Effects of non-periodic variations in periodic RF structures

Summary form only given. The theory of perfectly periodic RF structures has been extensively developed, motivated largely by the many applications, some of which are millimeter wave radiation sources, amplifiers, and slow-wave circuits. Of course, the realization of a periodic structure is never perfect, due to fabrication tolerances and variations in material properties from cell to cell. Such differences among cells may also be intentionally introduced in order to tailor the structure properties for a specific application. In the perfectly periodic case, the geometry and composition of a single cell determines the dispersive and other electromagnetic properties of the structure; these properties are also affected by the properties of the terminations, for structures of finite length. In this paper we present a theory that describes non-periodic perturbations in periodic RF structures. Departures from periodicity change the local impedances, which results in phase shift variations and reflections experienced by a wave as it traverses an imperfect cell. For small perturbations the accumulated phase errors are dominating and produce spatial modulation of the field. If the perturbations are large the structure modes become localized. The phenomenon is similar to Anderson, also known as strong, localization. Our analytical results compare favorably with a 3D finite element code in an example of a periodic circuit designed for a 670 GHz extended interaction klystron. In an ancillary result we document a limitation of finite element codes when applied to long periodic structures. Our results are applicable to both random structural variations and non-random geometry modifications. Our techniques can be used to help specify fabrication tolerances, which are especially critical for millimeter and submillimeter-wave structures and applications.