Jones’ matrix

If the principal axis of the real part of the refractive index tensor is oriented at an angle 0 relative to the laboratory frame, equation (2.11) must be used to rotate the Jones matrices used in the calculation of N in the rotated frame to obtain ... 

Using the Jones matrices of the optical effects presented earlier in this chapter, along with the rotation property of N expressed in (2.55), Table 2.1 listing the different N matrices, was constructed. 

The majority of Jones matrices for transmission polarizing elements have been presented in this chapter. As mentioned earlier, it is generally more convenient to use Mueller matrices and not Jones matrices when analyzing cascades of optical elements making up a particular experiment. For the purpose of such calculations, a list of Jones and Mueller matrices for most of the elements encountered in practice can be found compiled in Appendix I. 

Table 1 The Jones matrices of amplitude and phase anisotropy...

Table 9.1. Viewing angle range (in degrees) for contrast ratios (CR) of 5 and 10 of various LG / foil configurations as simulated using 2x2 Jones matrices (MD = monodomain, DD = dual domain). ...

To compare different operating modes, let us focus on the normalized transmittance by ignoring the optical losses from polarizers and indium-tin-oxide (ITO) layers, and the interface reflections from substrates. The normalized transmittance TV) of a TN cell can be described by the following Jones matrices as = mV [5] ... 

Table 2.1. Jones vectors for light traveling in the z-direction and Jones matrices for polarizers. The jc-direction is horizontal, the y-direction vertical...

The Jones representation shows its advantages when we consider the transmission of light through optical elements such as polarizers, A/4 plates, or beamsplitters (Fig. 2.12). These elements can be described by 2x2matrices Jones matrices), which are compiled for some elements in Table 2.1. The polarization state of the transmitted light is then obtained by multiplication of the Jones vector of the incident wave by the Jones matrix of the optical element. 

If the light wave passes through several polarizing elements their Jones matrices are multiplied, where the first matrix in the product represents the last element. We will illustrate this by some examples ... 

The optical properties of aTN cell were calculated using Jones matrices by Gooch and Tarry [12]. The normalized transmittance Ttn in the OFF state in the normally white mode is given by... 

As an example of the application of the Jones matrices, the director configuration in a thin liquid crystal film of a SmC material has been investigated [34] by measuring... 

It is more useful to be able to express the retardation from an arbitrary rotation of the fast axis by an angle y/ about the y axis. Rotation with Jones matrices can be done as with normal matrix rotation. If we define a counter-clockwise rotation of angle Y about the y axis as positive, then the rotation ma-... 

The interaction between the FLC molecules and the coherent polarized light can be modeled as a switchable wave plate with two possible axis positions. Hence we can use Jones matrices to model this interaction and polarizers to orient the light then we can analyze the light after propagation through the FLC. 

Such normalized Jones matrices can be expressed for Ihe different polarization states as ... 

---