Microwave resonator lattices for topological photonics [Invited]

Abstract

We present a microwave experimental setup emulating tight-binding systems that is now widely used in the realm of topological photonics. A thorough description of the experimental building blocks is presented, showing the advantages and the limits of this platform. Various experimental realizations are then described, ranging from the selective enhancement of a defect state in a non-Hermitian Su-Schrieffer-Heeger (SSH) chain, to the generation of giant pseudo-magnetic fields in deformed honeycomb lattices. Introducing nonlinear losses, the interplay between nonlinearity and topological protection can be engineered to realize a nonlinearly functionalized topological mode with promising applications in receiver protection.

Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

“…Here, we will utilize the defect waveguide modes to build chaotic graph structures. Note that these PC defect waveguide graphs are distinctly different from pho- tonic crystal slabs and billiards [12,35,36], and from coupled resonant dielectric cylinders [3,37] studied previously.…”

Experimental Observation of Multifractality in Fibonacci Chains

“…The variation of ν 0 for the resonators is within their width. For further details on the experimental setup and its relevance for topological photonics, see [34].…”

“…We measure the spectrum over each resonator for all permutations for the coupling strengths t A = 81 MHz and t B = 126 MHz, corresponding to distances d A = 8 mm and d B = 7 mm. The relation between coupling strength t and separation d between two resonators is extracted from two-resonator measurements [33,34]. We chose these values in order to have the least possible overlap between resonances in the spectra, while keeping ρ reasonably small, for the best visible contrast.…”

“…The resonance amplitudes ψ j (i) of each peak j of the measured spectrum above resonator i are extracted via a harmonic inversion method [38,39] and a density-based clustering algorithm [40]. Additionally, we symmetrize the results with respect to the central frequency-index as the resonance widths for the higher frequency bands are larger and thus stronger overlapping making it impossible to extract [34]. Finally we obtain a discretized form of the local density of states LDoS(i, j) = |ψ j (i)| 2 , where |ψ j (i)| 2 represents the wavefunction intensity of state j evaluated over resonator i [33,34].…”

Topological transitions and Anderson localization of light in disordered atomic arrays

“…Most successful experimental realizations of topological photonic phenomena involve two-dimensional (2D) arrays of microwave resonators [18,[24][25][26][27] or parallel waveguides [19,22]. Recently, a planar array of twolevel atoms arranged in a 2D honeycomb lattice embedded in three-dimensional (3D) free space (see Fig.…”