  Geometrically decorated two-dimensional (2D) discrete surfaces can be more
effective than conventional smooth reflectors in managing wave radiation.
Constructive non-specular wave scattering permits the scattering angle to be
other than twice that of incidence and can result in gross violations of the
law of reflection. Hence significant fraction of the phase space becomes
accessible. A wide range of novel reflective behaviors ensues; including the
phenomenon of negative reflection were energy transport remains on the same
side of the normal. Also, at a critical incidence coherent superposition can
force both the transmitted and reflected waves to graze the scattering surface
thus synergistically reinforcing the diffractive process in a behavior
reminiscent of critical internal reflection of ray optics. We experimentally
demonstrate the concept with measurements on a one-dimensionally periodic
system (grating) where the scattering angle is shown to be an inverse circular
function of a function that depends on the diffractive index and the two
angles. Excellent agreement is found between experimental data and theory.
