Abstract

PT-symmetric structures, such as a pair of coupled waveguides with balanced loss/gain, exhibit a singularity of their eigenvalues around an exceptional point, hence a large apparent differential gain. In the case of fixed losses and variable gain, typical of plasmonic systems, a similar behavior emerges but the singularity is smoothened, especially in more confined structures. This reduces the differential gain around the singular point. Our analysis ascribes the origin of this behavior to a complex coupling between the waveguides once gain is present in an unsymmetrical fashion, even if guides feature the same modal gains in isolation. We demonstrate that adjunction of a real index variation to the variable waveguide heals the singularity nearly perfectly, as it restores real coupling. We illustrate the success of the approach with two geometries, planar or channel, and with different underlying physics, namely dielectric or plasmonic.

© 2012 IEEE

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2012 (1)

H. Benisty, M. Besbes, "Confinement and optical properties of the plasmonic inverse-rib waveguide," J. Opt. Soc. Amer. B 29, 818-826 (2012).

2011 (2)

H. Benisty, A. Degiron, A. Lupu, A. De Lustrac, S. Chenais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, G. Lerondel, "Implementation of PT symmetric devices using plasmonics: Principle and applications," Opt. Express 19, 18004-18019 (2011).

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

2010 (7)

J. Ctyroky, V. Kuzmiak, S. Eyderman, "Waveguide structures with antisymmetric gain/loss profile," Opt. Express 18, 21585-21593 (2010).

S. Longhi, "PT-symmetric laser absorber," Phys. Rev. A 82, (2010).

I. De Leon, P. Berini, "Amplification of long-range surface plasmons by a dipolar gain medium," Nat. Photon. 4, 382-387 (2010).

M. C. Gather, K. Meerholz, N. Danz, K. Leosson, "Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer," Nat. Photon. 4, 457-461 (2010).

T. Kottos, "Broken symmetry makes light work," Nat. Phys. 6, 166-167 (2010).

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

H. Benisty, M. Besbes, "Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition," J. Appl. Phys. 108, 0631081-0631088 (2010).

2009 (3)

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, D. R. Smith, "Directional coupling between dielectric and long-range plasmon waveguides," New J. Phys. 11, 01500201-01500210 (2009).

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. MA, C. Gladden, L. Dai, G. Bartal, X. Zhang, "Plasmon lasers at deep subwavelength scale," Nature 461, 629-632 (2009).

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

2008 (4)

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

M. A. Noginov, V. A. Podolskiy, G. Zhul, M. Mayyl, M. Bahoural, J. A. Adegokel, B. A. Ritzo, K. Reynolds, "Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium," Opt. Express 16, 1385-1392 (2008).

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

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

2005 (2)

2002 (1)

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

1984 (1)

G. W. Ford, W. H. Weber, "Electromagnetic interaction of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).

J. Appl. Phys. (1)

H. Benisty, M. Besbes, "Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition," J. Appl. Phys. 108, 0631081-0631088 (2010).

J. Opt. Soc. Amer. B (1)

H. Benisty, M. Besbes, "Confinement and optical properties of the plasmonic inverse-rib waveguide," J. Opt. Soc. Amer. B 29, 818-826 (2012).

Nat. Photon. (2)

I. De Leon, P. Berini, "Amplification of long-range surface plasmons by a dipolar gain medium," Nat. Photon. 4, 382-387 (2010).

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

Nat. Photon. (1)

M. C. Gather, K. Meerholz, N. Danz, K. Leosson, "Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer," Nat. Photon. 4, 457-461 (2010).

Nat. Phys. (2)

T. Kottos, "Broken symmetry makes light work," Nat. Phys. 6, 166-167 (2010).

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

Nature (1)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. MA, C. Gladden, L. Dai, G. Bartal, X. Zhang, "Plasmon lasers at deep subwavelength scale," Nature 461, 629-632 (2009).

New J. Phys. (2)

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

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, D. R. Smith, "Directional coupling between dielectric and long-range plasmon waveguides," New J. Phys. 11, 01500201-01500210 (2009).

Opt. Express (2)

M. A. Noginov, V. A. Podolskiy, G. Zhul, M. Mayyl, M. Bahoural, J. A. Adegokel, B. A. Ritzo, K. Reynolds, "Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium," Opt. Express 16, 1385-1392 (2008).

H. Benisty, A. Degiron, A. Lupu, A. De Lustrac, S. Chenais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, G. Lerondel, "Implementation of PT symmetric devices using plasmonics: Principle and applications," Opt. Express 19, 18004-18019 (2011).

Opt. Quant. Electron. (1)

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

Opt. Express (3)

Phys. Rev. Lett. (1)

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

Phys. Rep. (1)

G. W. Ford, W. H. Weber, "Electromagnetic interaction of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).

Phys. Rev. A (1)

S. Longhi, "PT-symmetric laser absorber," Phys. Rev. A 82, (2010).

Phys. Rev. Lett. (2)

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

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

Other (2)

H. P. Nolting, G. Sztefka, M. Grawert, J. Ctyroky, "Wave propagation in a waveguide with a balance of gain and loss," Proc. Integr. Photon. Conf. (1996) pp. IMD5-1.

D. Felbacq, "Finding resonance poles by means of Cauchy integrals," Proc. 13th Int. Conf. Transp. Opt. Netw. (2011) pp. 4.

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