Refractive index ordinary dispersion

The velocity of light is decreased when it passes from a vacuum into a medium, and the amount of slowing depends on the properties of the medium and specifically on the interaction of light with the transition dipole moments of the medium. This effect is expressed in terms of the refractive index, n. 

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Birefridgence may be observed with optically anisotropic particles of dispersed phase as well as with optically isotropic but anisometric particles, whose refractive index, n, is different from the refractive index of the medium, n0. One can reveal these two components of birefringence by varying the refractive index of dispersion medium. The own double refraction of particles, characterized by the difference in the refractive indexes of extraordinary, nE, and ordinary, nm, beams, is independent of the refractive index of medium and is maintained when particles are placed into the medium with the same refractive index. For optically isotropic but anisometric particles undergoing co-orientation in the flow, the double refraction, nE - nm, is proportional to (n2 - n20)2. The proportionality constant is positive for rod-like particles and negative for plate-like ones. In the case of particles that are both optically anisotropic and anisometric these effects are additive. 

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... 

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.

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...

Optical rotation is a general term which is used to include both circular dichroism and optical rotatory dispersion. These are closely related phenomena in the same way that absorption and ordinary dispersion (refractive index) are related. They can be interconverted by mathematical transforms. Whereas the common element in absorption and ordinary dispersion is the dipole strength of the transition, the common quantity in circular dichroism and optical rotatory dispersion is rotational strength. And, as will be seen below, the rotational strength of a transition may be obtained from either measurement. 

In the Talbot-Rayleigh interferometer developed by Warenghem et al. [55, 56], the planar-oriented nematic cell is inserted in the focal plane of an ordinary spectroscope that covers only half of the field of polychromatic light. In this way dark bands (Talbot bands) appear due to the interference between the upper and the lower part of the beam. The position of the bands is correlated with the phase retardation (and, therefore, with the refractive index) induced by the nematic layer. By means of a proper spectrum analysis, dispersion curves of n and can also be determined. 

The absolute index for all ordinary transparent substances is greater than 1 (see Table 1) but there are some special cases (X-rays and light in metal films, which are discussed below) for which the index of refraction is less than unity. Since the absolute index for air exceeds unity by less than 0.0003, the relative indices for solids and liquids in air are very nearly equal to their absolute indices. It should be noted that since the refractive mdex vanes with the wavelength, any exact statement of its value must specify the wavelength to which it refers in Tables it is usually given for sodium light of frequency 5.893A. See also Dispersion. 

Phase-matching in dispersive media can be fulfilled in birefringent crystals which have two different refractive indices n, and n for the ordinary and the extraordinary waves. While the ordinary index n, does not depend on the propagation direction, the extraordinary index n depends on both the directions of E and k. The refractive indices can be illustrated by the index ellipsoid defined by the three principal axes of the dielectric susceptibility tensor. If these axes are aligned with the x, y, z axes we obtain the index ellipsoid. 

Figure 3.27 (a) The ordinary and extraordinary refractive indices of Mg i nO films (x = 0, 0.24, and 0.36). The solid curves are least-square fits to the first-order Sellmeier dispersion. The index of refraction of cubic MgO crystal measured by Stephens and Malitson [17 is... 

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