Inverse design of polymorphic Dirac-like cone dispersion relationship in photonic crystals

Abstract

Dirac-like cone linear dispersion relations in photonic crystals (PhCs) often endow them with unique properties, yet searching for such relations can be challenging. We introduce a generalized inverse design system that, given the dielectric constants and lattice of two-dimensional PhCs, can efficiently determine its structural parameters to obtain its Dirac-like cone dispersion. Employing this inverse design strategy, we design three types of Dirac cone PhCs, including triple degenerate, quadruple degenerate, and triple degenerate under dual polarization with the same frequency. Further investigations reveal a systematic relationship between the radius of the dielectric rods in these PhCs and their corresponding Dirac frequencies across varying dielectric constants. The zero refractive index characteristic is validated in two of the three PhCs studied, as confirmed through numerical simulations. Additionally, by leveraging our proposed inverse design method, we introduce an innovative shell dielectric rod model, which encapsulates a dielectric material, achieving a quadruple degenerate dispersion structure with dual Dirac cones. This research provides a potent tool for the inverse design of PhCs and expands its application in Dirac cone dispersion design.