Digitally Manufactured Spatially Variant Photonic Crystals
Metamaterials and photonic crystals are engineered composites that exhibit electromagnetic properties superior to those found in nature. They have been shown to produce novel and useful phenomena that allow extraordinary control over the electromagnetic field. One of these phenomena is self-collimation, an effect observed in photonic crystals in which a beam of light propagates without diffraction and is forced to flow in the direction of the crystal. Self-collimation however, like many of the mechanisms enabled through dispersion engineering, is effective in directions only along the principal axes of the lattice. To this effect, a general purpose synThesis procedure was developed that is capable of simultaneously spatially varying the orientation, lattice spacing, fill fraction, and other properties of a periodic structure throughout its volume in a way that leaves the overall structure smooth and continuous. This enables unprecedented control over a beam's propagation, one that is now dictated by the spatially variant orientation of the unit cells. The algorithm was also used to synthesize a spatially variant photonic crystal waveguide based on band gaps. The waveguide was designed to be multi-moded, and it was spatially varied in a manner that highly minimizes crosstalk between the modes. Designing these devices with only ordinary all-dielectric materials, 3D printing was well-suited to produce these novel sculpted dielectric devices.