Photonic Flat Bands Arising From Metallic Claw Structure

Flat band refers to dispersion-less spectral band,which represents one kind of ideal band.In photonics,the photonic flat bands are of significance in realizing slow light,enhancement of light-matter interaction and wave localization,and also greatly stimulating studies in nonlinear optics.Currently,researches about flat bands are mostly based on some classical model proposed in the last century,where the dispersion can be eliminated by adjusting the structural parameters.In this research,inspired by complete graph theory,we innovatively used graph theory as a tool to understand electromagnetic property in photonic crystal,and proposed a metallic claw structure.Combining the complete graph theory with analytical dynamics,we made the comparison analysis of Laplacian matrix and Euler-Lagrange equation.Using the systematic solving process promoted by us,the properties of metallic claw structure were predicted.We demonstrated that a large number of resonant modes could exist in the metallic claw structure,and frequency of those modes were nearly degenerate.The appearance of resonant mode is determined by the underlying connectivity nature of metallic claw structure instead of the symmetry.In addition,a linear relationship was observed between the number of resonant modes and the number of branches in the metallic claw structure.A photonic meta-crystal composing of a lattice of such metallic claw structure exhibits a large number of flat bands,and these flat bands can be designed to locate in a wide complete 3D bandgap,leading to an extremely high density of state(DOS).By finely tuning the parameter,those flat bands can be localized into a narrow frequency window,realizing highly degenerate flat bands which have no intersection with other dispersive bands.What’s interesting,the degeneracy dimension(Nf)of the flat bands is determined by the number of branches(Nb)of the metallic claw with Nf=Nb-3,which is geometrically related to the complete graph theory.Different from those flat bands emerging from special lattice arrangements,here the flat bands are enabled by the connectivity nature of the metallic claw structure,thus making them more robust against imperfections.To summarize,the mechanism proposed in our work offers a new platform for realizing various dispersion-less phenomena and a new paradigm to realize high density of states and spectra compressing.