Birefringent crystals

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

Comparison of these two polarizations shows that P2 Pi- Hence, in an isotropic medium such as a gas or a liquid x " = 0 and second order phenomena are not observable. Thus, only anisotropic media such as certain crystals are suitable for three-wave mixing processes. A consequence of a crystal being anisotropic is that it exhibits birefringence. However, the crystal birefringence enables phase matching to be achieved resulting in efficient generation of the new wave. 

Retardation (delta) is the distance that the slow light ray lags behind the fast ray and is directly related to crystal birefringence and thickness. In other words. 

FIGURE 2.2 Examples of liquid crystal birefringence textures imaged at lOOX magnification (a) a homeotropic texture of a columnar phase and (b) "fingerprint" texture of the cholesteric phase growing in from the isotropic liquid phase (black regions). 

Schlieren texture A planar liquid crystal birefringence texture characterized by dark brushes. ... 

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