Abstract

We propose a scheme to achieve a controllable unidirectional reflectionless propagation at exceptional point (EP) in a non-ideal parity-time metasurface consisting of two silver ring resonators. The unidirectional reflectionless propagation can be manipulated by simply adjusting the angle of incident wave and the distance s between two silver rings based on the far field coupling. In addition, the angle of incident wave in a wide range of ∼25° is available to achieve the unidirectional reflectionless propagation. Moreover, the unidirectional reflectionless propagation at EP is insensitive to the polarization of incident wave due to the two-ring structure.

© 2017 Optical Society of America

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References

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2017 (2)

Y. Aurégan and V. Pagneux, “PT-symmetric scattering in flow duct acoustics,” Phys. Rev. Lett. 118, 174301 (2017).
[Crossref]

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian enfineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

2016 (8)

K-H. Kim, M-S. Hwang, H-R. Kim, J-H. Choi, Y-S. No, and H-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref] [PubMed]

C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
[Crossref] [PubMed]

J. Christensen, M. Willatzen, V. R. Velasco, and M. H. Lu, “Parity-time synthetic phononic media,” Phys. Rev. Lett. 116, 207601 (2016).
[Crossref] [PubMed]

P. Y. Chen and J. Jung, “PT symmetry and singularity-enhanced sensing based on photoexcited graphene metasurfaces,” Phys. Rev. Appl. 5, 064018 (2016).
[Crossref]

Y. Y. Fu, Y. D. Xu, and H. Y. Chen, “Zero index metamaterials with PT symmetry in a waveguide system,” Opt. Express 24, 1648 (2016).
[Crossref] [PubMed]

E. Yang, Y. Lu, Y. Wang, Y. Dai, and P. Wang, “Unidirectional reflectionless phenomenon in periodic ternary layered material,” Opt. Express 24, 14311 (2016).
[Crossref] [PubMed]

Y. Huang, C. Min, and G. Veronis, “Broadband near total light absorption in non-PT-symmetric waveguide-cavity systems,” Opt. Express 24, 22219–22231 (2016).
[Crossref] [PubMed]

2015 (7)

Y. Choi, J. K. Hong, J. H. Cho, K. G. Lee, J. W. Yoon, and S. H. Song, “Parity-time-symmetry breaking in double-slab surface-plasmon-polariton waveguides,” Opt. Express 23, 11783–89 (2015).
[Crossref] [PubMed]

Y. Huang, G. Veronis, and C. J. Min, “Unidirectional reflectionless propagation in plasmonic waveguide-cavity systems at exceptional points,” Opt. Express 23, 29882–29895 (2015).
[Crossref] [PubMed]

K. Ding, Z. Q. Zhang, and C. T. Chan, “Coalescence of exceptional points and phase diagrams for one-dimensional PT-symmetric photonic crystals,” Phys. Rev. B 92, 235310 (2015).
[Crossref]

B. Baum, H. Alaeian, and J. Dionne, “A parity-time symmetric coherent plasmonic absorber-amplifier,” J. Appl. Phys. 117, 063106 (2015).
[Crossref]

R. Fleury, D. Sounas, and A. Alu, “An invisible acoustic sensor based on parity-time symmetry,” Nat. Commun. 6, 5905 (2015).
[Crossref] [PubMed]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

B. He, L. Yang, and M. Xiao, “Cyclic permutation-time symmetric structure with coupled gain-loss microcavities,” Phys. Rev. A 91, 033830 (2015).
[Crossref]

2014 (10)

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112, 1439032014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328 (2014).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref] [PubMed]

Y. L. Xu, L. Feng, M. H. Lu, and Y. F. Chen, “Unidirectional transmission based on a passive PT symmetric grating with a nonlinear silicon distributed Bragg reflector cavity,” IEEE. Photonics. J 6, 0600507 (2014).
[Crossref]

M. H. Teimourpour and R. El-Ganainy, “Light transport in PT-invariant photonic structures with hidden symmetries,” Phys. Rev. A 90, 053817 (2014).
[Crossref]

X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, “PT-symmetric acoustics,” Phys. Rev. X 4, 031042 (2014).

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
[Crossref]

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

H. Alaeian and J. Dionne, “Parity-time-symmetric plasmonic metamaterials,” Phys. Rev. A 89, 033829 (2014).
[Crossref]

2013 (3)

M. Kang, F. Liu, and J. Li, “Effective spontaneous PT-symmetry breaking in hybridized metamaterials,” Phys. Rev. A 87, 053824 (2013).
[Crossref]

X. R. Jin, Y. Q. Zhang, S. Zhang, Y. P. Lee, and J. Y. Rhee, “Polarization-independent electromagnetically induced transparency-like effects in stacked metamaterials based on Fabry-Pérot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

N. Lazarides and G. P. Tsironis, “Gain-driven discrete breathers in PT-symmetric nonlinear metamaterials,” Phys. Rev. Lett. 110, 053901 (2013).
[Crossref] [PubMed]

2012 (6)

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109, 3 (2012).
[Crossref]

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, 108 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167 (2012).
[Crossref] [PubMed]

H. Ramezani, J. Schindler, F. M. Ellis, U. Gunther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).
[Crossref]

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

J. J. Chen, C. Wang, R. Zhang, and J. H. Xiao, “Multiple plasmon-induced transparencies in coupled-resonator systems,” Opt. Lett. 37, 5133 (2012).
[Crossref] [PubMed]

2011 (6)

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023820 (2011).
[Crossref]

H. Benisty, A. Degiron, A. Lupu, A. D. Lustrac, S. Chénais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, and G. Lérondel, “Implementation of PT symmetric devices using plasmonics: principle and applications,” Opt. Express 19, 18004–18019 (2011).
[Crossref] [PubMed]

D. D. Scott and Y. N. Joglekar, “Degrees and signatures of broken PT symmetry in nonuniform lattices,” Phys. Rev. A 83, 050102 (2011).
[Crossref]

E-M. Graefe and H. F. Jones, “PT-symmetric sinusoidal optical lattices at the symmetry breaking threshold,” Phys. Rev. A 84, 013818 (2011).
[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref] [PubMed]

2010 (4)

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

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

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, 153601 (2010).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

2009 (4)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. V. Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758 (2009).
[Crossref]

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. 103, 134101 (2009).
[Crossref] [PubMed]

I. Rotter, “A non-Hermitian Hamilton operator and the physics of open quantum systems,” J. Phys. A: Math. Theor. 42, 153001 (2009).
[Crossref]

2008 (3)

K. G. Makris, R. E. Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

Z. H. Musslimani, K. G. Makris, R. E. Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

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

2005 (2)

M. Kulishov, J. M. Laniel, N. Bélanger, J. Azaña, and D. V. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13, 3068–3078 (2005).
[Crossref] [PubMed]

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A: Math. Gen. 38, L171–L176 (2005).
[Crossref]

2004 (1)

C. M. Bender, D. C. Brody, and H. F. Jones, “Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction,” Phys. Rev. D 70, 025001 (2004).
[Crossref]

2002 (1)

B. Bagchi and C. Quesne, “Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework,” Phys. Lett. A 300, 18–26 (2002).
[Crossref]

1998 (2)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamitonians having PT symmetry,” Phys. Rev. Lett. 80, 5243 (1998).
[Crossref]

I. Y. Goldsheid and B. A. Khoruzhenko, “Distribution of eigenvalues in non-Hermitian Anderson models,” Phys. Rev. Lett. 80, 2897 (1998).
[Crossref]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. V. Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Alaeian, H.

B. Baum, H. Alaeian, and J. Dionne, “A parity-time symmetric coherent plasmonic absorber-amplifier,” J. Appl. Phys. 117, 063106 (2015).
[Crossref]

H. Alaeian and J. Dionne, “Parity-time-symmetric plasmonic metamaterials,” Phys. Rev. A 89, 033829 (2014).
[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, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108 (2012).
[Crossref] [PubMed]

Alu, A.

R. Fleury, D. Sounas, and A. Alu, “An invisible acoustic sensor based on parity-time symmetry,” Nat. Commun. 6, 5905 (2015).
[Crossref] [PubMed]

An, K.

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, 153601 (2010).
[Crossref] [PubMed]

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. 103, 134101 (2009).
[Crossref] [PubMed]

Aurégan, Y.

Y. Aurégan and V. Pagneux, “PT-symmetric scattering in flow duct acoustics,” Phys. Rev. Lett. 118, 174301 (2017).
[Crossref]

Azaña, J.

Bagchi, B.

B. Bagchi and C. Quesne, “Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework,” Phys. Lett. A 300, 18–26 (2002).
[Crossref]

Barbillon, G.

Baum, B.

B. Baum, H. Alaeian, and J. Dionne, “A parity-time symmetric coherent plasmonic absorber-amplifier,” J. Appl. Phys. 117, 063106 (2015).
[Crossref]

Bélanger, N.

Bender, C. M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328 (2014).
[Crossref] [PubMed]

C. M. Bender, D. C. Brody, and H. F. Jones, “Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction,” Phys. Rev. D 70, 025001 (2004).
[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamitonians having PT symmetry,” Phys. Rev. Lett. 80, 5243 (1998).
[Crossref]

Benisty, H.

Bersch, C.

A. Regensburger, C. Bersch, M-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167 (2012).
[Crossref] [PubMed]

Besbes, M.

Blaize, S.

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamitonians having PT symmetry,” Phys. Rev. Lett. 80, 5243 (1998).
[Crossref]

Brandstetter, M.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Brody, D. C.

C. M. Bender, D. C. Brody, and H. F. Jones, “Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction,” Phys. Rev. D 70, 025001 (2004).
[Crossref]

Bruyant, A.

Cao, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Cerjan, A.

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

Chan, C. T.

K. Ding, Z. Q. Zhang, and C. T. Chan, “Coalescence of exceptional points and phase diagrams for one-dimensional PT-symmetric photonic crystals,” Phys. Rev. B 92, 235310 (2015).
[Crossref]

Chen, H.

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112, 1439032014).
[Crossref] [PubMed]

Chen, H. Y.

Chen, J. J.

Chen, P. Y.

P. Y. Chen and J. Jung, “PT symmetry and singularity-enhanced sensing based on photoexcited graphene metasurfaces,” Phys. Rev. Appl. 5, 064018 (2016).
[Crossref]

Chen, Y.

C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
[Crossref] [PubMed]

Chen, Y. F.

Y. L. Xu, L. Feng, M. H. Lu, and Y. F. Chen, “Unidirectional transmission based on a passive PT symmetric grating with a nonlinear silicon distributed Bragg reflector cavity,” IEEE. Photonics. J 6, 0600507 (2014).
[Crossref]

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, 108 (2012).
[Crossref] [PubMed]

Chénais, S.

Cheng, L.

C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
[Crossref] [PubMed]

Cho, J. H.

Choi, J-H.

K-H. Kim, M-S. Hwang, H-R. Kim, J-H. Choi, Y-S. No, and H-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Choi, Y.

Y. Choi, J. K. Hong, J. H. Cho, K. G. Lee, J. W. Yoon, and S. H. Song, “Parity-time-symmetry breaking in double-slab surface-plasmon-polariton waveguides,” Opt. Express 23, 11783–89 (2015).
[Crossref] [PubMed]

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, 153601 (2010).
[Crossref] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023820 (2011).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Christensen, J.

J. Christensen, M. Willatzen, V. R. Velasco, and M. H. Lu, “Parity-time synthetic phononic media,” Phys. Rev. Lett. 116, 207601 (2016).
[Crossref] [PubMed]

Christodoulides, D. N.

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167 (2012).
[Crossref] [PubMed]

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109, 3 (2012).
[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

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

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. V. Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

K. G. Makris, R. E. Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

Z. H. Musslimani, K. G. Makris, R. E. Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

Dai, Y.

Degiron, A.

Delgado, F.

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A: Math. Gen. 38, L171–L176 (2005).
[Crossref]

Deutsch, C.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Ding, K.

K. Ding, Z. Q. Zhang, and C. T. Chan, “Coalescence of exceptional points and phase diagrams for one-dimensional PT-symmetric photonic crystals,” Phys. Rev. B 92, 235310 (2015).
[Crossref]

Dionne, J.

B. Baum, H. Alaeian, and J. Dionne, “A parity-time symmetric coherent plasmonic absorber-amplifier,” J. Appl. Phys. 117, 063106 (2015).
[Crossref]

H. Alaeian and J. Dionne, “Parity-time-symmetric plasmonic metamaterials,” Phys. Rev. A 89, 033829 (2014).
[Crossref]

Dubois, M.

C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
[Crossref] [PubMed]

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. V. Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Eichelkraut, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

El-Ganainy, R.

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian enfineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref] [PubMed]

M. H. Teimourpour and R. El-Ganainy, “Light transport in PT-invariant photonic structures with hidden symmetries,” Phys. Rev. A 90, 053817 (2014).
[Crossref]

Ellis, F. M.

H. Ramezani, J. Schindler, F. M. Ellis, U. Gunther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).
[Crossref]

Fan, S.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394 (2014).
[Crossref]

Fegadolli, W. S.

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, 108 (2012).
[Crossref] [PubMed]

Feng, L.

Y. L. Xu, L. Feng, M. H. Lu, and Y. F. Chen, “Unidirectional transmission based on a passive PT symmetric grating with a nonlinear silicon distributed Bragg reflector cavity,” IEEE. Photonics. J 6, 0600507 (2014).
[Crossref]

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, 108 (2012).
[Crossref] [PubMed]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758 (2009).
[Crossref]

Fleury, R.

R. Fleury, D. Sounas, and A. Alu, “An invisible acoustic sensor based on parity-time symmetry,” Nat. Commun. 6, 5905 (2015).
[Crossref] [PubMed]

Forget, S.

Fu, Y. Y.

Ganainy, R. E.

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

Z. H. Musslimani, K. G. Makris, R. E. Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

K. G. Makris, R. E. Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

Ge, L.

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref] [PubMed]

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023820 (2011).
[Crossref]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Gianfreda, M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394 (2014).
[Crossref]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758 (2009).
[Crossref]

Goldsheid, I. Y.

I. Y. Goldsheid and B. A. Khoruzhenko, “Distribution of eigenvalues in non-Hermitian Anderson models,” Phys. Rev. Lett. 80, 2897 (1998).
[Crossref]

Graefe, E-M.

E-M. Graefe and H. F. Jones, “PT-symmetric sinusoidal optical lattices at the symmetry breaking threshold,” Phys. Rev. A 84, 013818 (2011).
[Crossref]

Gunther, U.

H. Ramezani, J. Schindler, F. M. Ellis, U. Gunther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).
[Crossref]

Günther, U.

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

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. V. Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Han, J. L.

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
[Crossref]

He, B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

B. He, L. Yang, and M. Xiao, “Cyclic permutation-time symmetric structure with coupled gain-loss microcavities,” Phys. Rev. A 91, 033830 (2015).
[Crossref]

Hong, J. K.

Huang, C. Y.

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
[Crossref]

Huang, Y.

Hwang, M-S.

K-H. Kim, M-S. Hwang, H-R. Kim, J-H. Choi, Y-S. No, and H-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Jin, X. R.

X. R. Jin, Y. Q. Zhang, S. Zhang, Y. P. Lee, and J. Y. Rhee, “Polarization-independent electromagnetically induced transparency-like effects in stacked metamaterials based on Fabry-Pérot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

Jing, H.

H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref] [PubMed]

Joglekar, Y. N.

D. D. Scott and Y. N. Joglekar, “Degrees and signatures of broken PT symmetry in nonuniform lattices,” Phys. Rev. A 83, 050102 (2011).
[Crossref]

Jones, H. F.

E-M. Graefe and H. F. Jones, “PT-symmetric sinusoidal optical lattices at the symmetry breaking threshold,” Phys. Rev. A 84, 013818 (2011).
[Crossref]

C. M. Bender, D. C. Brody, and H. F. Jones, “Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction,” Phys. Rev. D 70, 025001 (2004).
[Crossref]

Jung, J.

P. Y. Chen and J. Jung, “PT symmetry and singularity-enhanced sensing based on photoexcited graphene metasurfaces,” Phys. Rev. Appl. 5, 064018 (2016).
[Crossref]

Kang, M.

M. Kang, F. Liu, and J. Li, “Effective spontaneous PT-symmetry breaking in hybridized metamaterials,” Phys. Rev. A 87, 053824 (2013).
[Crossref]

Kang, S.

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, 153601 (2010).
[Crossref] [PubMed]

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758 (2009).
[Crossref]

Khoruzhenko, B. A.

I. Y. Goldsheid and B. A. Khoruzhenko, “Distribution of eigenvalues in non-Hermitian Anderson models,” Phys. Rev. Lett. 80, 2897 (1998).
[Crossref]

Kim, H-R.

K-H. Kim, M-S. Hwang, H-R. Kim, J-H. Choi, Y-S. No, and H-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Kim, J. R.

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, 153601 (2010).
[Crossref] [PubMed]

Kim, K-H.

K-H. Kim, M-S. Hwang, H-R. Kim, J-H. Choi, Y-S. No, and H-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Kim, S. W.

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. 103, 134101 (2009).
[Crossref] [PubMed]

Kim, W.

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, 153601 (2010).
[Crossref] [PubMed]

Kip, D.

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

Klaiman, S.

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

Klang, P.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Kottos, T.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109, 3 (2012).
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B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
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Wang, P.

Wang, Y.

E. Yang, Y. Lu, Y. Wang, Y. Dai, and P. Wang, “Unidirectional reflectionless phenomenon in periodic ternary layered material,” Opt. Express 24, 14311 (2016).
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C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
[Crossref] [PubMed]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758 (2009).
[Crossref]

Willatzen, M.

J. Christensen, M. Willatzen, V. R. Velasco, and M. H. Lu, “Parity-time synthetic phononic media,” Phys. Rev. Lett. 116, 207601 (2016).
[Crossref] [PubMed]

Xiao, J. H.

Xiao, M.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

B. He, L. Yang, and M. Xiao, “Cyclic permutation-time symmetric structure with coupled gain-loss microcavities,” Phys. Rev. A 91, 033830 (2015).
[Crossref]

Xu, J. Q.

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
[Crossref]

Xu, Y. D.

Xu, Y. L.

Y. L. Xu, L. Feng, M. H. Lu, and Y. F. Chen, “Unidirectional transmission based on a passive PT symmetric grating with a nonlinear silicon distributed Bragg reflector cavity,” IEEE. Photonics. J 6, 0600507 (2014).
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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, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108 (2012).
[Crossref] [PubMed]

Yan, S. B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
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Yang, E.

Yang, J.

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. 103, 134101 (2009).
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Yang, L.

B. He, L. Yang, and M. Xiao, “Cyclic permutation-time symmetric structure with coupled gain-loss microcavities,” Phys. Rev. A 91, 033830 (2015).
[Crossref]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328 (2014).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref] [PubMed]

Yilmaz, H.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328 (2014).
[Crossref] [PubMed]

Yoon, J. W.

Zhang, J.

H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref] [PubMed]

Zhang, R.

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
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J. J. Chen, C. Wang, R. Zhang, and J. H. Xiao, “Multiple plasmon-induced transparencies in coupled-resonator systems,” Opt. Lett. 37, 5133 (2012).
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Zhang, S.

X. R. Jin, Y. Q. Zhang, S. Zhang, Y. P. Lee, and J. Y. Rhee, “Polarization-independent electromagnetically induced transparency-like effects in stacked metamaterials based on Fabry-Pérot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

Zhang, X.

C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
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X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, “PT-symmetric acoustics,” Phys. Rev. X 4, 031042 (2014).

Zhang, Y. Q.

X. R. Jin, Y. Q. Zhang, S. Zhang, Y. P. Lee, and J. Y. Rhee, “Polarization-independent electromagnetically induced transparency-like effects in stacked metamaterials based on Fabry-Pérot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

Zhang, Z. Q.

K. Ding, Z. Q. Zhang, and C. T. Chan, “Coalescence of exceptional points and phase diagrams for one-dimensional PT-symmetric photonic crystals,” Phys. Rev. B 92, 235310 (2015).
[Crossref]

Zheng, J.

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
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Zhu, J.

X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, “PT-symmetric acoustics,” Phys. Rev. X 4, 031042 (2014).

Zhu, X.

X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, “PT-symmetric acoustics,” Phys. Rev. X 4, 031042 (2014).

IEEE. Photonics. J (1)

Y. L. Xu, L. Feng, M. H. Lu, and Y. F. Chen, “Unidirectional transmission based on a passive PT symmetric grating with a nonlinear silicon distributed Bragg reflector cavity,” IEEE. Photonics. J 6, 0600507 (2014).
[Crossref]

J. Appl. Phys. (1)

B. Baum, H. Alaeian, and J. Dionne, “A parity-time symmetric coherent plasmonic absorber-amplifier,” J. Appl. Phys. 117, 063106 (2015).
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J. Opt. (1)

X. R. Jin, Y. Q. Zhang, S. Zhang, Y. P. Lee, and J. Y. Rhee, “Polarization-independent electromagnetically induced transparency-like effects in stacked metamaterials based on Fabry-Pérot resonance,” J. Opt. 15, 125104 (2013).
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J. Phys. A: Math. Gen. (1)

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A: Math. Gen. 38, L171–L176 (2005).
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J. Phys. A: Math. Theor. (1)

I. Rotter, “A non-Hermitian Hamilton operator and the physics of open quantum systems,” J. Phys. A: Math. Theor. 42, 153001 (2009).
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Nat. Commun. (4)

R. Fleury, D. Sounas, and A. Alu, “An invisible acoustic sensor based on parity-time symmetry,” Nat. Commun. 6, 5905 (2015).
[Crossref] [PubMed]

C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, “Accessing the exceptional points of parity-time symmetric acoustics,” Nat. Commun. 7, 11110 (2016).
[Crossref] [PubMed]

K-H. Kim, M-S. Hwang, H-R. Kim, J-H. Choi, Y-S. No, and H-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
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M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
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Nat. Mater. (1)

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, 108 (2012).
[Crossref] [PubMed]

Nat. Phys. (2)

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394 (2014).
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C. E. Rüer, K. G. Makris, R. E. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Nature (1)

A. Regensburger, C. Bersch, M-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167 (2012).
[Crossref] [PubMed]

Nature Mater. (1)

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758 (2009).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Phys. Lett. A (1)

B. Bagchi and C. Quesne, “Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework,” Phys. Lett. A 300, 18–26 (2002).
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Phys. Rev. A (11)

H. Ramezani, J. Schindler, F. M. Ellis, U. Gunther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).
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D. D. Scott and Y. N. Joglekar, “Degrees and signatures of broken PT symmetry in nonuniform lattices,” Phys. Rev. A 83, 050102 (2011).
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E-M. Graefe and H. F. Jones, “PT-symmetric sinusoidal optical lattices at the symmetry breaking threshold,” Phys. Rev. A 84, 013818 (2011).
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M. H. Teimourpour and R. El-Ganainy, “Light transport in PT-invariant photonic structures with hidden symmetries,” Phys. Rev. A 90, 053817 (2014).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

H. Alaeian and J. Dionne, “Parity-time-symmetric plasmonic metamaterials,” Phys. Rev. A 89, 033829 (2014).
[Crossref]

M. Kang, F. Liu, and J. Li, “Effective spontaneous PT-symmetry breaking in hybridized metamaterials,” Phys. Rev. A 87, 053824 (2013).
[Crossref]

C. Y. Huang, R. Zhang, J. L. Han, J. Zheng, and J. Q. Xu, “Type II perfect absorption and amplification modes with controllable bandwidth in combined PT-symmetric and conventional Bragg-grating structures,” Phys. Rev. A 89, 023842 (2014).
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S. Longhi, “PT-symmetry laser absorber,” Phys. Rev. A 82, 031801 (2010).
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L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023820 (2011).
[Crossref]

B. He, L. Yang, and M. Xiao, “Cyclic permutation-time symmetric structure with coupled gain-loss microcavities,” Phys. Rev. A 91, 033830 (2015).
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Phys. Rev. Appl. (2)

P. Y. Chen and J. Jung, “PT symmetry and singularity-enhanced sensing based on photoexcited graphene metasurfaces,” Phys. Rev. Appl. 5, 064018 (2016).
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M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian enfineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
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Phys. Rev. B (1)

K. Ding, Z. Q. Zhang, and C. T. Chan, “Coalescence of exceptional points and phase diagrams for one-dimensional PT-symmetric photonic crystals,” Phys. Rev. B 92, 235310 (2015).
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Phys. Rev. D (1)

C. M. Bender, D. C. Brody, and H. F. Jones, “Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction,” Phys. Rev. D 70, 025001 (2004).
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Phys. Rev. Lett. (18)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamitonians having PT symmetry,” Phys. Rev. Lett. 80, 5243 (1998).
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Y. Aurégan and V. Pagneux, “PT-symmetric scattering in flow duct acoustics,” Phys. Rev. Lett. 118, 174301 (2017).
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Z. H. Musslimani, K. G. Makris, R. E. Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
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J. Christensen, M. Willatzen, V. R. Velasco, and M. H. Lu, “Parity-time synthetic phononic media,” Phys. Rev. Lett. 116, 207601 (2016).
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S. Klaiman, U. Günther, and N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
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A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. V. Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
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Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
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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. 103, 134101 (2009).
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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, 153601 (2010).
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Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112, 1439032014).
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H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109, 3 (2012).
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N. Lazarides and G. P. Tsironis, “Gain-driven discrete breathers in PT-symmetric nonlinear metamaterials,” Phys. Rev. Lett. 110, 053901 (2013).
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Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106, 093902 (2011).
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M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
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Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
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H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref] [PubMed]

Phys. Rev. X (1)

X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, “PT-symmetric acoustics,” Phys. Rev. X 4, 031042 (2014).

Sci. Rep. (1)

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref] [PubMed]

Science (1)

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328 (2014).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Schematic of unit cell of the non-ideal PT metasurface structure. The parameters are h = 20nm, r1 = 61nm, R1 = 122nm, r2 = 63nm, R2 = 170nm and t = 640nm, respectively. The distance s is variable. The incident wave is in xz plane and has an angle θ with +z axis.
Fig. 2
Fig. 2 (a)–(e): Dependency of the simulated (analytical) reflection spectra on the distance s (phase ϕ) and the wavelength of incident wave. (f) The relevant fitting parameters Γ1(2) and γ1(2) versus the distance s.
Fig. 3
Fig. 3 The z-component distributions of electric field of two silver rings for s = 485nm ((a)–(d)) and s = 395nm ((e)–(h)) at the wavelengths 1441nm and 1387nm in +z and −z directions, respectively.
Fig. 4
Fig. 4 Reflection as the functions of distance s ((a) and (b)) and phase ϕ ((c) and (d)) in excitation along +z and −z based on the numerical simulation (Sim) and analytical calculation (Ana), respectively.
Fig. 5
Fig. 5 Dependency of reflection on the angle of incident wave in excitation along +z and −z and wavelength for s = 485nm ((a) and (b)) and s = 395nm((c) and (d)), respectively.
Fig. 6
Fig. 6 Real and imaginary parts of eigenvalues of scattering matrix S as a function of wavelength in different ϕ. The black solid and red dash lines correspond to the two eigenvalues λ1 and λ2, respectively.

Equations (7)

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T all = T s 1 × T p × T s 2 = ( T 11 T 12 T 21 T 22 ) ,
T s 1 ( 2 ) = ( 1 i γ 1 ( 2 ) ω ω 1 ( 2 ) + i Γ 1 ( 2 ) 2 i γ 1 ( 2 ) ω ω 1 ( 2 ) + i Γ 1 ( 2 ) 2 i γ 1 ( 2 ) ω ω 1 ( 2 ) + i Γ 1 ( 2 ) 2 1 i γ 1 ( 2 ) ω ω 1 ( 2 ) + i Γ 1 ( 2 ) 2 ) ,
T p = ( exp ( i ϕ ) 0 0 exp ( i ϕ ) ) ,
ϕ 1 ( 2 ) = arctan [ Im ( T s , 21 1 ( 2 ) / T s , 22 1 ( 2 ) ) Re ( T s , 21 1 ( 2 ) / T s , 22 1 ( 2 ) ) ] = ( ω ω 1 ( 2 ) ) ( γ 1 ( 2 ) + Γ 1 ( 2 ) 2 ) ,
t = t + z = t z = 1 T 22 , r + z = T 21 T 22 , r z = T 12 T 22 .
S = ( t r z r + z t ) .
λ 1 ( 2 ) = t ± r + z r z ,

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