Jones matrix formalism

In the general case, when s-polarized light is converted into p-polarized light and/or vice versa, the standard SE approach is not adequate, because the off-diagonal elements of the reflection matrix r in the Jones matrix formalism are nonzero [114]. Generalized SE must be applied, for instance, to wurtzite-structure ZnO thin films, for which the c-axis is not parallel to the sample normal, i.e., (1120) ZnO thin films on (1102) sapphire [43,71]. Choosing a Cartesian coordinate system relative to the incident (Aj) and reflected plane waves ( > ), as shown in Fig. 3.4, the change of polarization upon reflection can be described by [117,120]... 

Model Using Jones Matrix Formalism Comments on the Models FACTORS INFLUENCING THE FORMATION OF SRGs... 

It is important to emphasize that this modeP explains the polarization dependence of the writing and reading beams, and it provides a full picture of what one should expect in terms of the diffraction efficiency for the various experimental conditions. Note, however, that the formation of the SRG, which contributes with a phase difference to be input in the Jones matrix formalism, was assumed a priori. The model is not, therefore, aimed at explaining the origin of the mass transport, unlike the case of the models in references 9, 30-33, 36, and 37. 

In the Jones matrix formalism, therefore, a retardation plate is described by a matrix IF( /,r) characterized by its phase retardation F and its azimuth angle / ... 

In Section V we used the system transfer matrix to study the effect of an optical system on the parameters of a Gaussian beam. A similar formalism exists for studying the polarization evolution of a Jones vector as a beam traverses a polarization-transforming system. In this case the system transfer matrix is called a Jones matrix. The simplest Jones matrix is the matrix that describes the polarization vector reflected from an ideal mirror. In order to satisfy the boundary conditions of vanishing tangential E, we need... 

In N and S liquid crystals, as well as in the twisted nematic cell, the formalism can be simplified, since the Jones matrix is independent of z, dcp/dz and being both constants in these cases. By setting k(0)=const=k2, the characteristic equation for the wave vectors of the forward propagating modes is simply... 

This setup allows the determination of the unknown ellipsometric angles and can be operated in various modes. Each optical component modifies the state of polarization. Since any state of polarization can be represented by a complex Jones vector consisting of two columns, the effect of each optical components is described by a complex 2x2 matrix. The Jones formalism provides an elegant means for a quantitative description [4]. 

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