Three-dimensional all-dielectric photonic topological insulator

Abstract

The discovery of two-dimensional topological photonic systems has transformed our views on electromagnetic propagation and scattering of classical waves, and a quest for similar states in three dimensions, known to exist in condensed matter systems, has been put forward. Here we demonstrate that symmetry protected three-dimensional topological states can be engineered in an all-dielectric platform with the electromagnetic duality between electric and magnetic fields ensured by the structure design. Magneto-electric coupling playing the role of a synthetic gauge field leads to a topological transition to an "insulating" regime with a complete three-dimensional photonic bandgap. An emergence of surface states with conical Dirac dispersion and spin-locking is unimpeded. Robust propagation of surface states along two-dimensional domain walls defined by the reversal of magneto-electric coupling is confirmed numerically by first principle studies. It is shown that the proposed system represents a table-top platform for emulating relativistic physics of massive Dirac fermions and the surface states revealed can be interpreted as Jackiw-Rebbi states confined to the interface between two domains with opposite particle masses.Following the footsteps of condensed matter topological systems, a significant progress has been recently made in understanding and realizing topological states for bosons [ 1,2,3,4,5] and in classical systems [ 6, 7, 8, 9, 10, 11, 12, 13, 14 15, 16, 17, 18, 19, 20, 21, 22, 23]. Unlike fermionic systems, achieving topological order for bosons meets several limitations. In particular, while fermions can support robust topological phases protected by time-reversal (TR) symmetry alone, in bosonic and classical systems TR symmetry is not sufficient to protect any nontrivial topological phases [ 24]. Consequently, the traditional approach to engineering topological order in classical systems relies on removal of TR symmetry. This approach requires either using magnetic materials, e.g. in magnetic-photonic crystals emulating Quantum Hall effect (QHE) which were successfully realized in 2D [ 9,25] and has also been recently extended theoretically to three dimensions [ 26], or temporal modulation emulating the effect of external magnetic field [ 27,28,29,17,30,13].

Guiding Waves Along an Infinitesimal Line between Impedance Surfaces

“…Notably, this includes photonic topological insulators based on symmetry-protected topological (SPT) phases [ 9, 10 , 11 ,12 ]. In these systems, where timereversal (TR) symmetry is not broken [13,14,15,16], crystalline or intrinsic symmetries of the wave fields and differing topology of bulk bands give rise to wavevector-locked states at the interface [12]. Analogously, opposite single-negative bulk materials [17] support bound states that exhibit a similar though limited robustness [18,19,20].…”

“…Bookmark not defined.]. This makes our system somewhat reminiscent of TR-invariant SPT states formed between two claddings of opposite bianisotropy [12], where intrinsic symmetries of the fields and differing topology of bulk bands give rise to counter propagating pseudo-spin states, ψ + and ψ − [36].…”

Type-II Dirac photons

“…These two elements are also at the heart of Z 2 topology in PT -symmetric (P is inversion) systems, as revealed in the seminal work of Fu and Kane. 33 Although there have been a few fine designs 29,31,32 showing the connection between type-I DPs and the Z 2 topology, type-II DPs [in analog of type-II Weyl Points (WPs), 34,35 see Fig. 1] have never been explored in photonics or in other classical/bosonic waves.…”

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

“…The discovery of topological insulators in condensed‐matter systems has promoted extensive research on analogous systems of classical waves including acoustics and photonics . Uniquely, these systems have insulating bulk but conducting interfaces that host chiral one‐way or helical spin‐polarized edge states. As a result, wave propagation is immune to backscattering unlike in ordinary photonic circuitry, where realistic fabrication imperfections, disorder, or arbitrary bends could severely reduce signal transmission, hence device performance.…”