🔬 optics

Topological photonics in one-dimensional settings

This chapter provides an overview of one-dimensional topological photonics, reviewing fundamental models like the SSH, recent experimental advances in nonlinear and non-Hermitian systems, and various topological phenomena such as Floquet systems and topological pumping.

Original authors: Shiqi Xia, Ziteng Wang, Domenico Bongiovanni, Dario Jukić, Daohong Song, Liqin Tang, Jingjun Xu, Roberto Morandotti, Hrvoje Buljan, Zhigang Chen

Published 2026-02-10

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Shiqi Xia, Ziteng Wang, Domenico Bongiovanni, Dario Jukić, Daohong Song, Liqin Tang, Jingjun Xu, Roberto Morandotti, Hrvoje Buljan, Zhigang Chen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Magic of "Topological" Light: A Guide to the Invisible Highways of Photons

Imagine you are trying to guide a crowd of people through a massive, chaotic music festival. Usually, people wander aimlessly, bumping into each other, getting lost in the crowd, or stuck in dead ends.

Now, imagine if you could build a set of invisible, indestructible highways through that crowd. No matter how much people push, shove, or how much the music changes, the people on these highways move perfectly from point A to point B, completely immune to the chaos around them.

That is essentially what this scientific paper is about. It explores a field called Topological Photonics, where scientists use the "math of shapes" to create special paths for light (photons) that are protected from interference.

1. The Star of the Show: The SSH Model (The "Perfectly Balanced Seesaw")

The paper focuses heavily on something called the SSH Model.

Think of a long line of people holding hands. In a normal line, everyone holds hands with equal strength. But in an SSH model, people hold hands in a specific pattern: a strong grip between two people, followed by a weak grip between the next pair.

Because of this "strong-weak-strong-weak" rhythm, something magical happens at the very ends of the line. Even if the middle of the line is shaking or messy, a "special person" (a topological state) will always appear at the very edge, standing perfectly still and protected. This is what scientists call an Edge State.

2. Adding "Spice": Nonlinearity (The "Shape-Shifting Highway")

The researchers didn't just want to build static highways; they wanted highways that could change based on how much "traffic" (light) was on them. This is called Nonlinearity.

Inherited Effects: Imagine a highway that is already built. If you add more cars, the highway stays the same, but the cars might start driving in a specific, synchronized formation.
Emergent Effects: This is even cooler. Imagine a regular, messy dirt road. But as soon as you drive enough heavy trucks over it, the weight of the trucks actually compresses the dirt into a smooth, paved highway. The "highway" didn't exist until the traffic arrived!

3. The "Ghostly" World: Non-Hermitian Physics (The "Leaky Pipe")

In most physics, we assume energy is perfectly conserved (nothing is lost). But in the real world, light leaks out, or we add "gain" (like a laser) to boost it. This is called Non-Hermitian physics.

The paper describes how scientists can use this "leakiness" to control light. It’s like having a plumbing system where you can precisely control which pipes leak and which ones spray extra water. By balancing the "leaks" (loss) and the "sprays" (gain), they can force light to behave in ways that were previously thought impossible, like creating "topological lasers" that are incredibly stable.

4. Why does this matter? (The "Future Tech" Toolbox)

You might ask, "Why spend all this time playing with light-highways?" The paper suggests several real-world "superpowers" this could give us:

Unstoppable Lasers: Creating lasers that don't flicker or fail even if the device is bumped or slightly damaged.
Ultra-Fast Computers: Using these "highways" to move information around tiny computer chips without the signals getting lost in the "noise."
Next-Gen Sensors: Creating sensors that can detect tiny changes in the environment (like biological molecules) because the light is so sensitive to the "shape" of its path.

Summary in a Nutshell

Scientists are learning how to use the deep, mathematical rules of geometry to "program" light. By building tiny, patterned structures, they can create protected lanes for light that are immune to chaos, can change their own shape, and can be controlled with incredible precision. It is the difference between throwing a ball into a crowd and launching a train on a high-speed rail.

This technical summary provides a detailed overview of the review chapter "Topological photonics in one-dimensional settings" by Xia et al.

1. Problem and Scope

The field of topological photonics has transitioned from theoretical explorations of quantum Hall analogs to the practical manipulation of light using topological principles. While much research has focused on two-dimensional (2D) systems, one-dimensional (1D) settings—specifically those based on the Su–Schrieffer–Heeger (SSH) model—offer a unique, simplified, yet incredibly rich platform for studying the interplay between topology, nonlinearity, and non-Hermiticity.

The central challenge addressed by this review is to synthesize the vast, rapidly evolving landscape of 1D topological photonics. The authors aim to bridge the gap between fundamental 1D models (like SSH, Rice–Mele, and Aubry–André–Harper) and their complex, real-world applications in nonlinear optics, non-Hermitian physics, and higher-order topological insulators (HOTIs).

2. Methodology and Theoretical Framework

The paper organizes its technical discussion around several core theoretical pillars:

The SSH Model: The authors define the 1D SSH model as a dimerized chain with intracell ( $v$ ) and intercell ( $w$ ) hopping amplitudes. They explain the role of chiral symmetry in protecting topological zero-modes and the use of the winding number ( $\mathcal{W}$ ) as a topological invariant.
Symmetry and Invariants: For systems where chiral symmetry is broken but inversion symmetry is preserved, the authors discuss the Zak phase ( $\mathcal{Z}$ ) and its relationship to Wannier centers and bulk polarization.
Topological Pumping: The review details the Rice–Mele model (an SSH model with staggered onsite potential) and the Aubry–André–Harper (AAH) model (quasiperiodic modulation). These are used to explain Thouless pumping, where adiabatic variation of parameters maps 1D dynamics to 2D Chern number physics.
Experimental Platforms: The authors highlight the use of photorefractive nonlinear crystals (using CW-laser-writing for reconfigurable lattices) and photonic crystal nanocavities as primary methodologies for implementing these theoretical models.

3. Key Contributions and Results

A. Nonlinear Topological Photonics

The authors categorize nonlinear effects into two types:

Inherited Phenomena: Where nonlinearity acts as a perturbation to a linear topological system. Examples include the formation of topological gap solitons and the nonlinearity-induced coupling of light into topological defects (breaking chiral symmetry to allow mode coupling).
Emergent Phenomena: Where nonlinearity creates topology that did not exist in the linear regime. A key result is the observation of dynamic topological phase transitions in interacting soliton lattices, where the system oscillates between trivial and nontrivial phases.

B. Non-Hermitian Topology

The review explores the intersection of topology and energy exchange (gain/loss).

PT-Symmetry Control: The authors demonstrate that optical nonlinearity can be used to tune Parity-Time (PT) symmetry. In a "passive" PT-symmetric SSH lattice, nonlinearity can trigger a phase transition from a PT-symmetric regime (real eigenvalues) to a non-PT regime (asymmetric eigenmodes), effectively controlling the "birth and death" of topological modes.

C. Higher-Order Topological Insulators (HOTIs)

The paper bridges 1D and 2D by discussing Topological Crystalline Insulators (TCIs).

2D SSH and Kagome Lattices: They review how 2D extensions of the SSH model and breathing Kagome lattices (BKLs) support corner states.
Orbital Degrees of Freedom: A significant technical highlight is the discussion of $p$ -orbital corner states in Kagome lattices, which require additional "orbital-hopping symmetry" for protection.
Sub-symmetry (SubSy): The authors discuss the discovery that corner states can be protected by symmetries of specific sublattices, even when the global symmetry of the system is broken.

D. Practical Applications

The review showcases successful implementations in:

Terahertz (THz) Technology: Topologically tuned THz confinement and generation in lithium niobate chips.
Topological Lasing: Robust, low-threshold lasing in polymer-cholesteric liquid crystal superlattices and silicon nanocavity chains.
Nonlinear Harmonic Generation: Giant enhancement of third-harmonic generation via topological edge-mode localization.

4. Significance and Outlook

The significance of this work lies in its comprehensive mapping of how 1D topological physics serves as a "laboratory" for more complex phenomena. By mastering 1D settings, researchers can develop:

Robust Photonic Devices: Lasers and signal processors that are immune to structural imperfections.
Programmable Photonics: Integrated chips that allow real-time switching between topological phases.
New Physics Discovery: Exploring the "triple phase transition" (intertwining topology, non-Hermiticity, and symmetry breaking) and the role of disorder as a constructive resource (Topological Anderson Insulators).

Future Directions: The authors identify the need for unified theoretical frameworks to handle the simultaneous presence of nonlinearity, non-Hermiticity, and disorder, and the challenge of scaling these systems into low-loss, integrated quantum-photonic architectures.