Physical Limitations on Ray Oscillation Suppressors

Light transmission systems can be built in various ways. A continuous dielectric medium of rotational symmetry with an index of refraction which depends on the distance r from the optical axis n = n(r) is capable of guiding light rays if n(r) decreases monotonically with increasing r. Another example is the beam-waveguide consisting of a series of lenses which refocuses the light beam periodically counteracting diffraction. Both of these examples have one point in common -- a ray which is launched off-axis into the waveguide follows an oscillatory trajectory. However, even if a light ray travels on-axis it will be forced into an oscillatory trajectory by any imperfection of the guidance medium. 1 To 743 744 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , M A Y - J U N E 19G6 keep the ray amplitudes small requires a veiy high precision of alignment which might be hard to obtain for long waveguides. It seemed natural, therefore, to consider means of suppressing these ray oscillations, and if all such efforts fail, to ask for a general physical principle which says that such ray oscillation suppressors are impossible. The search for such a general principle is even more important as it is easy to construct models of beam waveguides which violate physical principles in subtle ways thus seeming to lead to ray oscillation suppressors. One such system is shown in Fig. 1. Assume that we deform thin lenses as indicated in the figure and assume further that these lenses behave just like plane thin lenses in that they break each ray by an amount /3,, which depends only on the radius r,, of the ray but not on the input angle.