## Demonstration of a large-scale optical exceptional point structure |

Optics Express, Vol. 22, Issue 2, pp. 1760-1767 (2014)

http://dx.doi.org/10.1364/OE.22.001760

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### Abstract

We report a large-size (4-inch) optical exceptional point structure at visible frequencies by designing a multilayer structure of absorbing and non-absorbing dielectrics. The optical exceptional point was implemented as indicated by the realized unidirectional reflectionless light transport at a wafer scale. The associated abrupt phase transition is theoretically and experimentally confirmed when crossing over the exceptional point in wavelengths. The large scale demonstration of phase transition around exceptional points will open new possibilities in important applications in free space optical devices.

© 2013 Optical Society of America

## 1. Introduction

## 2. Exceptional point and phase transition

12. C. Dembowski, H. D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. **86**(5), 787–790 (2001). [CrossRef] [PubMed]

14. F. Cannata, J. P. Dedonder, and A. Ventura, “Scattering in *PT*-symmetric quantum mechanics,” Ann. Phys. **322**(2), 397–433 (2007). [CrossRef]

*t*is the transmission coefficient,

*r*and

_{f}*r*are reflection coefficients in forward and backward directions, respectively. As quantum exceptional points are designed by engineering the Hamiltonian matrix [10

_{b}10. Y. Choi, S. Kang, S. Lim, W. Kim, J. R. Kim, J. H. Lee, and K. An, “Quasieigenstate coalescence in an atom-cavity quantum composite,” Phys. Rev. Lett. **104**(15), 153601 (2010). [CrossRef] [PubMed]

*r*or

_{f}*r*is zero, i.e., the system is unidirectional reflectionless.

_{b}13. J. G. Muga, J. P. Palao, B. Navarroa, and I. L. Egusquiza, “Complex absorbing potentials,” Phys. Rep. **395**(6), 357–426 (2004). [CrossRef]

15. W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. Math. Gen. **37**(6), 2455–2464 (2004). [CrossRef]

8. L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. **12**(2), 108–113 (2013). [CrossRef] [PubMed]

10. Y. Choi, S. Kang, S. Lim, W. Kim, J. R. Kim, J. H. Lee, and K. An, “Quasieigenstate coalescence in an atom-cavity quantum composite,” Phys. Rev. Lett. **104**(15), 153601 (2010). [CrossRef] [PubMed]

16. H. Cartarius, J. Main, and G. Wunner, “Exceptional points in atomic spectra,” Phys. Rev. Lett. **99**(17), 173003 (2007). [CrossRef] [PubMed]

17. L. Ge, Y. D. Chong, and A. D. Stone, “Conservation relations and anisotropic transmission resonances in one-dimensional *PT*-symmetric photonic heterostructures,” Phys. Rev. A **85**(2), 023802 (2012). [CrossRef]

5. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. **6**(3), 192–195 (2010). [CrossRef]

8. L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. **12**(2), 108–113 (2013). [CrossRef] [PubMed]

## 3. Experimental validation

1. M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. **12**(1), 20–24 (2013). [CrossRef] [PubMed]

18. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. **10**(7), 2342–2348 (2010). [CrossRef] [PubMed]

19. Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. **12**(3), 1443–1447 (2012). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. |

2. | C. M. Bender and S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having |

3. | K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in |

4. | S. Klaiman, U. Günther, and N. Moiseyev, “Visualization of branch points in |

5. | C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. |

6. | Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by |

7. | A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature |

8. | L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. |

9. | S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A |

10. | Y. Choi, S. Kang, S. Lim, W. Kim, J. R. Kim, J. H. Lee, and K. An, “Quasieigenstate coalescence in an atom-cavity quantum composite,” Phys. Rev. Lett. |

11. | S. B. Lee, J. Yang, S. Moon, S. Y. Lee, J. B. Shim, S. W. Kim, J. H. Lee, and K. An, “Observation of an exceptional point in a chaotic optical microcavity,” Phys. Rev. Lett. |

12. | C. Dembowski, H. D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. |

13. | J. G. Muga, J. P. Palao, B. Navarroa, and I. L. Egusquiza, “Complex absorbing potentials,” Phys. Rep. |

14. | F. Cannata, J. P. Dedonder, and A. Ventura, “Scattering in |

15. | W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. Math. Gen. |

16. | H. Cartarius, J. Main, and G. Wunner, “Exceptional points in atomic spectra,” Phys. Rev. Lett. |

17. | L. Ge, Y. D. Chong, and A. D. Stone, “Conservation relations and anisotropic transmission resonances in one-dimensional |

18. | N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. |

19. | Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. |

**OCIS Codes**

(310.4165) Thin films : Multilayer design

(310.6845) Thin films : Thin film devices and applications

**ToC Category:**

Thin Films

**History**

Original Manuscript: November 4, 2013

Revised Manuscript: December 17, 2013

Manuscript Accepted: December 18, 2013

Published: January 17, 2013

**Citation**

Liang Feng, Xuefeng Zhu, Sui Yang, Hanyu Zhu, Peng Zhang, Xiaobo Yin, Yuan Wang, and Xiang Zhang, "Demonstration of a large-scale optical exceptional point structure," Opt. Express **22**, 1760-1767 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1760

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### References

- M. A. Kats, R. Blanchard, P. Genevet, F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013). [CrossRef] [PubMed]
- C. M. Bender, S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998). [CrossRef]
- K. G. Makris, R. El-Ganainy, D. N. Christodoulides, Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008). [CrossRef] [PubMed]
- S. Klaiman, U. Günther, N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008). [CrossRef] [PubMed]
- C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010). [CrossRef]
- Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011). [CrossRef] [PubMed]
- A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012). [CrossRef] [PubMed]
- L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013). [CrossRef] [PubMed]
- S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010). [CrossRef]
- Y. Choi, S. Kang, S. Lim, W. Kim, J. R. Kim, J. H. Lee, K. An, “Quasieigenstate coalescence in an atom-cavity quantum composite,” Phys. Rev. Lett. 104(15), 153601 (2010). [CrossRef] [PubMed]
- S. B. Lee, J. Yang, S. Moon, S. Y. Lee, J. B. Shim, S. W. Kim, J. H. Lee, K. An, “Observation of an exceptional point in a chaotic optical microcavity,” Phys. Rev. Lett. 103(13), 134101 (2009). [CrossRef] [PubMed]
- C. Dembowski, H. D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86(5), 787–790 (2001). [CrossRef] [PubMed]
- J. G. Muga, J. P. Palao, B. Navarroa, I. L. Egusquiza, “Complex absorbing potentials,” Phys. Rep. 395(6), 357–426 (2004). [CrossRef]
- F. Cannata, J. P. Dedonder, A. Ventura, “Scattering in PT-symmetric quantum mechanics,” Ann. Phys. 322(2), 397–433 (2007). [CrossRef]
- W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. Math. Gen. 37(6), 2455–2464 (2004). [CrossRef]
- H. Cartarius, J. Main, G. Wunner, “Exceptional points in atomic spectra,” Phys. Rev. Lett. 99(17), 173003 (2007). [CrossRef] [PubMed]
- L. Ge, Y. D. Chong, A. D. Stone, “Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures,” Phys. Rev. A 85(2), 023802 (2012). [CrossRef]
- N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]
- Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012). [CrossRef] [PubMed]

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