The speed of light in Birefringent material depends on the direction of oscillation (polarization) of the electric field vector in relation to the symmetry axis of the crystal (called the optic axis).

When the electric field vector is in the same direction as the optic axis, the light advance at certain speed. When the electric field vector is perpendicular to the optic axis, the velocity of light in the material is different.

When light enter such crystal the electric field vector is at certain angle to the optic axis. It is possible to separate the electric field vector into two perpendicular components, which advance through the material at different speeds.

When the light exit the crystal, these two components combines to create the electric field vector, which can have a different direction of polarization than the original electric field vector.

Conclusion:

It is possible to use Birefringent crystal to change the direction of polarization of light.

Linear polarized light is changed to elliptical polarized light by passing through Birefringent crystal.

There are many applications for Birefringent crystals, and usually a plate is used with a specific width.

At the entrance to the plate light is separated to its polarization components.

Each of the components travel at different speed, and they unite again when exiting the plate.

The specific width of the plate create a turn of the direction of polarization at specific angle.