Berreman 4×4 matrix method for reflective liquid crystal displays

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Abstract
The Berreman 4×4 matrix method is extended in order to calculate the optical behavior of reflective liquid crystal displays. Expressions for the reflection matrix and the reflection coefficient are derived. Possibly present uniaxial and/or biaxial retarders can be included in the calculation. Conservation of energy and time reversal invariance of Maxwell’s laws imply an important symmetry relation. This relation is used to reduce the computational time with a factor of 2. The new numerical method is illustrated by calculations of a direct-view twisted nematic effect, without and with a compensating biaxial retarder.