Critical states embedded in the continuum

We introduce a class of critical states which are embedded in the continuum (CSC) of a one-dimensional optical waveguide array with one non-Hermitian defect. These states are on the verge of being fractal and have real propagation constants. They emerge at a phase transition which is driven by the imaginary refractive index of the defective waveguide and it is accompanied by a mode segregation which reveals analogies with the Dicke super-radiance. Below this point the states are extended while above it they evolve to exponentially localized modes. An addition of a background gain or loss can turn these localized states into bound states in the continuum. (paper)