A dynamical system approach for multilayer dielectric slabs reflection and transmission coefficients calculation

An efficient method for evaluating the total transmission and reflection coefficients of multilayer slabs and planar radomes is presented. The proposed approach models multiple internal reflections using a simple dynamical system feedback framework, representing the interactions within the layers through a feedback loop mechanism. This formulation utilizes basic knowledge of dynamical feedback analysis and the well-known Fresnel transmission and reflection coefficients, thereby eliminating the need for series expansions or transmission-line–based input impedance calculations. The resulting approach closed-form solution can be easily cascaded to an arbitrary number of layers. Numerical benchmarking against commercial electromagnetic solvers is conducted to validate the accuracy of the approach. Owing to its closed-form nature, the method offers high computational efficiency and is particularly well suited for fast analysis and design of multi-dielectric structures such as planar antenna radomes. A simple planar radome design example is included to demonstrate the effectiveness of the method.