Scattering-free edge states between heterogeneous photonic topological insulators

Abstract

We propose a set of three simple photonic platforms capable of emulating quantum topologically insulating phases corresponding to Hall, spin-Hall, and valley-Hall effects. It is shown that an interface between any two of these heterogeneous photonic topological insulators supports scattering-free surface states. Spin and valley degrees of freedom characterizing such topologically protected surface waves determine their unique pathways through complex photonic circuits comprised of multiple heterogeneous interfaces.Light propagation through waveguides, photonic crystals, and other photonic system can often be reduced to a simple scalar wave equation that imposes fundamental limitations on how optical energy can be transported in space. For example, it is generally believed to be impossible to guide light along sharply bent trajectories without reflections. A new paradigm that calls into question this conventional wisdom has been recently introduced with the realization of a new class of photonic structures: photonic topological insulators (PTIs) [ 1, 2, 3, 4, 5, 6, 7, 8,9]. Just as their condensed matter counterparts, topological insulators (TIs) [ 10,11,12] from which they have been derived by analogy, PTIs enable reflections-free propagation of topologically protected surfaces waves (TPSWs) [ 5, 8] In this Letter, we demonstrate that these three condensed matter systems can be emulated by novel PTI structures. More significantly, while it is nearly impossible to realize lateral heterojunctions between different classes (e.g., between QSH and QH) of TIs in naturally occurring electronic materials, interfacing heterogeneous PTIs is relatively straightforward and, in fact, highly beneficial to developing novel photonic circuits. We demonstrate that reflectionsfree TPSWs are supported by the interfaces between such domains. It is shown that topological protection emerges not only from the conservation of the spin degree of freedom (DOF) [ 4, 5, 8], but also from the conservation of another binary DOF: the valley. While it has been recently recognized that the valley DOF can produce novel topological phases and chiral edge states of electrons [ 18,19,20], here we demonstrate its significance to reflections-free propagation of surface waves in photonic structures.The photonic analogues of the three topological phases are obtained by imposing three types of distinct symmetry-breaking perturbations on a simple symmetric "photonic graphene" (PhG) [ 21] structure shown in Fig.1(a). The PhG is comprised of a hexagonal arrays of metal posts symmetrically placed between two metal plates and separated from them by the gap 0 . A similar photonic structure was considered earlier in the narrower context of QSH-type [ 8] PTIs

All-Si Valley-Hall Photonic Topological Insulator

“…It has been shown [ 21] that any geometric perturbation that breaks the inversion ( )-symmetry yet preserves the 3 point symmetry does not couple the RCP and LCP modes. It means that the perturbation matrix (responsible for lifting the degeneracy of the RCP and LCP orbital states) is diagonalized:…”

“…Specific implementations of PTIs vary considerably, and can utilize large coupled optical resonators [ 3,4], wavelength-scale photonic structures [ 1,2,10,21], or metacrystals [ 6]. To date, most of the wavelength and sub-wavelength scale PTI concepts utilized metals.…”

“…To date, most of the wavelength and sub-wavelength scale PTI concepts utilized metals. For example, metallic metamaterials comprised of split-ring resonators [ 6] and meta-waveguides comprised of an array of metal rods attached to one of the two confining metal plates [ 10,21] have been used to emulate the binary spin degrees of freedom (DOF) by ensuring that the two polarization states of light, the transverse electric (TE) and transverse magnetic (TM) modes, propagate with the same speed. This, property, known as spin-degeneracy [ 6,7], is challenging to achieve without using metals.…”

Robustness of states at the interface between topological insulators of opposite spin Chern number

“…This raises the question of the interface between two TIs characterized by ν = 1 but opposite C s . Interestingly, recent theoretical and experimental works on photonic [31][32][33] and phononic [34] systems demonstrated scattering-free transport at the interface between two similar TIs but with reversed SOC (and therefore opposite C s ). However, we will see in the following that this remarkable robustness against disorder can be only obtained in very strict conditions.…”

“…In the recent studies on photonic [31][32][33] and phononic [34] systems reporting scattering-free transport at the interface between two similar TIs but with reversed SOC, the authors worked deliberately in conditions where the intrinsic SOC coupling is dominant and the k-dependent rotation of the spin is minimized. Our work demonstrates that it is compulsory to stay in this regime to maintain the topological protection of the interface states.…”