In the last decade we have elaborated an approach to the description of the interaction of the polarized light with the polarization
devices alternative to the standard matrix (Jones and Mueller) languages, namely a vectorial pure operatorial Pauli algebraic
approach. Here we present a complete, coherent and essentialized survey of this approach and we point out its advantages. The
operators of various static and dynamic polarization devices, the density operator of the partially polarized light and the light -
devices interactions are presented in this "non-matrix" or "coordinate-free" language. Some new results are obtained in this frame
illustrating the effectiveness and the compactness of this approach.
A vectorial Pauli algebraic analysis of the time-varying birefringent devices is performed. The general equations of evolution of the light polarization state interacting with such devices are applied in analyzing the modification of the polarization and spectral structure of light by electro-optic modulation in crystals of class 42m.
A theoretical approach to the interaction between the polarized light and the polarization devices based on the vectorial and
pure operatorial form of the Pauli algebra is presented. Unlike the standard (Jones and Mueller) approaches, this formalism is
coordinate-free, i.e. it does not appeal to any matrix representation of the involved operators. This approach addresses to
parameters that reveal the internal symmetries of both the polarization devices and the polarization state space. Therefore the
final equations giving the three relevant quantities that characterize the interaction - the gain, the Poincare vector of the
outgoing light and its degree of polarization - are symmetric, compact and physically expressive.
Unlike the homogeneous basic ("canonical") polarization devices, many inhomogeneous (multilayer) polarization
devices have non-orthogonal eigenvectors. They may be called non-orthogonal devices. Their operators pertain to a
class of operators unusual in physics and somewhat peripheral even in the linear operator theory the non-normal
operators. Moreover, the operators of some multilayer polarization devices are of a very pathological kind: singular and
defective (with the eigenvectors collapsed onto one and the corresponding eigenvalue equal to zero). In this paper we
give a comparative analysis of some of the most widespread orthogonal and non-orthogonal multilayer polarization
devices - to which correspond normal and non-normal operators, respectively - on the basis of the spectral theorem
of linear algebra in a pure operatorial (non-matrix) Dirac-dyadic language.
An analysis of the generalized coherence of multifrequency optical fields is given, both in terms of observable quantities (coherence functions) and in terms of field quantities (analytical signal and amplitude spectral density of the field). The spectral structure of the generalized coherence function for a widespread class of multifrequency optical fields is given. Experimental results obtained by interferometrical investigation of the generalized coherence of such fields are presented.
The spectral analysis of the device (instrument) operators, as an alternative approach to the dynamical polarization phenomena, is presented by means of two examples of classical time-varying optical device: the electro-optical modulator with longitudinal effect in crystals of KDP and the rotating birefringent plate. The polarization-spectral structure of the modulated light is analyzed on this basis, in terms of spectral Jones vectors.
Stationary and travelling waves of the states of optical polarization have been considered in the framework of Jones vector formalism. Feasibility for these waves by revealed in holographic and interference arrangements is grounded and demonstrated.
In analyzing the polarization spectral structure of the time- varying spinorial fields obtained by light modulation, the notions of spectral Jones vector and spectral coherence matrix are introduced. The KDP longitudinal electrooptic modulator is presented as an example.
Extending the idea of the intensity waves, a new term, that of polarization waves is introduced. Unlike the light waves, the intensity waves and the polarization waves belong to the class of observable phenomena. The formalism of intensity waves and of polarization waves is presented for some simple fundamental cases.
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