Information-entropy enabled identifying topological photonic phase in real space

The field of topological photonics has seen tremendous and wide‐ranging developments in recent years. Evolving from the broader field of topological insulators, topological photonics systems today harness a variety topological phases. These include the Su–Schreifer–Heeger, quantum Hall, quantum valley Hall and quantum spin Hall topologies. Importantly, the latter two generate edge states with opposite group velocities and opposite spin, respectively, allowing unidirectional light propagation and advanced photonic routing to occur. Amongst these exciting developments is a subset of advancements made in topological silicon photonics, which could potentially lend its appeal to complementary metal–oxide–semiconductor (CMOS) photonics applications, including telecommunications, data communications, quantum photonics, future exascale supercomputers, photonic neuromorphic computing, and infrared sensing. The fundamental underpinnings of these topological phases lead to interesting features, including chirality, scatter‐free light propagation around sharp bends, and importantly topological protection against defects, disorder, and scattering. This topological protection may be harnessed toward tunable light propagation, photon‐pair generation, quantum spatial entanglement, robust photonic routing, and beyond. Herein, the recent advancements made in the burgeoning field of topological silicon photonics are discussed.

Topological defects and disorder counteract each other1-5. Intuitively, disorder is considered detrimental, requiring efforts to mitigate its effects in conventional topological photonics6-9. We propose a counter-intuitive approach that exploits a real-momentum topological photonic crystal that harnesses real-space disorder to generate a Pancharatnam-Berry phase10,11, without disrupting the momentum-space singularity originating from bound states in the continuum12. This methodology allows flat optical devices to encode spatial information or even extra topological charge in real space while preserving the topology of bound states in the continuum in momentum space with inherent alignment. Here, as a proof of concept, we demonstrate the simultaneous and independent generation of a real-space broadband vortex or a holographic image alongside resonant momentum-space vortex beams with a narrow bandwidth, which cannot be achieved with conventional methods. Such engineered disorder contributes to vast intrinsic freedoms without adding extra dimensions or compromising the optical flatness13,14. Our findings of real-momentum duality not only lay the foundation for disorder engineering in topological photonics but also open new avenues for optical wavefront shaping, encryption and communications.

The polarization singularities in momentum space, rather than in real space, are capturing interest for active singular optics with exotic light scattering and various topological phenomena, which have potential applications in vortex nano-lasers, valley exciton emission, and others. Here, we propose to magnetically control the polarization singularities in momentum space in the photonic crystal slabs with inversion spatial symmetry (P symmetry). A pair of C points (circular polarization points) with the same topological charge is spawned from a V point (polarization vortex center), and they can be dynamically shifted in momentum space with the variation of the magnetic field. Moreover, the coupling between transverse electric (TE) and transverse magnetic (TM) modes induced by the magnetic field gives rise to a hybrid mode, which can close certain leaky channels to achieve an accidental V point. Such active manipulation of polarization singularities with magnetic field is promised for various applications in light-matter interactions and reveals novel phenomena and physics in singular optics and topological photonics.

Topological chiral edge states in photonic Chern insulators, which exhibit the one-way propagation property with reflection-free behavior and excellent robustness against perturbations, have become an important frontier in topological photonics. Currently, there have been many studies on its robust propagation behavior, but few studies have focused on its radiation properties. In developing functional photonic devices (e.g., topological antennas) for real-world applications, studying traveling-wave radiation characteristics based on chiral edge states deserves more attention. In this Letter, we propose a topological traveling-wave radiation system based on chiral edge states in photonic Chern insulators that show a steerable beam and reflection-free property. By introducing the perturbation controlled by magnetic fields, we demonstrate that exploiting a certain strength of perturbation can flexibly manipulate the radiation beam. In particular, the proposed dual-channel topological traveling-wave radiation system can not only improve the gain but also overcome the issue of impedance matching. The proposed configurations provide a novel way to manipulate topological-wave radiation and have potential applications for designing topological traveling-wave antennas with a reflection-free property.

Topological slow light exhibits potential to achieve stopped light by virtue of its widely known robust and non-reciprocal behaviours. Conventional approach for achieving topological slow light often involves flat-band engineering without disentangling the underlying physical mechanism. Here, we unveil the presence of counter-propagating waves within valley kink states as the distinctive hallmark of the slow light topological photonic waveguides. These counter-propagating waves, supported by topological vortices along glide-symmetric interface, provide significant flexibility for controlling the slowness of light. We tune the group velocity of light by changing the spatial separation between vortices adjacent to the glide-symmetric interface. We also dynamically control the group delay by introducing a non-Hermitian defect using photoexcitation to adjust the relative strength of the counter-propagating waves. This study introduces active slow light topological photonic device on a silicon chip, opening new horizons for topological photon transport through defects, topological light-matter interactions, nonlinear topological photonics, and topological quantum photonics.

Topological photonics attract significant interests due to their intriguing fundamental physics and potential applications. Researchers are actively exploring various artificial platforms to realize novel topological phenomena, which provides promising pathways for the development of robust photonic devices. Among these platforms, femtosecond laser direct-written photonic waveguides show unique ability to visualize intricate light dynamics in 2 + 1 dimensions, which rendering them ideal tools for investigating topological photonics. By integrating topological concepts into these waveguides, researchers not only deepen their understanding of topological physics but also provide potential methodology for developing advanced topological photonic integrated devices. In this review, we discuss recent experimental implementations of different topological phases within femtosecond laser direct-written photonic waveguides, as well as the fascinating physical phenomena induced by the interplay of topology with non-Hermiticity, nonlinearity and quantum physics are also introduced. The exploration of topological waveguide arrays shows great promise in advancing the field of topological photonics, providing a solid foundation for further research and innovation in this rapidly developing domain.

Topological photonics has expanded our understanding of electromagnetic wave propagation and unraveled new methods of electromagnetic wave shaping. Among the various topological photonic systems, valley photonic crystal (VPC) is a highly versatile platform for constructing interfaces that supports unidirectional edge state to enable the robust topological transport of light. Although silicon VPC waveguides has demonstrated the lossless propagation of terahertz (THz) waves through multiple sharp bends, existing designs are mostly based on the standard zigzag-interface. Here, we explore interfacial topological photonics by designing a composite interface junction for an air-slot-like VPC waveguide with a 60° bend and an unchanging bearded-interface to allow the topologically protected propagation of THz waves over a 20% relative bandwidth. We employ particle swarm optimization to design the geometry of a bearded-interface silicon VPC waveguide to achieve a 42% relative bandgap and a topological edge state spanning a usable 25% relative bandwidth. Our work illustrates the prospects and challenges of interfacial topological photonics in the design of broadband silicon topological waveguides for potential applications across the electromagnetic spectrum, including the on-chip THz sixth-generation (6G) communication.

Entanglement entropy and topological properties in a long-range non-Hermitian Su–Schrieffer–Heeger model

The discovery of nonlocal order parameters in real space provides a feasible scheme for studying dynamical critical behavior in topological systems. We study the critical phenomena in the one-dimensional Su-Schrieffer-Heeger (SSH) model by investigating the inhomogeneities in the local winding number in real space. By slowly quenching the system across the topological phase transition during a finite time interval, we find that the length scale defined through the local winding number satisfies the Kibble-Zurek mechanism. In contrast to the density of excitation, the scaling of this length scale is in full analog to the behavior of traditional continuous phase transitions with local order parameter and spontaneous symmetry breaking. In addition, the critical behavior and Kibble-Zurek mechanism in the generalized SSH with next-nearest-neighbor hopping are also studied. These results extend our understanding to the Kibble-Zurek mechanism and topological phase transition in nonequilibrium.

Ultrahigh-[formula omitted] Fano resonance in a cavity-waveguide coupled system based on second-order topological photonic crystals with elliptical holes

Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.

Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.

The emergence of non equilibrium topological phases in low dimensional systems offers an interesting route for material properties engineering. We analyze the dynamical modulation of two coupled one-dimensional chains, described by the Su–Schrieffer–Heeger model. We find that the interplay of driving interactions and interchain coupling leads to the emergence of non-equilibrium edge states with nontrivial topological properties. Using an effective Hamiltonian approach, we quantify the emergent topological phases via the winding number and show that oscillations in the mean pseudospin polarization arise as a consequence of the periodic modulation. The patterns of these pseudospin oscillations are different for the static trivial and topological phases offering a dynamical means to distinguish both physical configurations. The system also exhibits non integer values of the winding number, which have been recently reported experimentally in connection to spin textures.

Synthetic optical materials have been recently employed as a powerful platform for the emulation of topological phenomena in wave physics. Topological phases offer exciting opportunities, not only for fundamental physics demonstrations, but also for practical technologies. Yet, their impact has so far been primarily limited to their claimed enhanced robustness. Here, we clarify the role of robustness in topological photonic systems, and we discuss how topological photonics may offer a wider range of important opportunities in science and for practical technologies, discussing emergent and exciting research directions.

Contactless tuning of signals represents a promising avenue for advancing topological phononics and photonics devices, particularly in the frequency and spatial domains. For topological phase transitions, breaking the spatial inversion symmetry geometrically to obtain an open topological band gap is a typical way to introduce perturbations. This approach has great limitations in achieving reconfigurable topological protection routes. We present a thermally modulated two-dimensional elastic topological insulator made from a patterned substrate and a temperature-sensitive vanadium dioxide film, allowing elastic waves to propagate in the suspended region of the 2D material. The topological phase transition is activated by locally heating a portion of the unit cell. This heating induces a phase transition in the material by exploiting changes in mechanical properties, achieving symmetry breaking. The topological valley-locked states with strong localization at the interface are obtained by placing unit cells with different chirality adjacent to each other at the omnidirectional bulk band gap. Full-field simulations confirm both the reconfigurability of arbitrary paths and the robustness of the induced waves against defects. Eliminating the need for pre-etched topological protection paths on patterned substrates enhances flexibility in both manufacturing and application. This innovative scheme employs localized temperature control at the unit cell scale to achieve effects akin to approximately 10% geometric symmetry breaking, thereby significantly reducing precision manufacturing requirements. Moreover, localized thermal modulation holds considerable potential for improving modulation rates while minimizing energy loss.