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While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform…

Optics · Physics 2026-02-06 Zimeng Zeng , Zhuoyang Li , Jiayao Liu , Zelong He , Zhaona Wang

Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to back-scattering and deformations, as well as other platforms that feature extreme nonreciprocal wave…

Optics · Physics 2023-02-01 João C. Serra , Mário G. Silveirinha

Topological phases have prevailed across diverse disciplines, spanning electronics, photonics, and acoustics. Hitherto, the understanding of these phases has centred on energy (frequency) bandstructures, showcasing topological boundary…

Photonic time crystals are electromagnetic media with periodically time-varying parameters, enabling momentum band gaps, parametric amplification, and frequency conversion beyond what is possible in time-invariant systems. So far, they have…

Optics · Physics 2026-05-15 Z. Li , M. S. Mirmoosa , V. Asadchy , X. Wang

Photonic time crystals (PTCs) are materials whose dielectric permittivity is periodically modulated in time, giving rise to bandgaps not in energy-as in conventional photonic crystals-but in momentum, known as k-gaps. These k-gaps enable…

Time-variant systems have recently garnered considerable attention due to their unique potentials in manipulating electromagnetic waves. Here, a novel class of topological spacetime crystals is introduced, with a traveling-wave modulation…

Optics · Physics 2025-09-24 João C. Serra , Mário G. Silveirinha

We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…

Mesoscale and Nanoscale Physics · Physics 2022-05-06 Yang Peng

We introduce topological phases in Photonic Time-Crystals. Photonic Time-Crystals are materials in which the refractive index varies periodically and abruptly in time. When the refractive index changes abruptly, the light propagating in the…

Optics · Physics 2018-12-14 Eran Lustig , Yonatan Sharabi , Mordechai Segev

Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…

Time is, figuratively and literally, becoming the new dimension for crystalline matter. As such, rapid recent progress on time-varying media gave rise to the notion of temporal and spatiotemporal crystals. Fundamentally rethinking the role…

Studying the topology of spatiotemporal media poses a fundamental challenge: their remarkable properties stem from breaking spatial and temporal symmetries, yet this same breaking obscures their topological characterization. Here, we show…

Optics · Physics 2026-02-27 Alejandro Caballero , Thomas F. Allard , Paloma A. Huidobro

We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the…

Optics · Physics 2018-03-01 Xuan Zhu , Hai-Xiao Wang , Changqing Xu , Yun Lai , Jian-Hua Jiang , Sajeev John

Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch…

Optics · Physics 2022-11-01 Chang-Yin Ji , Wenze Lan , Peng Fu , Gang Wang , Changzhi Gu , Jiafang Li , Yugui Yao , Baoli Liu

Time-varying media have recently emerged as a new paradigm for wave manipulation, thanks to thesynergy between the discovery of novel, highly nonlinear materials, such as epsilon-near-zero materials, and the questfor novel wave…

This tutorial offers a comprehensive overview of photonic time crystals - artificial materials whose electromagnetic properties are periodically modulated in time at scales comparable to the oscillation period of light while remaining…

Optics · Physics 2024-12-04 M. M. Asgari , P. Garg , X. Wang , M. S. Mirmoosa , C. Rockstuhl , V. Asadchy

Topological phase transitions in condensed matter systems have shown extremely rich physics, unveiling such exotic states of matter as topological insulators, superconductors and superfluids. Photonic topological systems open a whole new…

Topological photonics provides a robust and flexible platform for controlling light, enabling functionalities such as backscattering-immune edge transport and slow-light propagation. In this work, we design and characterize photonic…

Optics · Physics 2025-05-12 Ondřej Novák , Martin Veis , Gervasi Herranz

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly…

Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological…

Mesoscale and Nanoscale Physics · Physics 2018-04-04 Noah P. Mitchell , Lisa M. Nash , William T. M. Irvine

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…

Materials Science · Physics 2020-05-11 Huaqing Huang , Feng Liu
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