Polarized light imaging is a potential tool to obtain an adequate description of the properties of depolarizing media such as biological tissues. In many biomedical applications, for instance, dermatology, ophthalmology, or urology, imaging polarimetry provides a noninvasive diagnosis of a wide range of disease states, and, likewise, it could be applied to the study of internal tissues though the use of endoscopes that use optical fibers. We introduce an algebraic method, based on the Mueller-coherence matrix, for a clearer analysis of the polarization characteristics of depolarizing media via the entropy factor. First-order errors introduced by the measurement system are corrected. Entropy defines three kinds of media according to their depolarizing behavior, and several examples corresponding to each region are shown. The calculation of this factor provides clearer information than that provided by the traditional Mueller matrix in the analysis of biological tissue properties by polarization measurement techniques.

theoretical Quaternions of a fibre subjected to a given by the next expressions: Quaternion (circular birefringence) suffers an magnetic field, that is, to a Faraday effect, would be almost sinusoidal variation which would be perfect if linear birefiingence would be neglected or it becomes small against the circular birehgece. Quaternions 5, and 5, (linear birefringence) interchange their values a Tel: +34 942 201537, Fax: +34 942 201 873, Email: d~ubi~~~teisa.unican.es, ilarcek3,teisa.unican.q bTel: +420 5 41182408, Fax: 4 2 0 5 41 182888, Email: Scs~unir.vlcckr~v.c~ -g = cos(v/2) 1-IntroductionOne of the most usual and practical methods for the analysis of an optical device is the employment of its Jones matrix [l]. However, although this ma& provides much information about an optical device, its behaviour cannot be clearly understood just only using its traditional expression. It would be very interesting to separate the different effects produced by the device.This is the main reason for the employment of Pauli matrices. These four matrices, usually employed in quantum theory [2], are 2x2 Jones matrices which represent the Jones matrices of ideal components, and they characterize different effects, like linear and circular birefiingences. Using these matrices, an unambiguously decomposition of the Jones matrices can be developed:From this decomposition, four different coefficients, 6, t,, t2 and 6, denominated Quaternions, are obtained. These coefficients are related with physical effects, as linear or circular birefringence [3,4], that is, they are a measure of its presence into the device. This is possible as every different matrix can be considered as a Jones matrix of an ideal and well known device: 0, + Free space propagation o2 + Circular retarder right polarization 0, + Linear retarder 2 2 45" to the x aris 0, + Linear retarder 2 2 0" to the anis xThe variation of the Quuternions with the magnetic field is studied and analysed for a Nd3+ doped fibre. Quaternions have to be obtained from the Jones matrix of a real optical device. In order to obtain this matrix, eleven different intensities lave to be measured [5]. A He-Ne laser source, whose wavelength is 633 nm, is used for the measurements 0-7803-7105-4/01/$1 O.OWOO1 IEEE 823

Giant photoinduced magneto-optic Kerr effects are predicted and measured in asymmetric semiconductor microcavities with a totally reflecting rear mirror operated in the limit of the strong coupling regime. The microcavity is modeled by two coupled Fabry-Perot cavities and use is made of the optical scattering matrices to derive its characteristics. The giant photoinduced rotations and phase changes are traced to the saturation, blueshift, and pseudo-Zeeman splitting of the exciton transition. Modeling the lower and upper polariton transitions by two different two-level systems qualitatively accounts for the main spectral features: the photoinduced Kerr rotations and phase changes are due to the modifications of the coupling existing between the cavity and exciton modes, due to the photoinduced changes of the exciton characteristics. The influence of spin relaxation on the rotation and ellipticity spectra is also analyzed; it confirms the gyrotropic nature of the interaction which depends strongly on the difference between the densities of counter-rotating circularly polarized excitons and only weakly on their sum as is the case in previous isotropic studies. Measurements of photoinduced Kerr rotations performed at a temperature of 50 K in a microcavity containing a single semimagnetic semiconductor quantum well confirm the effectiveness of the effect with polarization rotations of 10°a round the lower polariton frequency at a pump fluence of only 2 J/cm 2 .