## Theoretical investigation of fabrication-related disorders on the properties of subwavelength metal-dielectric-metal plasmonic waveguides |

Optics Express, Vol. 18, Issue 20, pp. 20939-20948 (2010)

http://dx.doi.org/10.1364/OE.18.020939

Acrobat PDF (2277 KB)

### Abstract

We theoretically investigate the effect of fabrication-related disorders on subwavelength metal-dielectric-metal plasmonic waveguides. We use a Monte Carlo method to calculate the roughness-induced excess attenuation coefficient with respect to a smooth waveguide. For small roughness height, the excess optical power loss due to disorder is small compared to the material loss in a smooth waveguide. However, for large roughness height, the excess attenuation increases rapidly with height and the propagation length of the optical mode is severely affected. We find that the excess attenuation is mainly due to reflection from the rough surfaces. However, for small roughness correlation lengths, enhanced absorption is the dominant loss mechanism due to disorder. We also find that the disorder attenuation due to reflection is approximately maximized when the power spectral density of the disordered surfaces at the Bragg spatial frequency is maximized. Finally, we show that increasing the modal confinement or decreasing the guide wavelength, increase the attenuation due to disorder.

© 2010 OSA

## 1. Introduction

*α*

_{s}. In a rough MDM waveguide, disorders induce additional attenuation on top of the material loss in the metal. The total optical power loss in the rough waveguide is characterized by an attenuation coefficient

*α*

_{r}. Thus, the difference of attenuation coefficients

*α*

_{r}-

*α*

_{s}is a measure of the excess losses in the plasmonic waveguides due to disorders, and will be referred to as the excess attenuation coefficient due to disorder. We use the Monte Carlo method to calculate the attenuation coefficient

*α*

_{r}in a rough waveguide by averaging over an ensemble of randomly-generated rough waveguide realizations. For each randomly-generated rough waveguide realization, the electromagnetic fields are calculated using a full-wave finite-difference frequency-domain (FDFD) method. For small roughness root-mean-square (rms) height, the excess optical power loss due to disorder is small compared to the material loss in a smooth waveguide. However, for large roughness height, the excess attenuation increases rapidly with height, and the propagation length of the optical mode is severely affected. We find that the disorder loss is mainly due to reflection from the rough surfaces. However, for small roughness correlation lengths, enhanced absorption in the metal is the dominant loss mechanism due to disorder. We also find that the disorder attenuation due to reflection is approximately maximized when the power spectral density of the disordered surfaces at the Bragg spatial frequency is maximized. Finally, we show that increasing the modal confinement or decreasing the guide wavelength, increase the attenuation due to disorder in the MDM waveguide.

11. S. P. Morgan Jr., “Effects of surface roughness on eddy current losses at microwave frequencies,” J. Appl. Phys. **20**(4), 352–362 (1949). [CrossRef]

13. R. Ding, L. Tsang, and H. Braunisch, “Wave Propagation in a Randomly Rough Parallel-Plate Waveguide,” IEEE Trans. Microw. Theory Tech. **57**(5), 1216–1223 (2009). [CrossRef]

17. A. Kolomenski, A. Kolomenskii, J. Noel, S. Peng, and H. Schuessler, “Propagation length of surface plasmons in a metal film with roughness,” Appl. Opt. **48**(30), 5683–5691 (2009). [CrossRef] [PubMed]

20. F. M. Izrailev and N. M. Makarov, “Onset of delocalization in quasi-one-dimensional waveguides with correlated surface disorder,” Phys. Rev. B **67**(11), 113402 (2003). [CrossRef]

19. A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today **62**(8), 24–29 (2009). [CrossRef]

21. P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Grémaud, C. A. Müller, and C. Miniatura, “One-dimensional Anderson localization in certain correlated random potentials,” Phys. Rev. A **80**(2), 023605 (2009). [CrossRef]

22. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. **69**(3), 731–808 (1997). [CrossRef]

20. F. M. Izrailev and N. M. Makarov, “Onset of delocalization in quasi-one-dimensional waveguides with correlated surface disorder,” Phys. Rev. B **67**(11), 113402 (2003). [CrossRef]

23. A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. **71**(14), 1912–1914 (1997). [CrossRef]

25. J. A. Sánchez-Gil, V. Freilikher, I. Yurkevich, and A. A. Maradudin, “Coexistence of Ballistic Transport, Diffusion, and Localization in Surface Disordered Waveguides,” Phys. Rev. Lett. **80**(5), 948–951 (1998). [CrossRef]

## 2. Simulation method

*T*through the waveguide section of length

*L*(Fig. 1(a)). This method allows us to directly use experimental data for the frequency-dependent dielectric constant of materials such as silver [29], including both the real and imaginary parts, with no approximation. Perfectly matched layer absorbing boundary conditions [30] are used at all boundaries of the simulation domain. We also note that, since we directly use a full-wave simulation method to calculate the fields in the disordered waveguides, our calculations take into account multiple scattering and localization effects [31

31. S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. **103**(6), 063903 (2009). [CrossRef] [PubMed]

22. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. **69**(3), 731–808 (1997). [CrossRef]

31. S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. **103**(6), 063903 (2009). [CrossRef] [PubMed]

*T*)> undergoes a linear variation with

*L*for large

*L*. This allows us to define an attenuation coefficient

*α*

_{r}for the rough MDM waveguide using [31

31. S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. **103**(6), 063903 (2009). [CrossRef] [PubMed]

*α*

_{r}is referred to in the literature on disordered systems as the Lyapunov exponent and its inverse as the localization length [18,20

20. F. M. Izrailev and N. M. Makarov, “Onset of delocalization in quasi-one-dimensional waveguides with correlated surface disorder,” Phys. Rev. B **67**(11), 113402 (2003). [CrossRef]

22. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. **69**(3), 731–808 (1997). [CrossRef]

*L*large enough to ensure that Eq. (5) holds. In Fig. 1(d), we show a typical result for the convergence of the calculated attenuation coefficient

*α*

_{r}of a rough MDM plasmonic waveguide, as a function of the number

*N*of randomly-generated rough waveguide realizations used in the Monte Carlo method. We observe that the method converges after a few hundred waveguide realization calculations. In all cases we found that

*N*= 1000 is sufficient for an accuracy of the results within 1%.

## 3. Results

*δ*and correlation length

*L*

_{c}on the attenuation coefficient. In Fig. 2 , we show the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}of a rough MDM plasmonic waveguide as a function of the roughness rms height

*δ*for

*L*

_{c}= 36nm. For convenience we also show the attenuation enhancement factor, defined as

*α*

_{r}/

*α*

_{s}. We observe that, as expected, the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}increases with

*δ*. We also found that for

*δ*>4nm, the increase is almost exponential. For

*δ*<4nm, we have

*α*

_{r}/

*α*

_{s}<1.2 for the attenuation enhancement factor. Thus, for small roughness height (

*δ*<4nm), the excess optical power loss due to disorder is small compared to the material loss in a smooth waveguide. On the other hand, for large roughness height (

*δ*>4nm),

*α*

_{r}/

*α*

_{s}increases rapidly with

*δ*, and the propagation length of the optical mode is severely affected. Thus, for

*δ*= 12nm the attenuation coefficient in the rough waveguide is enhanced by an order of magnitude compared to the smooth waveguide (

*α*

_{r}/

*α*

_{s}≈10).

*α*

_{r}-

*α*

_{s}for a rough MDM waveguide in which the metal in the MDM waveguide is lossless (

*ε*

_{metal}=

*ε*

_{metal,real}, neglecting the imaginary part of the dielectric permittivity

*ε*

_{metal,imag}). We observe that material losses in the metal do not significantly affect the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}. In the lossless metal case,

*α*

_{s}= 0 and the excess attenuation is only due to the reflection from the rough surfaces. Thus, we can conclude that the excess loss in a rough MDM plasmonic waveguide is mainly due to reflection from the rough surfaces. As mentioned in Section 1, this loss mechanism is connected to Anderson localization in one-dimensional disordered systems.

*α*

_{r}-

*α*

_{s}and the attenuation enhancement factor

*α*

_{r}/

*α*

_{s}of a rough MDM plasmonic waveguide as a function of the correlation length

*L*

_{c}for

*δ*= 4nm, 8nm. We observe that in both cases

*α*

_{r}-

*α*

_{s}is maximized for

*L*

_{c}= 120nm. In addition, the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}increases as

*L*

_{c}→0. In Fig. 3(a), we also show the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}for a rough MDM waveguide in which the metal in the MDM waveguide is lossless. The results in the lossless metal case agree well with the lossy metal case for

*L*

_{c}>20nm. Thus, we can conclude that for

*L*

_{c}>20nm, the excess attenuation is due to reflection from the rough surfaces.

*α*

_{r}-

*α*

_{s}at

*L*

_{c}= 120nm is associated with Bragg reflection from the rough surfaces. In a MDM plasmonic waveguide with a periodic perturbation with period

*P*, there is strong reflection associated with Bragg Scattering [4] when where

*λ*is the guide wavelength in the MDM plasmonic waveguide. The corresponding Bragg spatial frequency is Using Eqs. (4) and (6), we obtain the power spectral density

_{MDM}*W*(

*k*) of the disordered surfaces at

_{Bragg}*k*

_{Bragg}*W*(

*k*) as a function of

_{Bragg}*L*

_{c}. We observe that the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}due to reflection from disorders correlates very well with the power spectral density

*W*(

*k*). Thus, the disorder attenuation due to reflection is approximately maximized when the power spectral density of the disordered surfaces at the Bragg spatial frequency

_{Bragg}*W*(

*k*) is maximized. Using Eq. (7), we find that

_{Bragg}*W*(

*k*) is maximized for

_{Bragg}*L*

_{c}<20nm, there is a large difference between the lossy and lossless metal cases (Fig. 3(a)). In the lossless metal case, the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}decreases as

*L*

_{c}→0, due to the fact that

*α*

_{r}-

*α*

_{s}increases as

*L*

_{c}→0. This is because when

*L*

_{c}→0, the waveguide surfaces become extremely rough with disorder dimensions small compared to the skin depth, which allows light to directly pass through, and results in enhanced absorption in the metal. Thus, for

*L*

_{c}<20nm, the reflection from the rough surfaces is small, and enhanced absorption in the metal is the dominant loss mechanism due to disorder. Finally, for very large correlation lengths (

*L*

_{c}>400nm), the waveguide surfaces are almost flat, which results in a small reflection, hence the attenuation coefficient is only slightly enhanced with respect to the smooth waveguide (Figs. 2, 3(a)).

*ε*

_{metal}|>>

*ε*

_{diel}at near-infrared wavelengths [29], the electric field intensity in the metal is much smaller than the electric field intensity in the dielectric. In addition, we observe that the electric field intensity in the dielectric is enhanced at the peak of the metal roughness bumps. The enhancement is associated with the behavior of the electric field near sharp edges [32], which is often referred to as the lightning rod effect [33

33. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. **98**(1), 011101 (2005). [CrossRef]

*α*

_{r}(

*x*) for the random rough MDM waveguide. We observe that in certain locations of the disordered waveguide, corresponding to peaks of metal roughness bumps, the absorption is actually suppressed with respect to a smooth MDM waveguide. Even though the absorption is locally suppressed at certain locations, the overall absorption in the rough waveguide is enhanced with respect to the smooth waveguide. As mentioned above, this absorption enhancement is the dominant disorder loss mechanism in the case of small roughness correlation length. We finally note that the absorption properties described above are quite general and are not limited to random rough waveguides. As an example, periodically textured waveguides exhibit similar characteristics (Figs. 4(b), 4(d), 4(f)).

*w*, operating wavelength

*λ*, and dielectric constant

*ε*

_{r}of the material in the waveguide (Fig. 1(a)), on the attenuation in the rough MDM plasmonic waveguides. In Figs. 5(a) and 5(d), we show the attenuation coefficient

*α*

_{s}in a smooth MDM waveguide, and the excess attenuation coefficient due to disorder

*α*

_{r}-

*α*

_{s}, respectively, as a function of the waveguide width

*w*. In a smooth MDM waveguide, the fraction of the modal power in the metal increases as

*w*decreases, and the attenuation coefficient

*α*

_{s}therefore increases (Fig. 5(a)) [6

6. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A **21**(12), 2442–2446 (2004). [CrossRef]

*w*decreases and the optical mode confinement increases, the effect of the roughness becomes more severe (Fig. 5(d)). Several factors contribute to the increased disorder losses when

*w*is decreased. First, as

*w*decreases, the ratio

*δ*/

*w*of roughness rms height to waveguide width increases, and the fraction of the modal power reflected by disorders, therefore, increases. Second, as

*w*decreases, the fraction of the modal power in the metal increases, and the effective index of the propagating mode, therefore, increases. Thus, the guide wavelength

*λ*decreases. This in turn leads to increased disorder losses, since the scattering cross-section of metallic nanoparticles increases as the wavelength decreases [4,34]. Third, as

_{MDM}*w*decreases, the group velocity of the propagating optical mode in the MDM plasmonic waveguide decreases. This in turn leads to increased disorder losses, since a smaller group velocity means that light moves more slowly through the waveguide and thus has more time to sample the regions of disorder and roughness [31

**103**(6), 063903 (2009). [CrossRef] [PubMed]

35. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. **94**(3), 033903 (2005). [CrossRef] [PubMed]

*λ*on the attenuation coefficient in a smooth waveguide

*α*

_{s}, and the excess attenuation coefficient due to disorder

*α*

_{r}-

*α*

_{s}, respectively. In a smooth MDM waveguide the attenuation coefficient

*α*

_{s}increases as the wavelength decreases (Fig. 5(b)). This is due to the fact that the propagation length of surface plasmons scales with the wavelength [1

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

*ε*

_{r}of the material in the waveguide (Fig. 1(a)) on the attenuation coefficient in a smooth waveguide

*α*

_{s}, and the excess attenuation coefficient due to disorder

*α*

_{r}-

*α*

_{s}, respectively. In a smooth MDM waveguide

*α*

_{s}increases with

*ε*

_{r}(Fig. 5(c)). This is due in part to increased fraction of the modal power in the metal, as the permittivity of the dielectric increases, as well as decreased group velocity. In addition, we observe that the excess attenuation due to roughness also increases with

*ε*

_{r}(Fig. 5(f)). This is due to the fact that, as the permittivity of the dielectric increases, the guide wavelength and the group velocity decrease. Both of these factors contribute to increased disorder losses, as mentioned above.

## 4. Conclusions

*δ*and the correlation length

*L*

_{c}on the excess attenuation coefficient

*α*

_{r}-

*α*

_{s}. For small roughness rms height, the reflection from the rough surfaces is small, hence the excess optical power loss due to disorder is small compared to the material loss in a smooth waveguide. For large roughness height,

*α*

_{r}/

*α*

_{s}increases rapidly with

*δ*, and the propagation length of the optical mode is severely affected. We found that excess loss in rough MDM plasmonic waveguides is mainly due to reflection from the rough surfaces. However, for small roughness correlation lengths, enhanced absorption in the metal is the dominant loss mechanism due to disorder. We also found that the disorder attenuation due to reflection is approximately maximized when the power spectral density of the disordered surfaces at the Bragg spatial frequency is maximized.

*w*, operating wavelength

*λ*, and dielectric constant

*ε*

_{r}of the material in the waveguide, on the attenuation in rough MDM plasmonic waveguides. We found that variation of these waveguide parameters impacts several important factors that affect disorder losses, such as the ratio of disorder size to waveguide width, the guide wavelength, and the group velocity. Increasing the light confinement in a MDM plasmonic waveguide leads to increased ratio of disorder size to waveguide width, decreased guide wavelength, and decreased group velocity, and, therefore, to increased disorder losses.

36. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. **25**(9), 2511–2521 (2007). [CrossRef]

37. T. Barwicz and H. A. Haus, “Three-Dimensional Analysis of Scattering Losses Due to Sidewall Roughness in Microphotonic Waveguides,” J. Lightwave Technol. **23**(9), 2719–2732 (2005). [CrossRef]

38. C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation Modes and Roughness Loss in High Index-Contrast Waveguides,” IEEE J. Sel. Top. Quant. **12**(6), 1306–1321 (2006). [CrossRef]

39. C. L. Holloway and E. F. Kuester, “Power Loss Associated with Conducting and Superconducting Rough Interfaces,” IEEE Trans. Microw. Theory Tech. **48**(10), 1601–1610 (2000). [CrossRef]

**103**(6), 063903 (2009). [CrossRef] [PubMed]

## Acknowledgments

## References and links

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

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

3. | R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today |

4. | S. A. Maier, |

5. | H. A. Atwater, “The promise of plasmonics,” Sci. Am. |

6. | R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A |

7. | G. Veronis and S. Fan, “Bends and splitters in subwavelength metal-dielectric-metal plasmonic waveguides,” Appl. Phys. Lett. |

8. | S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B |

9. | D. M. Pozar, |

10. | E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. |

11. | S. P. Morgan Jr., “Effects of surface roughness on eddy current losses at microwave frequencies,” J. Appl. Phys. |

12. | M. V. Lukic and D. S. Filipovic, “Modeling of 3-D surface roughness effects with application to coaxial lines,” IEEE Trans. Microw. Theory Tech. |

13. | R. Ding, L. Tsang, and H. Braunisch, “Wave Propagation in a Randomly Rough Parallel-Plate Waveguide,” IEEE Trans. Microw. Theory Tech. |

14. | H. Raether, |

15. | J. A. Sánchez-Gil, “Localized surface-plasmon polaritons in disordered nanostructured metal surfaces: Shape versus Anderson-localized resonances,” Phys. Rev. B |

16. | A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. |

17. | A. Kolomenski, A. Kolomenskii, J. Noel, S. Peng, and H. Schuessler, “Propagation length of surface plasmons in a metal film with roughness,” Appl. Opt. |

18. | V. D. Freilikher, and S. A. Gredeskul, “Localization of waves in media with one-dimensional disorder,” in |

19. | A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today |

20. | F. M. Izrailev and N. M. Makarov, “Onset of delocalization in quasi-one-dimensional waveguides with correlated surface disorder,” Phys. Rev. B |

21. | P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Grémaud, C. A. Müller, and C. Miniatura, “One-dimensional Anderson localization in certain correlated random potentials,” Phys. Rev. A |

22. | C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. |

23. | A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. |

24. | A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Intensity Distribution of Modes in Surface Corrugated Waveguides,” Phys. Rev. Lett. |

25. | J. A. Sánchez-Gil, V. Freilikher, I. Yurkevich, and A. A. Maradudin, “Coexistence of Ballistic Transport, Diffusion, and Localization in Surface Disordered Waveguides,” Phys. Rev. Lett. |

26. | F. D. Hastings, J. B. Schneider, and S. L. Broschat, “A Monte-Carlo FDTD Technique for Rough Surface Scattering,” IEEE Trans. Antenn. Propag. |

27. | E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. |

28. | G. Veronis, and S. Fan, “Overview of Simulation Techniques for Plasmonic Devices,” in |

29. | E. D. Palik, |

30. | J. Jin, |

31. | S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. |

32. | J. D. Jackson, |

33. | S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. |

34. | C. F. Bohren, and D. R. Huffman, |

35. | S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. |

36. | G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. |

37. | T. Barwicz and H. A. Haus, “Three-Dimensional Analysis of Scattering Losses Due to Sidewall Roughness in Microphotonic Waveguides,” J. Lightwave Technol. |

38. | C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation Modes and Roughness Loss in High Index-Contrast Waveguides,” IEEE J. Sel. Top. Quant. |

39. | C. L. Holloway and E. F. Kuester, “Power Loss Associated with Conducting and Superconducting Rough Interfaces,” IEEE Trans. Microw. Theory Tech. |

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(240.5770) Optics at surfaces : Roughness

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: July 30, 2010

Revised Manuscript: September 9, 2010

Manuscript Accepted: September 9, 2010

Published: September 17, 2010

**Citation**

Changjun Min and Georgios Veronis, "Theoretical investigation of fabrication-related disorders on the properties of subwavelength metal-dielectric-metal plasmonic waveguides," Opt. Express **18**, 20939-20948 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-20939

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### References

- W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
- E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]
- R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7–8), 20–27 (2006). [CrossRef]
- S. A. Maier, Plasmonics: fundamentals and applications, (Springer, New York, 2007).
- H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–62 (2007). [CrossRef] [PubMed]
- R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef]
- G. Veronis and S. Fan, “Bends and splitters in subwavelength metal-dielectric-metal plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]
- S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B 79(3), 035120 (2009). [CrossRef]
- D. M. Pozar, Microwave Engineering, (Wiley, New York, 1998).
- E. N. Economou, “Surface plasmons in thin ﬁlms,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]
- S. P. Morgan., “Effects of surface roughness on eddy current losses at microwave frequencies,” J. Appl. Phys. 20(4), 352–362 (1949). [CrossRef]
- M. V. Lukic and D. S. Filipovic, “Modeling of 3-D surface roughness effects with application to coaxial lines,” IEEE Trans. Microw. Theory Tech. 55(3), 518–525 (2007). [CrossRef]
- R. Ding, L. Tsang, and H. Braunisch, “Wave Propagation in a Randomly Rough Parallel-Plate Waveguide,” IEEE Trans. Microw. Theory Tech. 57(5), 1216–1223 (2009). [CrossRef]
- H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer, Berlin, 1988).
- J. A. Sánchez-Gil, “Localized surface-plasmon polaritons in disordered nanostructured metal surfaces: Shape versus Anderson-localized resonances,” Phys. Rev. B 68(11), 113410 (2003). [CrossRef]
- A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005). [CrossRef]
- A. Kolomenski, A. Kolomenskii, J. Noel, S. Peng, and H. Schuessler, “Propagation length of surface plasmons in a metal film with roughness,” Appl. Opt. 48(30), 5683–5691 (2009). [CrossRef] [PubMed]
- V. D. Freilikher, and S. A. Gredeskul, “Localization of waves in media with one-dimensional disorder,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), V. XXX, pp. 137–203.
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