Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics

We provide a description of the far-field encountered in the diffraction problem resulting from the interaction of a monochromatic plane-wave and a right-angled no-contrast penetrable wedge. To achieve this, we employ a two-complex-variable framework and use the analytical continuation formulae derived in Kunz & Assier (2023, Diffraction by a right-angled No-contrast penetrable wedge: analytical continuation of spectral functions. Q. J. Mech. Appl. Math., 76, 211-241) to recover the wave-field's geometrical optics components, as well as the cylindrical and lateral diffracted waves. We prove that the corresponding cylindrical and lateral diffraction coefficients can be expressed in terms of certain two-complex-variable spectral functions, evaluated at some given points.