Diffraction by a plane sector

The problem of diffraction by a perfectly reflecting screen occupying an infinite sector of the equatorial plane is addressed by the random–walk method. The solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen. The diffracted field is explicitly represented as the mathematical expectation of a specified functional on trajectories of the random motion, the radial component of which runs in a complex space while the two–dimensional angular component remains real valued. The numerical results confirm the efficiency of the random–walk approach to the analysis of diffraction by wedge–shaped screens of arbitrary angles.