# Novel topological beam-splitting in photonic crystals

## TL;DR

This paper introduces a passive, geometry-based three-way beam splitter in photonic crystals using square lattice arrangements of dielectric pillars, leveraging accidental Dirac cones for efficient splitting and routing.

## Contribution

It presents a novel passive beam-splitting design in photonic crystals that relies solely on geometric arrangements and accidental Dirac cones, unlike symmetry-based methods.

## Key findings

- Effective three-way beam splitting demonstrated through simulations.
- Design works around sharp bends for robust transport.
- Splitting mechanism explained by pillar arrangements within the unit cell.

## Abstract

We create a passive wave splitter, created purely by geometry, to engineer three-way beam splitting in electromagnetism in transverse electric polarisation. We do so by considering arrangements of Indium Phosphide dielectric pillars in air, in particular we place several inclusions within a cell that is then extended periodically upon a square lattice. Hexagonal lattice structures more commonly used in topological valleytronics but, as we discuss, three-way splitting is only possible using a square, or rectangular, lattice. To achieve splitting and transport around a sharp bend we use accidental, and not symmetry-induced, Dirac cones. Within each cell pillars are either arranged around a triangle or square; we demonstrate the mechanism of splitting and why it does not occur for one of the cases. The theory is developed and full scattering simulations demonstrate the effectiveness of the proposed designs.