Universal form of arrays with spectral singularities.

An array of non-Hermitian optical waveguides can operate as a laser or as a coherent perfect absorber, which corresponds to a spectral singularity of the underlying discrete complex potential. We show that all lattice potentials with spectral singularities are characterized by the universal form of the gain-and-loss distribution. Using this result, we systematically construct potentials characterized by several spectral singularities at arbitrary wavelengths, as well as potentials with second-order spectral singularities in their spectra. Higher-order spectral singularities demonstrate a greatly enhanced response to incident beams, resulting in the excitation of high-intensity lasing modes.