photonic quasicrystals

photonic quasicrystals
Name	Photonic quasicrystals
Type	Aperiodic optical materials
Discovered	1984 (quasicrystals), adapted to photonics in 1990s
Applications	Waveguiding, lasers, filters, sensors

photonic quasicrystals Photonic quasicrystals are aperiodic dielectric arrangements that produce optical phenomena analogous to those in periodic Bragg diffraction materials, combining features of Shechtman-type quasicrystalline order and engineered electromagnetic responses. They bridge concepts from Paul Steinhardt-related quasicrystal theory, John von Neumann mathematics, and photonics research at institutions like Harvard University and Massachusetts Institute of Technology. Their study links experimental platforms developed at Bell Labs, University of Cambridge, and École Polytechnique Fédérale de Lausanne with theoretical work from groups at Max Planck Society, Imperial College London, and Caltech.

Introduction

Photonic quasicrystals were introduced by adapting structural ideas from Dan Shechtman's discovery to optical materials, informed by theoretical frameworks from Roger Penrose and Alan Mackay. Early experimental demonstrations by teams at University of Chicago and IBM Research used lithography techniques from Bell Labs and fabrication platforms influenced by Intel processes. Research was advanced through collaborations among National Science Foundation-funded centers, projects at DARPA, and academic groups at University of Pennsylvania and Stanford University.

Structure and Symmetry

Photonic quasicrystals display long-range aperiodic order characterized by noncrystallographic rotational symmetries first described by Roger Penrose and investigated in diffraction studies linked to A. L. Mackay. Structures often derive from tilings like the Penrose tiling, Ammann–Beenker tiling, and Danzer set constructions studied at Princeton University and University of Oxford. Symmetry analysis employs tools developed by mathematicians associated with Institute for Advanced Study and ETH Zurich, while reciprocal-space methods reference work from Paul Dirac and Hermann Weyl-inspired spectral theory. Fabrication geometries exploit motifs related to Islamic art tessellations and patterns investigated by Cairo University cultural heritage studies.

Photonic Bandgaps and Localization

Photonic bandgap behavior in quasicrystals parallels concepts from Eli Yablonovitch's photonic crystal work and complements studies from Sajeev John's localization theory. Band diagrams for quasicrystals are computed using methods influenced by Vladimir Arnold and Andrey Kolmogorov-type spectral analysis, with experimental comparisons drawn to measurements at Centre National de la Recherche Scientifique and National Institute of Standards and Technology. Localization phenomena are related to studies of electronic quasicrystals by researchers at University of California, Berkeley and are interpreted via scattering formalisms developed at Los Alamos National Laboratory.

Fabrication and Experimental Realizations

Realizations utilize techniques from Stanford University nanofabrication centers and cleanrooms at MIT Lincoln Laboratory, combining electron-beam lithography, focused ion beam methods, and additive manufacturing used at Lawrence Berkeley National Laboratory. Photonic quasicrystals have been implemented in platforms including dielectric slabs studied at Princeton Plasma Physics Laboratory, photonic glass fibers investigated at University of Cambridge, and microwave experiments conducted at NIST facilities. Integrated optics demonstrations involve collaboration with industry labs at IBM and Intel, and optics characterization often occurs in facilities affiliated with Max Planck Institute for the Science of Light.

Optical Properties and Applications

Optical responses of photonic quasicrystals enable low-threshold lasers akin to developments at Rochester Institute of Technology and sensor designs drawing on work from Georgia Institute of Technology. Applications range from filters explored by researchers at Columbia University to waveguides tested in collaborations between University of Tokyo and Osaka University. Devices leveraging quasicrystalline order are proposed for telecommunications research at Bell Labs and quantum photonics experiments at Caltech. Market-oriented projects have connections to initiatives at Nokia Bell Labs and technology transfer offices at University of Illinois Urbana-Champaign.

Theoretical Models and Numerical Methods

Modeling uses plane-wave expansion techniques refined by teams at École Normale Supérieure and finite-difference time-domain algorithms developed at MIT and University of Southampton. Computational efforts draw on supercell approaches influenced by John von Neumann-era numerical analysis and matrix methods pioneered at Courant Institute. Eigenvalue solvers from Lawrence Livermore National Laboratory and spectral methods from Argonne National Laboratory are commonly applied. Mathematical frameworks reference contributions from Henri Poincaré and operator theory associated with Stefan Banach.

Challenges and Future Directions

Outstanding challenges include scaling manufacturability addressed by initiatives at DARPA and improving disorder tolerance studied at National Renewable Energy Laboratory. Future directions intersect with integrated quantum networks designed at IQOQI Vienna, topological photonics research at KIT, and metamaterials programs at Harvard John A. Paulson School of Engineering and Applied Sciences. International collaborations among European Research Council grantees, Japan Science and Technology Agency projects, and Australian Research Council centers aim to translate quasicrystalline optical control into practical devices.

Category:Optical materials