Birefringent filters for tuning flashlamp-pumped dye lasers: simplified theory and design

The theory of a birefringent filter in a laser cavity simplifies when the Jones matrix of a tilted birefringent plate is reduced to its most fundamental form. Theorems relating to stacks of plates are deduced. For example, certain periodic stacks are shown to have no secondary peaks. Approximate expressions are derived for the important parameters of the filters. Designs with maximum tuning range and minimum total number of plates are achieved by tailoring the secondary peaks to meet the inverse of the laser gain curve.