Abstract
Geometrical dimensionality plays a fundamentally important role in the topological effects arising in discrete lattices. Although direct experiments are limited by three spatial dimensions, the research topic of synthetic dimensions implemented by the frequency degree of freedom in photonics is rapidly advancing. The manipulation of light in these artificial lattices is typically realized through electro-optic modulation; yet, their operating bandwidth imposes practical constraints on the range of interactions between different frequency components. Here we propose and experimentally realize all-optical synthetic dimensions involving specially tailored simultaneous short- and long-range interactions between discrete spectral lines mediated by frequency conversion in a nonlinear waveguide. We realize triangular chiral-tube lattices in three-dimensional space and explore their four-dimensional generalization. We implement a synthetic gauge field with nonzero magnetic flux and observe the associated multidimensional dynamics of frequency combs, all within one physical spatial port. We anticipate that our method will provide a new means for the fundamental study of high-dimensional physics and act as an important step towards using topological effects in optical devices operating in the time and frequency domains.
Highlights
1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Introduction Discrete photonic lattices constitute a versatile platform for topological photonics[1], with various implementations employing arrays of evanescently coupled waveguides[2], metamaterials[3], and coupled resonators[4]
We start by introducing a general approach for the implementation of spectral photonic lattices in a nonlinear waveguide
The working principle based on nonlinear frequency conversion enables an alloptical realization with large separation between the spectral lines, overcoming the bandwidth limitations of systems employing electrooptic modulation (EOM)
Summary
Discrete photonic lattices constitute a versatile platform for topological photonics[1], with various implementations employing arrays of evanescently coupled waveguides[2], metamaterials[3], and coupled resonators[4]. In these systems, the most commonly considered topological features originate from the dispersion associated with the wavevector space, where the geometrical dimensionality fundamentally limits the degrees of freedom that can contribute to the topological invariant. The possibility of accessing higher geometrical dimensions is a key factor enabling a drastic boost in the manifestations of topological effects This motivates the rapidly developing field of synthetic dimensions[5,6], where many schemes for. It is of fundamental interest to explore various lattice types in addition to honeycombs and analyse the possibility of realizing multidimensional analogues of chiral-tube structures
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