Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals

Abstract

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experiments are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.

Unidirectional Wave Propagation in a Topological Plasmonic Ring Resonator via a Symmetry-Broken Excitation Scheme

“…Even in a merged two-particle configuration, we still have two modes: the transverse and longitudinal modes. In addition, based on the momentum of the optical modes, some of the modes could appear as degenerate in some parts of the bands, while they hybridize and open a band gap in other points of the Brillouin zone . The photonic band structures, shown in Figure a–c, reveal both topological and trivial photonic band gaps.…”

“…In addition, based on the momentum of the optical modes, some of the modes could appear as degenerate in some parts of the bands, while they hybridize and open a band gap in other points of the Brillouin zone. 17 The photonic band structures, shown in Figure 4a−c, reveal both topological and trivial photonic band gaps. By increasing the value of v with respect to w, the band structure undergoes a transition from gapped to gapless and again to gapped around the energy of 1.59 (eV), corresponding to changes in the distance between two nanoparticles, indicating a topological phase transition.…”

“…In recent years, topological plasmonics has emerged as a new frontier in manipulating light on the nanoscale. Topological systems, characterized by intriguing nontrivial properties that are robust against perturbations, have captivated the attention of researchers across diverse disciplines. − Analogous to their electronic counterparts, topological plasmonic systems and materials , exhibit remarkable phenomena, such as protected edge states, rendering them highly promising for novel applications in nanophotonics, , quantum information processing, , and beyond. − One of the pioneering topological systems in the realm of plasmonics has been realized by the one-dimensional Su–Schrieffer–Heeger (SSH) model. − This model, originally introduced to describe the behavior of electrons in polyacetylene chains, has been adapted to the realm of plasmonic nanostructures. − In the context of plasmonic SSH nanochains, a chain of metallic nanoparticles with alternating spacings serves as the ideal platform to explore and harness topological properties. By controlling the interplay between the nanoparticle interactions via dimerization and periodicity within these chains, the system unveils a plethora of intriguing phenomena.…”