C. Alberdi

Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media

The propagation of a homogeneous plane wave in uniaxial and absorbing dielectric media is described in detail. Complete expressions for electric displacement field, electric field, magnetic field and Poynting vector are derived using a new formalism that simplifies the interpretation of polarization. These expressions are analysed and verified in some particular situations. Whilst absorption is directly determined by the absorption coeffcient k, the field geometry depends exclusively on the absorption index X for given ordinary and extraordinary refractive indices. When ordinary and extraordinary absorption indices are equal, the field geometry coincides with the field geometry in a transparent medium with the same refractive index as the absorbing medium.

Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media

We introduce a formalism based on complex unitary vectors for the direction of propagation and for the polarization in order to describe in detail the propagation of inhomogeneous plane waves in absorbing isotropic media. We obtain analytic expressions for the displacement vector, the electric field, the magnetic field, and the Poynting vector, and we study their geometry in terms of the geometrical interpretation of the complex directions of propagation inside the material. We introduce a complex coordinate system based on complex unitary vectors, where the description of the polarization states of the field vectors and the Poynting vector becomes simpler. The physical meaning and the interpretation of the mathematical operations involving these complex unitary vectors is provided.

Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media

The propagation of inhomogeneous and elliptically polarized plane waves in absorbing uniaxial anisotropic media is described using complex unitary vectors to represent the direction of propagation and the direction of polarization. Detailed expressions for electric displacement, electric field, and magnetic field vectors are obtained for the ordinary and extraordinary waves, and their geometry is discussed. According to the complex direction of propagation, three particular cases are studied: the real case (homogeneous wave), the case perpendicular to the optical axis, and the case coplanar with the optic axis. The case of isotropic media is also analyzed.

Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation

In this work we analyze the propagation of a plane wave that passes from an isotropic transparent medium to a uniaxial absorbing medium. Detailed expressions that give the real directions of propagation of the wave and the energy of the reflected and refracted ordinary and extraordinary waves are obtained. These expressions are valid for every orientation of the optic axis of the uniaxial medium and for every direction of propagation of the incident wave. Expressions are tested in the case of an interface between a transparent and an absorbing isotropic media and for the air-rutile (TiO2) interface. The effect of absorption has been evaluated by comparing the results obtained in rutile with the results obtained in a transparent uniaxial medium with the same real refractive indices. Results are presented for different values of the angle of incidence and the orientation of the plane of incidence.

Influence of absorption on the anomalous negative refraction in right-handed uniaxial absorbing dielectric media

In this work we study the anomalous negative refraction when a plane wave is incident from an isotropic medium to a uniaxial absorbing medium. We study the influence of the anisotropy on the refractive indices and the anisotropy on the absorption coefficients in the negative refraction of these materials. Negative refraction can occur for the ordinary and extraordinary waves for a wide range of values of the angle of incidence. The allowed values of the angle of incidence that lead to negative refraction are analyzed in detail as a function of the orientation of the optic axis and the values of the refractive indices and absorption coefficients.

Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media

The optical properties are an important characteristic of a mineral. These properties can be studied with a photometer microscope using the indicating surface of natural reflectance (ISRN). Transparent uniaxial media have been studied. Biaxial transparent media, in the same way as uniaxial media, can be analysed by knowing the statistical parameters of the ISRN. To analyse these media, we need the expressions that relate these parameters to the refractive index of the incident medium and to the principal indices of the medium under observation.

Colour Evolution of Rosé Wines after Bottling

This research reports on the colour evolution of six rose wines during sixteen months of storage in the bottle. Colour changes were determined in terms of CIELAB colour parameters and in terms of the common colour categories used in visual assessment. The colour measurement method reproduces the visual assessment conditions during wine tasting with respect to wine sampler, illuminating source, observing background and sample-observer geometry. CIELAB L*, a*, b*, C* and hab colour coordinates were determined at seven different times (t = 0, 20, 80, 153, 217, 300 and 473 days). The time evolution of colour coordinate values was studied using models related to linear, quadratic and exponential rise to a maximum. Adjusted R2, average standard error and CIELAB ΔE* colour difference were used to compare models and evaluate their performance. For each colour coordinate, the accuracy of model predictions was similar to the standard deviation associated with a single measurement. An average ΔE* = 0.92 with a 90 percentile value ΔE*90% = 1.50 was obtained between measured and predicted colour. These values are smaller than human colour discrimination thresholds. The classification into colour categories at different times depends on the wine sample. It was found that all wines take three to four months to change from raspberry to strawberry colour and seven to eight months to reach the redcurrant category. Only two wines had developed salmon colour by the end of the experiment.

Uniaxial absorbing media: conditions for refraction in the direction of the optical axis

When a plane wave is incident from an isotropic medium into a uniaxial transparent medium so that the ordinary wave propagates in the direction of the optical axis, the extraordinary wave will also propagate in the same direction and with the same refractive index. We will show that this is not the case when the second medium is a uniaxial absorbing material. In this work, we will state a clear and precise interpretation of the meaning of propagation in the direction of the optical axis in the case of uniaxial absorbing media. Assuming that the ordinary wave is refracted in the direction of the optical axis we will analyze the refraction of the extraordinary wave and we will compare it with the case of transparent media. The necessary conditions to have both ordinary and extraordinary waves refracted in the direction of the optical axis will be obtained.

General expressions for the refractive indices of absorbing biaxial media as a function of the angle of incidence.

In this work we obtain general expressions for the complex refractive indices of refracted waves as a function of the angle of incidence in the case of an electromagnetic wave propagating in a transparent isotropic medium that reaches an interface with a biaxial absorbing medium. The biaxial absorbing medium is only required to have a diagonalizable complex dielectric tensor. Obtained expressions can be applied to any orientation of the principal axes and can be specialized for isotropic, uniaxial or biaxial, or transparent or absorbing media. By using these expressions we have also obtained the surface of indices and the surface of absorption coefficients for an example of a biaxial absorbing medium.

The Number of Linearly Independent Vectors in Spectral Databases

Linear dependence among spectra in spectral databases affects the eigenvectors obtained from principal component analysis. This affects the values of usual spectral and colorimetric metrics. The effective dependence is proposed as a tool to quantify the maximum number of linearly independent vectors in the database. The results of the proposed algorithm do not depend on the selection of the first seed vector and are consistent with the results based on reduction of the bivariate coefficient of determination.