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

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2009 (6)

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]

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]

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]

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

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]

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]

2007 (3)

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

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–62 (2007).
[CrossRef] [PubMed]

2006 (3)

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]

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]

2005 (5)

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]

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]

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]

G. Veronis and S. Fan, “Bends and splitters in subwavelength metal-dielectric-metal plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[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]

2004 (1)

2003 (3)

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

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]

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]

2000 (1)

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]

1998 (2)

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Intensity Distribution of Modes in Surface Corrugated Waveguides,” Phys. Rev. Lett. 80(19), 4165–4168 (1998).
[CrossRef]

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]

1997 (2)

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

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]

1995 (1)

F. D. Hastings, J. B. Schneider, and S. L. Broschat, “A Monte-Carlo FDTD Technique for Rough Surface Scattering,” IEEE Trans. Antenn. Propag. 43(11), 1183–1191 (1995).

1988 (1)

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83(1), 78–92 (1988).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

1949 (1)

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

Aspect, A.

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]

Atwater, H. A.

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–62 (2007).
[CrossRef] [PubMed]

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]

Barnes, W. L.

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

Barwicz, T.

Beenakker, C. W. J.

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

Braunisch, H.

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]

Brongersma, M. L.

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]

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]

Broschat, S. L.

F. D. Hastings, J. B. Schneider, and S. L. Broschat, “A Monte-Carlo FDTD Technique for Rough Surface Scattering,” IEEE Trans. Antenn. Propag. 43(11), 1183–1191 (1995).

Catrysse, P. B.

Chandran, A.

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]

Delande, D.

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]

Dereux, A.

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

Ding, R.

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]

Ebbesen, T. W.

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

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Fan, S.

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]

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

G. Veronis and S. Fan, “Bends and splitters in subwavelength metal-dielectric-metal plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

Filipovic, D. S.

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]

Freilikher, V.

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]

Freude, W.

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]

Fujii, M.

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]

García-Martín, A.

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Intensity Distribution of Modes in Surface Corrugated Waveguides,” Phys. Rev. Lett. 80(19), 4165–4168 (1998).
[CrossRef]

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]

Grémaud, B.

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]

Hastings, F. D.

F. D. Hastings, J. B. Schneider, and S. L. Broschat, “A Monte-Carlo FDTD Technique for Rough Surface Scattering,” IEEE Trans. Antenn. Propag. 43(11), 1183–1191 (1995).

Haus, H. A.

Holloway, C. L.

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]

Hughes, S.

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]

Hugonin, J. P.

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]

Izrailev, F. M.

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]

Kocabas, S. E.

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]

Kolomenski, A.

Kolomenskii, A.

Koos, C.

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]

Kuester, E. F.

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]

Lagendijk, A.

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

Lalanne, P.

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]

Leuthold, J.

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]

Lugan, P.

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]

Lukic, M. V.

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]

Maier, S. A.

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]

Makarov, N. M.

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]

Maradudin, A. A.

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]

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]

Mazoyer, S.

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]

Miller, D. A. B.

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]

Miniatura, C.

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]

Morgan, S. P.

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

Müller, C. A.

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]

Nieto-Vesperinas, M.

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Intensity Distribution of Modes in Surface Corrugated Waveguides,” Phys. Rev. Lett. 80(19), 4165–4168 (1998).
[CrossRef]

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]

Noel, J.

Ozbay, E.

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

Peng, S.

Pfrang, A.

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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).
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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).
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Schuessler, H.

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Selker, M. D.

Sipe, J. E.

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).
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E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83(1), 78–92 (1988).
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A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Intensity Distribution of Modes in Surface Corrugated Waveguides,” Phys. Rev. Lett. 80(19), 4165–4168 (1998).
[CrossRef]

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

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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).
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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]

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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]

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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).
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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).
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[CrossRef]

IEEE J. Sel. Top. Quant. (1)

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).
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IEEE Trans. Antenn. Propag. (1)

F. D. Hastings, J. B. Schneider, and S. L. Broschat, “A Monte-Carlo FDTD Technique for Rough Surface Scattering,” IEEE Trans. Antenn. Propag. 43(11), 1183–1191 (1995).

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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).
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W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
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E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
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Phys. Rev. A (1)

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).
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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).
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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).
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Phys. Rev. Lett. (4)

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Intensity Distribution of Modes in Surface Corrugated Waveguides,” Phys. Rev. Lett. 80(19), 4165–4168 (1998).
[CrossRef]

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).
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A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the simulation configuration used to calculate the attenuation coefficient α r of a rough MDM waveguide. It consists of a section of the rough waveguide of length L sandwiched between two smooth MDM waveguides. (b) Theoretical normalized probability density of the roughness height at metal-dielectric interfaces. We also show the probability density calculated from the generated profile of a random interface realization. (c) Theoretical normalized autocorrelation function R(u) = <f(x)f(x + u)> of the roughness. Results are shown for Lc = 36nm. We also show the autocorrelation function calculated from the generated profile of a random interface realization. (d) Averaged attenuation coefficient α r as a function of the number N of random rough waveguide realizations used in the Monte Carlo method. Results are shown for a silver-air-silver MDM waveguide with w = 50nm, L = 2μm, Lc = 36nm, δ = 4nm, and λ = 1.55μm.

Fig. 2
Fig. 2

Excess attenuation coefficient α r-α s of a rough MDM plasmonic waveguide and attenuation enhancement factor αrs with respect to a smooth waveguide as a function of roughness rms height δ for L c = 36nm (solid line) and L c = 500nm (dashed line). Also shown is the excess attenuation coefficient α r-α s of a rough MDM plasmonic waveguide as a function of δ for L c = 36nm (filled circles) and L c = 500nm (empty circles), if the metal in the MDM waveguide is lossless. All other parameters are as in Fig. 1(d).

Fig. 3
Fig. 3

(a) Excess attenuation coefficient α r-α s of a rough MDM plasmonic waveguide and attenuation enhancement factor αrs as a function of correlation length Lc for δ = 4nm (black solid line) and δ = 8nm (black dashed line). Also shown is the excess attenuation coefficient α r-α s of a rough MDM plasmonic waveguide as a function of Lc for δ = 4nm (red solid line) and δ = 8nm (red dashed line), if the metal in the MDM waveguide is lossless. All other parameters are as in Fig. 1(d). (b) Normalized power spectral density of the disordered surfaces at the Bragg spatial frequency kBragg as a function of Lc . All other parameters are as in Fig. 1(d).

Fig. 4
Fig. 4

(a)-(b) Electric field intensity profiles for a random rough MDM plasmonic waveguide and a MDM waveguide with periodic perturbation. Results are shown for perturbation periodicity P = 200nm and amplitude A = 2 2 δ in the sine periodic waveguide. All other parameters are as in Fig. 1(d). (c)-(d) Absorbed power density profiles for a random rough MDM waveguide and a MDM waveguide with periodic perturbation. (e)-(f) Local absorption coefficient for a random rough MDM plasmonic waveguide and a MDM waveguide with periodic perturbation. We also show the local absorption coefficient for a smooth MDM waveguide (black dashed line).

Fig. 5
Fig. 5

(a)-(c) Attenuation coefficient αs in a smooth MDM plasmonic waveguide as a function of width w, wavelength λ, and dielectric constant ε r of the material in the waveguide. All other parameters are as in Fig. 1(d). (d)-(f) Excess attenuation coefficient due to disorder α r-α s as a function of w, λ, and ε r. All other parameters are as in Fig. 1(d).

Equations (9)

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R ( u ) = < f ( x ) f ( x + u ) > ,
R ( u ) = δ 2 exp ( u 2 / L c 2 ) ,
f ( x n ) = 1 L j = M / 2 M / 2 1 F ( k j ) e i k j x n ,
F ( k j ) = 2 π L W ( k j ) { [ M ( 0 , 1 ) + i M ( 0 , 1 ) ] / 2 ,   for   j 0 , M / 2 M ( 0 , 1 ) ,   for   j = 0 , M / 2 ,
W ( k ) 1 2 π R ( u ) e i k u d u = δ 2 L c 2 π exp ( k 2 L c 2 4 ) .
< ln ( T ) > = α r L     .
P = P B r a g g = λ M D M / 2 ,
k B r a g g 2 π P B r a g g = 4 π λ M D M .
W ( k B r a g g ) = δ 2 L c 2 π exp [ ( 2 π L c λ M D M ) 2 ] .

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