Optical Topology and Protected Light States

By Ankit SinghReviewed by Susha Cheriyedath, M.Sc.Sep 3 2026

Optical topology describes how the bands of an engineered photonic medium carry a global property that survives small changes in shape or material. Researchers build these media from photonic lattices, coupled ring resonators, waveguide arrays, and photonic crystals, then tune couplings, phase delays, and lattice geometry until the bands acquire that property.

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Topology is a design parameter alongside frequency, polarization, and phase. The consequence appears at the boundaries rather than within the bulk material. A medium with nontrivial bands hosts protected light states along its edges, which can carry energy unidirectionally along a domain wall. Disorder scatters light weakly here because the bulk band gap forbids propagation away from the boundary, which leaves backward channels unavailable.¹

Invariants that Count Protected States

The Su-Schrieffer-Heeger chain provides the clearest illustration. Two sites per unit cell couple via intra-cell and inter-cell amplitudes, and the Bloch Hamiltonian maps each wave vector to a circle. When inter-cell coupling dominates, the circle encloses the origin and the winding number equals one. Otherwise, the circle misses the origin, and the number vanishes.²

The chain's gap equals the difference between its two coupling amplitudes at the Brillouin zone edge. Equal couplings close the gap and turn the chain into a uniform lattice. Passing through that point inverts the sublattice phases, a band inversion signaling a change in band topology. The Zak phase, the one-dimensional Berry phase, records the outcome as 0 or π.²

Bulk-boundary correspondence links these numbers to observable modes. Where the invariant changes across an interface, including the interface between a topological chain and space, localized states appear, and their count matches the difference in invariant values. Such a state occupies roughly one lattice cell and decays exponentially outward, with stronger coupling contrast producing tighter confinement.²

Chiral Edge States Measured Directly

Gyromagnetic photonic crystals under a magnetic field provide the original demonstration. Breaking time-reversal symmetry opens a gap labeled by a Chern number, measured as -1 in a recent microwave experiment, and that gap fills with chiral edge modes. Measured edge transmission dominates between roughly 8.96 and 9.27 GHz, while a source at 9.12 GHz drives robust counterclockwise circulation around the boundary.³

Valley photonic crystals achieve similar on-chip confinement without magnetic bias. Two triangular air holes of unequal side lengths per cell break spatial inversion symmetry, and a zigzag interface between two such lattices supports a single edge state spanning nearly the whole Brillouin zone inside the gap. Bending that interface into a closed triangular loop turns guided light into a resonator.⁴

Finite loop size quantizes the edge wave vector, so each cavity mode corresponds to an edge state at a momentum set by the effective round-trip length. Lower-order modes cut across the corners via local Poynting-vector vortices, shortening the trip. The free spectral range peaks near the valley momenta, where edge dispersion steepens and the group index is at its minimum.⁴

Corner States and Higher-order Topology

Protected light states can occupy dimensions well below that of the host lattice. In an n-dimensional structure, higher-order phases confine light to regions of dimension n-m where m≥2. This produces corner-localized modes inside a two-dimensional crystal. Such states rely on quantized multipole moments rather than on the Chern numbers that govern unidirectional chiral edge transport.¹

A quadrupole phase realized on the same gyromagnetic platform carries a trivial Chern number and a quadrupole moment of 1/2. Bulk and edge transmission both dip between about 8.04 and 8.38 GHz, showing that no edge channel exists there, while corner transmission peaks sharply at 8.23 GHz. Field scanning resolves 4 degenerate corner modes with strong spatial localization.³

Tuning the applied field from 0.18 to 0.42 Tesla sweeps these corner states through the gap and into the surrounding bulk continuum. At 0.38 Tesla, a corner peak appears at 8.51 GHz, a frequency at which bulk modes also exist, and measured field patterns confirm that the corner state remains localized while sharing its frequency with extended states.³

Gain, Loss, and Complex Bands

Real photonic devices absorb, radiate, and amplify light, so their spectra become complex and the Hermitian bookkeeping needs revision. Bands avoiding a baseline in the complex plane define a line gap that resembles the familiar gapped case, while bands avoiding a single base point define a point gap. Winding of the bands around that point yields a spectral winding number.¹

Exceptional points in these complex spectra push this accounting further. Two eigenvalues swap places after one loop in parameter space and return only after a second loop, giving a Berry phase of π and a half-integer winding number. Bands then braid around one another, and under open boundaries, the standard correspondence between bulk invariants and boundary modes requires modified formulations.¹

Protected Light States Inside Lasers

Dirac-vortex microcavities show what these ideas deliver in a working light source. A hexagonal photonic crystal with 6 triangular holes per cell interpolates between a photonic quantum spin Hall regime and a valley Hall regime through two geometric parameters, and winding that interpolation angle once around the cavity center produces a tightly bound vortex state at the center.⁵

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Built with a 641 nm lattice constant and quantum dot layers grown directly on a 300 mm silicon wafer, the cavity lases continuously at room temperature at a telecom wavelength with single-mode, linearly polarized, vertical emission. Lasing pins to the Dirac frequency, and the mode spacing departs from the usual inverse volume scaling, a combination that suits silicon nanophotonic integration.⁵

Boundaries of Protection

Protection addresses backscattering caused by geometric imperfections while leaving all other loss channels intact. This dramatically influences the device's performance. Measured edge propagation still decays due to material absorption, corner-state frequencies shift by around 0.02 GHz due to fabrication errors, and closed-loop edge cavities lose light through bending, radiation, and coupling paths that the topology never addresses in the first place.³

Current experimental work is expanding the range of accessible phases into three dimensions. Gyrotropic crystals with a periodic structural modulation host neighboring domains separated by an axion angle of π that still share identical Chern vectors throughout, and tilting the magnetic bias selects which hinges of an embedded wire carry the guided states that follow from that choice.⁶

References and Further Reading

1. Yan, Q. et al. (2023). Advances and applications on non-Hermitian topological photonics. Nanophotonics, 12(13), 2247-2271. DOI:10.1515/nanoph-2022-0775. https://onlinelibrary.wiley.com/doi/10.1515/nanoph-2022-0775
2. Hotte-Kilburn, A. et al. (2025). Integrated topological photonics in one dimension. Advances in Physics: X, Vol. 25. DOI:10.1080/23746149.2025.2476417. https://www.tandfonline.com/doi/full/10.1080/23746149.2025.2476417
3. Zhou, P. et al. (2024). Realization of a quadrupole topological insulator phase in a gyromagnetic photonic crystal. National Science Review, 11(11). DOI:10.1093/nsr/nwae121. https://academic.oup.com/nsr/article/11/11/nwae121/7638834
4. Wang, W. et al. (2025). On-chip topological edge state cavities. Light: Science & Applications, 14(1), 330. DOI:10.1038/s41377-025-02017-3. https://www.nature.com/articles/s41377-025-02017-3
5. Ma, J. et al. (2023). Room-temperature continuous-wave topological Dirac-vortex microcavity lasers on silicon. Light: Science & Applications, 12(1), 255. DOI:10.1038/s41377-023-01290-4. https://www.nature.com/articles/s41377-023-01290-4
6. Devescovi, C. et al. (2024). Axion topology in photonic crystal domain walls. Nature Communications, 15(1), 6814. DOI:10.1038/s41467-024-50766-3. https://www.nature.com/articles/s41467-024-50766-3

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