Abstract

We introduce a non-parity-time-symmetric three-layer structure, consisting of a gain medium layer sandwiched between two phase-change medium layers for switching of the direction of reflectionless light propagation. We show that for this structure unidirectional reflectionlessness in the forward direction can be switched to unidirectional reflectionlessness in the backward direction at the optical communication wavelength by switching the phase-change material Ge2Sb2Te5 (GST) from its amorphous to its crystalline phase. We also show that it is the existence of exceptional points for this structure with GST in both its amorphous and crystalline phases which leads to unidirectional reflectionless propagation in the forward direction for GST in its amorphous phase, and in the backward direction for GST in its crystalline phase. Our results could be potentially important for developing a new generation of compact active free-space optical devices.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (5)

V. Achilleos, G. Theocharis, O. Richoux, and V. Pagneux, “Non-Hermitian acoustic metamaterials: Role of exceptional points in sound absorption,” Phys. Rev. B 95, 144303 (2017).
[Crossref]

Y. Huang, Y. Shen, C. Min, S. Fan, and G. Veronis, “Unidirectional reflectionless light propagation at exceptional points,” Nanophotonics 6, 977–996 (2017).
[Crossref]

S. Kim, H. Yun, K. Park, J. Hong, J. Yun, K. Lee, J. Kim, S. Jeong, S. Mun, J. Sung, Y. Lee, and B. Lee, “Active directional switching of surface plasmon polaritons using a phase transition material,” Sci. Rep. 7, 43723 (2017).
[Crossref] [PubMed]

V. K. Mkhitaryan, D. S. Ghosh, M. Rude, J. Canet-Ferrer, R. A. Maniyara, K. K. Gopalan, and V. Pruneri, “Tunable complete optical absorption in multilayer structures including Ge2Sb2Te5 without lithographic patterns,” Adv. Optical Mater. 5, 1600452 (2017).
[Crossref]

Q. Liu, B. Wang, S. Ke, H. Long, K. Wang, and P. Lu, “Exceptional points in Fano-resonant graphene metamaterials,” Opt. Express 25, 7203–7212 (2017).
[Crossref] [PubMed]

2016 (11)

J. Doppler, A. A. Mailybaev, J. Bohm, 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, 76–80 (2016).
[Crossref] [PubMed]

S. Yoo, T. Gwon, T. Eom, S. Kim, and C. Hwang, “Multicolor changeable optical coating by adopting multiple layers of ultrathin phase change material film,” ACS Photonics 3, 1265–1270 (2016).
[Crossref]

Q. Wang, E. T. F. Rogers, B. Gholipour, C. Wang, G. Yuan, J. Teng, and N. I. Zheludev, “Optically reconfigurable metasurfaces and photonic devices based on phase change materials,” Nat. Photonics 10, 60–65 (2016).
[Crossref]

P. Li, X. Yang, T. W. W. Mab, J. Hanss, M. Lewin, A. U. Michel, M. Wuttig, and T. Taubner, “Reversible optical switching of highly confined phonon-polaritons with an ultrathin phase-change material,” Nat. Mater. 15, 870–876 (2016).
[Crossref] [PubMed]

M. Rude, V. Mkhitaryan, A. E. Cetin, T. A. Miller, A. Carrilero, S. Wall, F. J. Abajo, H. Altug, and V. Pruneri, “Ultrafast and broadband tuning of resonant optical nanostructures using phase-change materials,” Adv. Optical Mater. 4, 1060–1066 (2016).
[Crossref]

S. Longhi, “Bidirectional invisibility in Kramers-Kronig optical media,” Opt. Lett. 41, 2727–2730 (2016).
[Crossref]

B. Peng, S. K. Ozdemir, M. Liertzer, W. Chen, K. Johannes, 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]

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]

E. Yang, Y. Lu, Y. Wang, Y. Dai, and P. Wang, “Unidirectional reflectionless phenomenon in periodic ternary layered material,” Opt. Express 24, 14311–14321 (2016).
[Crossref] [PubMed]

S. Yu, X. Piao, and N. Park, “Acceleration toward polarization singularity inspired by relativistic E ×B drift,” Sci. Rep. 6, 37754 (2016).
[Crossref]

S. Yu, H. Park, X. Piao, B. Min, and N. Park, “Low-dimensional optical chirality in complex potentials,” Optica 3, 1025–1032 (2016).
[Crossref]

2015 (9)

J. W. Ryu, W. S. Son, D. U. Hwang, S. Y. Lee, and S. W. Kim, “Exceptional points in coupled dissipative dynamical systems,” Nano Lett. 91, 052910 (2015).

S. Yu, X. Piao, K. Yoo, J. Shin, and N. Park, “One-way optical modal transition based on causality in momentum space,” Opt. Express 23, 24997–25008 (2015).
[Crossref] [PubMed]

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

Y. Jia, Y. Yan, S. V. Kesava, Z. D. Gomez, and N. C. Giebink, “Passive parity-time symmetry in organic thin film waveguides,” ACS Photonics 2, 319–325 (2015).
[Crossref]

S. A. R. Horsley, M. Artoni, and G. C. La Rocca, “Spatial Kramer-Kronig relations and the reflection of waves,” Nat. Photonics 9, 436–439 (2015).
[Crossref]

T. Hira, T. Homma, T. Uchiyama, K. Kuwamura, Y. Kihara, and T. Saiki, “All-optical switching of localized surface plasmon resonance in single gold nanosandwich using GeSbTe film as an active medium,” Appl. Phys. Lett. 106, 031105 (2015).
[Crossref]

F. F. Schlich, P. Zalden, A. M. Lindenberg, and R. Spolenak, “Color switching with enhanced optical contrast in ultrathin phase change materials and semiconductors induced by femtosecond laser pulses,” ACS Photonics 2, 178–182 (2015).
[Crossref]

M. Rude, R. E. Simpson, R. Quidant, V. Pruneri, and J. Renger, “Active control of surface plasmon waveguides with a phase change material,” ACS Photonics 2, 669–674 (2015).
[Crossref]

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. Chua, J. D. Joannopoulos, and M. Soljacic, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (6)

X. Yin and X. Zhang, “Unidirectional light propagation at exceptional points,” Nat. Mater. 12, 175–177 (2013).
[Crossref] [PubMed]

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, 108–113 (2013).
[Crossref]

A. Lupu, H. Benisty, and A. Degiron, “Switching using PT-symmetry in plasmonic systems: positive role of the losses,” Opt. Express 21, 21651–21668 (2013).
[Crossref] [PubMed]

O. N. Kirillov, “Exceptional and diabolical points in stability questions,” Fortschr. Phys. 61, 205–224 (2013).
[Crossref]

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref] [PubMed]

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

2012 (7)

V. E. Babicheva, I. V. Kulkova, R. Malureanu, K. Yvind, and A. V. Lavrinenko, “Plasmonic modulator based on gain-assisted metal-semiconductor-metal waveguide,” Photon. Nanostructures 10, 389–399 (2012).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ’Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[Crossref]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
[Crossref]

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, C. T. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336, 1556–1569 (2012).
[Crossref]

W. D. Heiss, “The physics of exceptional points,” J. Phys. A 45, 444016 (2012).
[Crossref]

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

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

2011 (4)

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]

X. Li, Q. Tan, B. Bai, and G. Jin, “Experimental demonstration of tunable directional excitation of surface plasmon polaritons with a subwavelength metallic double slit,” Appl. Phys. Lett. 98, 251109 (2011).
[Crossref]

E. S. Semenova, I. V. Kulkova, S. Kadkhodazadeh, M. Schubert, and K. Yvind, “Metal organic vapor-phase epitaxy of InAs/InGaAsP quantum dots for laser applications at 1.5 μm,” Appl. Phys. Lett. 99, 101106 (2011).
[Crossref]

K. Akahane, N. Yamamoto, and T. Kawanishi, “Fabrication of ultra-high-density InAs quantum dots using the strain-compensation technique,” Phys. Status Solidi A 208, 425–428 (2011).
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2008 (2)

K. Kawaguchi, N. Yasuoka, M. Ekawa, H. Ebe, T. Akiyama, M. Sugawara, and Y. Arakawa, “Demonstration of transverse-magnetic dominant gain in quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 93, 121908 (2008).
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K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7, 653–658 (2008).
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2007 (2)

M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage,” Nat. Mater. 6, 824–832 (2007).
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E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics. 1, 395–401 (2007).
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2005 (1)

M. H. R. Lankhorst, B. W. Ketelaarsand, and R. A. M. Wolters, “Low-cost and nanoscale non-volatile memory concept for future silicon chips,” Nat. Mater. 4, 347–352 (2005).
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2004 (5)

G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29, 2288–2290 (2004).
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M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12, 4072–4079 (2004).
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T. Stehmann, W. S. Heiss, and F. G. Scholtz, “Observation of exceptional points in electronic circuits,” J. Phys. Math. Gen. 37, 7813–7819 (2004).
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M. V. Berry, “Physics of nonhermitian degeneracies,” Czech. J. Phys. 54, 1039–1047 (2004).
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W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. Math. Gen. 37, 2455–2464 (2004).
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2002 (1)

K. Akahane, N. Ohtani, Y. Okada, and M. Kawabe, “Fabrication of ultra-high density InAs-stacked quantum dots by strain-controlled growth on InP(3 1 1)B substrate,” J. Cryst. growth 245, 31–36 (2002).
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2001 (1)

C. Dembowski, H. Graf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86, 787–790 (2001).
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2000 (1)

W. D. Heiss, “Repulsion of resonance states and exceptional points,” Phys. Rev. E 61, 929–932 (2000).
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1998 (2)

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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1996 (1)

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, M. V. Maximov, P. S. Kopev, and Zh. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
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M. Rude, V. Mkhitaryan, A. E. Cetin, T. A. Miller, A. Carrilero, S. Wall, F. J. Abajo, H. Altug, and V. Pruneri, “Ultrafast and broadband tuning of resonant optical nanostructures using phase-change materials,” Adv. Optical Mater. 4, 1060–1066 (2016).
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V. Achilleos, G. Theocharis, O. Richoux, and V. Pagneux, “Non-Hermitian acoustic metamaterials: Role of exceptional points in sound absorption,” Phys. Rev. B 95, 144303 (2017).
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Akahane, K.

K. Akahane, N. Yamamoto, and T. Kawanishi, “Fabrication of ultra-high-density InAs quantum dots using the strain-compensation technique,” Phys. Status Solidi A 208, 425–428 (2011).
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K. Akahane, N. Ohtani, Y. Okada, and M. Kawabe, “Fabrication of ultra-high density InAs-stacked quantum dots by strain-controlled growth on InP(3 1 1)B substrate,” J. Cryst. growth 245, 31–36 (2002).
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Akiyama, T.

K. Kawaguchi, N. Yasuoka, M. Ekawa, H. Ebe, T. Akiyama, M. Sugawara, and Y. Arakawa, “Demonstration of transverse-magnetic dominant gain in quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 93, 121908 (2008).
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D. Bimberg, N. N. Ledentsov, M. Grundmann, F. Heinrichsdorff, V. M. Ustinov, P. S. Kopev, Z. I. Alferov, and J. A. Lott, “Edge and vertical cavity surface emitting InAs quantum dot lasers,” Solid St. Electron. 42, 1433–1437 (1998).
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N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, M. V. Maximov, P. S. Kopev, and Zh. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
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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, 108–113 (2013).
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Altug, H.

M. Rude, V. Mkhitaryan, A. E. Cetin, T. A. Miller, A. Carrilero, S. Wall, F. J. Abajo, H. Altug, and V. Pruneri, “Ultrafast and broadband tuning of resonant optical nanostructures using phase-change materials,” Adv. Optical Mater. 4, 1060–1066 (2016).
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Antoniou, N.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
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Arakawa, Y.

K. Kawaguchi, N. Yasuoka, M. Ekawa, H. Ebe, T. Akiyama, M. Sugawara, and Y. Arakawa, “Demonstration of transverse-magnetic dominant gain in quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 93, 121908 (2008).
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Artoni, M.

S. A. R. Horsley, M. Artoni, and G. C. La Rocca, “Spatial Kramer-Kronig relations and the reflection of waves,” Nat. Photonics 9, 436–439 (2015).
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V. E. Babicheva, I. V. Kulkova, R. Malureanu, K. Yvind, and A. V. Lavrinenko, “Plasmonic modulator based on gain-assisted metal-semiconductor-metal waveguide,” Photon. Nanostructures 10, 389–399 (2012).
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M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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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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A. Lupu, H. Benisty, and A. Degiron, “Using optical PT-symmetry for switching applications,” Photon. Nanostructures 12, 305–311 (2014).
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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, 21651–21668 (2013).
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M. V. Berry, “Physics of nonhermitian degeneracies,” Czech. J. Phys. 54, 1039–1047 (2004).
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A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
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D. Bimberg, N. N. Ledentsov, M. Grundmann, F. Heinrichsdorff, V. M. Ustinov, P. S. Kopev, Z. I. Alferov, and J. A. Lott, “Edge and vertical cavity surface emitting InAs quantum dot lasers,” Solid St. Electron. 42, 1433–1437 (1998).
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N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, M. V. Maximov, P. S. Kopev, and Zh. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
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M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12, 20–24 (2013).
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M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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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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J. Doppler, A. A. Mailybaev, J. Bohm, 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, 76–80 (2016).
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Brinkmeyer, E.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ’Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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Canet-Ferrer, J.

V. K. Mkhitaryan, D. S. Ghosh, M. Rude, J. Canet-Ferrer, R. A. Maniyara, K. K. Gopalan, and V. Pruneri, “Tunable complete optical absorption in multilayer structures including Ge2Sb2Te5 without lithographic patterns,” Adv. Optical Mater. 5, 1600452 (2017).
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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).
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Capasso, F.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
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M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12, 20–24 (2013).
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M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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Carrilero, A.

M. Rude, V. Mkhitaryan, A. E. Cetin, T. A. Miller, A. Carrilero, S. Wall, F. J. Abajo, H. Altug, and V. Pruneri, “Ultrafast and broadband tuning of resonant optical nanostructures using phase-change materials,” Adv. Optical Mater. 4, 1060–1066 (2016).
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E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics. 1, 395–401 (2007).
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M. Rude, V. Mkhitaryan, A. E. Cetin, T. A. Miller, A. Carrilero, S. Wall, F. J. Abajo, H. Altug, and V. Pruneri, “Ultrafast and broadband tuning of resonant optical nanostructures using phase-change materials,” Adv. Optical Mater. 4, 1060–1066 (2016).
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Chen, L.

Chen, W.

B. Peng, S. K. Ozdemir, M. Liertzer, W. Chen, K. Johannes, 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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Chen, Y. F.

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, 108–113 (2013).
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Chong, C. T.

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, C. T. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336, 1556–1569 (2012).
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Chong, Y. D.

L. Ge, Y. D. Chong, and A. D. Stone, “Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures,” Phys. Rev. A 85, 023802 (2012).
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A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
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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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Chua, S.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. Chua, J. D. Joannopoulos, and M. Soljacic, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
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Dai, Y.

Degiron, A.

A. Lupu, H. Benisty, and A. Degiron, “Using optical PT-symmetry for switching applications,” Photon. Nanostructures 12, 305–311 (2014).
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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, 21651–21668 (2013).
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Dembowski, C.

C. Dembowski, H. Graf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86, 787–790 (2001).
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Deng, X. H.

Doerr, C. R.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ’Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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J. Doppler, A. A. Mailybaev, J. Bohm, 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, 76–80 (2016).
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Dutton, R. W.

Ebe, H.

K. Kawaguchi, N. Yasuoka, M. Ekawa, H. Ebe, T. Akiyama, M. Sugawara, and Y. Arakawa, “Demonstration of transverse-magnetic dominant gain in quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 93, 121908 (2008).
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N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, M. V. Maximov, P. S. Kopev, and Zh. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ’Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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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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K. Kawaguchi, N. Yasuoka, M. Ekawa, H. Ebe, T. Akiyama, M. Sugawara, and Y. Arakawa, “Demonstration of transverse-magnetic dominant gain in quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 93, 121908 (2008).
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D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, C. T. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336, 1556–1569 (2012).
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S. Yoo, T. Gwon, T. Eom, S. Kim, and C. Hwang, “Multicolor changeable optical coating by adopting multiple layers of ultrathin phase change material film,” ACS Photonics 3, 1265–1270 (2016).
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Fan, S.

Y. Huang, Y. Shen, C. Min, S. Fan, and G. Veronis, “Unidirectional reflectionless light propagation at exceptional points,” Nanophotonics 6, 977–996 (2017).
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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, 108–113 (2013).
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L. Ge, Y. D. Chong, and A. D. Stone, “Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures,” Phys. Rev. A 85, 023802 (2012).
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M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12, 20–24 (2013).
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V. K. Mkhitaryan, D. S. Ghosh, M. Rude, J. Canet-Ferrer, R. A. Maniyara, K. K. Gopalan, and V. Pruneri, “Tunable complete optical absorption in multilayer structures including Ge2Sb2Te5 without lithographic patterns,” Adv. Optical Mater. 5, 1600452 (2017).
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V. K. Mkhitaryan, D. S. Ghosh, M. Rude, J. Canet-Ferrer, R. A. Maniyara, K. K. Gopalan, and V. Pruneri, “Tunable complete optical absorption in multilayer structures including Ge2Sb2Te5 without lithographic patterns,” Adv. Optical Mater. 5, 1600452 (2017).
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C. Dembowski, H. Graf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86, 787–790 (2001).
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D. Bimberg, N. N. Ledentsov, M. Grundmann, F. Heinrichsdorff, V. M. Ustinov, P. S. Kopev, Z. I. Alferov, and J. A. Lott, “Edge and vertical cavity surface emitting InAs quantum dot lasers,” Solid St. Electron. 42, 1433–1437 (1998).
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S. Yoo, T. Gwon, T. Eom, S. Kim, and C. Hwang, “Multicolor changeable optical coating by adopting multiple layers of ultrathin phase change material film,” ACS Photonics 3, 1265–1270 (2016).
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Figures (8)

Fig. 1
Fig. 1 Schematic of a non-PT-symmetric three-layer structure composed of a gain medium layer sandwiched between two GST layers for switching of the direction of reflectionless light propagation at exceptional points.
Fig. 2
Fig. 2 (a) Reflection spectra for the optimized structure of Fig. 1 with GST in its crystalline phase calculated for normal incidence from both the forward and backward directions using FDFD. Results are shown for L1 = 276 nm, L2 = 84 nm, and L3 = 2 nm. The gain medium is InGaAsP with InAs QDs (ñg = n + jk = 3.44 − j0.67). (b) Contrast ratio spectra for the optimized structure of Fig. 1 with GST in its crystalline phase. All parameters are as in Fig. 2(a). (c) and (d) Magnetic field amplitude profiles for the optimized structure of Fig. 1 with GST in its crystalline phase at f = 193.4 THz (λ0 =1.55μm), when a plane wave is normally incident from the left and right, respectively. All other parameters are as in Fig. 2(a). (e) and (f) Magnetic field amplitude in the optimized structure of Fig. 1 with GST in its crystalline phase at f = 193.4 THz (λ0 =1.55μm), normalized with respect to the field amplitude of the incident plane wave, when the light is incident from the left and right, respectively. The two vertical dashed lines indicate the left boundary of the left GST layer, and the right boundary of the right GST layer. All other parameters are as in Fig. 2(a).
Fig. 3
Fig. 3 (a) Reflection spectra for the optimized structure of Fig. 1 with GST in its amorphous phase calculated for normal incidence from both the forward and backward directions using FDFD. All parameters are as in Fig. 2(a). (b) Contrast ratio spectra for the optimized structure of Fig. 1 with GST in its amorphous phase. All parameters are as in Fig. 2(a). (c) and (d) Magnetic field amplitude profiles for the optimized structure of Fig. 1 with GST in its amorphous phase at f = 193.4 THz (λ0 =1.55μm), when a plane wave is normally incident from the left and right, respectively. All other parameters are as in Fig. 2(a). (e) and (f) Magnetic field amplitude in the optimized structure of Fig. 1 with GST in its amorphous phase at f = 193.4 THz (λ0 =1.55μm), normalized with respect to the field amplitude of the incident plane wave, when the light is incident from the left and right, respectively. The two vertical dashed lines indicate the left boundary of the left GST layer, and the right boundary of the right GST layer. All other parameters are as in Fig. 2(a).
Fig. 4
Fig. 4 (a) The reflection process at normal incidence from a three-layer structure composed of a gain medium layer sandwiched between two GST layers showing the partial waves. GST is in its crystalline phase. (b) Schematic defining the reflection coefficient reff when a plane wave is normally incident on the boundary between GST and a two-layer structure composed of a gain medium layer and a GST layer above an air substrate. GST is in its crystalline phase. (c) Phasor diagram demonstrating that a zero-reflection condition is achievable via destructive interference for the optimized structure of Fig. 1 with GST in its crystalline phase. A plane wave is incident from the right (backward direction) at f = 193.4 THz (λ0 =1.55 μm). All other parameters are as in Fig. 2(a). (d) Phasor diagram demonstrating that a zero-reflection condition is achievable via destructive interference for the structure of Fig. 1 with GST in its amorphous phase. A plane wave is incident from the left (forward direction) at f = 193.4 THz. All other parameters are as in Fig. 2(a).
Fig. 5
Fig. 5 (a) Calculated reflection for the structure of Fig. 1 with GST in its crystalline phase as a function of the real and imaginary parts, n and k, of the refractive index of the gain material. Results are shown for normal incidence from the backward direction at f = 193.4 THz (λ0 =1.55 μm). All other parameters are as in Fig. 2(a). The dashed lines correspond to the n and k of the optimized structure (ñg = n + jk = 3.44 − j0.67). (b) Same as in (a) except that GST is in its amorphous phase and results are shown for normal incidence from the forward direction.
Fig. 6
Fig. 6 (a) Phase spectra of the reflection coefficients in the forward (rf, black) and backward (rb, red) directions for the structure of Fig. 1 with GST in its crystalline phase. All parameters are as in Fig. 2(a). (b) Same as in (a) except that GST is in its amorphous phase.
Fig. 7
Fig. 7 (a) Schematic representation of the coalescence of the two eigenvalues λ s ± of the scattering matrix S [Eq. (1)], as the thickness L2 is varied for the structure of Fig. 1 with GST in its crystalline phase. The red lines correspond to the eigenvalues for L2 ≧ 84 nm, the blue lines correspond to the eigenvalues for L2 < 84 nm, and the meeting-point of the arrows corresponds to the exceptional point. Results are shown for f = 193.4 THz (λ0 =1.55 μm). All other parameters are as in Fig. 2(a). (b) Same as in (a) except that GST is in its amorphous phase.
Fig. 8
Fig. 8 (a) A circular loop in the parameter space of the real and imaginary parts, n and k, of the complex refractive index of the gain material. The circle is centered at the exceptional point (red dot with ñg = 3.44 − j0.67), and its radius R is set to be 0.05. The blue dot represents the starting position of the loop (point A with ñg = 3.49 − j0.67). (b) and (c) The trajectories of the real and imaginary parts of the eigenvalues λ s ± of the scattering matrix S [Eq. (1)] for the structure of Fig. 1, as the path of the complex refractive index of the gain material traces the circular loop of Fig. 8(a) in the counterclockwise orientation. Results are shown for GST in its crystalline phase and f = 193.4 THz (λ0 =1.55 μm). All other parameters are as in Fig. 2(a). (d) and (e). Same as in (b) and (c) except that GST is in its amorphous phase.

Equations (5)

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( H R H L ) = S ( H L + H R + ) = ( t r b r f t ) ( H L + H R + ) ,
r b = m = 0 r m = r 12 + r eff e 2 j γ L 3 1 + r 12 r eff e 2 j γ L 3 ,
E ± ( x ) = E E P ± α x x E P ,
n ˜ g n ˜ g , E P = R e j ϕ ,
λ s ± ( 2 π ) = λ s ( 0 ) .

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