When a wave interacts with a convex obstacle, it creates reflected waves, as well as waves in the geometric shadow of the obstacle. This phenomenon is called wave diffraction. To describe the propagation of oscillations in wave diffraction, we construct highly oscillatory asymptotic solutions to semilinear wave equations, allowing arbitrary order of grazing. As a corollary, we found that no high frequency oscillation can be observed in the geometric shadow in $H^1$ norms. This talk is based on joint work with Mark Williams.