Localization of light in disordered topological metamaterials – LOLITOP

We use a microwave platform to study Anderson localization and topological phenomena in 2D metamaterials composed of subwavelength resonators. Due to the scaling of Maxwell’s equations with frequency, our findings extend beyond the microwave range and pave the way for new designs of nanostructured optical metamaterials.

Our experimental setup, consisting of dielectric resonators that can be placed at arbitrary positions, allows us to control the opening of spectral gaps in the system, as well as their topological nature. We can design photonic metamaterials with ordered, disordered, or quasi-periodic structures.

The experimental activity is supported by a strong theoretical framework, both in the design phase and for result interpretation. Our theoretical models are based on the coupled dipole method and the tight-binding model. Disorder is introduced by displacing resonators and accounting for the dependence of coupling between resonators on their spacing. We can model both open systems (with resonators in 3D free space) and closed systems (with resonators confined in a Fabry-Pérot cavity). The topological properties of the spectra are characterized by topological invariants such as Chern number and Bott index, with calculations adapted to account for the non-Hermitian nature of the system.

- Realization of a microwave analog of the quantum spin Hall effect. We demonstrated the opening of a topological gap in a deformed 2D lattice of resonators without breaking time-reversal symmetry. The spin 1/2 of electrons is replaced by a pseudo-spin, simulated by the orbital angular momentum of the electromagnetic wave in a cluster of six resonators arranged in a hexagon. The band structure topology is characterized by spin Chern number or spin Bott index and manifests itself through the existence of helical edge states in a sample of finite size.

- Achievement of unidirectional propagation of a pseudo-spin-polarized signal and its frequency-dependent routing. The synthetic nature of spin 1/2 in our device makes the analogy with the quantum spin Hall effect imperfect near the sample edges. This prevents the edge-state bands from crossing the gap and makes their shape sensitive to the edge type, enabling control over the propagation direction by adjusting the frequency of the wave emitted by an antenna.

- Measurement of the propagation speed of signals carried by topological edge states. We measured the group velocity of a signal carried by topological edge states, as well as the transport velocity of the pseudo-spin (orbital angular momentum) of the electromagnetic wave. Both velocities are equal and 100 to 1000 times slower than the speed of light in a vacuum. This result aligns with findings from a 1D chain of resonators, confirming the one-dimensional nature of edge states.

- Demonstration of the robustness of topological edge states against disorder. We showed that signals propagating along the sample edges via helical edge modes are unaffected by introduced defects and immune to backscattering.

- Study of the role of disorder for light in cold-atom lattices. A theoretical study allowed us to propose an experiment to investigate the role of disorder for light in cold-atom lattices and to establish the precise conditions under which such an experiment should be conducted.

- Theoretical proposal for an experiment demonstrating the existence of a topological Anderson insulator for photons in a cold-atom lattice. We established that a topological Anderson insulator can be realized for light in a 2D lattice of cold atoms and determined the experimental conditions for its existence.

- Theoretical study of the role of dimensionality (2D vs 3D) in topological phenomena in resonator networks. The topological properties of 2D resonator networks confined in a Fabry-Pérot cavity and those suspended in 3D space are shown to be very similar.

In the short term, the LOLITOP project is expected to have a strong impact on fundamental research in optics, electromagnetism, and, more broadly, on wave propagation in complex media. In the medium term, our results will advance knowledge in condensed matter physics as a whole. Beyond addressing fundamental questions, the LOLITOP project will also contribute to the development of new optical technologies. In the long term, a deeper understanding of the combined impact of disorder and topology on wave propagation should enable their controlled use to create useful functionalities, thus paving the way for future functional optical materials.

S.E. Skipetrov and P. Wulles, Topological transitions and Anderson localization of light in disordered atomic arrays, Phys. Rev. A 105, 043514 (2022)

The main objective of the LOLITOP project is to study the interplay between topological physics and disorder-induced effects for light in two-dimensional (2D) metamaterials made of subwavelength resonators. On the one hand, disorder may induce a topologically nontrivial phase – the so-called topological Anderson insulator (TAI). On the other hand, the properties of disorder-induced spatially localized states with energies inside band gaps may depend on the topological indices of adjacent energy bands. We will use a flexible microwave experimental platform to investigate Anderson localization in topologically nontrivial 2D metamaterials and to demonstrate a TAI in gyromagnetic or non-uniformly strained materials. The experimental activity will benefit from a solid theoretical support both at the stage of experiment design and for interpretation of results. A separate theoretical study will aim at extending the 2D analysis to higher dimensions (3D, 4D). Owing to the scaling of Maxwell equations with frequency, our results will apply beyond the microwave frequency range and will open a door to novel designs of nano-structured optical metamaterials.

The main innovation of the LOLITOP project with respect to the state of the art is the full consideration given to the aspects specific to photonics (polarization of light, resonant nature of scattering, possibility of strong deformations of a lattice) in the study of the impact of disorder on light propagation in topologically nontrivial metamaterials. The main scientific barriers to overcome are due to the needs of adapting the methodology existing to deal with electronic systems to vector electromagnetic waves, and of coping with the fundamental differences between photons and electrons: the absence of charge and the “volatility” of photons that can easily leave the material or be absorbed by it. Fortunately, these difficulties also open a number of new opportunities arising from the possibility of manipulating the polarization of electromagnetic waves (TM or TE) and controlling the number of modes allowed to propagate inside the metamaterial. We will fully exploit these opportunities to reach various propagation regimes in our experimental setup composed of dielectric resonators that can be equipped with patches of magnetic material for controlling the time-reversal symmetry in light propagation by an external magnetic field. The freedom in the choice of the spatial arrangement of resonators allows for designing photonic metamaterials with ordered, disordered, or quasi-periodic structure. The expected results of the project include the understanding of the interplay between topology and disorder in 2D photonic metamaterials, the theoretical description and experimental realization of the first 2D photonic TAI based on the use of gyromagnetic materials, the theoretical description and experimental realization of the first 2D photonic pseudo-TAI making use of a nonuniform lattice deformation, the theoretical description of the first quasi-periodic 2D photonic TAI, and the theoretical investigation of a 3D photonic TAI to motivate future experiments.

In the short-time perspective, the LOLITOP project is expected to have a strong impact on fundamental research in optics, electromagnetism, and more generally, wave propagation in complex media. In the mid-term, our results will help to advance knowledge in condensed-matter physics in general. Finally, in addition to addressing fundamental questions, the LOLITOP project will contribute to the development of new optical technologies. Better understanding of the combined impact of disorder and topology on wave propagation is expected to allow for their controlled use in order to create useful functionalities and thus to pave a way towards future functional optical materials in the long term.