Stability of astigmatic and twisted optical lensguides

We study theoretically the stability problem of ray and wave propagation in a general astigmatic and twisted paraxial optical lensguide obtained by successive rotations of a basic astigmatic optical system around its paraxial optical axis. A generalized stability condition in terms of the ray matrix elements of the basic astigmatic optical system and twist rotation angle is derived in a closed form. It is shown that, for stable (unstable) astigmatic lensguides, the introduction of the twist generally leads to the appearance of a region of ray instability (ray stability) within a finite range of twist angle due to non-orthogonal effects induced by the twist. The general theory is applied to the noteworthy continuous limit of ray and wave propagation in a twisted astigmatic graded-index optical fiber.