10 February 2015; published 3 June 2015 | Long-Hua Wu and Xiao Hu
This paper presents a method to achieve a topological photonic crystal using conventional dielectric materials. By deforming a honeycomb lattice of cylinders into a triangular lattice of hexagonal clusters, the authors demonstrate a photonic system with nontrivial topology. The photonic topology is associated with a pseudo-time-reversal (TR) symmetry, which is constructed from the TR symmetry of Maxwell equations and the C6 crystal symmetry. This symmetry leads to Kramers doubling, similar to electronic systems. The role of pseudospin is played by the angular momentum of the out-of-plane electric field of transverse magnetic modes.
The authors solve Maxwell equations to demonstrate the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors. The system is designed with a triangular lattice of hexagonal clusters, where each cluster acts as an "artificial atom." The photonic bands exhibit electronic-like p- and d-wave shapes, and the system shows a band gap opening at the Γ point. The topological phase is confirmed by evaluating the Berry curvatures of bulk photonic bands and edge states.
The study shows that the photonic system exhibits a quantum spin Hall effect, with unidirectional energy propagation at the edges of the crystal. The topological photonic state is achieved without the need for external fields or special materials, making it promising for future applications. The design is based on symmetry considerations and can be fabricated relatively easily compared to other proposals. The results demonstrate that a topological photonic crystal can be created using conventional dielectric materials, opening new possibilities for topological physics and related materials science.This paper presents a method to achieve a topological photonic crystal using conventional dielectric materials. By deforming a honeycomb lattice of cylinders into a triangular lattice of hexagonal clusters, the authors demonstrate a photonic system with nontrivial topology. The photonic topology is associated with a pseudo-time-reversal (TR) symmetry, which is constructed from the TR symmetry of Maxwell equations and the C6 crystal symmetry. This symmetry leads to Kramers doubling, similar to electronic systems. The role of pseudospin is played by the angular momentum of the out-of-plane electric field of transverse magnetic modes.
The authors solve Maxwell equations to demonstrate the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors. The system is designed with a triangular lattice of hexagonal clusters, where each cluster acts as an "artificial atom." The photonic bands exhibit electronic-like p- and d-wave shapes, and the system shows a band gap opening at the Γ point. The topological phase is confirmed by evaluating the Berry curvatures of bulk photonic bands and edge states.
The study shows that the photonic system exhibits a quantum spin Hall effect, with unidirectional energy propagation at the edges of the crystal. The topological photonic state is achieved without the need for external fields or special materials, making it promising for future applications. The design is based on symmetry considerations and can be fabricated relatively easily compared to other proposals. The results demonstrate that a topological photonic crystal can be created using conventional dielectric materials, opening new possibilities for topological physics and related materials science.