The knife-edge effect is explained by Huygens-Fresnel principle, which states that a well-defined obstruction to an electromagnetic wave acts as a secondary source, and creates a new wavefront. This new wavefront propagates into the geometric shadow area of the obstacle.
The knife-edge effect is an outgrowth of the half-plane problem, originally solved by Arnold Sommerfeld using a plane wave spectrum formulation. A generalization of the halfplane problem is the wedge problem, solvable as a boundary value problem in cylindrical coordinates. The solution in cylindrical coordinates was then extended to the optical regime by Joseph B. Keller, who introduced the notion of diffraction coefficients through his geometrical theory of diffraction (GTD). Pathak and Kouyoumjian extended the (singular) Keller coefficients via the uniform theory of diffraction (UTD).