Extraordinary index

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.

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

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...

Due to the linear profile of 9(z) it is very easy to calculate the phase retardation of the initially homeotropic cell for the normal light incidence, kHz. Without electric field, the longest axis of the dielectric ellipsoid coincides with the director axis z. Therefore, refraction index for any polarization is o = With increasing field E, due to deflection of the director within plane xz, the y- and -components of the refraction index will correspond to the ordinary and extraordinary rays, Uy = no = n , rix(z) = rig(z). Integration provides us with the average extraordinary index ... 

In the Si02 coated cell the molecules were oriented with their long axis along the surface of the coated electrodes in the plane of incidence. As shown in Fig. 6, the reflectivity minimum is now at 18. Assuming the ordinary refractive index oriented perpendicularly to the surface, we calculated the extraordinary index to be 1.742, very close to TFE case, but now oriented 90 from it. 

Birefringence In an optically anisotropic medium with axial symmetry, the difference between the refractive index for light polarized parallel to the symmetry axis (extraordinary index) and that for light polarized perpendicular to the axis (ordinary index). 

Because the extraordinary index is, in general, more temperature dependent than the ordinary index, one can adjust the birefringence of the crystal by varying the temperature, until phase matching is obtained. However, as already stated above, the B = 90° condition can only be achieved for a relatively narrow range of frequencies. 

This condition can be fulfilled in unaxial birefringent crystals that have two different refractive indices no and n for the ordinary and the extraordinary waves. The ordinary wave is polarized in the x-y-plane perpendicular to the optical axis, while the extraordinary wave has its -vector in a plane defined by the optical axis and the incident beam. While the ordinary index no does not depend on the propagation direction, the extraordinary index n depends on the directions of both E and k. The refractive indices Uo, and their dependence on the propagation direction in uniaxial birefringent crystals can be illustrated by the index ellipsoid defined by the three principal axes of the dielectric tensor. If these axes are aligned with the jc-, y-, z-axes, we obtain with n = the index ellipsoid. 

As predicted by Eq. 4, one would expect to see a poling-induced birefringence in the refractive index. In fact, this difference between the two refractive indices (ordinary index and extraordinary index n ) can be measured. Figure 3 shows the example of a poled DANS side-chain polymer, where the indices have been measured using m-line spectroscopy with a grating coupler. The diagram also reveals a wavelength dependence of the indices, an effect that will be further discussed in Section II.E. 

Because the voltage on the electrodes is designed to change as the square of the distance from the center of the lens device, a square change in the LC index of refraction occurs if the LC is operated in the linear portion of its characteristic curve. Figure 5.5 illustrates LC molecules in their rotated positions as results of the different voltage levels generated by the resistor bias network in the device, n represents the extraordinary index of refraction of the LC material, is the ordinary index of refraction, and dn = > 0 is... 

This is the refractive index experienced by the electric vector of the light that has a component along the director, and is called extraordinary index. 

This condition 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 ng does not depend on the propagation direction the extraordinary index n depends on both the directions of E and k. 

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