Using both direct mathematical analysis and numerical modeling based on the predictions by Jones  it is shown that if the director in a liquid crystal cell is in a plane which lies at 45° to the incident polarization, then, for normally incident light, the transmission signal which conserves polarization will always have a phase difference of π/2 from the transmission signal of the orthogonal polarization. This is independent of the director profile in the plane, the cell thickness, the anisotropy of the liquid crystal refractive index and the optical parameters of other isotropic layers in the cell. Based on this realization a hybrid aligned nematic liquid crystal cell has been tested as a thresholdless voltage-controlled polarization rotator. By using a quarter-wave plate to compensate for the phase difference between the two orthogonal output polarizations a simple liquid crystal spatial light modulator has been realized.
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