Digital Planar Holography (DPH) has arrived due to progress in microlithography, planar waveguide fabrication, and theoretical physics. A computer-generated hologram can be written by microlithography means on the surface of a planar waveguide. DPH combines flexibility of digital holograms, superposition property of volume (thick) holograms, and convenience of microlithographic mass production. DPH is a powerful passive light processor, and could be used to connect multiple optical devices in planar lightwave circuits (PLCs), and if combined with active elements on the same chip, may perform not only analog operations but also logical ones. A DPH implementation of a multiplexer/demultiplexer with discrete dispersion is proposed and demonstrated, avoiding communication signal distortion inherent in multiplexers/demultiplexers with continuous dispersion. The concept of discrete dispersion leads to a device with a flat top transfer function without a loss penalty. The dispersion is created with custom-designed bandgaps for specific directions. A DPH hologram resembles a poly-crystal with long-range correlations, and it exhibits the properties of a quasi-crystal. Unlike photonic crystals, light in quasi-crystal may propagate in almost any direction. Single mode planar waveguides are specially designed to suppress parasitic reflections that appear due to mixture of TE-modes, TM-modes, and cladding modes. Demultiplexers with 2-32 channels were demonstrated on planar waveguides with binary single-layer lithography.