Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field

Abstract

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

Mueller Coherency matrix method for contrast image in tissue polarimetry

“…These errors are optical activity ($>), strain (<5>) and leakage (y P ) in the linear polarizer and optical activity ($?) and dichroism (a R ) in the linear retarder [3]. As polarization devices are supposed to produce no modification of the degree of polarization, they could be analyzed by simple Jones matrix [19].…”

“…Polarimetric techniques are specially appropriate for biological tissues, due to the fact that their properties show dependence with the polarization of light, and they usually exhibit a depolarising behaviour. Methods of analysis that do not take into account tissue depolarisation, like Jones matrix, produce limited results [3]. The extension of these characterization techniques to Mueller matrix measurement adds data to the image obtained, but further information can be extracted [4].…”

Mueller Matrix Group Theory Formalism for Tissue Imaging Polarimetry Contrast Increase

“…This parameter indicates how much losses the device introduces. Their calculus is based on the Quaternions i ξ analysis [8]:…”

Characterization of depolarizing optical media by means of the entropy factor: application to biological tissues

“…13,14 In a equivalent way, by means of the homomorphism SU͑4͒ ↔ O ϩ ͑6͒, the Mueller-coherence matrix C 4ϫ4 and the Mueller matrix can be connected by use of the Dirac matrices ͑ ij ͒ basis 15 :…”