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

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  1. 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]
  2. C. M. Bender, S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
    [CrossRef]
  3. 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]
  4. S. Klaiman, U. Günther, N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
    [CrossRef]
  10. 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]
  11. 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]
  12. 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]
  13. J. G. Muga, J. P. Palao, B. Navarroa, I. L. Egusquiza, “Complex absorbing potentials,” Phys. Rep. 395(6), 357–426 (2004).
    [CrossRef]
  14. F. Cannata, J. P. Dedonder, A. Ventura, “Scattering in PT-symmetric quantum mechanics,” Ann. Phys. 322(2), 397–433 (2007).
    [CrossRef]
  15. W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. Math. Gen. 37(6), 2455–2464 (2004).
    [CrossRef]
  16. H. Cartarius, J. Main, G. Wunner, “Exceptional points in atomic spectra,” Phys. Rev. Lett. 99(17), 173003 (2007).
    [CrossRef] [PubMed]
  17. 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]
  18. 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]
  19. 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]

2013

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]

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]

2012

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. 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]

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]

2011

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]

2010

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]

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]

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]

2009

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]

2008

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]

2007

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

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

2004

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

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

2001

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]

1998

C. M. Bender, S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[CrossRef]

Almeida, V. R.

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]

An, K.

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]

Bender, C. M.

C. M. Bender, S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[CrossRef]

Bersch, C.

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]

Blanchard, R.

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]

Böttcher, S.

C. M. Bender, S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[CrossRef]

Cannata, F.

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

Cao, H.

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]

Capasso, F.

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]

Cartarius, H.

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

Chen, Y. F.

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]

Choi, Y.

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]

Chong, Y. D.

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]

Christodoulides, D. N.

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]

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]

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]

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]

Cui, Y.

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]

Dedonder, J. P.

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

Dembowski, C.

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]

Egusquiza, I. L.

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

Eichelkraut, T.

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]

El-Ganainy, R.

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]

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]

Fang, N. X.

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]

Fegadolli, W. S.

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]

Feng, L.

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]

Fung, K. H.

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]

Ge, L.

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]

Genevet, P.

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]

Giessen, H.

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]

Gräf, H. D.

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]

Günther, U.

S. Klaiman, U. Günther, N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
[CrossRef] [PubMed]

Harney, H. L.

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]

He, S.

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]

Heine, A.

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]

Heiss, W. D.

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

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]

Hentschel, M.

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]

Jin, Y.

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]

Kang, S.

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]

Kats, M. A.

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]

Kim, J. R.

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]

Kim, S. W.

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]

Kim, W.

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]

Kip, D.

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]

Klaiman, S.

S. Klaiman, U. Günther, N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
[CrossRef] [PubMed]

Kottos, T.

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]

Lee, J. H.

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]

Lee, S. B.

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]

Lee, S. Y.

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]

Lim, S.

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]

Lin, Z.

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]

Liu, N.

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]

Longhi, S.

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[CrossRef]

Lu, M. H.

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]

Ma, H.

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]

Main, J.

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

Makris, K. G.

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]

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]

Mesch, M.

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]

Miri, M. A.

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]

Moiseyev, N.

S. Klaiman, U. Günther, N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
[CrossRef] [PubMed]

Moon, S.

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]

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J. G. Muga, J. P. Palao, B. Navarroa, I. L. Egusquiza, “Complex absorbing potentials,” Phys. Rep. 395(6), 357–426 (2004).
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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).
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Onishchukov, G.

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]

Palao, J. P.

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

Peschel, U.

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]

Ramezani, H.

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]

Regensburger, A.

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]

Rehfeld, H.

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]

Richter, A.

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]

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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]

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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]

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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]

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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]

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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).
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Wunner, G.

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

Yang, J.

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]

Ann. Phys.

F. Cannata, J. P. Dedonder, A. Ventura, “Scattering in PT-symmetric quantum mechanics,” Ann. Phys. 322(2), 397–433 (2007).
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W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. Math. Gen. 37(6), 2455–2464 (2004).
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Nano Lett.

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).
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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).
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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).
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Nat. Phys.

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]

Nature

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]

Phys. Rep.

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

Phys. Rev. A

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[CrossRef]

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]

Phys. Rev. Lett.

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).
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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]

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]

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]

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

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the optical exceptional point structure on a glass wafer designed at the wavelength of 532 nm, where nSi = 4.86 – j0.65 and nsilica = 1.46. (b) Complex eigen value solutions of the modified scattering matrix at 532 nm construct a multi-valued Riemann surface as a function of Im( n Si ) , where red color indicates optical gain and blue corresponds to absorption as we have in Si layers. (c) Simulations of light propagating through the exceptional point structure in the forward (upper panel) and backward (lower panel) directions, in which the distribution of the amplitude of the magnetic field is shown normalized to the incident magnetic field of 1. (d) and (e) are amplitude and phase of the magnetic field in the device as light propagate in the forward (red) and backward (black) directions, respectively.

Fig. 2
Fig. 2

(a) and (b) are calculated spectra of generalized total power and its partial derivatives as a function of wavelength detuning. The red curves denote the spectra with the exact exceptional point design, while the blue dash curves are the case near the exceptional point.

Fig. 3
Fig. 3

(a) SEM pictures of the cross-section of the fabricated exceptional point structure. Scale bar, 50 nm. (b) and (c) are numerically calculated and experimentally measured reflection spectra of the exceptional point structure from 450 nm to 600 nm, respectively, for both forward (red) and backward (black) incidence.

Fig. 4
Fig. 4

Experimentally measured generalized power spectrum (a) and its differential spectrum (b) around the exceptional point.

Fig. 5
Fig. 5

(a) and (b) are photographs of the wafer-scale exceptional point structure in forward and backward directions, respectively with a 10 nm band pass filter centered at the wavelength of 520 nm. (c) and (d) show numerically and experimentally the angular dependence of reflection spectra of unpolarized light at the exceptional point in both forward (red) and backward (black) directions for incident angle from 0 to 45°. The reflectance for non-zero incident angle is the corresponding intensity of light at the reflection angle symmetric to the incident angle with respect to the normal.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

M j =( cos k j L j 1 k j sin k j L j k j sin k j L j cos k j L j ) , j=1,2,...,N
t=2i k 0 e i k 0 L [ M 11 f M 22 f M 12 f M 21 f M 21 f + k 0 2 M 21 f +i k 0 ( M 11 f + M 22 f ) ]
r f =[ ( M 21 f + k 0 2 M 12 f )+i k 0 ( M 22 f M 11 f ) ( M 21 f + k 0 2 M 12 f )+i k 0 ( M 22 f + M 11 f ) ],
r b =[ ( M 21 b + k 0 2 M 12 b )+i k 0 ( M 22 b M 11 b ) ( M 21 b + k 0 2 M 12 b )+i k 0 ( M 22 b + M 11 b ) ].

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