Multislice Approach to Lens Analysis

Abstract

This chapter presents a multislice approach to lens analysis. The standard multislice approach is used to analyze electromagnetic cyclindrical lenses from the wave optical standpoint. It is shown how the results obtained by Storbeck are recovered without any modification of the basic equations. It is also shown how Aharonov–Bohm effects are framed quite naturally in this formulation. The shortcomings arising in the analysis of round symmetric electromagnetic lenses are analyzed, where it is shown how to implement the basic equations to obtain the correct results. The propagation of general spherical waves within a thick electromagnetic lens is investigated, as a first step toward a general theory of image formation. The analogy between electron and light optics is employed to discuss improved beam propagation method (BPM) equations and to study the propagation of a Gaussian beam in an integrated optic lens. It is shown that this approach removes an inconsistency pointed out by Gribble and Arnold between the predictions of standard BPM and those of geometrical optics. The chapter also presents an extension of the phase-object approximation that is able to encompass the problem of lens aberrations. The case of spherical aberration is discussed, and it is shown in the chapter that the same results are recovered as those predicted by the geometric optical analysis.