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