Abstract

A novel surface impedance model is developed to analyze plasmonic circuits supporting long range surface plasmon polaritons (LR-SPP). The analysis is carried out in two steps. First, a higher order approximation of the surface impedance is obtained for the metal strip through a 2-D analysis of the waveguide cross section. Second, the developed surface impedance boundary condition is incorporated in the mixed potential integral equation formulation of the problem, and the method of moments is employed to find the unknown surface current distributions on the strips carrying LR-SPP. In other words, in this method, the volumetric currents flowing inside the metal are substituted by a surface current model flowing on an infinitely thin strip characterized by the developed surface impedance model. This procedure reduces the number of unknowns significantly, in this way increasing the speed of simulation. Validity and accuracy of the proposed model are demonstrated by analyzing three popular LR-SPP circuits.

© 2013 IEEE

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  1. R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Exp. 13, 977-984 (2005).
  2. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, S. I. Bozhevolnyi, "Integrated optical components utilizing long-range surface plasmon polaritons," J. Lightw. Technol. 23 , 413-422 (2005).
  3. M.-S. Kwon, "Metal stripe waveguide based interferometer-type sensor working in an aqueous solution with a low refractive index," J. Lightw. Technol. 30, 2035-2041 (2012).
  4. I. Kim, D. Seok Jeong, T. Seong Lee, W. Seong Lee, K.-S. Lee, " Plasmonic absorption enhancement in organic solar cells by nano disks in a buffer layer," J. Appl. Phys. 111, 103121-1-103121-6 (2012).
  5. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61 , 10484-10503 (2000).
  6. A. Ludwig, G. V. Eleftheriades, C. D. Sarris, "FDTD analysis of sub-wavelength focusing phenomena in plasmonic meta-screens," J. Lightw. Technol. 30, 2054-2061 (2012).
  7. M.-Y. Chen, H.-C. Chang, "Determination of surface plasmon modes and guided modes supported by periodic subwavelength slits on metals using a finite-difference frequency-domain method based eigenvalue algorithm," J. Lightw. Technol. 30, 76-83 (2012).
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  9. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag , 1986).
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  11. W. Chien, T. Szkopek, "Multiple-multipole simulation of optical nearfields in discrete metal nanosphere assemblies ," Opt. Exp. 16, 1820-1835 (2008).
  12. C. Rockstuhl, M. G. Salt, H. P. Herzig, "Application of the boundary-element method to the interaction of light with single and coupled metallic nanoparticles," J. Opt. Soc. Amer. A 20, 1960-1964 (2003).
  13. S. He, W. E. I. Sha, L. Jiang, W. C. H. Choy, W. Cho Chew, Z. Nie, "Finite-element-based generalized impedance boundary condition for modeling plasmonic nanostructures," IEEE Trans. Nanotechnol. 11, 336-345 (2012).
  14. A. Boltasseva, S. I. Bozhevolnyi, "Directional couplers using long-range surface plasmon polariton waveguides," IEEE J. Select. Topics Quantum Electron. 12, 1233-1241 (2006).
  15. F. P. G. de Arquer, V. Volski, N. Verellen, G. A. E. Vandenbosch, V. V. Moshchalkov, "Engineering the input impedance of optical nano dipole antennas: Materials, geometry and excitation effect," IEEE Trans. Antennas Propag. 59, 3144-3153 (2011).
  16. T. B. A. Senior, J. L. Volakis, Approximate Boundary Conditions In Electromagnetic (The Institution of Electrical Engineering, 1995).
  17. J. R. Mosig, F. E. Gardiol, "General integral equation formulation for microstrip antennas and scatters," IEE Proc. H Microw. Antennas Propag. 132, 424-432 (1985).
  18. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  19. D. W. Lynch, W. R. Hunter, Handbook of Optical Constants of Solids (Academic, 1985) pp. 275 -367.
  20. R. Faraji-Dana, Y. L. Chow, "The current distribution and AC resistance of a microstrip structure," IEEE Trans. Microw. Theory Techn. 38, 1268 -1277 (1990).
  21. R. Faraji-Dana, Y. L. Chow, "AC resistance of two coupled strip conductors," Proc. IEE H Microw., Antennas Propag. 138, 37- 45 (1991).
  22. H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, S. I. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 011110-1-011110-3 (2006).
  23. S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides," Opt. Exp. 13, 4674-4682 (2005).
  24. Y.-J. Chang, Y.-C. Liu, " A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).

2012 (5)

M.-S. Kwon, "Metal stripe waveguide based interferometer-type sensor working in an aqueous solution with a low refractive index," J. Lightw. Technol. 30, 2035-2041 (2012).

I. Kim, D. Seok Jeong, T. Seong Lee, W. Seong Lee, K.-S. Lee, " Plasmonic absorption enhancement in organic solar cells by nano disks in a buffer layer," J. Appl. Phys. 111, 103121-1-103121-6 (2012).

A. Ludwig, G. V. Eleftheriades, C. D. Sarris, "FDTD analysis of sub-wavelength focusing phenomena in plasmonic meta-screens," J. Lightw. Technol. 30, 2054-2061 (2012).

M.-Y. Chen, H.-C. Chang, "Determination of surface plasmon modes and guided modes supported by periodic subwavelength slits on metals using a finite-difference frequency-domain method based eigenvalue algorithm," J. Lightw. Technol. 30, 76-83 (2012).

S. He, W. E. I. Sha, L. Jiang, W. C. H. Choy, W. Cho Chew, Z. Nie, "Finite-element-based generalized impedance boundary condition for modeling plasmonic nanostructures," IEEE Trans. Nanotechnol. 11, 336-345 (2012).

2011 (2)

F. P. G. de Arquer, V. Volski, N. Verellen, G. A. E. Vandenbosch, V. V. Moshchalkov, "Engineering the input impedance of optical nano dipole antennas: Materials, geometry and excitation effect," IEEE Trans. Antennas Propag. 59, 3144-3153 (2011).

Y.-J. Chang, Y.-C. Liu, " A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).

2009 (1)

K. Tanaka, T. T. Minh, M. Tanaka, "Analysis of propagation characteristics in the surface plasmon polariton gap waveguides by method of lines," Opt. Exp. 17, 1078-92 (2009).

2008 (1)

W. Chien, T. Szkopek, "Multiple-multipole simulation of optical nearfields in discrete metal nanosphere assemblies ," Opt. Exp. 16, 1820-1835 (2008).

2007 (1)

M. Yan, M. Qiu, " Analysis of surface plasmon polariton using anisotropic finite elements," IEEE Photon. Technol. Lett. 19, 1804- 1806 (2007).

2006 (2)

A. Boltasseva, S. I. Bozhevolnyi, "Directional couplers using long-range surface plasmon polariton waveguides," IEEE J. Select. Topics Quantum Electron. 12, 1233-1241 (2006).

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, S. I. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 011110-1-011110-3 (2006).

2005 (3)

S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides," Opt. Exp. 13, 4674-4682 (2005).

R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Exp. 13, 977-984 (2005).

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, S. I. Bozhevolnyi, "Integrated optical components utilizing long-range surface plasmon polaritons," J. Lightw. Technol. 23 , 413-422 (2005).

2003 (1)

C. Rockstuhl, M. G. Salt, H. P. Herzig, "Application of the boundary-element method to the interaction of light with single and coupled metallic nanoparticles," J. Opt. Soc. Amer. A 20, 1960-1964 (2003).

2000 (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61 , 10484-10503 (2000).

1991 (1)

R. Faraji-Dana, Y. L. Chow, "AC resistance of two coupled strip conductors," Proc. IEE H Microw., Antennas Propag. 138, 37- 45 (1991).

1990 (1)

R. Faraji-Dana, Y. L. Chow, "The current distribution and AC resistance of a microstrip structure," IEEE Trans. Microw. Theory Techn. 38, 1268 -1277 (1990).

1985 (1)

J. R. Mosig, F. E. Gardiol, "General integral equation formulation for microstrip antennas and scatters," IEE Proc. H Microw. Antennas Propag. 132, 424-432 (1985).

IEEE Trans. Microw. Theory Techn. (1)

R. Faraji-Dana, Y. L. Chow, "The current distribution and AC resistance of a microstrip structure," IEEE Trans. Microw. Theory Techn. 38, 1268 -1277 (1990).

J. Appl. Phys. (1)

I. Kim, D. Seok Jeong, T. Seong Lee, W. Seong Lee, K.-S. Lee, " Plasmonic absorption enhancement in organic solar cells by nano disks in a buffer layer," J. Appl. Phys. 111, 103121-1-103121-6 (2012).

Appl. Phys. Lett. (1)

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, S. I. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 011110-1-011110-3 (2006).

IEE Proc. H Microw. Antennas Propag. (1)

J. R. Mosig, F. E. Gardiol, "General integral equation formulation for microstrip antennas and scatters," IEE Proc. H Microw. Antennas Propag. 132, 424-432 (1985).

IEEE J. Select. Topics Quantum Electron. (1)

A. Boltasseva, S. I. Bozhevolnyi, "Directional couplers using long-range surface plasmon polariton waveguides," IEEE J. Select. Topics Quantum Electron. 12, 1233-1241 (2006).

IEEE Photon. Technol. Lett. (2)

M. Yan, M. Qiu, " Analysis of surface plasmon polariton using anisotropic finite elements," IEEE Photon. Technol. Lett. 19, 1804- 1806 (2007).

Y.-J. Chang, Y.-C. Liu, " A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).

IEEE Trans. Antennas Propag. (1)

F. P. G. de Arquer, V. Volski, N. Verellen, G. A. E. Vandenbosch, V. V. Moshchalkov, "Engineering the input impedance of optical nano dipole antennas: Materials, geometry and excitation effect," IEEE Trans. Antennas Propag. 59, 3144-3153 (2011).

IEEE Trans. Nanotechnol. (1)

S. He, W. E. I. Sha, L. Jiang, W. C. H. Choy, W. Cho Chew, Z. Nie, "Finite-element-based generalized impedance boundary condition for modeling plasmonic nanostructures," IEEE Trans. Nanotechnol. 11, 336-345 (2012).

J. Lightw. Technol. (4)

A. Ludwig, G. V. Eleftheriades, C. D. Sarris, "FDTD analysis of sub-wavelength focusing phenomena in plasmonic meta-screens," J. Lightw. Technol. 30, 2054-2061 (2012).

M.-Y. Chen, H.-C. Chang, "Determination of surface plasmon modes and guided modes supported by periodic subwavelength slits on metals using a finite-difference frequency-domain method based eigenvalue algorithm," J. Lightw. Technol. 30, 76-83 (2012).

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, S. I. Bozhevolnyi, "Integrated optical components utilizing long-range surface plasmon polaritons," J. Lightw. Technol. 23 , 413-422 (2005).

M.-S. Kwon, "Metal stripe waveguide based interferometer-type sensor working in an aqueous solution with a low refractive index," J. Lightw. Technol. 30, 2035-2041 (2012).

J. Opt. Soc. Amer. A (1)

C. Rockstuhl, M. G. Salt, H. P. Herzig, "Application of the boundary-element method to the interaction of light with single and coupled metallic nanoparticles," J. Opt. Soc. Amer. A 20, 1960-1964 (2003).

Opt. Exp. (3)

R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Exp. 13, 977-984 (2005).

Opt. Exp. (1)

K. Tanaka, T. T. Minh, M. Tanaka, "Analysis of propagation characteristics in the surface plasmon polariton gap waveguides by method of lines," Opt. Exp. 17, 1078-92 (2009).

Opt. Exp. (3)

W. Chien, T. Szkopek, "Multiple-multipole simulation of optical nearfields in discrete metal nanosphere assemblies ," Opt. Exp. 16, 1820-1835 (2008).

S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides," Opt. Exp. 13, 4674-4682 (2005).

Phys. Rev. B (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61 , 10484-10503 (2000).

Proc. IEE H Microw., Antennas Propag. (1)

R. Faraji-Dana, Y. L. Chow, "AC resistance of two coupled strip conductors," Proc. IEE H Microw., Antennas Propag. 138, 37- 45 (1991).

Other (4)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag , 1986).

T. B. A. Senior, J. L. Volakis, Approximate Boundary Conditions In Electromagnetic (The Institution of Electrical Engineering, 1995).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

D. W. Lynch, W. R. Hunter, Handbook of Optical Constants of Solids (Academic, 1985) pp. 275 -367.

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