Second Order Transition Boundary Condition for not Dense Thin Sheets Analysis with MoM

The paper presents a new second-order approximated transition boundary condition that can be used to analyze penetrable thin sheets with low density. This new condition can be easily incorporated into existing method of moment codes that use the Poggio-Miller-Chang-Harrington-Wu-Tsai formulation. The new boundary condition is expressed as an ABCD matrix, allowing it to be applied to multiple thin layers without the need for transverse electric and magnetic decomposition of the field. The proposed formulation ensures accurate modeling of thin slabs with low dielectric constants, even if the thickness of the slab is as small as one-tenth of the wavelength within the slab. This accurate modeling is achieved with an error of less than 1%. Despite its accuracy, the proposed formulation has a computational complexity similar to that of the widely used zero-order approximated transition boundary condition in the method of moments codes.