Keynote speaker 4: A new transformation solution to Sommerfeld integrals & analytical removal of Gibbs phenomena for multilayered media

The wave propagation in a multilayered medium has been an important topic since the last century and can find many practical and useful applications in realistic engineering applications. In this talk, multilayered media of planar stratified and spherically multilayered structures are re-visited and the general solutions are obtained for general applications to microstrip antennas and arrays radiation in the multilayered structures. Associated with the spherical and planar structures, the Gibbs phenomena are again looked into, and analytic removal of such phenomena has been proposed and its implementation is conducted. Associated with the new solution, the fields and waves in multilayered spherical structures are formulated and their solutions are obtained in close form. Using the transformation electromagnetics approach, the waves and fields in planar stratified multilayers are obtained in series form, where the Sommerfeld integrals occurring in the planar multilayers can be avoided and accurate and rigorous solutions are obtained in explicit form. In the analysis, some numerical examples are obtained and comparison results are obtained to check the validity and accuracy. The new solution procedure serves as an alternative approach for evaluating the Sommerfeld integrals, for validating these approximate solutions from some well-known numerical approaches such as steepest saddle-point method, branch cut method and curve fitting approximations, and for setting a unified solution to the same problem of where various different solutions exist in literature.