Scattering of proper waves of a generalized double-sided slot waveguide by a slot-width jump

Abstract

1. Nowadays, advances of activity in fundamental science representing the basis of the pioneering technology and also in commerce (a small-scale and largescale business), etc. depend principally on the possibility and ability of gaining and properly processing large and super-large data arrays. This fact implies the urgent necessity in convenient and reliable systems of highperformance data processing [1]. The design of such systems satisfying a variety of requirements for quality, high performance, cost, etc. is impossible without using three-dimensional integrated circuits capable of operating in microwave and extremely high-frequency wave ranges [2]. For solving the problem of designing basis components of three-dimensional integrated circuits (“structural units” of these integrated circuits), it is necessary to have good mathematical models for both transmission lines and various-type heterogeneities in them (basis components). Such models must primarily satisfy the requirement for consistency with the actual physical conditions. Indeed, for example, after a monolithic chip has been fabricated, it is impossible to a designer “manual” refining a ready device. This requirement is well satisfied by the mathematical models for transmission lines and their heterogeneities, which are constructed on the basis of a rigorous electrodynamic approach. (We imply, e.g., the method of partial domains [3‐5], as well as the universal analytical method based on solving singular integral equations with application of the Schwinger transformation [4]). In this paper, we formulate and solve the problem of transmitting a proper electromagnetic wave through a jump of a slot width in a generalized double-sided slot waveguide. The solution is given by both the rigorous electrodynamic method and using the approximate model based on the classical theory of a long transmission line. This is the key problem for three-dimensional integrated circuits operating in the microwave and extremely high-frequency wave ranges. 2. A generalized double-sided slot waveguide pre