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Light Propagation in Anisotropic Media
Published in Myeongkyu Lee, Optics for Materials Scientists, 2019
This is the equation of an ellipsoid whose semi-axes parallel to the x, y, and z directions are equal to the principal indices of refraction. The ellipsoid is called the index ellipsoid or the optical indicatrix. The index ellipsoid can be used to find the polarizations and refractive indices of a plane wave traveling along an arbitrary direction k in an anisotropic crystal. The procedure is explained with Figure 6.3. First we draw a plane passing through the origin of the ellipsoid, normal to k. The intersection of this plane with the ellipsoid is an ellipse. The intersection ellipse has two principal axes (long and short axes). These axes are parallel to the directions of two allowed D vectors, denoted as D1 and D2 in Figure 6.3. D1 and D2 are both perpendicular to k. The two polarizations D1 and D2 have refractive indices n1 and n2, respectively, which are the lengths of the principal semi-axes. The wave propagating along k can have its polarization (i.e., the direction of its D vector) only parallel to either of the principal axes of the intersection ellipse. No other D directions are allowed. This restriction vanishes in an isotropic crystal (such as a cubic crystal) where the curve of the intersection becomes a circle due to nx = ny = nz.
Uniaxial Materials and Components
Published in Russell A. Chipman, Wai-Sze Tiffany Lam, Garam Young, Polarized Light and Optical Systems, 2018
Russell A. Chipman, Wai-Sze Tiffany Lam, Garam Young
Understanding the resultant wavefronts and their aberrations aids in finding suitable configurations of optical elements and balancing aberrations. Chapter 19 developed the general method for polarization ray tracing through all types of birefringent materials, including uniaxial materials, where each material is represented by its dielectric tensor. The algorithm allows optical design software to trace rays through general systems of birefringent materials. This chapter presents the index ellipsoid or the optical indicatrix, which represents the dielectric tensor in the shape of an ellipsoid to help visualize the birefringent wavefronts.
Optical Materials for Ultraviolet, Visible, and Infrared
Published in Moriaki Wakaki, Optical Materials and Applications, 2017
Arai Toshihiro, Wakaki Moriaki
The ellipsoid given by this equation is called the refractive index ellipsoid. In the optically uniaxial crystal (ε1 = ε2), the index ellipsoid is formed from a sphere and an ellipse, and it has a rotating symmetry axis as is shown in Figure 2.11. Figures 2.12a and 2.12b show the cross section cut by the plane including the optical axis. As is known from this figure, the light velocity of an extraordinary ray varies depending on the propagating direction of the light.
Low gamma shift blue-phase liquid crystal display with electric field induced multi-domain electrode structure
Published in Liquid Crystals, 2020
Yuqiang Guo, Xiaoshuai Li, Yan Sun, Chi Zhang, Yanling Yang, Hui Zhang, Hongmei Ma, Yubao Sun
BPLC is not the self-luminescent material, while BPLCD can adjust the transmittance of backlight to achieve the different light intensities. Thus, BPLCD is usually regarded as the optical modulator. In voltage-off state, BPLC exhibits isotropic state, and it can be visualised as refractive index sphere. Thus, the excellent dark state can be obtained by adding the crossed polarisers at two sides of BPLC cell. When an appropriate electric field is applied, the BPLC refractive index sphere turns into refractive index ellipsoid, and so the birefringence generates, this phenomenon is called as the electric field induced birefringence effect. In this case, the backlight can pass through BPLCD to realise the bright state. The induced birefringence (Δnind(E)) of BPLC can be described by the extended Kerr equation [43]: