Abstract

Plasmonic inverse-rib optical waveguides, consisting of a high-index inverse rib embedded in low-index medium above a flat metallic surface, are investigated under four aspects: (i) the optimal angle θ of the rib sidewall for tight modal confinement is assessed, (ii) the effect of the geometric parameters and the wavelength on propagation losses is given, (iii) we use a 3D simulation to assess how well light from an emitting dipole is captured by such a tightly guiding structure, and (iv) we show that for two such parallel hybrid waveguiding systems, when one of them has added gain, we have a plasmonic version of the PT-symmetric waveguide arrangement, and we additionally show that complex gain is needed to restore a truly exceptional point in its propagation constant evolution.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
    [CrossRef]
  2. M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
    [CrossRef]
  3. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
    [CrossRef]
  4. J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
    [CrossRef]
  5. H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys. 108, 063108 (2010).
    [CrossRef]
  6. D. X. Dai and S. L. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009).
  7. M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21, 362–364 (2009).
    [CrossRef]
  8. X. Y. Zhang, A. Hu, J. Z. Wen, T. Zhang, X. J. Xue, Y. Zhou, and W. W. Duley, “Numerical analysis of deep sub-wavelength integrated plasmonic devices based on semiconductor-insulator-metal strip waveguides,” Opt. Express 18, 18945–18959 (2010).
  9. A. V. Krasavin and A. V. Zayats, “Numerical analysis of long-range surface plasmon polariton modes in nanoscale plasmonic waveguides,” Opt. Lett. 35, 2118–2120 (2010).
    [CrossRef]
  10. J. Ctyroky, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express 18, 21585–21593 (2010).
    [CrossRef]
  11. M. Kulishov, J. M. Laniel, N. Bélanger, and D. V. Plant, “Trapping light in a ring resonator using a grating-assisted coupler with asymmetric transmission,” Opt. Express 13, 3567–3578 (2005).
    [CrossRef]
  12. S. Klaiman and L. S. Cederbaum, “Non-Hermitian Hamiltonians with space–time symmetry,” Phys. Rev. A 78, 062113 (2008).
  13. S. Klainman, U. Günther, and N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
  14. K. G. Makris, R. El-Gaininy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef]
  15. O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
    [CrossRef]
  16. J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Hybrid long-range surface plasmon-polariton modes with tight field confinement guided by asymmetrical waveguides,” Opt. Express 17, 23603–23609 (2009).
  17. A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).
  18. T. Kottos, “Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
    [CrossRef]
  19. C. E. Rüter, K. G. Makris, R. El-Gaininy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
    [CrossRef]
  20. A. A. Sukhorukov, Z. Xu, and Y. Kivshar, “Nonlinear breaking of PT symmetry in coupled waveguides with balanced gain and loss,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC19.
  21. C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).
  22. H. Benisty, A. Degiron, A. Lupu, A. De Lustrac, S. Chenais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, and G. Lerondel, “Implementation of PT symmetric devices using plasmonics: principle and applications,” Opt. Express 19, 18004–18019 (2011).
    [CrossRef]
  23. A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
    [CrossRef]
  24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  25. J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley–IEEE, 2002).
  26. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
    [CrossRef]
  27. J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
  28. W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
    [CrossRef]
  29. R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
    [CrossRef]
  30. G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]
  31. Z. Han, A. Y. Elezzabi, and V. Van, “Experimental realization of subwavelength plasmonic slot waveguides on a silicon platform,” Opt. Lett. 35, 502–504 (2010).
    [CrossRef]

2011

2010

Z. Han, A. Y. Elezzabi, and V. Van, “Experimental realization of subwavelength plasmonic slot waveguides on a silicon platform,” Opt. Lett. 35, 502–504 (2010).
[CrossRef]

A. V. Krasavin and A. V. Zayats, “Numerical analysis of long-range surface plasmon polariton modes in nanoscale plasmonic waveguides,” Opt. Lett. 35, 2118–2120 (2010).
[CrossRef]

X. Y. Zhang, A. Hu, J. Z. Wen, T. Zhang, X. J. Xue, Y. Zhou, and W. W. Duley, “Numerical analysis of deep sub-wavelength integrated plasmonic devices based on semiconductor-insulator-metal strip waveguides,” Opt. Express 18, 18945–18959 (2010).

J. Ctyroky, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express 18, 21585–21593 (2010).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys. 108, 063108 (2010).
[CrossRef]

T. Kottos, “Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
[CrossRef]

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

C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

2009

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
[CrossRef]

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21, 362–364 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

D. X. Dai and S. L. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009).

J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Hybrid long-range surface plasmon-polariton modes with tight field confinement guided by asymmetrical waveguides,” Opt. Express 17, 23603–23609 (2009).

2008

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

S. Klaiman and L. S. Cederbaum, “Non-Hermitian Hamiltonians with space–time symmetry,” Phys. Rev. A 78, 062113 (2008).

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

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

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
[CrossRef]

2005

2002

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

1984

G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

1977

W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Aimez, V.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Alivisatos, A. P.

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

Baets, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Bakker, R.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Barbillon, G.

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
[CrossRef]

Bélanger, N.

Belgrave, A. M.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Bendix, O.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Benisty, H.

Besbes, M.

Bienstman, P.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Blaize, S.

Bruyant, A.

Cederbaum, L. S.

S. Klaiman and L. S. Cederbaum, “Non-Hermitian Hamiltonians with space–time symmetry,” Phys. Rev. A 78, 062113 (2008).

Chen, J. J.

Chenais, S.

Cho, S. Y.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
[CrossRef]

Christodoulides, D. N.

C. E. Rüter, K. G. Makris, R. El-Gaininy, 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, R. Duchesne, R. Morandotti, M. Volatier-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).

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

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Ctyroky, J.

J. Ctyroky, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express 18, 21585–21593 (2010).
[CrossRef]

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Dai, D. X.

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

De La Rue, R. M.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

De Lustrac, A.

De Ridder, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Degiron, A.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

Duchesne, R.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Duley, W. W.

Elezzabi, A. Y.

El-Gaininy, R.

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

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

Esteban, R.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

Eyderman, S.

Fleischmann, R.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Forget, S.

Freude, W.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21, 362–364 (2009).
[CrossRef]

Fujii, M.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21, 362–364 (2009).
[CrossRef]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Gong, Q. H.

Greffet, J. J.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

Günther, U.

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

Guo, A.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Han, Z.

He, S. L.

Helfert, S.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Herz, E.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Hu, A.

Hugonin, J. P.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Jin, J.-M.

J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley–IEEE, 2002).

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Jokerst, N. M.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
[CrossRef]

Kip, D.

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

Kivshar, Y.

A. A. Sukhorukov, Z. Xu, and Y. Kivshar, “Nonlinear breaking of PT symmetry in coupled waveguides with balanced gain and loss,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC19.

Klaasse, G.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Klaiman, S.

S. Klaiman and L. S. Cederbaum, “Non-Hermitian Hamiltonians with space–time symmetry,” Phys. Rev. A 78, 062113 (2008).

Klainman, S.

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

Kottos, T.

C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).

T. Kottos, “Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Krasavin, A. V.

Kulishov, M.

Kunz, R. E.

W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
[CrossRef]

Kuzmiak, V.

Lalanne, P.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Laniel, J. M.

Lerondel, G.

Leuthold, J.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21, 362–364 (2009).
[CrossRef]

Li, Z.

Lukosz, W.

W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
[CrossRef]

Lupu, A.

Ma, R.-M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Makris, K. G.

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

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

Moiseyev, N.

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

Morandotti, R.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Musslimani, Z. H.

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

Narimanov, E. E.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Noginov, M. A.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
[CrossRef]

Petracek, J.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
[CrossRef]

Plant, D. V.

Pregla, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Prosen, T.

C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).

Rüter, C. E.

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

Salamo, G. J.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Segev, M.

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

Shalaev, V. M.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Shapior, B.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Sheldon, M. T.

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

Siviloglou, G. A.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Smith, D. R.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

Stoffer, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Stout, S.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Sukhorukov, A. A.

A. A. Sukhorukov, Z. Xu, and Y. Kivshar, “Nonlinear breaking of PT symmetry in coupled waveguides with balanced gain and loss,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC19.

Suteewong, T.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

Teperik, T. V.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

Tyler, T.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
[CrossRef]

Van, V.

Volatier-Ravat, M.

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

Weber, W. H.

G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Wen, J. Z.

West, C. T.

C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).

Wiesner, U.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Xu, Z.

A. A. Sukhorukov, Z. Xu, and Y. Kivshar, “Nonlinear breaking of PT symmetry in coupled waveguides with balanced gain and loss,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC19.

Xue, X. J.

Yue, S.

Zayats, A. V.

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Zhang, T.

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

Zhang, X. Y.

Zhou, Y.

Zhul, G.

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, “Silicon-based plasmonics for on-chip photonics,” IEEE J. Sel. Top. Quantum Electron. 16, 295–306 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21, 362–364 (2009).
[CrossRef]

J. Appl. Phys.

H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys. 108, 063108 (2010).
[CrossRef]

Nat. Photon.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photon. 2, 496–500 (2008).
[CrossRef]

Nat. Phys.

T. Kottos, “Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
[CrossRef]

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

Nature

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

M. A. Noginov, G. Zhul, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

New J. Phys.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” New J. Phys. 11, 015002 (2009).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10, 105018 (2008).
[CrossRef]

Opt. Commun.

W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).

Phys. Rep.

G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Phys. Rev. A

S. Klaiman and L. S. Cederbaum, “Non-Hermitian Hamiltonians with space–time symmetry,” Phys. Rev. A 78, 062113 (2008).

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett.

C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).

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

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

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

A. Guo, G. J. Salamo, R. Duchesne, R. Morandotti, M. Volatier-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).

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

Other

A. A. Sukhorukov, Z. Xu, and Y. Kivshar, “Nonlinear breaking of PT symmetry in coupled waveguides with balanced gain and loss,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC19.

J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley–IEEE, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

(a) Structure of the PIROW, the red spot being indicative for the confined mode profile and (b) optogeometric parameters of the rib and layer sequence.

Fig. 2.
Fig. 2.

PIROW modal characteristics for tip width Ltip=20nm, nL=1.40, and variable inverse-rib angle θ. (a), (b) Field profiles along the cuts indicated in their inset. (c) (Re(neff)) trend versus angle θ (dashed line), with comparison to nL=1.50 (solid line with dots). (d) Area enclosed in the range |Ey|>αEymax versus angle for different values of α.

Fig. 3.
Fig. 3.

Comparison of confinement for two low-index values differing by Δn=0.1, as a function of the inverse-rib sidewall angle: (a) nL=1.40 and (b) nL=1.50.

Fig. 4.
Fig. 4.

Losses as a function of the inverse-rib angle at 633 nm, given through the imaginary effective index. Note however the substantial real effective index variation on the same range in Fig. 2.

Fig. 5.
Fig. 5.

Losses as a function of wavelength for a 45° PIROW and a 15° PIROW as indicated, using gold. Inset, the associated absorption lengths that become larger than a typical penetration length in a periodic system of given modulation Δneff at wavelengths between 600 and 700 nm.

Fig. 6.
Fig. 6.

(a) Effective index versus wavelength for a 45° PIROW with Au (top curve) or Ag (lower curve) and (b) same as Fig. 5, but comparing Ag (dashed line) and Au (solid line) losses Im(neff). The inset transforms the same comparison into an absorption length one, as in Fig. 5. Note that Ag may behave well at wavelengths as short as 550–600 nm.

Fig. 7.
Fig. 7.

Purcell factor FP for a vertical dipole at wavelength λ=700nm in a PIROW: (a) dipole at variable height, either in the symmetry plane x=0 or along the rib edge and (b) dipole lying along x at height z=d, the height of the tip bottom. Insets, scanned positions.

Fig. 8.
Fig. 8.

Light capture efficiency by a PIROW on both sides for a dipole lying along the vertical direction at x=0. Insets show (left) the scanned position and the nominal and (right) the two “nested” collection boxes used to check that extraction is in the far-field regime.

Fig. 9.
Fig. 9.

(a) Map of coupled PIROW guides with attempt to implement PT symmetry onto the left one with the same variable added gain g in the inverse ridge and in the shaded region above it, (b) real part of neff, and (c) imaginary part of neff

Fig. 10.
Fig. 10.

Exceptional point restoration: by adding complex gain (i.e., simultaneous gain and index change) in the region above the inverse-rib [see Fig. 9(a)], a nearly perfect singularity in the vicinity of the exceptional point can be restored. (a) Real part of neff and (b) imaginary part of neff.

Metrics