## Ultrahigh nonlinear nanoshell plasmonic waveguide with total energy confinement |

Optics Express, Vol. 19, Issue 24, pp. 23800-23808 (2011)

http://dx.doi.org/10.1364/OE.19.023800

Acrobat PDF (1670 KB)

### Abstract

Dielectric nonlinear waveguides have reached their maximum potential in achieving high nonlinearity due to the limitation of mode confinement beyond the diffraction limit. We theoretically demonstrate that a plasmonic waveguide consisted of a nonlinear subwavelength core coated by a metallic nanoshell can achieve ultrahigh nonlinearity and complete mode confinement. Our results show that the subwavelength nanoshell plasmonic waveguide can possess an ultrahigh Kerr nonlinearity up to 4.1 × 10^{4}W^{−1}m^{−1} with nearly 100% of the mode energy residing inside the waveguide at λ = 1.55 µm. The optical properties are explored with detailed numerical simulations and are explained in terms of their dispersive properties.

© 2011 OSA

## 1. Introduction

1. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics **3**(4), 216–219 (2009). [CrossRef]

3. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

1. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics **3**(4), 216–219 (2009). [CrossRef]

*n*

_{2}. To greatly enhance the Kerr nonlinearity, a dramatic reduction of the effective mode area is required. A major problem of current dielectric nonlinear dielectric waveguides is the inability of confining the mode beyond the fundamental diffraction limit. On the other hand, plasmonic waveguides provide mode confinement beyond the diffraction limit; however, they are not explored for potential applications in nonlinear optics. Here, we propose a novel concept for an ultrahigh nonlinear nanoshell plasmonic waveguides with total energy confinement. We show that the silicon-core nanoshell plasmonic waveguide operating at the free-space wavelength 1.55 µm, can possess an ultrahigh Kerr nonlinearity up to 4.1×10

^{4}W

^{−1}m

^{−1}with nearly 100% of the mode energy residing inside the waveguide. Our results show that this new class of nanoshell plasmonic waveguides could lead to the realization of truly ultra-compact, high-density, integrated nanophotonic devices.

## 2. Nanoshell plasmonic waveguide beyond the diffraction limit with complete mode confinement

4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature **424**(6950), 824–830 (2003). [CrossRef] [PubMed]

6. A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Solids **69**(11), 2936–2938 (2008). [CrossRef]

4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature **424**(6950), 824–830 (2003). [CrossRef] [PubMed]

7. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature **440**(7083), 508–511 (2006). [CrossRef] [PubMed]

8. 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. Photonics **2**(8), 496–500 (2008). [CrossRef]

1. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics **3**(4), 216–219 (2009). [CrossRef]

3. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

8. 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. Photonics **2**(8), 496–500 (2008). [CrossRef]

10. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. **87**(6), 061106 (2005). [CrossRef]

^{−2}. Secondly, nearly 100% of the total mode energy can be confined within the subwavelength waveguide. Thirdly, the vectorial nature of the electromagnetic (EM) fields within the cylindrical subwavelength waveguide results in significant increase of the optical Kerr nonlinearity and reaches up to 41251.05W

^{−1}m

^{−1}. Our results show experimentally realizable [11

11. J. Li, M. M. Hossain, B. Jia, D. Buso, and M. Gu, “Three-dimensional hybrid photonic crystals merged with localized plasmon resonances,” Opt. Express **18**(5), 4491–4498 (2010). [CrossRef] [PubMed]

12. M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. **7**(7), 543–546 (2008). [CrossRef] [PubMed]

13. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. **85**(24), 5833–5835 (2004). [CrossRef]

14. C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express **17**(13), 10757–10766 (2009). [CrossRef] [PubMed]

15. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. **9**(2), 897–902 (2009). [CrossRef] [PubMed]

16. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. **9**(12), 4403–4411 (2009). [CrossRef] [PubMed]

17. Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. **104**(20), 207402 (2010). [CrossRef] [PubMed]

18. 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**(7264), 629–632 (2009). [CrossRef] [PubMed]

19. M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. De Vries, P. J. Van Veldhoven, F. W. M. Van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics **1**(10), 589–594 (2007). [CrossRef]

11. J. Li, M. M. Hossain, B. Jia, D. Buso, and M. Gu, “Three-dimensional hybrid photonic crystals merged with localized plasmon resonances,” Opt. Express **18**(5), 4491–4498 (2010). [CrossRef] [PubMed]

12. M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. **7**(7), 543–546 (2008). [CrossRef] [PubMed]

*w,*height

*h*, an aspect ratio

*s*(where s is defined as

*h*/

*w*) and the nonlinear core is considered as silicon with a bulk refractive index of 3.48 and a nonlinear coefficient n

_{2}of 14.5×10

^{−18}m

^{2}/W [20

20. H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. **44**(9A), 6541–6545 (2005). [CrossRef]

*n*+

*ik*of 0.145263+11.3587i [21

21. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

*d*. To illustrate the fundamental modal behavior of our plasmon waveguide we characterized the nonlinearity, the mode confinement and the effective mode index for a variety of

*d*,

*w*, and

*s*. The eigenmodes were extracted numerically with the finite element based eigenmode solver (COMSOL Multiphysics) within the plasmonic waveguide at the telecommunications free-space wavelength of 1.55 µm. Figure 1(c) demonstrates the mode energy distribution for the plasmonic waveguide with the same core size as in Fig. 1(b) but with a 50 nm silver coating. The mode energy is tightly confined within the dielectric core of the waveguides. In comparison, the state-of-the-art silicon nanowire waveguides [2

2. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express **16**(2), 1300–1320 (2008). [CrossRef] [PubMed]

3. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

8. 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. Photonics **2**(8), 496–500 (2008). [CrossRef]

*d*is further illustrated by the normalized electric field shown in Figs. 1(d)-1(f). For a metallic shell with thickness < 50 nm the coupling between the plasmons of the inner and outer surfaces of the metallic shell becomes stronger and results in hybridization of the plasmon modes causing the fields to spread outside of the nanoshell as depicted in Figs. 1(d) and 1(e). On the other hand, Fig. 1(f) demonstrates that for metallic shell thickness ≥ 50 nm, the coupling between the plasmons of the two surfaces becomes almost negligible and the mode is strictly confined within the dielectric core.

## 3. Mode characteristics of the nonlinear nanoshell plasmonic waveguide

*w*with fixed values of

*s*and

*d*to 3 and 50 nm, respectively. Due to the ellipsoidal symmetry of the waveguide structure the single fundamental mode is x polarized and thus the strong discontinuity of the normal component of the electric fields at the metal-dielectric interface creates an ultrahigh mode confinement. The plasmon mode contains 97.7% of its modal energy within the dielectric core and 99.9% of its modal energy is confined within the waveguide including the metallic shell.

**15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

23. S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express **17**(4), 2298–2318 (2009). [CrossRef] [PubMed]

25. M. D. Turner, T. M. Monro, and S. Afshar V, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman Scattering,” Opt. Express **17**(14), 11565–11581 (2009). [CrossRef] [PubMed]

23. S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express **17**(4), 2298–2318 (2009). [CrossRef] [PubMed]

26. S. Afshar V, W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett. **34**(22), 3577–3579 (2009). [CrossRef] [PubMed]

23. S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express **17**(4), 2298–2318 (2009). [CrossRef] [PubMed]

**E**and

**H**are the electric and magnetic vector fields of the propagating mode and n(x,y) and n

_{2}(x,y) are the linear and nonlinear refractive index distributions with respect to the waveguide cross-sections. The effective mode area

*A*

_{eff}represents a statistical measure for the mode energy density distribution. The effective mode area also possesses its full vector nature as opposed to the scalar field definition [22]. The statistical definition for

*A*

_{eff}provides the complete electromagnetic (EM) mode area compared to its counterparts [8

**2**(8), 496–500 (2008). [CrossRef]

*A*

_{eff}of the nanoshell plasmonic waveguide is 0.0196 µm

^{−2}, which, to the best of our knowledge, is the smallest effective mode area (based on the statistical measure) so far for optical waveguides at wavelength 1.55 µm. The inset of Fig. 3(a) shows the propagation lengths of the plasmon mode is less than that of the SPP modes (~24.5µm at the wavelength of 1.55 µm) at a flat silver-silicon interface. These higher losses arise from the strong localization of the fields to the metallic nanostructure. However, the high subwavelength localization and total energy confinement of the nanoshell plasmon waveguide make them unique candidates for photonic integration on the nanoscale. Further decrease of the core width leads to smaller effective areas and larger nonlinearity; however, this also greatly increases the propagation loss. Here we have restricted the results to a regime where the propagation length is of practical use.

*γ*is inversely proportional to

*A*

_{eff}, surprisingly, our results show that

*γ*increases at a much faster rate than the decreasing rate of

*A*

_{eff}. The reason behind this enhanced increasing rate is that the effective nonlinear index coefficient

11. J. Li, M. M. Hossain, B. Jia, D. Buso, and M. Gu, “Three-dimensional hybrid photonic crystals merged with localized plasmon resonances,” Opt. Express **18**(5), 4491–4498 (2010). [CrossRef] [PubMed]

*A*

_{eff}decreases 0.52 times, while

_{2}). Thus, the combined effect enhances the optical nonlinearity

*γ*to 2.64 times and reaches a highly enhanced value of 7514W

^{−1}m

^{−1}. Undoubtedly,

## 4. Ultrahigh nonlinearity with geometrical alteration

*s*for a constant cross-sectional area of the nonlinear core. Here we restrict our results to modes with an effective mode index n

_{eff}>1 where the plasmon mode wavevector

*k*

_{mode}>

*k*

_{0}(

*k*

_{mode}→

*n*

_{eff}

*k*

_{0}[27]). Figure 4(a) shows that

*A*

_{eff}clearly confirm that it is not

*A*

_{eff}that plays the dominating role to significantly enhance the nonlinearity rather it is

*γ*reaches an ultrahigh value of 41251.05W

^{−1}m

^{−1}for an aspect ratio of 1.333. For a fair comparison of the enhancement of

*γ*we compare with other highly nonlinear optical waveguides with the same waveguide core material. Our results show that this ultrahigh value of

*γ*in our plasmonic waveguide is 25 times higher than that of the state-of-the-art nonlinear silicon-on-insulator slot waveguide [3

**15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

**2**(8), 496–500 (2008). [CrossRef]

## 5. Origin of the ultrahigh nonlinearity

*E*and

_{x}*H*are strongly dominant over the

_{y}*E*and

_{y}*H*fields respectively. Thus the second term inside the integral of the right hand side of the above equation becomes the multiplication of the weak modal fields and thus can be ignored. So, Eq. (4) can be re-written as

_{x}*E*and

_{x}*H*. Figure 5(a) depicts the magnitudes of the modal fields for the changing aspect ratios i.e. for the varying wavevector. The field components

_{y}*E*component is dominant over the other components of the electric fields over the whole aspect ratio range. On the other hand, both the

_{x}*H*and

_{y}*H*components contribute for the high aspect ratio. However, as the aspect ratio decreases,

_{z}*H*becomes dominant over

_{z}*H*, as can be found in Fig. 5(a) for the aspect ratio of 1.333. The reduced magnitude of

_{y}*H*drastically weakens the energy flow along the propagation direction and effectively yields a much higher value of

_{y}_{z}component of the magnetic field for low aspect ratios is reasonable from the variation of the effective mode index

*n*

_{eff}shown in the inset of Fig. 4(a). This feature states that the

*n*

_{eff}value of the plasmon mode reduces for decreasing aspect ratios, indicating the reduction of the plasmon mode wavevector, i.e. it approaches the stationary limit (i.e.

*k*

_{mode}→0) when the aspect ratio is reduced.

*k*

_{mode}→0, the mode becomes stationary and the current density flows only along the azimuthal direction within the metallic nanoshell cross section. This rotational current flow in the two dimensions causes the magnetic fields to be directed purely along the propagation direction. Figure 5(a) evidently demonstrates the growing dominance of

*H*over

_{z}*H*for reducing plasmon wave vector (i.e. for approaching to the stationary limit) and illustrates the enhancement of the optical nonlinearity. Figures 5(b) and 5(c) show the distributions of the magnetic field components

_{y}*H*and

_{y}*H*for the lowest aspect ratio 1.333 and depict the dominance of

_{z}*H*over

_{z}*H*.

_{y}28. I. W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express **15**(3), 1135–1146 (2007). [CrossRef] [PubMed]

_{g}→c/v

_{g}) of the nanoshell plasmon modes over the varying values of the aspect ratio, shown in Fig. 4(b), exactly replicates the trend of the optical Kerr nonlinearity, illustrating the role of the reduction of the group velocity for the ultrahigh nonlinearity. This large group index greatly prolongs the nonlinear interaction between light and matter i.e. induces the enhanced nonlinear index coefficient

## 6. Conclusion

^{−1}m

^{−1}due to the significant enhancement of the effective nonlinear index coefficient along with the subwavelength confinement by controlling the geometrical properties of the plasmonic waveguide. The combined properties of the enhanced nonlinearity, the subwavelength mode area and complete mode energy confinement forms an excellent silicon based nanoplasmonic platform for the realization of high-density photonic integration of nonlinear optical switching [13

13. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. **85**(24), 5833–5835 (2004). [CrossRef]

14. C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express **17**(13), 10757–10766 (2009). [CrossRef] [PubMed]

17. Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. **104**(20), 207402 (2010). [CrossRef] [PubMed]

29. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics **1**(7), 402–406 (2007). [CrossRef]

19. M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. De Vries, P. J. Van Veldhoven, F. W. M. Van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics **1**(10), 589–594 (2007). [CrossRef]

20. H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. **44**(9A), 6541–6545 (2005). [CrossRef]

30. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature **466**(7307), 735–738 (2010). [CrossRef] [PubMed]

## Acknowledgement

## References and links

1. | C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics |

2. | M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express |

3. | C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express |

4. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature |

5. | E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science |

6. | A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Solids |

7. | S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature |

8. | 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. Photonics |

9. | E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. |

10. | D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. |

11. | J. Li, M. M. Hossain, B. Jia, D. Buso, and M. Gu, “Three-dimensional hybrid photonic crystals merged with localized plasmon resonances,” Opt. Express |

12. | M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. |

13. | T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. |

14. | C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express |

15. | J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. |

16. | W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. |

17. | Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. |

18. | 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 |

19. | M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. De Vries, P. J. Van Veldhoven, F. W. M. Van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics |

20. | H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. |

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

22. | G. P. Agrawal, “Nonlinear Fiber Optics, 4th ed,” (Academic press, San Diego, 2007). |

23. | S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express |

24. | M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express |

25. | M. D. Turner, T. M. Monro, and S. Afshar V, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman Scattering,” Opt. Express |

26. | S. Afshar V, W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett. |

27. | A. W. Snyder and J. D. Love, “Optical Waveguide Theory,” (Chapman & Hall, London, New York, 1983). |

28. | I. W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express |

29. | D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics |

30. | S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature |

**OCIS Codes**

(130.4310) Integrated optics : Nonlinear

(190.3270) Nonlinear optics : Kerr effect

(190.4360) Nonlinear optics : Nonlinear optics, devices

(250.5300) Optoelectronics : Photonic integrated circuits

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 20, 2011

Revised Manuscript: October 28, 2011

Manuscript Accepted: October 29, 2011

Published: November 8, 2011

**Citation**

Md M. Hossain, Mark D. Turner, and Min Gu, "Ultrahigh nonlinear nanoshell plasmonic waveguide with total energy confinement," Opt. Express **19**, 23800-23808 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23800

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### References

- C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009). [CrossRef]
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