Birefringence material

Figure 11. (a) An image (b) appears to be doubled when viewed through a birefringent material. 

As will be discussed further in Chapter 2, this is an example of a birefringent material, with birefringence, A = hv Clearly, two other birefringences, An and... 

Equation (2.52) satisfies the requirement that the ordering of the lamellae will not affect the final result. Furthermore, the differential propagation Jones matrix for a composite material is simply the sum of the matrices, N., for each of the separate optical effects. The N matrices for different optical properties can be derived using equation (2.44). As an example, consider a birefringent material with retardation S = (InAn z) /X. One form of the Jones matrix for this material is... 

Figure 5.8 The Raman scattering process in a birefringent material.

From Eq. (8.40), because the intensity is inversely proportional to (nx— n2)2, the efficient production of SHG radiation in a crystal of appreciable thickness requires the matching of nl and n2. In certain birefringent materials it is possible to choose a direction of propagation such that the refractive indices of the ordinary and extraordinary rays are equal. This is possible in, for example, the crystal potassium dihydrogen phosphate (KDP). 

Solution For weakly birefringent materials A and B, Table P.9.e gives the free energy of interaction with respect to infinite separation in the form... 

Ordinary refractive index of birefringent material X Wavelength... 

The high calcium content in the majolica found in Mexico City— 21.4% calculated as pure calcium carbonate compared with 5.9% in sherds of Teotihuacan—suggests that a calcium compound such as calcium or calcium magnesium carbonate may have been added to the majolica either as a temper or through deposition during burial. Petrographic examination of cross sections of representative Mexico City majolica sherds show heavy deposits of birefringent material with structures... 

After passage through a birefringent material of thickness e, the two components of linearly polarized light show a phase difference 6 equal to ... 

Fig. 9. Drawing showing how a phase difference between Ey and Ez arises in a birefringent material. In this diagram nz > ny...

The anisotropy of the optical properties in the wavelength range of visible light is generally described by the birefringence An, defined by the first part of Equation 8.12. A birefringent material has different refractive indices in two different principal axis directions. For a specimen that is under uniaxial tension, nn and n denote the refractive indices parallel and perpendicular to the orientation direction, respectively. The second part of Equation 8.12 defines the stress-optic coefficient C0 describing the dependence of An on the applied stress. 

Note A birefringent material has two or even three optical axes, which causes the refractive index to vary with the direction of the wave vector of the polarized light. 

By contrast with the transmission case, where the phase difference induced by birefringent materials is smooth and progressive, the phase and amplitude changes of the p and s components induced by reflection at a boundary between two materials are discontinuous. Figure 2 shows the effect of these stepwise changes on the polarization of light obliquely incident on a metallic mirror. 

Carbon is found free in nature in three allotropic forms amorphous, graphite, and diamond. A fourth form, known as white carbon, is now thought to exist. Ceraphite is one of the softest known materials, while diamond is one of the hardest. White carbon is a transparent birefringent material. Little information is presently available about this allotrope. 

Using the Fresnel coefficients of stratified surfaces, the theoretical angles S and A can be calculated of a surface, whether it consists of a single homogeneous material, a birefringent material, or a combination of absorbing and transparent coatings on a surface. 

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