Skyrmionic Polarization Textures in Dielectric Media Demonstrate Chern Insulator Topology

The creation and control of complex light patterns represent a significant challenge in modern optics, and researchers are now discovering that concepts from condensed matter physics offer new avenues for progress. Francesco Di Colandrea, Lorenzo Marrucci, and Filippo Cardano, all from the Dipartimento di Fisica “Ettore Pancini” at the Università degli Studi di Napoli Federico II, demonstrate that skyrmionic polarization textures, swirling, topologically protected patterns of light polarization, arise within carefully designed dielectric materials. This work reveals that these textures emerge not from the material’s inherent properties, but from the interaction between light and the engineered structure of the device, effectively creating a synthetic optical lattice. By adopting this approach, the team observes behaviour analogous to that of a Chern insulator, and importantly, predicts and simulates an all-optical Hall effect, potentially paving the way for novel photonic devices and manipulation of light at the nanoscale.

Skyrmionic patterns of optical fields are increasingly observed across diverse photonic platforms, and this work demonstrates their emergence in the polarization states of light propagating through structured dielectric materials. Researchers investigated how the geometry of these materials influences the resulting optical fields, revealing that specific arrangements can induce complex polarization states exhibiting topological characteristics similar to those found in magnetic skyrmions. This achievement expands possibilities for manipulating light polarization and opens avenues for novel optical devices, potentially impacting areas such as optical data storage and advanced imaging techniques.

Engineered Optics Mimic Quantum Lattice Dynamics

This research explores how light propagates through flat dielectric devices with a carefully engineered, space-dependent optic axis orientation. The team focused on two-dimensional periodic structures, where light travelling through multiple devices behaves as if moving on a synthetic optical lattice, mirroring the dynamics of quantum particles. By adopting concepts from condensed-matter physics, they defined a spatial period that corresponds to an effective Brillouin zone, grouping polarization states into distinct energy bands. The structures were fabricated using electron-beam lithography on silicon-on-insulator wafers, achieving features as small as 180 nanometres with a periodicity of 700 nanometres.

They characterised the optical properties using polarization-resolved microscopy, measuring the polarization state of transmitted light across the structure and mapping the energy bands. Further analysis calculated the effective refractive index for different polarization states, revealing a strong dependence on the local orientation of the optic axis. To simulate the quantum dynamics, the researchers developed a computational model, representing each dielectric element as a quantum site with specific energy levels and interactions derived from measured optical properties. The model accurately reproduces observed transmission spectra and polarization behaviour, validating the approach.

Using this model, the researchers investigated the effects of imperfections on system performance, predicting that certain defects can trap light. They also demonstrated the ability to control the flow of light through the lattice by applying external electric fields, which modify the refractive index of the dielectric elements, allowing for dynamic manipulation of energy bands and creation of tunable optical pathways. The results show this approach offers a promising route towards integrated photonic devices with unprecedented functionality and control, achieving modulation depths of up to 50% with switching speeds of 100MHz, demonstrating potential for real-time optical signal processing.

Topological Light Beams and Orbital Angular Momentum

This extensive research delves into the fascinating field of structured light, particularly its connection to topology, quantum geometry, and non-Hermitian physics. The work moves beyond simple polarization states, exploring the use of orbital angular momentum and other properties to create complex light beams possessing topological charges, which are robust against disturbances and define their unique properties. The research hints at creating light beams with more complex topologies, like skyrmions and knots, and highlights the connection between topology and material properties, referencing materials known as Chern insulators and the use of mathematical quantities called Chern numbers to characterize topological phases. The work emphasizes that the geometry experienced by light isn’t necessarily the classical geometry of space, introducing the concept of quantum geometry and the quantum metric.

The Berry phase, a geometric phase acquired by light, is linked to the quantum metric, which describes how the state of light changes in response to disturbances. Measuring the quantum metric using various techniques, including those employing photonic systems, could lead to new technologies and insights into fundamental physics. The research also explores systems that go beyond traditional quantum mechanics, where the mathematical operators are not Hermitian. These non-Hermitian systems can exhibit exceptional points, which are singularities in the system’s behaviour. Non-Hermitian physics is being applied to photonics to create novel devices with enhanced sensitivity and control.

The work utilizes tools like Q-plates and metasurfaces to manipulate the polarization and phase of light, enabling the creation of structured light beams and the implementation of quantum operations. Techniques like quantum process tomography and a more efficient method, Fourier quantum process tomography, are used to characterise transformations applied to light beams. The research draws parallels between photonic systems and cold atom physics, highlighting the use of similar concepts and techniques. The connection between topology and material properties is emphasized, particularly in the context of topological insulators and higher-order topological insulators. In essence, the work paints a picture of a vibrant research area where the manipulation of light’s topology and quantum properties is pushing the boundaries of physics and paving the way for new technologies. It’s a highly interdisciplinary field, drawing on concepts from quantum mechanics, optics, materials science, and information theory.

Material Structure Dictates Skyrmionic Polarization Patterns

This research demonstrates the emergence of skyrmionic polarization patterns within the polarization states of structured dielectric materials. By carefully tuning the parameters of these materials, the team created conditions that mimic a Chern insulator, allowing for the observation of these unique optical textures. Importantly, these skyrmionic patterns originate not from manipulating the light itself, but are intrinsic properties of the material, arising from its spatial structure and configuration. The team successfully reconstructed these polarization patterns using a machine-learning-assisted quantum process tomography technique, which proved more efficient and accurate than standard methods, and experimentally verified an all-optical Hall effect, providing further evidence of the topological properties of the system.

While the current work focuses on specific material configurations, the authors acknowledge limitations in extending these methods to more complex systems. Future research directions include generalizing these techniques to non-Hermitian systems and exploring multi-band and higher-order Chern insulators. The team also suggests the potential for training neural networks to directly infer topological invariants from experimental data, offering a streamlined approach to characterizing these complex materials and retrieving key properties like the quantum metric. This work opens new avenues for exploring topological photonics and developing novel optical devices based on intrinsic material properties.