Dielectric permittivity and refractive index

When an electric field is applied to a liquid crystal, it will induce dipole moments in the liquid crystal. For a uniaxial hquid crystal, the molecule can be regarded as a cylinder, and it has different molecular polarizabihties along and perpendicular to the long molecular axis a. Similar 

In order to illustrate the principle, let us first consider an isotropic medium. The cavity can be regarded as a sphere. The field is produced by the dipole moment inside the sphere, which can be calculated in the following way. In the calculation of the field, the dipole moment can be replaced by the surface charge produced by the dipole moment on the surface of the sphere. The 

1 -Na/3Eo 1 -Na/3Eo where the defined AT = 1/(1 -NuBeo) is called the internal field constant. 

Liquid crystals are anisotropic. In them the local field Eiocai depends on the macroscopic field 

E as well as the angles between E and the long molecular axis a and the liquid crystal director n. They are related to each other by 

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