On-chip photonic guides as efficient as topological channels?
Gaëtan Lévêque1, Pascal Szriftgiser2, Alberto Amo2, Yan Pennec1
1Institute of Electronics, de Microelectronics and Nanotechnology (IEMN, CNRS-8520), Cité Scientifique, Avenue Poincaré, 59652 Villeneuve d’Ascq, France
2University of Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
Photonic topology, by proposing a particular way of creating an interface between two periodic structures of the same insulating membrane, promises to guide an electromagnetic signal with minimal losses in complex miniaturized circuits.It is thus a key element in the development of terahertz telecommunications or quantum technologies. We propose a new structuring of the membrane, enriching the possible forms of interfaces, in order to question the topological origin of the remarkable performance of photonic crystals built using the “valley” approach.
Photonic topological insulators are systems that use photons to mimic the quantum Hall effects observed in their electronic counterparts in solid-state physics, with the aim of transporting electromagnetic signals via “robust” interface modes, i.e. propagating without backscattering despite the presence of defects or sharp bends along their path. However, the bosonic nature of photons means that in two-dimensional systems, time-reversal symmetry must be broken (e.g. by applying a magnetic field).
Figure 1: (a) Diagram showing the geometry of the photonic crystal, composed of three sets of diamonds of different sizes, grouped by color on the left half. The lozenges represent air holes in a silicon matrix. (b) Band diagram for the insert geometry. (c) Berry curvature distribution in the first Brillouin zone, along the lowest frequency band. (d) Interface constructed between an original grating A and an image grating B.
Another approach can be found in certain photonic crystals known as “valley crystals”. These materials exploit a geometric property of the electromagnetic wave, called Berry curvature, which can be represented on a map in two-dimensional space of wave propagation directions (reciprocal space).
To better understand this, let’s imagine an ant trying to move “as straight as possible” over a bumpy surface: it will be deflected by passing over the side of a bump, which has a non-zero curvature unlike a flat surface. Similarly, Berry’s curvature causes a rotation (phase) in the state of a photon moving in a given direction.
By construction, valley photonic crystals are not symmetrical with respect to a central symmetry, which gives them a non-zero Berry curvature, concentrated around certain propagation directions (noted K and K’ in reciprocal space). When two crystals forming a mirror image of each other are placed side by side along these directions, this curvature changes sign at the interface, creating a topological transition. It is this transition that is often proposed to explain why light can propagate robustly along the interface. However, several recent works question this interpretation [1].
Our work introduces an original photonic crystal pattern [2], consisting of three subsets of diamonds whose size is varied independently, see Figure 1(a). For well-chosen parameters, the system exhibits a band gap between the first and second bands, Figure 1(b). In reciprocal space, the Berry curvature is concentrated around the propagation directions K and K’, with opposite signs, Figure 1(c). The originality of our structure lies in the fact that the number of possible interfaces is greater than in conventional systems with only two asymmetric holes. Instead of just two mirror-symmetrical interfaces with topological transition in the latter case, we obtain 18 interfaces, similar to those shown in Fig. 1(d), some with topological transition and some without.
Figure 2: Transmission curves and magnetic field amplitude distributions in circuits corresponding to a triangular cavity coupled to a straight guide (a-e), or to a path of arbitrary shape (f-h). The green star in figures (a) and (f) indicates the position of the source, and the dotted arrows indicate the directions of propagation without backscatter. Figures (b,c,g) (resp. d,e,h) correspond to the interface with (resp. without) topological transition. The detailed shape of the interface is shown as an insert to the transmission curves. Maps (c) and (d) are plotted for frequencies indicated by arrows.
We have compared the propagation of interface modes along circuits of increasing complexity (Figure 2). In the situation traditionally used as a test for topological protection, Figure 2(a), the circuit features only 120° turns, in this case with a triangular cavity, along which the mode propagates only in the K or K’ directions, without passing from one to the other (dotted arrows in Figure 2(a)). In particular, reflection is not possible and transmission through the circuit is flat, the shape of the field is regular, whether for an interface with, (b,c), or without, (d,e), topological transition. The latter case is surprising, and is attributed to the chirality of the interface. On the other hand, simulations carried out on circuits of arbitrary shape, figure 2(f), show that the topological transition ensures much better transmission than a trivial interface, reflections distributed along the path being much less in the former case. Our study, while highlighting the possibility of transmitting a signal along a non-topological interface with virtually no backscattering, nevertheless establishes a hierarchy between topological and trivial interfaces for arbitrary-form circuits, in which the former perform better.
This study is the result of a collaboration begun in 2019 between the Physics (G. Lévêque and Y. Pennec), THz Photonics (G. Ducournau) and NAM6 (M. Faucher) groups at IEMN and the PhLAM laboratory (A. Amo and P. Szriftgiser). A first publication focused on the evaluation of topological protection in valley photonic crystals using semi-analytical and numerical methods [3], followed by a second demonstrating the applicability of valley topology to the design of terahertz telecommunication devices, notably for 5G and 6G networks [4].
[1] Impact of Transforming Interface Geometry on Edge States in Valley Photonic Crystals, D. Yu, S. Arora, L. Kuipers, Phys. Rev. Lett. 132, 116901 (2024) ; Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend, T. Torres, C. Bellis, R. Cottereau, A. Coutant, Proc. R. Soc. A 480, 20230905 (2024).
[2] Relation between interface symmetry and propagation robustness along domain walls based on valley topological photonic crystals, G. Lévêque, P. Szriftgiser, A. Amo, Y. Pennec, APL Photonics 9, 126107 (2024).
[3] Scattering matrix approach for a quantitative evaluation of the topological protection in valley photonic crystals, G. Lévêque, Y. Pennec, P. Szriftgiser, A. Amo, and A. Martínez, Phys. Rev. A 108, 043505 (2023).
[4] Engineering the breaking of topological protection in valley photonic crystals enables to design chip level functions for THz 6G communications and beyond, A. S. Mohammed, G. Lévêque, E. Lebouvier, Y. Pennec, M. Faucher, A. Amo, P. Szriftgiser, and G. Ducournau, J. Lightwave Technol. 42(23), 8323–8335 (2024).
