Theory of intrinsic propagation losses in topological edge states of planar photonic crystals

Abstract

Using a semianalytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the intrinsic propagation losses of these structures are not well understood and the concept of the light line can become blurred. For four example topological edge state structures, photonic band diagrams, loss parameters, and electromagnetic fields of the guided modes are computed. Two of these structures, based on armchair edge states, are found to have significant intrinsic losses for modes inside the photonic bandgap, more than 100 dB/cm, which is comparable to or larger than typical disorder-induced losses using slow-light modes in conventional photonic crystal waveguides, while the other two structures, using the valley Hall effect and inversion symmetry, are found to have a good bandwidth for exploiting lossless propagation modes below the light line (at least in the absence of disorder).

Chiral quantum optics in broken-symmetry and topological photonic crystal waveguides

“…These have been designed to guide light near λ = 930 nm (see Appendix A for further design parameters) for use with high-quality self-assembled Indium Arsenide quantum dots in a Galium Arsenide membrane [41] with a fixed lattice constant a = 266 nm, but their design can readily be scaled [33] for use with any other quantum photonic platform. Similarly, we limit our designs to circular holes but note that in practice more complex and fabricationally-challenging shapes such as triangles [68] or shamrocks [79] are possible.…”

“…In analogy with the electronic QVH insulators [18], we expect that the difference between these invariants (here 1) denotes the number of topological interface modes that span the bandgap, although recent experiments suggest the existence of spectral regions where the mode does not afford protection to sharp bends [49]. Regardless, we use QVH insulators as their guided modes are known to lie below the light lines and hence do not couple to the free-space continuum, in contrast to topological PhCWs based on the photonic analog of the Quantum Spin-Hall effect, whose modes lie above the light line and are therefore leaky [7,68]. Here, we consider QVH waveguide designs formed by bearded-type interface (BIW) and zig-zag-type (ZIW) interfaces [57] as shown in Fig.…”

Inverse design of broadband and lossless topological photonic crystal waveguide modes

“…Moreover, PCS waveguides also exhibit Bloch modes with local chirality [12][13][14], which can be used to couple to spin charged quantum dots, manifesting in unidirectional single photon emission. Unfortunately, many of the topological PCS waveguide modes fall above the light line and are thus intrinsically lossy, with significant propagation losses [15]. Very recently, new classes of topological PCS waveguides have been presented, using the so-called Valley Hall effect [16,17], which more easily allow edge state modes to fall below the light line.…”

Quantifying the Robustness of Topological Slow Light

“…In principle, these edge states have no intrinsic out-of plane losses and only fabrication imperfection can induce coupling to radiating modes. Even in that situation, in-plane backscattering is largely the dominant loss mechanism at large values of n g [17] so it is enough to consider the system as two dimensional to capture the physics of slow-light backscattering, something not possible with other implementations of topological photonics [18]. Here, we set up twodimensional simulations instead of the more computationally expensive three-dimensional slab.…”

“…Despite substantial theoretical work on ξ in nontopological electronic [26][27][28] and photonic transport [17,25,29], this parameter has only been explored recently in topological waveguides [30] although ignoring n g . Besides this, only intrinsic out-of plane losses of topological guided modes in nondisordered photonic crystal slabs have been analyzed [31]. We calculate ξ in perturbed topological and conventional photonic crystal waveguides as…”