Explicit Jones transformation matrix for a tilted birefringent plate with its optic axis parallel to the plate surface

It is shown that, for a tilted birefringent plate (BP) with its optic axis parallel to the plate surface, an explicit Jones transformation matrix can be derived without neglecting the birefringent splitting.Differences in calculating the desired thickness(es) of a BP by use of different formulas of phase difference between ordinary and extraordinary waves are also presented.