Uniaxial media

For comparison, the results obtained using the Maier-Meier theory [4] are also shown this is a generalization of the Onsager model [13] to uniaxial media. The same dipole moment used for the calculations with the molecular shaped cavity was assumed, and the radius a was taken to be 3.9 A, a value derived from the density of the system. Improvement of the predictions, when the sphere is replaced by a molecular shaped... 

Phase retardation of uniaxial media at oblique angles... 

Both uniaxial compensation film and nematic LC layer can be treated as uniaxial media. When a light propagates into a uniaxial film, generally two forward eigenwaves (one ordinary wave... 

Pseudo-Stokes parameter representation of light propagation in layered inhomogeneous uniaxial media in the geometric optics approximation... 

The GOA has been widely used in the study of light propagation in photoelastic materials and liquid crystals. Recently, Ong and Meyer presented a general GOA formalism for wave propagation in optically inhomogeneous, planar, uniaxial media and found excellent agreement between the zeroth-order GOA and the exact solution for the case of a periodically bent nematic liquid crystal. The approach of Ong and Meyer, however, is restricted to linearly polarized light in planar structures. 

See also Yang, K. H., 1990. Elimination of the Fabiy-Perot effect in the 4X4 matrix method for inhomogeneous uniaxial media. J. Appl. Phys. 68 1550. 

For the sake of illustration, the determination of the electrooptic coefficient for a uniaxial crystal is described below. Considering the nonlinear uniaxial medium of Figure 11, a D.C. electric field is applied in the z direction. The effect of the electric field is to modify the refractive index in the z direction by an amount proportional to the electric field, the modified ellipsoid is given as... 

During 1980-1981 the possibility of the existence of nonlinear surface polaritons of various types was predicted in the literature (18), (19)-(20). In particular, Tomlinson (19) and Maradudin (21) derived s-polarized surface polaritons at a plane interface between two dielectrics, one of which has an isotropic and linear (e1) dielectric constant whereas the dielectric constant of the other is that of a nonlinear uniaxial medium... 

Certain amphiphatic molecules arrange themselves in discoidal bilayered structures known as bicelles. The bicelles have highly anisotropy magnetic susceptibility and thus the property to align themselves in the magnetic field with the plane normal perpendicular to the field [434]. This results in a uniaxial medium suitable for... 

In low MW nematic liquids, the application of a magnetic field H leads to uniform alignment of the molecules owing to the diamagnetic anisotropy of the volume elements and the free mobility of the molecules. The anisotropy of the magnetic susceptibility Ax is the difference between the susceptibilities parallel and pe rpendicu-lar to the main axis of the uniaxial medium (the director n) ... 

Note that are t)-dependent numbers, not functions. Finally we can write the orientational distribution function for a uniaxial medium composed of... 

First we consider a uniaxial medium whose dielectric constants along the principal frame axes are ex = ey = nl4 e = n, and n and are the ordinary and extraordinary refractive index, respectively. When the propagation direction is along s= sin cos y/x+ sin0sinyry+ cosOz, as shown in Figure 2.4, Equation (2.62) becomes... 

In general, the phase retardation of a uniaxial medium at oblique incidence can be expressed as [28]... 

Figure 8.8 Schematic view of an arbitrary light impinging on a uniaxial medium. Zhu 2006. Reproduced with permission from IEEE.

Figure 8.9 Schematic diagram of Poincare sphere representation and the effect of uniaxial medium on the polarization state change of a polarized incident hght.

The poled polymer acts as a uniaxial medium with the optical axis along the poling axis. The complex linear susceptibility x P determines the refractive index n as well as the absorption coefficient a of the material as can be seen from the following equations ... 

We have shown that the zeroth-order geometric optics approximation can be used to describe the propagation of normally incident, elliptically polarized light in an inhomogeneous, locally uniaxial medium. The approximation corresponds to finding an asymptotic solution of the wave equation in the short-wavelength limit. It is found that a set of pseudo-Stokes parameters, linearly related to the usual Stokes parameters, can be defined to characterize the propa-... 

It has been shown that the evolution of the beam polarization of an optical wave propagating in an inhomogeneous uniaxial medium is approximately governed by the precession equation ... 

Optically, a nematic phase can be uniaxial or biaxial. The latter is formed by elongated lath-like molecules. Conventional nematic liquid crystals formed by rod-like molecules constitute a uniaxial medium with nonpolar symmetry. The constituent molecules rotate (freely or hindered) around both their short and long axes. Nonoriented samples are analogous in some measure to polycrystalline powders they consist of individual (liquid) crystallites, each of which has as a definite feature, a directed optical axis, which... 

The diamagnetic susceptibility tensor x in a. uniaxial medium has two principal components X and X-L which are along and normal to the director, respectively. The diamagnetism is particularly strong when the... 

When both Q and P are non-zero, this corresponds to a biaxial nematic phase. In the isotropic phase, both order parameters vanish. Now P is identical to zero in a uniaxial medium, such as nematic and smectic A phases. This is because Xxx — Xyy — Xxj the component of diamagnetic... 

Using Eqs. (3.9) and (3.10) in Ax = 3x Qzz — Qxx)j it is found that, as before, Qzz = 2 A x/9x This shows that a knowledge of A% and Aij is sufficient to determine the macroscopic order parameter Qzz, which distinguishes the nematic phase from the isotropic phase. However, in Eq. (3.9), it is seen that at least two microscopic parameters are needed to describe the orientational order of a biaxial molecule in a uniaxial medium. Unless the molecule possesses a threefold (C3) symmetry or higher, it is necessary to use S and D to describe its orientational order. These microscopic order parameters cannot be simultaneously determined from a single measurement of a bulk property like Xa/3- If> however, the molecule has a Cs or higher symmetry axis (772 = rjs and D = 0), then Qzz (2n A rj/9x)S ... 

In anisotropic systems there is an intrinsic mechanism which raises the orientational degeneracy by inducing preferred directions for the wavevectors characterizing the structures. e illustrate this property on the rather academic problem of the Turing instability in the Brusselator model in a 2D uniaxial medium (the... 

The nonchiral nematic is optically a positive uniaxial medium. A cholesteric is a nematic with twist. The local structure of a cholesteric is believed to be the same as that of the nematic except that it lacks reflection symmetry. This means that the director and therefore the local extraordinary optic axis is rotating around the helix axis making the cholesteric a negative uniaxial medium with the optic axis coinciding with the twist axis. The question has been asked as to why the nematic with twist could not be biaxial, and attempts have been made to measure a slight biaxiality of the cholesteric phase. In other words, why could the twist not be realized in such a way that the long molecular axis is inclined to the twist axis Why does it have to be perpendicular ... 

This orientational degeneracy is of course raised in anisotropic systems such as in the case of the patterns formed during catalysis at single crystal surfaces [25] or in metals under irradiation [16-18]. The diffusion coefficients of some species are then highest along some crystallographic directions. In a 2D uniaxial medium the reaction-diffusion equations are now ... 

Figure 7.4. Index ellipsoid for a uniaxial medium such as nematic liquid crystal, is the propagation direction [in the y-z plane].

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

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