PRECISE AND VERSATILE FORMULA FOR BIREFRINGENT FILTERS

In an investigation of extraordinary- (E-) ray behavior and the index of refraction for E waves in a uniaxial crystal, a precise and versati le formula for birefringent filters, based on the exact construction o f the optical path difference, is set up with neither the approximatio n Delta n = n(o) - n(e) less than or equal to n(e) (or n(2)), nor the ambiguity sin(theta)/sin(r(w)) = n(e). The exact construction gives th e correct variation of the position and the dimension in each path, yi elding the path difference while the filter is tuning. The formula is applicable not only to a filter with its optical axis parallel to the entrance surface (FAPS) but also to a filter with its axis inclined to the surface (FATS). Also, the formula indicates that a FATS allows la ser wavelengths to be tuned over a wider range than does a FAPS. The o rigin of the wider range is interpreted to be the greater Variation in the index for the FAIS while the filter is tuning. With the help of t he formula we design a FAIS for tuning a cw Ti:sapphire laser.