**Time-Domain Electromagnetic Wave Propagation in Confined Environments**

Jorge Avella-Castiblanco, Divitha Seetharamdoo, Marion Berbineau, Michel Ney, Ibrahim Massy and Franois Gallée 1∗ 1 1 2 2 2

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### **Abstract**

Confined environments like tunnels are electrically large structures for guided wave propagation. They can have arbitrary cross sections, and the design and optimization of antenna for communication system requires the knowledge of a "full-wave" solution in nearby zones. Current models based on asymptotic approaches do not describe adequately the wave propagation under the above conditions. In addition, a complete "full-wave" analysis of the tunnel propagation performances is not feasible in terms of computer expenditure. After a survey of the most commonly used techniques for propagation in tunnels, some investigation regarding an appropriate approach to find the fields is proposed. It is based on a modal decomposition of the wave propagation that allows an optimization of the coupling with the antenna. To find the mode characteristic for arbitrary cross section, a full-wave method, namely, the transmission-line matrix (TLM), is modified to a so-called 2.5-dimensional TLM algorithm and presented in details. This approach is validated for a canonical structure. Then, it is applied to study the wave propagation in a realistic rectangular tunnel. The concept of surface impedance boundary condition (SIBC) is introduced to reduce the TLM computational domain and model the tunnel walls that can be considered as lossy dielectric. Results show that guided structures with lossy dielectric walls of arbitrary cross section can be studied with this approach.

**Keywords**: wave propagation, wave-guides, Transmission Line Matrix Method, arbitrary cross-section wave-guides, dielectric waveguides, Modes
