Abstract

In this paper, we present a full-vector finite difference method to solve for optical modes in one and two dimensional subwavelength plasmonic waveguides. We have used the Implicitly Restarted Arnoldi method to directly calculate the propagation constants of the dominant modes. The method has low computational complexity and can be applied to accurately model complex geometries and structures with fast-varying field profiles. When applied to solve for purely bounded modes, our method automatically separates evanescent and low-loss guided modes.

© 2006 Optical Society of America

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  1. M. Hochberg, T. Baehr-Jones, C. Walker, and A. Scherer, "Integrated plasmon and dielectric waveguides," Opt. Express 12, 5481-5486 (2004).
    [CrossRef]
  2. K. Tanaka, M. Tanaka, and T. Sugiyama, "Simulation of practical nanometric circuits based on surface plasmon polariton gap waveguide," Opt. Express 13, 256-266 (2005).
    [CrossRef]
  3. G. I. Stegeman, R. F. Wallias, and A. Maradudin, "Excitation of surface polaritons by end-fire coupling," Opt. Lett. 8, 386 (1983).
  4. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).
  5. R. Zia,M. D. Selker, P. B. Catrysse, andM. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A 21, 2442-2446 (2004).
    [CrossRef]
  6. S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE J. Quantum Electron 40, 325-329 (2004).
    [CrossRef]
  7. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric strucutres," J. Phys. Rev. B 61, 10484-10503 (2000).
    [CrossRef]
  8. P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
    [CrossRef]
  9. R. Zia, M. D. Selker, and M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguide," Phys. Rev. B 71, 165431 (2005).
    [CrossRef]
  10. C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).
  11. J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model," J. Phys. Rev. B 72, 075405 (2005).
    [CrossRef]
  12. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
    [CrossRef]
  13. P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
    [CrossRef]
  14. K. Ramm, P. Lusse, and H.-G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides," IEEE Photonics Technol. Lett. 9, 967-969 (1997).
    [CrossRef]
  15. V. Hernandez, J. E. Roman, A. Tomas, and V. Vidal, "A Survey of Software for Sparse Eigenvalue Problems," Technical report, Universidad Politecnica de Valencia, (2005).
  16. W. J. Stewart and A. Jennings, "Algorithm 570: LOPSI: A Simultaneous Iteration Method for Real Matrices [F2]," ACM Trans. Math. Softw. 7, 230-232 (1981).
    [CrossRef]
  17. R. B. Lehoucq and D. C. Sorensen, "Deflation techniques within an implicitly restarted iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
    [CrossRef]
  18. D. C. Sorensen, "Implicit application of polynomial filters in a K-step Arnoldi method," SIAM J. Matrix Anal. Appl. 13, 357-385, (1992).
    [CrossRef]
  19. R. Radke, "A MATLAB implementation of the implicitly restarted Arnoldi method for solving large scale eigenvalue problems," Technical report, Dept. of Applied and Computational Mathematics, Rice University, Houston, TX, (1996).
  20. R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005).
    [CrossRef]

2005 (4)

R. Zia, M. D. Selker, and M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguide," Phys. Rev. B 71, 165431 (2005).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model," J. Phys. Rev. B 72, 075405 (2005).
[CrossRef]

K. Tanaka, M. Tanaka, and T. Sugiyama, "Simulation of practical nanometric circuits based on surface plasmon polariton gap waveguide," Opt. Express 13, 256-266 (2005).
[CrossRef]

R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005).
[CrossRef]

2004 (3)

2000 (4)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric strucutres," J. Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).

C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).

1997 (1)

K. Ramm, P. Lusse, and H.-G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides," IEEE Photonics Technol. Lett. 9, 967-969 (1997).
[CrossRef]

1996 (2)

P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
[CrossRef]

R. B. Lehoucq and D. C. Sorensen, "Deflation techniques within an implicitly restarted iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
[CrossRef]

1994 (1)

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
[CrossRef]

1992 (1)

D. C. Sorensen, "Implicit application of polynomial filters in a K-step Arnoldi method," SIAM J. Matrix Anal. Appl. 13, 357-385, (1992).
[CrossRef]

1983 (1)

1981 (1)

W. J. Stewart and A. Jennings, "Algorithm 570: LOPSI: A Simultaneous Iteration Method for Real Matrices [F2]," ACM Trans. Math. Softw. 7, 230-232 (1981).
[CrossRef]

Al-Bader, S. J.

S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE J. Quantum Electron 40, 325-329 (2004).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model," J. Phys. Rev. B 72, 075405 (2005).
[CrossRef]

Baehr-Jones, T.

Berini, P.

C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric strucutres," J. Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).

P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
[CrossRef]

Berolo, E.

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Brongersma, M. L.

R. Zia, M. D. Selker, and M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguide," Phys. Rev. B 71, 165431 (2005).
[CrossRef]

R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005).
[CrossRef]

Catrysse, P. B.

Chandran, A.

Charbonneau, R.

Chen, C.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model," J. Phys. Rev. B 72, 075405 (2005).
[CrossRef]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Feng, D.

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Hochberg, M.

Jager, D.

P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
[CrossRef]

Jennings, A.

W. J. Stewart and A. Jennings, "Algorithm 570: LOPSI: A Simultaneous Iteration Method for Real Matrices [F2]," ACM Trans. Math. Softw. 7, 230-232 (1981).
[CrossRef]

Lehoucq, R. B.

R. B. Lehoucq and D. C. Sorensen, "Deflation techniques within an implicitly restarted iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
[CrossRef]

Lisicka-Shrzek, E.

Lusse, P.

K. Ramm, P. Lusse, and H.-G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides," IEEE Photonics Technol. Lett. 9, 967-969 (1997).
[CrossRef]

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
[CrossRef]

Maradudin, A.

Ramm, K.

K. Ramm, P. Lusse, and H.-G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides," IEEE Photonics Technol. Lett. 9, 967-969 (1997).
[CrossRef]

Scherer, A.

Schule, J.

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
[CrossRef]

Selker, M. D.

R. Zia, M. D. Selker, and M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguide," Phys. Rev. B 71, 165431 (2005).
[CrossRef]

R. Zia,M. D. Selker, P. B. Catrysse, andM. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A 21, 2442-2446 (2004).
[CrossRef]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Sorensen, D. C.

R. B. Lehoucq and D. C. Sorensen, "Deflation techniques within an implicitly restarted iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
[CrossRef]

D. C. Sorensen, "Implicit application of polynomial filters in a K-step Arnoldi method," SIAM J. Matrix Anal. Appl. 13, 357-385, (1992).
[CrossRef]

Soukoulis, C. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Stegeman, G. I.

Stewart, W. J.

W. J. Stewart and A. Jennings, "Algorithm 570: LOPSI: A Simultaneous Iteration Method for Real Matrices [F2]," ACM Trans. Math. Softw. 7, 230-232 (1981).
[CrossRef]

Stohr, A.

P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
[CrossRef]

Stuwe, P.

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
[CrossRef]

Sugiyama, T.

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model," J. Phys. Rev. B 72, 075405 (2005).
[CrossRef]

Tanaka, K.

Tanaka, M.

Tanev, S.

Tzolov, V.

Unger, H.-G.

K. Ramm, P. Lusse, and H.-G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides," IEEE Photonics Technol. Lett. 9, 967-969 (1997).
[CrossRef]

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
[CrossRef]

Walker, C.

Wallias, R. F.

Wu, K.

P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
[CrossRef]

Zia, R.

ACM Trans. Math. Softw. (1)

W. J. Stewart and A. Jennings, "Algorithm 570: LOPSI: A Simultaneous Iteration Method for Real Matrices [F2]," ACM Trans. Math. Softw. 7, 230-232 (1981).
[CrossRef]

IEEE J. Quantum Electron (1)

S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE J. Quantum Electron 40, 325-329 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

K. Ramm, P. Lusse, and H.-G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides," IEEE Photonics Technol. Lett. 9, 967-969 (1997).
[CrossRef]

J. Lightwave Technol. (2)

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by new finite difference method," J. Lightwave Technol. 12, 487-494 (1994).
[CrossRef]

P. Berini, A. Stohr, K. Wu, D. Jager, "Normal mode analysis and characterization of an InGaAs/GaAs MQW field-induced optical waveguide including electrode effects," J. Lightwave Technol. 14, 2422-2435 (1996).
[CrossRef]

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

J. Phys. Rev. B (3)

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model," J. Phys. Rev. B 72, 075405 (2005).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelength," J. Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric strucutres," J. Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. B (1)

R. Zia, M. D. Selker, and M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguide," Phys. Rev. B 71, 165431 (2005).
[CrossRef]

SIAM J. Matrix Anal. Appl. (2)

R. B. Lehoucq and D. C. Sorensen, "Deflation techniques within an implicitly restarted iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
[CrossRef]

D. C. Sorensen, "Implicit application of polynomial filters in a K-step Arnoldi method," SIAM J. Matrix Anal. Appl. 13, 357-385, (1992).
[CrossRef]

Other (2)

R. Radke, "A MATLAB implementation of the implicitly restarted Arnoldi method for solving large scale eigenvalue problems," Technical report, Dept. of Applied and Computational Mathematics, Rice University, Houston, TX, (1996).

V. Hernandez, J. E. Roman, A. Tomas, and V. Vidal, "A Survey of Software for Sparse Eigenvalue Problems," Technical report, Universidad Politecnica de Valencia, (2005).

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