Birefringence

The term, birefringence, is an optical property exhibited by anisotropic material where the refractive index is determined by both the polarisation and the propagation direction of light, incident on the materials interface. Birefringence, arising naturally in anisotropic, or birefractive materials, can be described using the simplest case, uniaxial anisotropy, meaning that the crystal has an axis of symmetry with all perpendicular directions and can be described by the tetragonal, hexangonal and trigonal crystal lattices

uniaxial anisotropic

This optical axis of a crystal is the axis in which a beam of light does not undergo birefringence effects. In other words, light behaves differently when propagation is along, or parallel, with the optical axis than in any other directions. Plane polarized light with its vibration direction parallel with this axis is called the ordinary ray, whilst that ray vibrating perpendicular is called the extraordinary ray. In both directions, the refractive indices are no and ne, respectively.

If random polarized light is incident on the anisotropic interface at some angle of incidence θi,the beam will split into two components, one perpendicular to the other. The component parallel with the optical axis is called the ordinary ray, which refracts into the medium with accordance to Snell’s law. This index of refraction is this termed as the ordinary refractive index no, whilst the component parallel with the optical axis is known as the extraordinary ray, which refracts at a slightly different angle which depends on the angle θ between the orientation of the optical axis and the angle of incidence θi.

The uniaxial anisotropic crystals, above, can be described by modelling the atomic bonds as springs, such that in one plane, the atoms are connected to one another by loosely damped springs, whilst in the orthogonal direction, they are connected by higher damped springs. Electrons, when driven by an incoming electric field vector E, of an electromagnetic field, will vibrate with a different characteristic frequency ω, than those in the perpendicular plane. In summary, an electromagnetic field propagates through a material by the excitation of its constituent atoms along the direction of travel. Thus, the atoms, according to Huygen’s principle, can be considered as sources of secondary wave fronts, and the resultant wave continues to advance onward. The stiffness of the springs determine the refractive index in a particular direction. The greater the electronic binding force (spring stiffness), therefore the higher the natural frequency ω of the electrons in this plane and the lower the value of refractive index in this direction . The graphical plot below illustrates an example of such phenomena, showing …………………

[Insert dispersion curves (refractive index vs freq) img for birefractive material]

To be continued…..

 

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