Anisotropic materials, polarized light

The analyzer is removed and the color of the sample is observed in plane-polarized light. If the sample is colored, the stage is rotated. Colored, anisotropic materials may show pleochroism—a change in color or hue when the orientation with respect to the vibration direction of the polarizer is changed. Any pleochroism should be noted and recorded. 

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. 

Circular birefringence will induce a differential retardation in the phase of the orthogonal states of circularly polarized light. Circular dichroism, on the other hand, results in anisotropic attenuation of left- and right-circularly polarized light. The Jones matrix of circularly dichroic materials is normally written as ... 

Refractive index is dimensionless. For anisotropic materials the state of polarization of the light (and its direction, where appropriate) must be defined relative to a reference axis in the sample. It is then customary to quote two refractive indices additionally, the maximum difference between the two indices measured in two mutually perpendicular directions is termed the birefringence of the material. 

---