  We prove that the Cauchy data of Dirichlet or Neumann $\Delta$-
eigenfunctions of Riemannian manifolds with concave (diffractive) boundary can
only achieve maximal sup norm bounds if there exists a self-focal point on the
boundary, i.e. a point at which a positive measure of geodesics leaving the
point return to the point. As an application, the Dirichlet or Neumann
eigenfunctions of Riemannian manifolds with concave boundary and non-positive
curvature never have eigenfunctions whose boundary traces achieve maximal sup
norm bounds.
