Plane-Wave Diffraction by a Slit Formed by Two Half-Planes with a Fractional Boundary Condition: Higher Order Asymptotics

The analysis of the scattering by a slit formed by two half-planes is a crucial subject in electromagnetic theory and relevant to many engineering applications. A number of scientists have analyzed slit diffraction problems using various analytical and numerical methods. In our previous paper [1], we analyzed the diffraction by a slit in a thin material screen using the Wiener-Hopf technique and generalized boundary conditions [2]. Recently, the diffraction problems related to a fractional boundary condition (FBC) have been analyzed in several papers [3]. Several scientists have analyzed the diffraction problem related to FBC so far. For example, Karaçuha et al. solved the diffraction by a slotted cylinder with FBC and clarified the near- and far-fields, total radar cross-sections (TRCS), and resonances [3]. FBC shows intermediate scattering properties between perfect electric conductor (PEC) and perfect magnetic conductor (PMC). ‘Fractional’ means the fractional derivative of this paper’s total electric field components. In this paper, we shall consider a slit in an infinite plate with the FBC and analyze the E-polarized plane wave diffraction by using a Wiener-Hopf approach similar to that employed in our previous paper $[1]$.