Refractive indices extraordinary

Fig. 1. (a) Phase matched second harmonic generation (2cJ = 0.49 fiTo) at cj = 0.98 where = refractive index by ordinary rays and = by extraordinary rays, (b) Hypothetical anomalous dispersion phase matching at 850 nm in similar a crystal having a Lorent2ian absorption centered at 650... 

Note 2 In the case of a short pitch, when P is less than the wavelength X, the macroscopic extraordinary axis for the refractive index is orthogonal to the director. 

Note 1 The nematic liquid crystal must have a negative dielectric anisotropy (Af < 0), and a positive anisotropy (Aa > 0). The optical texture corresponding to the flow pattern consists of a set of regularly spaced, black and white stripes perpendicular to the initial direction of the director. These stripes are caused by the periodicity of the change in the refractive index for the extraordinary ray due to variations in the director orientation. 

Ellipsometiy is unrivaled for the measurement of the properties of thin films, particularly those on electrodes in solution. It has extraordinary sensitivity and can measure films from submonolayers up to films having a thickness near to that of the wavelength of the light incident upon the electrode surface. Moreover, ellipsometiy gives not only the thickness of the film but also its refractive index and, in the case of conducting films, the absorption coefficient. 

According to the helical structure, the cholesteric phase (n ) is optically uniaxial negative, where the ordinary refractive index n0 nt is larger than the extraordinary... 

Figure 6. The guided mode dispersion curves for a birefringent film and an optically isotropic substrate. Both the fundamental and harmonic curves are shown. The TE mode utilizes the ordinary refractive index and TM primarily the extraordinary index. Note the change in horizontal axis needed to plot both the fundamental and harmonic dispersion curves. Phase-matching of the TEq(co) to the TMo(2o>) is obtained at the intersection of the appropriate fundamental and harmonic curves.

LiI03 is called a negative crystal, because the extraordinary refractive index is smaller than the ordinary one ne - n0 = 1.78 - 1.93 < 0 (values for 514.5 nm). When the scattering geometry is chosen in such a way that the incident light is an extraordinary ray, a greater polariton shift is obtained because smaller k values can be realized, as in the case of ZnO. 

For optically uniaxial crystals we know that the refractive index values for extraordinary waves are variable, with that for ordinary waves fixed. We can link this observation with that concerning the vibration directions for the two waves travelling along a general wave normal direction the ordinary vibration direction is always perpendicular to the optic axis, while the extraordinary vibration is always in the plane containing the optic axis and wave normal direction. This suggests that we may connect the variation of the refractive index in the crystal with the vibration direction of the light. This concept allows a convenient representation of anisotropic optical properties in the form of a spatial plot of the variation of refractive index as a function of vibration direction. Such a surface is known as the optical indicatrix. 

Those rays, e.g. SE, for which the electric displacement component lies in the principal section travel at a speed which depends on direction they are the extraordinary or e rays. The refractive index ne for an e ray propagating along SX is one of the two principal refractive indices of a uniaxial crystal the other, n0, refers to the o rays. 

The direction of the principal axes of the index of refraction tensor n can be described by the indicatrix. For isotropic crystals the indicatrix is a sphere. For positive uniaxial crystals it is a prolate spheroid (ns > n0j) for negative uniaxial crystals it is an oblate spheroid (nol > n,). For orientations away from the principal axis orientations, the extraordinary ray will have a refractive index h - intermediate between nm and ne. 

Figure 2.7 The refractive index ellipsoid of a uniaxial liquid crystal phase with the optical axis parallel to ihe x-axis. The refractive index, no, of the ordinary ray is independent of the direction of propagation. The refractive index, ng, of the extraordinary ray is larger than n if the liquid crystalline phase is of positive birefringence. ...

Figure 2.8 The dependence of the refractive indices, n and ng, of the ordinary and extraordinary rays, respectively, on the temperature, T.for a typical nematic liquid crystal. Above the clearing point, Tg, there is no birefringence and only one refractive index,is observed. ...

The use of birefringence to determine the behavior of 5( 7) is a natural choice since the principal characteristic of the nematic phase is optical birefringence i.e., the refractive index differs for light polarized parallel (/ n) or perpendicular (%) to the axis of molecular alignment. Eor a nematic liquid crystal, the director n specifies this optical z axis and / n = and = Dg are called the extraordinary and ordinary refractive indices, respectively. In general, rig > rig and the difference is the refractive index anisotropy (birefringence)... 

Figure 4.6-5 Infrared linear dichroism of a nematic sample (EBBA/MBBA equimolar mixture of N-(p-ethoxybenzylidene)-//- -butylaniline and its methoxy analogue 2 of Table 4.6-1 Riedel-de Haen) expressed as the difference of the absorption indices k and ke (imaginary part of the complex refractive index) for the ordinary and the extraordinary beam, resp. the temperature increases and thus, the degree of order decreases from spectrum a to spectrum d, the latter was taken close to the clearing point F, where the order and consequently the anisotropy vanishes (Reins et al., 1993).

In a uniaxial crystal, for any light traveling along c (vibrating in any direction perpendicular to its propagation direction) there is only one refractive index and therefore only one image. The extraordinary... 

Birefringence The difference between the refractive index for the extraordinary and ordinary rays (he — no) in a uniaxial or biaxial crystal. If a crystal, such as quartz, is positively birefringent, no is less than ns, and the velocity of the ordinary-ray is greater than that of the extraordinary ray. The reverse is true for a negatively birefringent crystal. 

Figure 18. Refractive index dispersion in evaporated thin films of pure (triangles), monosubstitued (circles) and disubstitued fumrot (squares) (cf. Fig. 10). Full figures show ordinary whereas the open the extraordinary index of refraction, respectively. Solid lines are Sellmeier fits...

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