Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices

TL;DR

This paper investigates tilted Dirac cones in photonic Lieb-kagome lattices, demonstrating their engineering, conical diffraction effects, and experimental validation, thereby advancing understanding of tunable lattice systems with potential applications in photonics.

Contribution

It introduces the study of tilted Dirac cones in Lieb-kagome lattices, combining theoretical modeling, simulations, and experimental validation for the first time.

Findings

Tilted Dirac cones can be engineered into types I, II, and III.

Conical diffraction is observed in photonic Lieb-kagome lattices.

Experimental results confirm the simulation predictions.

Abstract

The Lieb lattice and the kagome lattice, which are both well known for their Dirac cones and flat bands, can be continuously converted into each other by a shearing transformation. During this transformation, the flat band is destroyed, but the Dirac cones remain and become tilted, with types I, II, and III occurring for different parameters. In this work, we first study these tilted Dirac cones using a tight-binding model, revealing how they can be engineered into the different types. We then demonstrate conical diffraction in a photonic lattice realization of the Lieb-kagome lattice using split-step beam propagation simulations, obtaining evidence of the presence of Dirac cones tilted in different directions. Finally, we performed experiments with photonic lattices laser-written in fused silica (SiO$_2$) to validate the results of the simulations. These studies advance the understanding of the Lieb-kagome lattice and tilted Dirac cones in general and provide a basis for further research into this interesting tunable lattice system.