Abstract

Dual-band unidirectional reflectionlessness and coherent perfect absorption (CPA) are demonstrated in a non-Hermitian plasmonic waveguide system based on near-field coupling between a single resonator and the resonant modes of two resonators showing an electromagnetically induced-transparency-like (EIT-like) effect. The non-Hermitian plasmonic system consists of three metal-insulator-metal (MIM) resonators coupled to a MIM plasmonic waveguide.

© 2017 Optical Society of America

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References

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2017 (3)

C. Hang, G. Gabadadze, and G. X. Huang, “Realization of non-PT-symmetric optical potentials with all-real spectra in a coherent atomic system,” Phys. Rev. A. 95, 023833 (2017).
[Crossref]

H. Jing, S. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref] [PubMed]

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

2016 (10)

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]

S. Nixon and J. K. Yang, “Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides,” Opt. Lett. 41, 2747 (2016).
[Crossref] [PubMed]

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

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

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

S. Nixon and J. K. Yang, “Bifurcation of soliton families from linear modes in non-PT-symmetric complex potentials,” Stud. Appl. Math. 136, 459 (2016)
[Crossref]

S. Nixon and J. K. Yang, “All-real spectra in optical systems with arbitrary gain-and-loss distributions,” Phys. Rev. A. 93, 031802 (2016).
[Crossref]

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

L. Ge and R. EI-Ganainy, “Nonlinear modal interactions in parity-time (PT) symmetric lasers,” Sci. Rep. 6, 24889 (2016).
[Crossref] [PubMed]

2015 (5)

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

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

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[Crossref]

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodouldes, and M. Khajavikhan, “Parity-time-symmetric coupled microring lasers operating around an exceptional point,” Opt. Lett. 40, 4955–4958 (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 (2015).
[Crossref] [PubMed]

2014 (9)

Y. Shen, X. H. Deng, and L. Chen, “Unidirectional invisibility in a two-layer non-PT-symmetric slab,” Opt. Express 22, 19440 (2014).
[Crossref] [PubMed]

G. T. Cao, H. J. Li, S. P. Zhan, Z. H. He, Z. B. Guo, X. K. Xu, and H. Yang, “Uniform theoretical description of plasmon-induced transparency in plasmonic stub waveguide,” Opt. Lett. 39, 216 (2014).
[Crossref] [PubMed]

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

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, 143903 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

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, 328–332 (2014).
[Crossref] [PubMed]

2013 (5)

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

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

L. Feng, X. F. Zhu, S. Yang, H. Y. Zhu, P. Zhang, X. B. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22, 1760 (2013).
[Crossref]

A. Lupu, H. Benisty, and A. Degiron, “Switching using PT symmetry in plasmonic systems: positive role of the losses,” Opt. Express 21, 21651 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (5)

2009 (1)

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

2008 (2)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16, 413 (2008).
[Crossref] [PubMed]

2007 (1)

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947 (2007).
[Crossref]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
[Crossref] [PubMed]

1998 (1)

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

1983 (1)

Alaeian, H.

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

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

Alexander, R. W.

Almeida, V. R.

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

Bai, R. P.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

Barbillon, G.

Baum, B.

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

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bender, C. M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (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, 328–332 (2014).
[Crossref] [PubMed]

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947 (2007).
[Crossref]

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

Benisty, H.

Besbes, M.

Blaize, S.

Boettcher, S.

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

BÖhm, J.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

Bruyant, A.

Cao, G. T.

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]

Chang, L.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[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, 143903 (2014).
[Crossref] [PubMed]

Chen, H. Y.

Chen, J. J.

Chen, L.

Chen, W. J.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Chen, Y. F.

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

Chénais, S.

Christodouldes, D. N.

Christodoulides, D. N.

M. A. Miri, P. LiKamWa, and D. N. Christodoulides, “Large area single-mode parity-time-symmetric laser amplifiers,” Opt. Lett. 37, 764 (2012).
[Crossref] [PubMed]

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]

Chu, S. T.

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[Crossref]

Dai, Y. M.

Degiron, A.

Deng, X. H.

Dionne, J. A.

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

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

Doppler, J.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Dorpe, P. V.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (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]

EI-Ganainy, R.

L. Ge and R. EI-Ganainy, “Nonlinear modal interactions in parity-time (PT) symmetric lasers,” Sci. Rep. 6, 24889 (2016).
[Crossref] [PubMed]

Fan, S. H.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Fegadolli, W. S.

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

Feng, L.

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

L. Feng, X. F. Zhu, S. Yang, H. Y. Zhu, P. Zhang, X. B. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22, 1760 (2013).
[Crossref]

Forget, S.

Fu, Y. Y.

Gabadadze, G.

C. Hang, G. Gabadadze, and G. X. Huang, “Realization of non-PT-symmetric optical potentials with all-real spectra in a coherent atomic system,” Phys. Rev. A. 95, 023833 (2017).
[Crossref]

Ge, L.

L. Ge and R. EI-Ganainy, “Nonlinear modal interactions in parity-time (PT) symmetric lasers,” Sci. Rep. 6, 24889 (2016).
[Crossref] [PubMed]

Gear, J.

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[Crossref]

Geng, Z.

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Gianfreda, M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Girschik, A.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Gong, Y. K.

Gu, X. T.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

Gu, Z. Y.

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

Guo, Z. B.

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
[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]

Han, Z. H.

Hang, C.

C. Hang, G. Gabadadze, and G. X. Huang, “Realization of non-PT-symmetric optical potentials with all-real spectra in a coherent atomic system,” Phys. Rev. A. 95, 023833 (2017).
[Crossref]

Hao, F.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Hassan, A. U.

Hayenga, W. E.

He, Z. H.

Heinrich, M.

Hodaei, H.

Hua, S. Y.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

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, G. X.

C. Hang, G. Gabadadze, and G. X. Huang, “Realization of non-PT-symmetric optical potentials with all-real spectra in a coherent atomic system,” Phys. Rev. A. 95, 023833 (2017).
[Crossref]

Huang, Y.

Jiang, L.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Jiang, X. S.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Jin, X. R.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

Jing, H.

H. Jing, S. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

Khajavikhan, M.

Kim, H.

Kim, M. S.

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Kottos, 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]

Kramer, J.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

Kuhl, U.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Lee, B.

Lee, J.

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Lee, Y. P.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

Lei, F.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Lérondel, G.

Li, G. Y.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
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Li, H. J.

Li, H. Q.

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, 143903 (2014).
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Li, J.

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, 143903 (2014).
[Crossref] [PubMed]

Li, J. S.

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[Crossref]

Li, M.

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

Libisch, F.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Liertzer, M.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

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, 328–332 (2014).
[Crossref] [PubMed]

LiKamWa, P.

Lin, Z.

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]

Liu, F.

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[Crossref]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Liu, X. M.

Long, G. L.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Long, L. L.

Lu, H.

Lu, M. H.

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

Lu, Y. H.

Lü, H.

H. Jing, S. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref] [PubMed]

Lü, X. Y.

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

Lupu, A.

Lustrac, A. D

Lyu, Q.

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

Maier, S. A.

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Mailybaev, A. A.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Mao, D.

McEnery, K. R.

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Milburn, T. J.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Min, C. J.

Miri, M. A.

Moiseyev, N.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Monifi, F.

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, 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Moshchalkov, V. V.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Nixon, S.

S. Nixon and J. K. Yang, “Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides,” Opt. Lett. 41, 2747 (2016).
[Crossref] [PubMed]

S. Nixon and J. K. Yang, “Bifurcation of soliton families from linear modes in non-PT-symmetric complex potentials,” Stud. Appl. Math. 136, 459 (2016)
[Crossref]

S. Nixon and J. K. Yang, “All-real spectra in optical systems with arbitrary gain-and-loss distributions,” Phys. Rev. A. 93, 031802 (2016).
[Crossref]

Nordlander, P.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
[Crossref] [PubMed]

Nori, F.

H. Jing, S. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (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, 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Oliveria, J. E. B.

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

Ordal, M. A.

Özdemir, S. K.

H. Jing, S. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (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, 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Park, J.

Park, N.

Peng, B.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (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, 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Piao, X. J.

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
[Crossref] [PubMed]

Rabl, P.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
[Crossref] [PubMed]

Ramezani, 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]

Rhee, J. Y.

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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

Rotter, S.

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[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, 328–332 (2014).
[Crossref] [PubMed]

Scherer, A.

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

Shen, Y.

Sobhani, H.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Song, Q. H.

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

Sonnefraud, Y.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Sun, Y.

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, 143903 (2014).
[Crossref] [PubMed]

Tame, M. S.

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Tan, W.

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, 143903 (2014).
[Crossref] [PubMed]

Verellen, N.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Veronis, G.

Wang, C.

Wang, G. X.

Wang, G. Z.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Wang, P.

Wang, Y.

Ward, C. A.

Wen, J. M.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Wiersig, J.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

Xiao, J. H.

Xiao, M.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Xiao, S. M.

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[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, X. K.

Xu, Y. D.

Xu, Y. L.

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

Yang, C.

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Yang, E. C.

Yang, H.

Yang, J. K.

S. Nixon and J. K. Yang, “Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides,” Opt. Lett. 41, 2747 (2016).
[Crossref] [PubMed]

S. Nixon and J. K. Yang, “Bifurcation of soliton families from linear modes in non-PT-symmetric complex potentials,” Stud. Appl. Math. 136, 459 (2016)
[Crossref]

S. Nixon and J. K. Yang, “All-real spectra in optical systems with arbitrary gain-and-loss distributions,” Phys. Rev. A. 93, 031802 (2016).
[Crossref]

Yang, L.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (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, 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Yang, S.

Yilmaz, H.

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
[Crossref] [PubMed]

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, 328–332 (2014).
[Crossref] [PubMed]

Yin, X. B.

Yu, S.

Zhan, S. P.

Zhang, C.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

Zhang, J.

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

Zhang, N.

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

Zhang, P.

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).
[Crossref]

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]

Zhang, S.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

Zhang, X.

L. Feng, X. F. Zhu, S. Yang, H. Y. Zhu, P. Zhang, X. B. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22, 1760 (2013).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zhang, Y. Q.

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[Crossref] [PubMed]

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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

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).
[Crossref]

Zhu, H. Y.

Zhu, X. F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Huang, C. J. Min, and G. Veronis, “Subwavelength slow-light waveguides based on a plasmonic analogue of electromagnetically induced transparency,” Appl. Phys. Lett. 99, 143117 (2011).
[Crossref]

J. Appl. Phys. (1)

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

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-Perot resonance,” J. Opt. 15, 125104 (2013).
[Crossref]

Laser. Photonics. Rev. (1)

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” Laser. Photonics. Rev. 10588–594 (2016).
[Crossref]

Nano Lett. (1)

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Nanotechnology (1)

H. Lu, X. M. Liu, G. X. Wang, and D. Mao, “Tunable high-channel-count bandpass plasmonic filters based on an analogue of electromagnetically induced transparency,” Nanotechnology 23, 444003 (2012).
[Crossref] [PubMed]

Nat. Commun. (1)

B. Peng, S. K. Özdemir, W. J. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

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

Nat. Photonics. (1)

L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Nat. Phys. (2)

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Nature (1)

J. Doppler, A. A. Mailybaev, J. BÖhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537, 76–79 (2016).
[Crossref] [PubMed]

Opt. Express (12)

X. J. Piao, S. Yu, and N. Park, “Control of Fano asymmetry in plasmon induced transparency and its application to plasmonic waveguide modulator,” Opt. Express 20, 18994 (2012).
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A. Lupu, H. Benisty, and A. Degiron, “Switching using PT symmetry in plasmonic systems: positive role of the losses,” Opt. Express 21, 21651 (2013).
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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 (2011).
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J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16, 413 (2008).
[Crossref] [PubMed]

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).
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L. Feng, X. F. Zhu, S. Yang, H. Y. Zhu, P. Zhang, X. B. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22, 1760 (2013).
[Crossref]

E. C. Yang, Y. H. Lu, Y. Wang, Y. M. Dai, and P. Wang, “Unidirectional reflectionless phenomenon in periodic ternary layered material,” Opt. Express 24, 14311 (2016).
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Y. Shen, X. H. Deng, and L. Chen, “Unidirectional invisibility in a two-layer non-PT-symmetric slab,” Opt. Express 22, 19440 (2014).
[Crossref] [PubMed]

X. T. Gu, R. P. Bai, C. Zhang, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling,” Opt. Express 25, 11778 (2017).
[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 (2015).
[Crossref] [PubMed]

Y. Huang, C. J. Min, and G. Veronis, “Broadband near total light absorption in non-PT-symmetric waveguide-cavity systems,” Opt. Express 24, 22219 (2016).
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Z. H. Han and S. I. Bozhevolnyi, “Plasmon-induced transparency with detuned ultracompact Fabry-Perot resonators in integrated plasmonic devices,” Opt. Express 19, 3251 (2011).
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Opt. Lett. (7)

Phys. Rev. A (1)

J. Gear, F. Liu, S. T. Chu, S. Rotter, and J. S. Li, “Parity-time symmetry from stacking purely dielectric and magnetic slabs,” Phys. Rev. A 91, 033825 (2015).
[Crossref]

Phys. Rev. A. (4)

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

S. Nixon and J. K. Yang, “All-real spectra in optical systems with arbitrary gain-and-loss distributions,” Phys. Rev. A. 93, 031802 (2016).
[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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C. Hang, G. Gabadadze, and G. X. Huang, “Realization of non-PT-symmetric optical potentials with all-real spectra in a coherent atomic system,” Phys. Rev. A. 95, 023833 (2017).
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Phys. Rev. Lett. (4)

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, 143903 (2014).
[Crossref] [PubMed]

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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C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243 (1998).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. Usa. (1)

B. Peng, S. K. Özdemir, M. Liertzer, W. J. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. Usa. 113, 6845–6850 (2016).
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C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947 (2007).
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Sci. Rep. (3)

H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 09663 (2015).
[Crossref]

L. Ge and R. EI-Ganainy, “Nonlinear modal interactions in parity-time (PT) symmetric lasers,” Sci. Rep. 6, 24889 (2016).
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H. Jing, S. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
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Science (2)

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, 328–332 (2014).
[Crossref] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
[Crossref] [PubMed]

Stud. Appl. Math. (1)

S. Nixon and J. K. Yang, “Bifurcation of soliton families from linear modes in non-PT-symmetric complex potentials,” Stud. Appl. Math. 136, 459 (2016)
[Crossref]

Other (1)

C. Zhang, R. P. Bai, X. T. Gu, X. R. Jin, Y. Q. Zhang, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless propagation in plasmonic waveguide system based on phase coupling between two stub resonators,” Submitted.

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Figures (5)

Fig. 1
Fig. 1 Schematic of an MIM waveguide side coupled to resonators A and B, and resonator A coupled to resonator C. The geometric parameters of the structure are lA = 250 nm, lB = 270 nm, lC = 530 nm, e = 10 nm, w = 50 nm, L = W = 2000nm, and d is variable.
Fig. 2
Fig. 2 (a) Reflection and transmission spectra versus frequency ω for resonators A and C (solid line) and the single resonator B (dotted line) based on numerical simulation and (b) forward and backward reflectivities for the coupled system of the three resonators A, B, and C as functions of frequency ω where d = 42 nm and phase difference φ = 0.075π based on numerical simulation (Num) and analytical calculation (Analy). The parameters related to the analytical calculation are γA = 1.588 THz, γB = 1.38 THz, Γ A = 55 THz, Γ B = 42 THz, Γ C = 3.4 THz, δ = 0.97, ϕ = 1.156π, and k = 1.6 THz.
Fig. 3
Fig. 3 z-component distributions of the magnetic field of the SPPs when d = 42 nm at a frequency of 174.96 THz [(a), (b)] and 196 THz [(c), (d)] in the forward and backward directions.
Fig. 4
Fig. 4 Real (a) and imaginary (b) parts of eigenvalues s± of the scattering matrix S as a function of frequency ω when φ = 0.075π. s+ and s are represented by a blue dashed line and red short dotted line, respectively. The positions of CPAs are marked by two black arrows and green arrows. All parameters γA, γB, Γ A , Γ B , Γ C , δ, ϕ and k are same as that in Fig. 2(b).
Fig. 5
Fig. 5 The real [(a), (c)] and imaginary [(b), (d)] parts of the eigenvalues s± as the function of the frequency ω and the phase φ. The horizontal magenta dashed line corresponds to the case of phase φ = 0.075π. All parameters γA, γB, Γ A , Γ B , Γ C , δ, ϕ and k are same as that in Fig. 2(b).

Equations (5)

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d a d t = ( i ω A γ A Γ A Γ C ) a + S + 11 Γ A + S + 21 Γ A + S 13 2 Γ C i k b , d b d t = ( i ω B γ B Γ B ) b + S + 12 Γ B + S + 22 Γ B i k a .
S 11 = S + 11 Γ A a , S 21 = S + 21 Γ A a , S 12 = S + 12 Γ B b , S 22 = S + 22 Γ B b , S 13 = S + 13 + 2 Γ C a ,
S + 12 = S 11 e i φ , S + 21 = S 22 e i φ ,
t = t f = S 12 S + 11 = t b = S 21 S + 22 , r f = S 21 S + 11 , and r b = S 12 S + 22 .
S = ( t r b r f t ) .

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