## Confinement and optical properties of the plasmonic inverse-rib waveguide |

JOSA B, Vol. 29, Issue 4, pp. 818-826 (2012)

http://dx.doi.org/10.1364/JOSAB.29.000818

Acrobat PDF (1079 KB)

### 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

© 2012 Optical Society of America

## 1. INTRODUCTION

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]

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]

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

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]

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

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]

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]

## 2. ANGLE-DEPENDENT CONFINEMENT

**108**, 063108 (2010). [CrossRef]

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

**108**, 063108 (2010). [CrossRef]

**108**, 063108 (2010). [CrossRef]

**108**, 063108 (2010). [CrossRef]

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]

## 3. LOSSES OF A PLASMONIC INVERSE-RIB WAVEGUIDE

**108**, 063108 (2010). [CrossRef]

## 4. LIGHT CONCENTRATION CAPABILITIES

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]

## 5. COUPLED GUIDES WITH GAIN AND LOSS: ATTAINMENT OF EXCEPTIONAL POINT

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]

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]

**19**, 18004–18019 (2011). [CrossRef]

**19**, 18004–18019 (2011). [CrossRef]

**19**, 18004–18019 (2011). [CrossRef]

## 6. CONCLUSIONS

**108**, 063108 (2010). [CrossRef]

**19**, 18004–18019 (2011). [CrossRef]

## ACKNOWLEDGMENTS

## REFERENCES

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 |

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 |

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. |

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. |

5. | H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys. |

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 |

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. |

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 |

9. | A. V. Krasavin and A. V. Zayats, “Numerical analysis of long-range surface plasmon polariton modes in nanoscale plasmonic waveguides,” Opt. Lett. |

10. | J. Ctyroky, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express |

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 |

12. | S. Klaiman and L. S. Cederbaum, “Non-Hermitian Hamiltonians with space–time symmetry,” Phys. Rev. A |

13. | S. Klainman, U. Günther, and N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. |

14. | K. G. Makris, R. El-Gaininy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. |

15. | O. Bendix, R. Fleischmann, T. Kottos, and B. Shapior, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. |

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. | 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. |

18. | T. Kottos, “Broken symmetry makes light work,” Nat. Phys. |

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. |

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. |

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 |

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. |

24. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

25. | J.-M. Jin, |

26. | R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. |

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. |

28. | W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. |

29. | R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. |

30. | G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. |

31. | Z. Han, A. Y. Elezzabi, and V. Van, “Experimental realization of subwavelength plasmonic slot waveguides on a silicon platform,” Opt. Lett. |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(230.7380) Optical devices : Waveguides, channeled

(240.6680) Optics at surfaces : Surface plasmons

(250.3680) Optoelectronics : Light-emitting polymers

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(130.4110) Integrated optics : Modulators

**ToC Category:**

Plasmonics

**History**

Original Manuscript: November 30, 2011

Manuscript Accepted: January 2, 2012

Published: March 30, 2012

**Citation**

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

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-4-818

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### References

- 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]
- 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]
- 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]
- 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).
- 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]
- 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).
- 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]
- J. Ctyroky, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express 18, 21585–21593 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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).
- 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).
- 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]
- 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.
- C. T. West, T. Kottos, and T. Prosen, “PT-symmetric wave chaos,” Phys. Rev. Lett. 104, 054102 (2010).
- 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]
- 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]
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
- J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley–IEEE, 2002).
- 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]
- 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).
- W. Lukosz and R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977). [CrossRef]
- 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]
- G. W. Ford and W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984). [CrossRef]
- 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]

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