Iterative Tree Algorithm to Evaluate Terahertz Signal Contribution of Specific Optical Paths Within Multilayered Materials

Terahertz time-domain spectroscopy is a specifically appropriated technique to analyze layered structure composition and dimension. Inverse electromagnetic problems are commonly solved to extract, from a recorded terahertz-signal, the distinctive layer dielectric properties and thicknesses. However, main origins and formation routes of the signal are left unassessed while it could be of great value to deepen and to enlarge stratified material terahertz-probing property knowledge and understanding. In this article, a new numerical method to reconstruct and to analyze terahertz experimental signals is reported. It consists of an iterative algorithm implementing a connected propagation tree where each node of the tree denotes the occurrence of the incident pulse division. Descendent pulses are individually monitored and their carried proportion of the incident power can be evaluated. Therefore, it provides a flowchart of the predominant optical paths contributing to the structure response. On this basis, a simplified global transfer function is automatically derived by the algorithm. The effectiveness of the numerical procedure is demonstrated through the reconstruction and the analysis of a reflected terahertz-signal from an aerospace coating structure with individual and different thicknesses of several tens of microns. The recovered signal is first discussed as a function of the sum of pulses detected at each iteration. Then, the power proportion distribution for each iteration is studied to delimit the meaningful number of required algorithm iteration. Finally, within each iteration are sorted the most contributing optical paths and a simplified global transfer function is derived. The present algorithm allowed to identify the main propagations inside this stratified material giving arise to the recorded signal and to reduce by 98.23% the number of considered and calculated optical paths compared to the standard signal reconstruction procedure.