           ! ""# $ INTERACTION OF EIGENWAVES OF THE INSULATED IMAGE DIELECTRIC WAVEGUIDE WITH SYSTEM OF TRANSVERSE SLOTS IN THE SCREEN Mayboroda D.V., Pogarsky S.A. and Saprykin I.I. Karazin Kharkiv National University, Kharkiv, Ukraine E-mail: Sergey.A.Pogarsky@univer.kharkov.ua Abstract The present work is devoted to the generalisation of operator approach for the solv- ing electromagnetic waves diffraction problems by periodic systems of discontinuities (such transverse slot) in hybrid metal-dielectric structures. The diffraction problem solu- tion of single eigenwave of the hybrid metal-dielectric structure by bounded periodical slot sequences in the metal has been presented. The approach based on the using of semi-infinite periodical structures conception. On the first stage the reflection and propagation coefficients of single slot was found. On the second stage the reflection and propagation coefficients of the semi-infinite sequences of identical discontinuities was found. On the third stage the electrodynamical characteristics of the bounded sequence of identical slot discontinuities was found. By the numerical simulation the dependen- cies 11 S and 12 S of the structure with single slot and bounded sequences arranged equidistantly was founded. The pattern characteristics are presented. Keywords:, transverse slot, eigenwave, diffraction problem. 1. INTRODUCTION At present day in the antenna techniques the radiating structures which are based on various combinations of elements and guides are widely applied. One of such combinations is the hybrid metal-dielectric structure (HMDS) on the basis of the insulated dielectric wave guide (IDW) and slot radiators. Simplicity, rather small dimensions and weight concerns advantages of such antenna systems. The particular interest to HMDS, which combine pe- riodic sequences of the discontinuities various type (strip, slots, etc.) has detected. It is caused by a number of the important practical applies such as: antennas of leaky waves [1,2], frequency-selective devices [3] and a number of others. Antennas and antenna gratings on the basis of HMDS are difficult for theoretical electrodynamic analysis. There are a number of factors which cause complexity of a problem by the description of hybrid structures. The main from them are: necessity of con- sideration of three-dimensional structures; impossibility of use various asymptotic methods, which are correctly at the big or small length of waves in comparison with the linear sizes of radiators; necessity of the account of characteristics of fields near radiator edges; complexity of eigenwave spectrum in a basic line. The comprehensive information on characteristics of such systems can be received, using numerically- analytical methods of applied electrodynamics. Taking into account multiparametric of problems, the algo- rithms of calculation even the single slot radiators based on rigorous methods are very difficult, lengthy and, besides, there are difficulties of basic character, for example because of absence now a rigorous analyti- cal method for the decision of a problem diffraction by waves rectangular slot of the finite sizes. Therefore to use rigorous methods for the decision of slot antenna or problem of slot gratings, as a rule, either it is not obvi- ously possible, or it appears not reasonable because of lengthy algorithm and time-taking of procedure even with use of modern computer. The present work is devoted to the generalisation of operator approach [4] for the solving electromagnetic waves diffraction problems by periodic systems of dis- continuities (such transverse slot) in hybrid metal- dielectric structures. 2. FORMULATION AND DECISION PROBLEM Let's consider a problem of diffraction of one of eigen- waves of the metal-dielectric structure which is pre- sented in Fig. 1, by the bounded sequence of the trans- verse slots placed equidistantly in the metallized screen. The problem solves in a single mode approach. The approach based on the using of semi-infinite peri- odical structures conception in some stages.