## Characterization of bending losses for curved plasmonic nanowire waveguides |

Optics Express, Vol. 18, Issue 15, pp. 16112-16119 (2010)

http://dx.doi.org/10.1364/OE.18.016112

Acrobat PDF (1053 KB)

### Abstract

We characterize bending losses of curved plasmonic nanowire waveguides for radii of curvature ranging from 1 to 12 μm and widths down to 40 nm. We use near-field measurements to separate bending losses from propagation losses. The attenuation due to bending loss is found to be as low as 0.1 μm^{−1} for a curved waveguide with a width of 70 nm and a radius of curvature of 2 μm. Experimental results are supported by Finite Difference Time Domain simulations. An analytical model developed for dielectric waveguides is used to predict the trend of rising bending losses with decreasing radius of curvature in plasmonic nanowires.

© 2010 OSA

## 1. Introduction

1. S. A. Maier, “Plasmonics – Towards Subwavelength Optical Devices,” Curr. Nanosci. **1**(1), 17–22 (2005). [CrossRef]

2. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuactors B **54**(1-2), 3–15 (1999). [CrossRef]

3. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B **76**(3), 035420 (2007). [CrossRef]

4. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. **97**(14), 146102 (2006). [CrossRef] [PubMed]

5. Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics **2**(4), 242–246 (2008). [CrossRef]

6. D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Ultracompact and low-power optical switch based on silicon photonic crystals,” Opt. Lett. **33**(2), 147–149 (2008). [CrossRef] [PubMed]

7. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express **16**(12), 8395–8405 (2008). [CrossRef] [PubMed]

8. N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express **16**(20), 15915–15922 (2008). [CrossRef] [PubMed]

9. M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, S.-J. Choi, J. D. O’Brien, and P. D. Dapkus, “Experimental characterization of the reflectance of 60° waveguide bends in photonic crystal waveguides,” Appl. Phys. Lett. **86**(19), 191104 (2005). [CrossRef]

11. I. Ntakis, P. Pottier, and R. M. De La Rue, “Optimization of transmission properties of two-dimensional photonic crystal channel waveguide bends through local lattice deformation,” J. Appl. Phys. **96**(1), 12–18 (2004). [CrossRef]

12. M. Lipson, “Guiding, modulating, and emitting light on Silicon – challenges and opportunities,” J. Lightwave Technol. **23**(12), 4222–4238 (2005). [CrossRef]

13. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express **12**(8), 1622–1631 (2004). [CrossRef] [PubMed]

14. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today **61**(5), 44 (2008). [CrossRef]

16. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B **61**(15), 10484–10503 (2000). [CrossRef]

17. D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. **85**(26), 6323–6325 (2004). [CrossRef]

18. B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides,” Appl. Phys. Lett. **88**(9), 094104 (2006). [CrossRef]

19. L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. **31**(14), 2133–2135 (2006). [CrossRef] [PubMed]

21. M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. **95**(20), 203109 (2009). [CrossRef]

22. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. **22**(7), 475–477 (1997). [CrossRef] [PubMed]

23. 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]

24. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express **16**(18), 13585–13592 (2008). [CrossRef] [PubMed]

25. B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. **91**(8), 081111 (2007). [CrossRef]

22. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. **22**(7), 475–477 (1997). [CrossRef] [PubMed]

26. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. **93**(13), 137404 (2004). [CrossRef] [PubMed]

27. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. **102**(20), 203904 (2009). [CrossRef] [PubMed]

27. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. **102**(20), 203904 (2009). [CrossRef] [PubMed]

_{C}) ranging from 1 to 12 μm. With a phase- and polarization-sensitive near-field microscope we measure the electric field in the wire in both straight and curved segments. We determine the transmission through the bends as a function of R

_{C}. We use the straight wire segments to measure propagation losses due to Ohmic damping and surface roughness, and then subtract that from the overall transmission losses in bends to reveal pure bending loss. Our data is supported by Finite Difference Time Domain (FDTD) modeling. A simple analytical model is used to describe the trend of the bending losses as a function of R

_{C}.

## 2. Sample fabrication and near-field measurement

_{o}= 1.55 µm. A beam of SPPs propagates into the tapered waveguide, and is adiabatically funneled to a nanowire [27

27. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. **102**(20), 203904 (2009). [CrossRef] [PubMed]

_{C}ranging from 1 to 12 μm.

28. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. **19**(8), 1169–1176 (2001). [CrossRef]

29. M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. **102**(3), 033902 (2009). [CrossRef] [PubMed]

_{C}= 6 μm (c). Figure 1(c) depicts SPPs approaching the nanowire from the right, propagating in the direction of the white arrow. We observe that the NPPs propagate along the curved nanowire waveguide without significant leakage of light around the bend.

## 3. Characterization of losses

### 3.1 Transmission through nanowire bends

_{C}lies significantly beneath the fitted line in both cases, which indicates that for small R

_{C}an additional loss component plays a role.

^{”}_{propagation}represents the attenuation of the electric field per unit length due to propagation losses, k

^{”}_{bending}represents the attenuation due to bending losses, and x is the length along the waveguide. A

_{out}/A

_{in}is the amplitude transmittance around the bend, which can also be expressed as exp(-k

^{”}_{total}x), where k

^{”}_{total}is the total attenuation of the electric field per unit length through the bend.

### 3.2 Propagation losses

_{C}. In contrast to the case of a dielectric waveguide, where the mode is gradually expelled as the guide is narrowed, in the case of nanowire plasmons the mode retracts into the wire as it gets narrower [22

22. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. **22**(7), 475–477 (1997). [CrossRef] [PubMed]

26. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. **93**(13), 137404 (2004). [CrossRef] [PubMed]

**102**(20), 203904 (2009). [CrossRef] [PubMed]

^{”}_{propagation}= 0.2 ± 0.05 μm

^{−1}in 40 nm wide waveguides, and k

^{”}_{propagation}= 0.085 ± 0.006 μm

^{−1}in 70 nm wide waveguides. As expected, the propagation attenuation is smaller in the wider waveguide.

### 3.3 Isolating the bending losses

^{”}_{bending}by substituting x by R

_{C}π/2 (the path traversed in a 90° bend). This yieldsIn the above equation, we have made the assumption that propagation losses are the same in straight sections of the waveguide as in the curved sections. The assumption is verified with FDTD simulations, which show that the mode profile does not change significantly even in bends with small R

_{C}. A similar mode profile lets us assume that the surface scattering losses are the same for straight and curved waveguide sections. Ohmic losses and bulk scattering losses stay the same, irrespective of bending radius. Figure 3(a) depicts the measured attenuation in 70 nm wide waveguides. The total attenuation (k

^{”}_{total}) is measured as described in section 3.1, the propagation attenuation (k

^{”}_{propagation}) as described in section 3.2, after which k

^{”}_{bending}is extracted according to Eq. (2). The rise in attenuation (green circles) for small R

_{C}in Fig. 3(a) corresponds to the drop in amplitude transmittance seen in Fig. 2. Propagation losses (blue circles) remain constant for all waveguides with the same width, apart from small fluctuations, which we attribute to small variations in the width of wires for different realizations. As a result, the attenuation due to bending (orange circles) increases as R

_{C}decreases. At radii of curvature larger than ~6 μm, bending losses are negligible compared to propagation losses, however at radii smaller than ~4 μm the two loss mechanisms become comparable in magnitude. At curvatures with radii smaller than ~2 μm, bending losses appear to become dominant.

### 3.4 Simulation

30. Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express **10**(17), 853–864 (2002). [PubMed]

_{C}, becoming the dominant loss component at a radius of curvature below 2 μm.

## 4. Discussion

_{C}[31]:C

_{1}depends on the dimensions of the waveguide, β is the propagation constant of the mode, and Δn

_{eff}is the difference between the modal effective index n

_{eff}and the index of the surroundings. Equation (3) was derived for dielectric slab waveguides [32], for which electric field intensity decays exponentially outside of the waveguide. In a waveguide curve, at a certain distance X

_{o}away from the center of the waveguide, the wavevector of the guided light matches that of light freely propagating in the surroundings. The bending losses of the waveguide scale with the fraction of the total modal energy beyond this distance X

_{o}. This leads to exponentially decreasing losses with increasing R

_{C}, as in Eq. (3). In the curved plasmonic nanowires considered in this work, the mode has an effective index slightly higher than that of the glass substrate, hence in a bend the energy primarily leaks into the glass, and not the air. To verify that Eq. (3) is valid in plasmonic nanowire waveguides, we perform simulations to show that the electric field intensity in the substrate decays exponentially outside of the waveguide. In Fig. 4 we show the fraction of the total energy which lies in the glass substrate, outside a distance X away from the center of the waveguide, for straight nanowires with widths of 40 nm and 70 nm. The blue and green data points were obtained from a numerical mode solver (COMSOL). The overlaid red lines are exponential fits. In both cases, the exponential fit matches well to the numerical data, especially at distances close to the waveguide, where most of the energy resides. This observation shows that the assumption underlying Eq. (3) is fulfilled for NPPs just like for dielectric waveguides. We therefore fit Eq. (3) to the experimental and simulated data, shown as dashed orange lines in Fig. 3. Table 1 displays the resultant fit coefficients.

**102**(20), 203904 (2009). [CrossRef] [PubMed]

_{2}is higher at a width of 40 nm than at 70 nm, which results in smaller bending losses. The simulated C

_{1}is equal for the two widths, which is not surprising since the difference in waveguide widths in the two cases is small. The values extracted from experiments are close to simulation results, although the absolute numbers do not match. As the bending losses become the dominant loss mechanism for only the smallest of the measured R

_{C}, more measurements at radii below 1 micrometer would be required to find the combination of C1 and C2 that describes the bending losses best.

13. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express **12**(8), 1622–1631 (2004). [CrossRef] [PubMed]

11. I. Ntakis, P. Pottier, and R. M. De La Rue, “Optimization of transmission properties of two-dimensional photonic crystal channel waveguide bends through local lattice deformation,” J. Appl. Phys. **96**(1), 12–18 (2004). [CrossRef]

13. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express **12**(8), 1622–1631 (2004). [CrossRef] [PubMed]

## 5. Conclusion

^{−1}in the same wire. Measurements were supported by FDTD simulations. An analytical model developed for dielectric waveguides is employed to describe the losses, which exponentially decay as a function of the radius of curvature. Further improvements in the fabrication procedure could decrease bending losses by generating narrower wires.

## Acknowledgments

## References and links

1. | S. A. Maier, “Plasmonics – Towards Subwavelength Optical Devices,” Curr. Nanosci. |

2. | J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuactors B |

3. | D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B |

4. | J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. |

5. | Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics |

6. | D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Ultracompact and low-power optical switch based on silicon photonic crystals,” Opt. Lett. |

7. | F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express |

8. | N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express |

9. | M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, S.-J. Choi, J. D. O’Brien, and P. D. Dapkus, “Experimental characterization of the reflectance of 60° waveguide bends in photonic crystal waveguides,” Appl. Phys. Lett. |

10. | M. Ayre, T. J. Karle, T. Lijun Wu, T. Davies, and T. F. Krauss, “Experimental verification of numerically optimized photonic crystal injector, Y-splitter, and bend,” IEEE J. Sel. Areas Commun. |

11. | I. Ntakis, P. Pottier, and R. M. De La Rue, “Optimization of transmission properties of two-dimensional photonic crystal channel waveguide bends through local lattice deformation,” J. Appl. Phys. |

12. | M. Lipson, “Guiding, modulating, and emitting light on Silicon – challenges and opportunities,” J. Lightwave Technol. |

13. | Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express |

14. | T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today |

15. | H. Raether, “Surface Plasmons on Smooth and Rough Surfaces and on Gratings,” |

16. | P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B |

17. | D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. |

18. | B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides,” Appl. Phys. Lett. |

19. | L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. |

20. | J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B |

21. | M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. |

22. | J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. |

23. | 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 |

24. | T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express |

25. | B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. |

26. | M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. |

27. | E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. |

28. | M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. |

29. | M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. |

30. | Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express |

31. | E. A. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. |

32. | R. G. Hunsperger, |

**OCIS Codes**

(230.7370) Optical devices : Waveguides

(250.5300) Optoelectronics : Photonic integrated circuits

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: May 20, 2010

Revised Manuscript: June 21, 2010

Manuscript Accepted: June 25, 2010

Published: July 15, 2010

**Citation**

Dirk Jan Dikken, Marko Spasenović, Ewold Verhagen, Dries van Oosten, and L. (Kobus) Kuipers, "Characterization of bending losses for curved plasmonic nanowire waveguides," Opt. Express **18**, 16112-16119 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-16112

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### References

- S. A. Maier, “Plasmonics – Towards Subwavelength Optical Devices,” Curr. Nanosci. 1(1), 17–22 (2005). [CrossRef]
- J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuactors B 54(1-2), 3–15 (1999). [CrossRef]
- D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007). [CrossRef]
- J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006). [CrossRef] [PubMed]
- Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008). [CrossRef]
- D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Ultracompact and low-power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008). [CrossRef] [PubMed]
- F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16(12), 8395–8405 (2008). [CrossRef] [PubMed]
- N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008). [CrossRef] [PubMed]
- M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, S.-J. Choi, J. D. O’Brien, and P. D. Dapkus, “Experimental characterization of the reflectance of 60° waveguide bends in photonic crystal waveguides,” Appl. Phys. Lett. 86(19), 191104 (2005). [CrossRef]
- M. Ayre, T. J. Karle, T. Lijun Wu, T. Davies, and T. F. Krauss, “Experimental verification of numerically optimized photonic crystal injector, Y-splitter, and bend,” IEEE J. Sel. Areas Commun. 23(7), 1390–1395 (2005). [CrossRef]
- I. Ntakis, P. Pottier, and R. M. De La Rue, “Optimization of transmission properties of two-dimensional photonic crystal channel waveguide bends through local lattice deformation,” J. Appl. Phys. 96(1), 12–18 (2004). [CrossRef]
- M. Lipson, “Guiding, modulating, and emitting light on Silicon – challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]
- Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004). [CrossRef] [PubMed]
- T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44 (2008). [CrossRef]
- H. Raether, “Surface Plasmons on Smooth and Rough Surfaces and on Gratings,” Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1988) Vol. 3.
- P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]
- D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004). [CrossRef]
- B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006). [CrossRef]
- L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31(14), 2133–2135 (2006). [CrossRef] [PubMed]
- J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
- M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009). [CrossRef]
- J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]
- 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]
- T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008). [CrossRef] [PubMed]
- B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007). [CrossRef]
- M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]
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- M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. 19(8), 1169–1176 (2001). [CrossRef]
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