as PMC in antenna engineering and finding structures for its realization is a challenge.

Snow Fork for Field Determination of the Density and Wetness Profiles of a Snow Pack

A radiowave sensor (a snow fork) for determining the density and wetness profiles of a snow pack with a single measurement has been developed. The snow fork is based on the measurement of the dielectric properties (real and imaginary part) of snow around 1 GHz. Due to the open structure of the resonator the measurement is nondestructive. Automatic measuring equipment guarantees instantaneous measurement results that can be recorded in the field.

A comparative study of instruments for measuring the liquid water content of snow

Different dielectric sensors for measuring the liquid water content of snow are compared and described in detail. The instruments make use of the significant difference in the dielectric properties of ice and liquid water at radio frequencies; they are operated with frequencies ranging from 1 MHz up to 1.3 GHz. Plate condensers in connection with ac bridges are used as sensors in the frequency range up to 100 MHz whereas open resonators are used in the GHz regime. Test measurements with the different sensors on homogeneous samples like dry sand and mixed and prepared snow showed the same results for the dielectric constant: the discrepancies are less than 1%. In the natural, inhomogeneous snow cover, the special properties of the different sensors appear. Snow wetness is calculated from the measured dielectric constant and the snow density using the model of Polder and van Santen. The comparative field measurements were made with Alpine snow in the Stubai Alps in Austria.