# Topological protection of photonic mid-gap defect modes

## Abstract

Defect modes in two-dimensional periodic photonic structures have found use in diverse optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for enhancement of nonlinearity, lasing and cavity quantum electrodynamics. Defect-core photonic crystal fibres allow for supercontinuum generation and endlessly single-mode fibres with large cores. However, these modes are notoriously fragile: small structural change leads to significant detuning of resonance frequency and mode volume. Here, we show that photonic topological crystalline insulator structures can be used to topologically protect the mode frequency at mid-gap and minimize the volume of a photonic defect mode. We experimentally demonstrate this in a femtosecond-laser-written waveguide array by observing the presence of a topological zero mode confined to the corner of the array. The robustness of this mode is guaranteed by a topological invariant that protects zero-dimensional states embedded in a two-dimensional environment—a novel form of topological protection that has not been previously demonstrated.

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## Acknowledgements

W.A.B. and T.L.H. are supported by the Office of Naval Research Young Investigator Program Award N00014-15-1-2383. M.C.R. acknowledges support from the National Science Foundation under grant number ECCS-1509546 and the Penn State Materials Research Science and Engineering Center, DMR-1420620 as well as from the Alfred P. Sloan Foundation under fellowship number FG-2016-6418. K.P.C. acknowledges the National Science Foundation under grant numbers ECCS-1509199 and DMS-1620218.

## Author information

Authors

### Contributions

J.N. built the experimental probing station (with assistance from M.J.C.), performed the experimental measurements, numerical simulations and data analysis under the guidance of M.C.R. S.H. developed the laser fabrication process and characterized the samples under the supervision of K.P.C. and M.C.R. W.A.B. proposed the model and provided theoretical analysis and simulations. T.L.H. provided theoretical analysis. J.N., W.A.B., T.L.H. and M.C.R. wrote the paper. M.C.R. supervised the project.

### Corresponding author

Correspondence to Mikael C. Rechtsman.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary discussion; Supplementary Figures 1–8; Supplementary references 1–3. [In this file initially published, some characters did not display properly; this file has now been replaced.]

### Supplementary Video 1

Excitation of zero mode.

### Supplementary Video 2

Beating of two modes as wavelength is swept.

### Supplementary Video 3

Injection of light at the corner.

### Supplementary Video 4

Response due to detuning of refractive index at corner.

### Supplementary Video 5

Response due to detuning of wavelength at corner.

## Rights and permissions

Reprints and Permissions

Noh, J., Benalcazar, W.A., Huang, S. et al. Topological protection of photonic mid-gap defect modes. Nature Photon 12, 408–415 (2018). https://doi.org/10.1038/s41566-018-0179-3

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