Alternating-Gradient Focusing and Related Properties of Conventional Convergent Lens Focusing

Abstract

A series of lenses whose focusing properties are alternately convergent and divergent (alternating-gradient focusing) is of potential interest in the guidance of light waves, and has previously been used to focus electron beams and high-energy particle streams. New information is provided herein on such focusing for the case of equal focal length f (but alternating-gradient) lenses equally spaced a distance L. The alternating-gradient system formed by adding diverging lenses between the lenses of an all-converging sequence of lenses is found to have the same stability condition as the original system for 0 < L/f < 2. A physical argument leads to the conclusion that weaker divergent lenses would also leave the stability criterion unchanged. The focusing effect of the alternating-gradient system is surprisingly close to that of an all-converging lens system. After the focal length of each has been adjusted to an optimum value, the ray departure from the system axis is only 1.67 times as great for the alternating-gradient system as for an all-convergent lens system with the same spacing of convergent lenses. For weak lenses (i.e. 2f/L ≫ 1) the output ray departure due to input ray displacement is independent of both the focal length and spacing of the lenses, and is independent of lens spacing but proportional to focal length for input ray slope. Both the alternating-gradient system and all-convergent lens focusing arrangements exhibit discontinuities in the maximum ray displacement versus focal strength relation. Viewed over-all, alternating-gradient focusing for light guidance does a surprisingly efficient job and may be advantageous over all-convergent lens systems if the alternating-gradient arrangement has structural or economic advantages.