Frequency range dependent topological phases and photonic detouring in valley photonic crystals

Abstract

The recent exploration of the valley degree of freedom in photonic systems has enriched the topological phases of light and brought the robust transport of edge states around sharp bends. The two and more simultaneous band gaps in valley-Hall systems have attracted researchers' attention for enlarging the working bandwidth. However, band gaps with frequency-dependent topologies were not reported and the demonstrated flow of electromagnetic waves is limited to the robust transport of edge states. Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic valley photonic crystals are demonstrated as examples in which all four topological phases are found. At the domain walls between topologically distinct valley photonic crystals, frequency-dependent edge states are demonstrated and a broadband photonic detouring is proposed. Our findings provide the guidance for designing the frequency-dependent property of topological structures and show its potential applications in wavelength division multiplexers.

Magnetic-Optic Effect-Based Topological State: Realization and Application

“…The topological photonic states with the MO effect are essential for exploring abundant physical laws and unique physical effects. In addition to utilizing the MO effect, other configurations can achieve photonic topological states, such as the systems breaking IS (Chen et al, 2018;Tang et al, 2020;Shi et al, 2021) or the systems breaking TRS with an effective magnetic field (Fang et al, 2016). Topological protected edge states ensure the absence of backscattering of waves by defects and disorders, which suggest abundant applications, such as oneway fiber, on-chip isolation, and slow light effect.…”

“…Pairs of Dirac points are allowed to exist when inversion symmetry (IS) and TRS are existed, which means F ab n (k) 0. When IS is alone broken, F ab n (−k) −F ab n (k), Chern number is zero, but another topological invariant named the valley Chern number can be created (Chen et al, 2018;Tang et al, 2020;Shi et al, 2021). When TRS is alone broken by adding a Faraday term in permittivity tensor or permeability tensor (applying an external magnetic field on gyrotropic medium), tensors acquire imaginary off-diagonal components having the periodicity of the unit cell (Haldane and Raghu, 2008):…”

“…When Dirac point is separated by breaking IS, the Chern number is zero, but the structures with valley Chern numbers (another topological invariant) can be constructed to realize TESs (Chen et al, 2018;Tang et al, 2020;Shi et al, 2021). In 2018, Lu et al introduced the valley concept in magnetic PhC with broken IS and TRS (Lu et al, 2018a).…”

Topological Nanophotonic Wavelength Router Based on Topology Optimization

“…These facts make VPC convenient for experiments and give a fascinating prospect in designing on-chip integrated high-performance nanophotonic devices [14][15][16][17]. Works of devices designed with VPC are presented in recent years, including topological Mach-Zehnder interferometers [18], topological photonic routing structure [11,19], valley beam filter [20], photonic detouring structure [21], and splitters [22]. However, much attention has been paid to engineer the bulk band dispersion to realize topological states in the realm of topological photonics, and a topological wavelength router working in optical telecom band has not been reported to date, which has restricted the practical application of topological states and the development of robust nanophotonic devices.…”

Topological photonic crystals: a review

“…Here, the HTPCs give rise to the simultaneous emergence of the chiral and valley edge states in different band gaps [Fig. 1 tion of the QAH and VH topological phenomena in a single photonic system is more remarkable than previous realization on dual band topology of both photonic VH effects [25,26].…”