Generalized conditions of eigenpolarizations orthogonality: Jones matrix calculus Sergey N. Savenkov, * Yevgeny A. Oberemok Department of Radiophysics, Taras Shevchenko Kiev National University, 01033 Kiev, Ukraine ABSTRACT It is known that all four basic types of anisotropy, circular and linear birefringence and circular and linear dichroism, each taken separately, possess orthogonal eigenpolarizations. Generalized birefringence, i.e. the case of medium exhibiting linear and circular birefringence simultaneously, is characterized by unitary matrix model and has orthogonal eigenpolarizations. At the same time, simultaneous presence of dichroism and birefringence in a medium may lead to nonorthogonal eigenpolarizations. However, to the best of our knowledge, so far there has been no systematic study of conditions under which such medium possesses orthogonal eigenpolarizations. Ascertainment of generalized conditions for orthogonality of medium's eigenpolarizations allows determining the structure and symmetry of matrix model Keywords: Jones matrix, eigenpolarizations, orthogonality 1. INTRODUCTION Deterministic polarization element can be described within a formalism of a 2 2 × Jones matrices: 1,2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 22 21 12 11 t t t t T (1) Eigenvalues and eigenpolarizations of the Jones matrix characterize completely polarization element described by this matrix. 1 Eigenpolarizations, 2 , 1 χ , are those polarization states of light that do not change when passing through a polarization element. 21 21 12 2 11 22 11 22 2 , 1 4 ) ( 2 1 t t t t t t t ⋅ + − ± − = χ (2) The amplitude and the overall phase of the light beam with an eigenpolarization do, however, change. These changes are described by the corresponding eigenvalues. Physically clear definition of eigenpolarizations and eigenvalues has motivated their active use in polarimetry. Based on the properties of eigenpolarizations and eigenvalues, a number of classifications of polarization elements have been suggested in the literature. Two well-known examples are the elliptical retarders and polarizers of Azzam and Bashara 1 and the homogeneous and inhomogeneous elements of Lu and Chipman. 3 Classification of polarization elements and its Jones matrices as homogeneous or inhomogeneous is based on the orthogonality of their eigenpolarizations. In such a way, a homogeneous polarization element has two orthogonal eigenpolarizations and is described by a homogeneous sns@univ.kiev.ua ; phone 3 8 044 526 05 90; fax 3 8 044 521 35 90 Polarization: Measurement, Analysis, and Remote Sensing VIII, edited by David B. Chenault, Dennis H. Goldstein, Proc. of SPIE Vol. 6972, 697210, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.783958 Proc. of SPIE Vol. 6972 697210-1 2008 SPIE Digital Library -- Subscriber Archive Copy