# Asymmetric conical diffraction in dislocated edge-centered square lattices

## TL;DR

This paper explores the linear and nonlinear propagation of light in a novel dislocated edge-centered square lattice, revealing asymmetric Dirac cones and conical diffraction phenomena influenced by nonlinearities.

## Contribution

It introduces a new lattice structure with analytical and numerical analysis of its band structure, Dirac cones, and diffraction properties, including nonlinear effects.

## Key findings

- Asymmetric Dirac cones are identified in the lattice.
- Both focusing and defocusing nonlinearities enhance conical diffraction asymmetry.
- Linear and nonlinear asymmetric conical diffraction are demonstrated.

## Abstract

We investigate linear and nonlinear evolution dynamics of light beams propagating along a dislocated edge-centered square lattice. The band structure and Brillouin zones of this novel lattice are analyzed analytically and numerically. Asymmetric Dirac cones as well as the corresponding Bloch modes of the lattice are obtained. By adopting the tight-binding approximation, we give an explanation of the asymmetry of Dirac cones. By utilizing the appropriate Bloch modes, linear and nonlinear asymmetric conical diffraction is demonstrated. We find that both the focusing and defocusing nonlinearities can enhance the asymmetry of the conical diffraction.