  The Helmholtz equation can be written as coupled equations for the amplitude
and phase. By considering spatial phase distributions corresponding to
reflectionless wave propagation in the plane and solving for the amplitude in
terms of this phase, we designed two-dimensional graded-index media which do
not scatter light. We give two illustrative examples, the first of which is a
periodic grating for which diffraction is completely suppressed at a single
frequency at normal incidence to the periodicity. The second example is a
medium which behaves as a 'beam shifter' at a single frequency; acting to
laterally shift a plane wave, or sufficiently wide beam, without reflection.
