Creation of circular polarization by a twisted birefringent polarizing medium

We consider the passage of initially unpolarized light through a medium possessing both birefringence and differential attenuation with respect to the same pair of perpendicular axes. Circular polarization is produced if the axes undergo rotation as the light path progresses. The twisting rate that maximizes $N_2$ (the circular Stokes parameter) is found to be an elliptic function with modulus depending on the path length. Various limits are discussed, and the maximized $N_2$ is tabulated and graphed against path length for several ratios of birefringence to differential attenuation. These results are pertinent to the polarization of hard x rays by a slightly tilted crystal.