How does a twisted-nematic liquid crystal cell rotate polarized light by 90 degrees?

In a twisted-nematic cell, the rotation of polarized light is achieved through the specific structural arrangement of the liquid crystal molecules between two crossed polarizers.12

The cell's substrate plates are coated with an aligning polymer that is rubbed in a single direction. These plates are assembled so that their alignment directions are perpendicular to each other. This forces the liquid crystal molecules to adopt a smooth, 90-degree twisted configuration across the gap between the plates.12

When light passes through the first polarizer, its polarization becomes aligned with the liquid crystal molecules at the bottom of the cell. As the light travels through the layer, the twisted structure of the liquid crystal acts as a waveguide, gradually rotating the polarization of the light along with the molecular twist. By the time the light reaches the top of the layer, its polarization has been rotated by 90 degrees, matching the orientation of the second (top) polarizer and allowing the light to pass through the assembly. Applying an electric field destroys this twist, preventing the rotation and causing the cell to appear dark.21