Sommerfeld's Diffraction Problem in A Bi-Isotropic Medium

We analyse the diffraction of a harmonic plane wave incident normally on the edge of a perfectly conducting half-plane S immersed in a bi-isotropic medium. This 2D-diffraction problem is essentially of scalar nature and we first discuss the 2D-solutions of Maxwell's equations in a bi-isotropic medium. Then, using a Bateman's theorem to get the diffracted components of the electromagnetic field, we prove that the total field (incident, reflected, diffracted) is a solution of the 2D-Helmholtz equation continuous outside S and such as the tangential components of the electric field and the normal derivative of the tangential components of the magnetic field are zero on S.