The wonders of anisotropy

Birefringent materials have two main orthogonal axes of symmetry along which the index of refraction differs. When a wave of light passes through a material like this, one part of it is phase shifted from the other so we can achieve different sorts of polarizations.

We align a birefringent material such that the axis with a lower index of refraction is along the x-axis and the axis with a higher index of refraction is along the y-axis. We shine onto the crystal a plane wave of light traveling along the z-axis and polarized at an angle \(\theta\) with respect to the x-axis.

How long should the sample of the birefringent material be in micrometers in order for the polarization of the input light to be rotated to where it makes an angle of \(-\theta\) with the x-axis?

Details and assumptions

  • Input light is green, i.e. its wavelength is \(510~\mbox{nm}\)
  • The difference between the refraction indexes is \(0.001\)

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