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In this work, we focused on the resonant cavity effect of the air plasma, formed during femtosecond laser filamentation, on the near- and far-field profiles of the generated terahertz (THz) radiation. Via the method of ray tracing, it has been demonstrated that both on-axis propagation and conical forward emission of THz wave could be qualitatively interpreted in case of considering the filament as a Fabry-Perot-like micro-cavity with radial step refractive index distribution in THz domain. Our theory might potentially solve the contradictions of different experimental observations on THz spatial profiles reported in publications, and renew the understanding of THz wave propagation inside the filament plasma column. [ABSTRACT FROM AUTHOR]

In this paper, the shortcut D-bar method is introduced to electrical capacitance tomography to directly reconstruct the permittivity distribution within the region of interest. The method reveals the analytic relationship between the permittivity distribution and the Dirichlet-to-Neumann (DN) map. The DN map can be directly estimated with measured capacitances. However, the direct estimate of the DN map is inaccurate in the cases of small electrode numbers. To better adapt the method to real applications of small electrode numbers, the original shortcut D-bar method is modified by splitting estimation of the DN map into the analytical expression of a homogeneous background and the estimation of the other variation part. Comparisons are made among the original, modified shortcut D-bar methods, and the classical Landweber iteration method through simulation and experiment, respectively. Results confirm the improved tomographic imaging quality by using the modified shortcut D-bar method. [ABSTRACT FROM AUTHOR]