Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies

## Abstract

Invisibility by metamaterials is of great interest, where optical properties are manipulated in the real permittivity–permeability plane1,2. However, the most effective approach to achieving invisibility in various military applications is to absorb the electromagnetic waves emitted from radar to minimize the corresponding reflection and scattering, such that no signal gets bounced back. Here, we show the experimental realization of chip-scale unidirectional reflectionless optical metamaterials near the spontaneous parity-time symmetry phase transition point where reflection from one side is significantly suppressed. This is enabled by engineering the corresponding optical properties of the designed parity-time metamaterial in the complex dielectric permittivity plane. Numerical simulations and experimental verification consistently exhibit asymmetric reflection with high contrast ratios around a wavelength of of 1,550 nm. The demonstrated unidirectional phenomenon at the corresponding parity-time exceptional point on-a-chip confirms the feasibility of creating complicated on-chip parity-time metamaterials and optical devices based on their properties.

This is a preview of subscription content, access via your institution

## Relevant articles

• ### Band structures and scattering properties of the simplest one-dimensional $${\mathscr {P}}{\mathscr {T}}$$-symmetric photonic crystal

Scientific Reports Open Access 27 September 2022

• ### Linear response theory of open systems with exceptional points

Nature Communications Open Access 07 June 2022

• ### Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Nature Communications Open Access 19 April 2022

## Access options

\$32.00

All prices are NET prices.

## References

1. Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006).

2. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

3. Bender, C. M. & Böttcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).

4. Bender, C. M. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947–1018 (2007).

5. Bender, C. M., Brody, D. C. & Jones, H. F. Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction. Phys. Rev. D 70, 025001 (2004).

6. Longhi, S. & Della Valle, G. Photonic realization of PT-symmetric quantum field theories. Phys. Rev. A 85, 012112 (2012).

7. Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT-symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008).

8. Musslimani, Z. H., El-Ganainy, R., Makris, K. G. & Christodoulides, D. N. Optical solitons in PT periodic potentials. Phys. Rev. Lett. 100, 030402 (2008).

9. Klaiman, S., Guenther, U. & Moiseyev, N. Visualization of branch points in PT symmetric waveguides. Phys. Rev. Lett. 101, 080402 (2008).

10. Longhi, S. Bloch oscillations in complex crystals with PT symmetry. Phys. Rev. Lett. 103, 123601 (2009).

11. Zheng, M. C., Christodoulides, D. N., Fleischmann, R. & Kottos, T. PT optical lattices and universality in beam dynamics. Phys. Rev. A 82, 010103(R) (2010).

12. Graefe, E. M. & Jones, H. F. PT-symmetric sinusoidal optical lattices at the symmetry-breaking threshold. Phys. Rev. A 84, 013818 (2011).

13. Miroshnichenko, A. E., Malomed, B. A. & Kivshar, Y. S. Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances. Phys. Rev. A 84, 012123 (2011).

14. Longhi, S. PT-symmetric laser absorber. Phys. Rev. A 82, 031801 (2010).

15. Chong, Y. D., Ge, L. & Stone, A. D. PT-symmetry breaking and laser-absorber modes in optical scattering systems. Phys. Rev. Lett. 106, 093902 (2011).

16. Ge, L. et al. Unconventional modes in lasers with spatially varying gain and loss. Phys. Rev. A 84, 023820 (2011).

17. Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nature Phys. 6, 192–195 (2010).

18. Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009).

19. Schindler, J., Li, A., Zheng, M. C., Ellis, F. M. & Kottos, T. Experimental study of active LRC circuits with PT symmetries. Phys. Rev. A 84, 040101(R) (2011).

20. Kulishov, M., Laniel, J., Bélanger, N., Azaña, J. & Plant, D. Nonreciprocal waveguide Bragg gratings. Opt. Express 13, 3068–3078 (2005).

21. Lin, Z. et al. Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett. 106, 213901 (2011).

22. Longhi, S. Invisibility in PT-symmetric complex crystals. J. Phys. A 44, 485302 (2011).

23. Jones, H. F. Analytic results for a PT-symmetric optical structure. J. Phys. A 45, 135306 (2012).

24. Mostafazadeh, A. Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies. Phys. Rev. Lett. 102, 220402 (2009).

25. Muga, J. G., Palaob, J. P., Navarroa, B. & Egusquizac, I. L. Complex absorbing potentials. Phys. Rep. 395, 357–426 (2004).

26. Cannata, F., Dedonder, J-P. & Ventura, A. Scattering in PT-symmetric quantum mechanics. Ann. Phys. 322, 397–433 (2007).

27. Regensburger, A. et al. Parity–time synthetic photonic lattices. Nature 488, 167–171 (2012).

28. Razzari, L. & Morandotti, R. Gain and loss mixed in the same cauldron. Nature 488, 163–164 (2012).

29. Kottos, T. Optical physics: Broken symmetry makes light work. Nature Phys. 6, 166–167 (2010).

30. Berry, M. V. Optical lattices with PT symmetry are not transparent. J. Phys. A 41, 244007 (2008).

31. Zhang, S., Xia, C. & Fang, N. Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett. 106, 024301 (2011).

## Acknowledgements

We acknowledge critical support and infrastructure provided for this work by the Kavli Nanoscience Institute at Caltech. This work was supported by the NSF ERC Center for Integrated Access Networks (no. EEC-0812072), the National Basic Research of China (no. 2012CB921503 and no. 2013CB632702), the National Nature Science Foundation of China (no. 11134006), the Nature Science Foundation of Jiangsu Province (no. BK2009007), the Priority Academic Program Development of Jiangsu Higher Education, and CAPES and CNPQ—Brazilian Foundations. M-H.L. also acknowledges the support of FANEDD of China.

## Author information

Authors

### Contributions

L.F. and M-H.L. conceived the idea. L.F., Y-L.X. and M-H.L. designed the device. Y-L.X., L.F. and M-H.L. performed the theoretical analysis of parity-time symmetry. W.S.F. and L.F. designed the chip and carried out fabrications and measurements. All the authors contributed to discussion of the project. Y-F.C. and A.S. guided the project. L.F. wrote the manuscript with revisions from other authors.

### Corresponding authors

Correspondence to Liang Feng, Ye-Long Xu, William S. Fegadolli or Ming-Hui Lu.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary Information (PDF 870 kb)

## Rights and permissions

Reprints and Permissions

Feng, L., Xu, YL., Fegadolli, W. et al. Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nature Mater 12, 108–113 (2013). https://doi.org/10.1038/nmat3495

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/nmat3495

• ### Unidirectional amplification with acoustic non-Hermitian space−time varying metamaterial

• Xinhua Wen
• Xinghong Zhu
• Jensen Li

Communications Physics (2022)

• ### Band structures and scattering properties of the simplest one-dimensional $${\mathscr {P}}{\mathscr {T}}$$-symmetric photonic crystal

• Tiecheng Wang
• Xiang Gou

Scientific Reports (2022)

• ### Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss

• Alexander Yulaev
• Sangsik Kim

Nature Nanotechnology (2022)

• ### Linear response theory of open systems with exceptional points

• A. Hashemi
• K. Busch
• R. El-Ganainy

Nature Communications (2022)

• ### Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

• Xiaoqian Shu
• Aodong Li
• Lin Chen

Nature Communications (2022)