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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 23800–23808
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Ultrahigh nonlinear nanoshell plasmonic waveguide with total energy confinement

Md M. Hossain, Mark D. Turner, and Min Gu  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 23800-23808 (2011)
http://dx.doi.org/10.1364/OE.19.023800


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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 × 104W−1m−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

Recent advancement in the state-of-the-art nanofabrication facilities have led to the development of optical waveguides with subwavelength features and inhomogeneous cross-sections, providing enhanced optical nonlinearities and small effective mode areas [1

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

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]

]. Such nonlinear optical waveguides are emerging as vital components for all-optical high speed signal processing [1

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]

]. The Kerr nonlinear coefficient within a waveguide is determined by the mode confinement and on the bulk nonlinear index coefficient n2. 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 4.1×104W−1m−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

Confining the mode energy totally within the waveguide cross-section becomes a great challenge when approaching the subwavelength regime. Due to the fundamental diffraction limit, the mode energy cannot be confined to dielectric waveguides with subwavelength core sizes. Taking as an example, a silicon waveguide, embedded in air, depicted in Figs. 1(a)
Fig. 1 Concept of the nanoshell plasmonic waveguide and associated total mode confinement. (a, b) Mode energy density distribution of a silicon waveguide with an aspect ratio of 3, calculated numerically for a 200 nm and a 100 nm core width respectively. (c), Mode energy distributions for a nanoshell plasmonic waveguide with a silicon core width of 100 nm and silver nanoshell of thickness 50 nm. (d) The normalized electric field |E| of the plasmonic mode for a 10 nm thick silver shell on the silicon core, showing large leaking of the fields outside of the waveguide. (e) |E| for a 25 nm silver shell, showing less field leakage. (f) |E| for a 50 nm thick silver shell, showing minimal field leakage and leading to nearly total confinement of the fields to the nonlinear core region.
and 1(b), operating at a free-space wavelength of 1.55 µm, we find that a reduction of the core width from 200 nm to 100 nm results in the dramatic loss of the mode energy confined within the waveguide from 77.4% to 0.22%. On the other hand, plasmonics provides an unmatchable ability to confine fields far beyond the diffraction limit [4

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

6

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

]. Surface plasmon polaritons (SPP) can facilitate guiding light with concentrated electromagnetic (EM) energies at the metal-dielectric interfaces [4

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

, 7

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

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]

]. However, confining the mode energy completely within the waveguides physical region is very important for realizing compact integrated nanophotonic components with zero-crosstalk, which has not been addressed in both the current dielectric and plasmonic waveguide designs [1

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

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

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

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]

].

The dependence of the mode confinement on the nanoshell thickness 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

It is clear from Fig. 3(a)
Fig. 3 Effective mode area, Kerr nonlinearity and effective nonlinear index of the plasmon mode for w=100 nm, d=50 nm and s=3. (a) Calculated Aeff of the plasmonic waveguide for varying w. Inset: The propagation length L of the plasmon mode for varying core width. (b) Calculated γ and normalized effective nonlinear index of the nanoshell plasmonic waveguide. Inset: Calculated effective mode indices over a range of w.
that the mode possesses an ultra-small effective mode area due to the plasmonic confinement of the system. For a core width of 100 nm, Aeff 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.

Even though the nonlinearity γ is inversely proportional to Aeff, surprisingly, our results show that γ increases at a much faster rate than the decreasing rate of Aeff. The reason behind this enhanced increasing rate is that the effective nonlinear index coefficient n¯2 of the nanoshell plasmonic waveguide emerges much larger than the bulk n¯2, which has not been reported before. Figures 3(a) and 3(b) show that as the core width decreases from 140 nm to 100 nm [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]

], Aeff decreases 0.52 times, while n¯2 increases 1.37 times (from 1.82 to 2.506 times the bulk silicon n2). Thus, the combined effect enhances the optical nonlinearity γ to 2.64 times and reaches a highly enhanced value of 7514W−1m−1. Undoubtedly, n¯2plays an intriguing role to stimulate the γ value of the nanoshell plasmonic waveguide which could demonstrate an ultrahigh optical nonlinearity. It should also be noted that the nearly total energy confinement of the plasmonic waveguide holds regardless the variation of the waveguide core cross-section sizes shown in Fig. (3).

4. Ultrahigh nonlinearity with geometrical alteration

We now turn our attention to the dependence of this nonlinear enhancement on geometrical properties via the variation of the waveguide aspect ratio s for a constant cross-sectional area of the nonlinear core. Here we restrict our results to modes with an effective mode index neff >1 where the plasmon mode wavevector kmode>k0 (kmodeneffk0 [27

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

]). Figure 4(a)
Fig. 4 Characteristics of the effective nonlinear index, mode area, Kerr nonlinearity and group index for d = 50 nm and varying s while the nonlinear core cross-sectional area was kept same as in Fig. 3. (a) The normalized n¯2and Aeff for decreasing aspect ratios of plasmon waveguide. Inset: the neff versus aspect ratio s. (b) Kerr nonlinearity and square of the group index as function of aspect ratios for the plasmonic waveguide with a silicon core. Inset: The propagation length L and product of γ and L as a figure of merit.
shows that n¯2/n2 increases from 2.51 to 15.03 as the aspect ratio decreases from 3 to 1.333. Once again, the ultra-small but almost constant values of Aeff clearly confirm that it is not Aeff that plays the dominating role to significantly enhance the nonlinearity rather it is n¯2of the waveguide core. Figure 4(b) shows that γ reaches an ultrahigh value of 41251.05W−1m−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

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]

]. More importantly, at this ultrahigh nonlinearity the mode contains 99.1% of energy within the entire waveguide region. It is the strong lateral localization of the nanoshell plasmonic waveguide that provides almost all the mode energy confined within the tiny silicon core with immense nonlinearity. In contrast, other geometries such as the hybrid plasmonic waveguide [8

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]

] contain only 15 to 20% of the mode energy within the low index dielectric region for the mode confinement. As a result, our nanoshell plasmonic waveguide geometry is more suitable for ultrahigh nonlinear interactions with nearly total energy confinement as well as minimal cross-talk at a subwavelength scale.

It can also be noticed from the inset of Fig. 4b that the propagation length decreases with a reduction of aspect ratios, giving a trade-off between the ultrahigh nonlinearity and the propagation length. As a figure of merit, we plot the product of the nonlinearity and the propagation length in the inset of Fig. 4b which shows a gain of a factor of two for decreasing aspect ratios. Further decrease of the aspect ratio of the nonlinear core leads to even greater enhancement of the Kerr nonlinearity; however, in this regime, the propagation length of the mode becomes less than the wavelength of operation. Thus we have not included these results here.

5. Origin of the ultrahigh nonlinearity

|(E×H*).z^|2dA=|ExHy*EyHx*|2dA
(4)

|(E×H*).z^|2dA|Ex|2|Hy*|2dA
(5)

In the limit of kmode→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 Hz over Hy 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 Hy and Hz for the lowest aspect ratio 1.333 and depict the dominance of Hz over Hy.

An alternative explanation of the enhancement of the effective nonlinear coefficient n¯2can be derived by analyzing the dispersive properties of the nanoshell plasmonic waveguide for varying aspect ratios. We investigate the dispersive properties of the nanoshell plasmon waveguide by using the eigenmodes and analyze the relation with the group velocity [28

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]

]. Figure 6
Fig. 6 Dispersion relation of the plasmon mode approaching of the stationary limit at 1.55 µm for d = 50 nm and varying s while the nonlinear core cross-sectional area was kept same as in Fig. 3.
depicts the dispersion of the plasmon modes for a range of aspect ratios. Interestingly, for the transition from the high to low aspect ratios, where the plasmon modes approach the stationary limit, the dispersion curves flatten out. As pointed out at Fig. 6, at the wavelength of 1.55 µm the dispersion curve is almost flat for the low aspect ratio of 1.333 which indicates a very small group velocity in contrast to the high group velocity for the high aspect ratio of 3. The square of the group index (ng→c/vg) 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 n¯2 of the system and hence, yields the ultrahigh Kerr nonlinearity.

6. Conclusion

We have shown that total mode energy confinement is achievable in a nanoshell nonlinear plasmonic waveguide. We have theoretically demonstrated that an ultrahigh nonlinearity can be achieved up to 41,251 W−1m−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

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

], higher order nonlinear signal generation [17

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]

] and all optical modulators [29

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]

], nano-lasers [19

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

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]

] and gain assisted plasmonic propagation [30

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

This research was conducted by the Australian Research Council Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (project number CE110001018)

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 3(4), 216–219 (2009). [CrossRef]

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]

4.

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

5.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

6.

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

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]

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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. 100(2), 023901 (2008). [CrossRef] [PubMed]

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]

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]

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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]

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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]

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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]

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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]

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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]

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M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004). [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]

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]

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 15(3), 1135–1146 (2007). [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]

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]

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

  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. Photonics3(4), 216–219 (2009). [CrossRef]
  2. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express16(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. Express15(10), 5976–5990 (2007). [CrossRef] [PubMed]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  5. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
  6. A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Solids69(11), 2936–2938 (2008). [CrossRef]
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