Abstract

The Fourier expansion-based transmission line (TL) formulation has been modified using the Lanczos correction factor for the full-wave modal analysis of dielectric optical waveguides. Also, an algorithm for systematic determination of the optimum values for the main simulation parameters of the presented formulation has been proposed. These optimum parameters provide a trade-off between accuracy, speed, and memory usage and consequently improve the efficiency of simulations. This algorithmic formulation has been applied for the modal analysis of optical channel, strip, and strip-based slot waveguides, and good results have been obtained for dispersion characteristics and electromagnetic (EM) field distributions of their guided modes.

© 2012 Optical Society of America

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  6. W. Huang and H. A. Haus, “A simple variational approach to optical rib waveguides,” J. Lightwave Technol. 9, 56–61 (1991).
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  7. M. S. Stern, P. C. Kendall, and P. W. A. Mcllroy, “Analysis of the spectral index method for vector modes of rib waveguides,” IEE Proc. J. Optoelectron. 137, 21–26 (1990).
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  9. M. S. Stern, “Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles,” IEE Proc. J. Optoelectron. 135, 56–63 (1988).
    [CrossRef]
  10. H. Dong, A. Chronopoulos, J. Zou, and A. Gopinath, “Vectorial integrated finite-difference analysis of dielectric waveguides,” J. Lightwave Technol. 11, 1559–1564 (1993).
    [CrossRef]
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
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  14. S. Selleri and A. Petracek, “Modal analysis of rib waveguide through finite element and mode matching methods,” Opt. Quantum Electron. 33, 373–386 (2001).
    [CrossRef]
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  16. P. C. Lee and E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1994).
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    [CrossRef]
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  23. M. Lohmeyer, “Wave-matching method for mode analysis of dielectric waveguides,” Opt. Quantum Electron. 29, 907–922 (1997).
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  25. C. C. Huang, “Numerical calculations of ARROW structures by pseudospectral approach with Mur’s absorbing boundary conditions,” Opt. Express 14, 11631–11652 (2006).
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  27. Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
    [CrossRef]
  28. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
    [CrossRef]
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    [CrossRef]
  32. Z. G. Kashani, N. Hojjat, and M. Shahabadi, “Full-wave analysis of coupled waveguides in a two-dimensional photonic crystal,” Prog. Electromagn. Res. 49, 291–307 (2004).
    [CrossRef]
  33. M. Ahmadi-Boroujeni and M. Shahabadi, “Modal analysis of multilayer planar lossy anisotropic optical waveguides,” J. Opt. A 8, 856–863 (2006).
    [CrossRef]
  34. M. Ahmadi-Boroujeni and M. Shahabadi, “Full-wave analysis of lossy anisotropic optical waveguides using a transmission line approach based on a Fourier method,” J. Opt. A 8, 1080–1087 (2006).
    [CrossRef]
  35. N. Dabidian, M. Shahabadi, and A. Tavakoli, “Diffraction analysis of photonic metamaterials using a transmission line formulation,” Proc. SPIE 6581, 658111 (2007).
    [CrossRef]
  36. V. R. Almeida, Q. Xu, R. R. Panepucci, C. A. Barrios, and M. Lipson, “Light guiding in low index materials using high-index-contrast waveguides,” Mater. Res. Soc. Symp. Proc. 797, W6.10.1–W6.10.6 (2004).
  37. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
    [CrossRef]
  38. Q. Xu, V. R. Almeida, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29, 1626–1628 (2004).
    [CrossRef]
  39. C. Lanczos, Applied Analysis, (Prentice Hall, 1956).

2008 (1)

2007 (1)

N. Dabidian, M. Shahabadi, and A. Tavakoli, “Diffraction analysis of photonic metamaterials using a transmission line formulation,” Proc. SPIE 6581, 658111 (2007).
[CrossRef]

2006 (3)

M. Ahmadi-Boroujeni and M. Shahabadi, “Modal analysis of multilayer planar lossy anisotropic optical waveguides,” J. Opt. A 8, 856–863 (2006).
[CrossRef]

M. Ahmadi-Boroujeni and M. Shahabadi, “Full-wave analysis of lossy anisotropic optical waveguides using a transmission line approach based on a Fourier method,” J. Opt. A 8, 1080–1087 (2006).
[CrossRef]

C. C. Huang, “Numerical calculations of ARROW structures by pseudospectral approach with Mur’s absorbing boundary conditions,” Opt. Express 14, 11631–11652 (2006).
[CrossRef]

2005 (2)

2004 (5)

M. Shahabadi, S. Atakaramians, and N. Hojjat, “Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals,” IEE Proc. Sci. Measure. Tech. 151, 327–334 (2004).
[CrossRef]

Z. G. Kashani, N. Hojjat, and M. Shahabadi, “Full-wave analysis of coupled waveguides in a two-dimensional photonic crystal,” Prog. Electromagn. Res. 49, 291–307 (2004).
[CrossRef]

V. R. Almeida, Q. Xu, R. R. Panepucci, C. A. Barrios, and M. Lipson, “Light guiding in low index materials using high-index-contrast waveguides,” Mater. Res. Soc. Symp. Proc. 797, W6.10.1–W6.10.6 (2004).

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
[CrossRef]

Q. Xu, V. R. Almeida, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29, 1626–1628 (2004).
[CrossRef]

2003 (1)

2001 (1)

S. Selleri and A. Petracek, “Modal analysis of rib waveguide through finite element and mode matching methods,” Opt. Quantum Electron. 33, 373–386 (2001).
[CrossRef]

2000 (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

1998 (1)

M. Lohmeyer, “Vectorial wave-matching mode analysis of integrated optical waveguides,” Opt. Quantum Electron. 30, 385–396 (1998).
[CrossRef]

1997 (2)

M. Lohmeyer, “Wave-matching method for mode analysis of dielectric waveguides,” Opt. Quantum Electron. 29, 907–922 (1997).
[CrossRef]

C. Vassallo, “1993-1995 optical mode solvers,” Opt. Quantum Electron. 29, 95–114 (1997).
[CrossRef]

1994 (2)

S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” Pure Appl. Opt. 3, 381–388 (1994).
[CrossRef]

P. C. Lee and E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1994).
[CrossRef]

1993 (2)

H. Dong, A. Chronopoulos, J. Zou, and A. Gopinath, “Vectorial integrated finite-difference analysis of dielectric waveguides,” J. Lightwave Technol. 11, 1559–1564 (1993).
[CrossRef]

U. Rogge, and R. Pregla, “Method of lines for the analysis of dielectric waveguides,” J. Lightwave Technol. 11, 2015–2020 (1993).
[CrossRef]

1992 (2)

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J. Quantum Electron. 28, 459–465 (1992).
[CrossRef]

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method-analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[CrossRef]

1991 (2)

U. Rogge and R. Pregla, “Method of lines for the analysis of strip-loaded optical waveguides,” J. Opt. Soc. Am. B 8, 459–463 (1991).
[CrossRef]

W. Huang and H. A. Haus, “A simple variational approach to optical rib waveguides,” J. Lightwave Technol. 9, 56–61 (1991).
[CrossRef]

1990 (3)

M. S. Stern, P. C. Kendall, and P. W. A. Mcllroy, “Analysis of the spectral index method for vector modes of rib waveguides,” IEE Proc. J. Optoelectron. 137, 21–26 (1990).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef]

1988 (1)

M. S. Stern, “Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles,” IEE Proc. J. Optoelectron. 135, 56–63 (1988).
[CrossRef]

1986 (1)

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguides by a new finite difference method,” J. Lightwave Technol. 34, 1104–1113 (1986).

1984 (1)

B. M. A. Rahman and J. B. Davies, “Finite-element analysis of optical and microwave waveguide problems,” IEEE Trans. Microwave Theory Tech. 32, 20–28 (1984).
[CrossRef]

1981 (1)

N. Mabaya and P. E. Lagasse, “Finite element analysis of optical waveguides,” IEEE Trans. Microwave Theory Tech. 29, 600–605 (1981).
[CrossRef]

1969 (1)

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).

Ahmadi-Boroujeni, M.

M. Ahmadi-Boroujeni and M. Shahabadi, “Modal analysis of multilayer planar lossy anisotropic optical waveguides,” J. Opt. A 8, 856–863 (2006).
[CrossRef]

M. Ahmadi-Boroujeni and M. Shahabadi, “Full-wave analysis of lossy anisotropic optical waveguides using a transmission line approach based on a Fourier method,” J. Opt. A 8, 1080–1087 (2006).
[CrossRef]

Almeida, V. R.

Arndt, F.

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguides by a new finite difference method,” J. Lightwave Technol. 34, 1104–1113 (1986).

Atakaramians, S.

M. Shahabadi, S. Atakaramians, and N. Hojjat, “Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals,” IEE Proc. Sci. Measure. Tech. 151, 327–334 (2004).
[CrossRef]

Barrios, C. A.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
[CrossRef]

V. R. Almeida, Q. Xu, R. R. Panepucci, C. A. Barrios, and M. Lipson, “Light guiding in low index materials using high-index-contrast waveguides,” Mater. Res. Soc. Symp. Proc. 797, W6.10.1–W6.10.6 (2004).

Bierwirth, K.

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguides by a new finite difference method,” J. Lightwave Technol. 34, 1104–1113 (1986).

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef]

Chaudhuri, S. K.

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method-analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[CrossRef]

Chronopoulos, A.

H. Dong, A. Chronopoulos, J. Zou, and A. Gopinath, “Vectorial integrated finite-difference analysis of dielectric waveguides,” J. Lightwave Technol. 11, 1559–1564 (1993).
[CrossRef]

Chu, S. T.

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method-analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[CrossRef]

Dabidian, N.

N. Dabidian, M. Shahabadi, and A. Tavakoli, “Diffraction analysis of photonic metamaterials using a transmission line formulation,” Proc. SPIE 6581, 658111 (2007).
[CrossRef]

Davies, J. B.

B. M. A. Rahman and J. B. Davies, “Finite-element analysis of optical and microwave waveguide problems,” IEEE Trans. Microwave Theory Tech. 32, 20–28 (1984).
[CrossRef]

Dong, H.

H. Dong, A. Chronopoulos, J. Zou, and A. Gopinath, “Vectorial integrated finite-difference analysis of dielectric waveguides,” J. Lightwave Technol. 11, 1559–1564 (1993).
[CrossRef]

Eghlidi, M. H.

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

H. Dong, A. Chronopoulos, J. Zou, and A. Gopinath, “Vectorial integrated finite-difference analysis of dielectric waveguides,” J. Lightwave Technol. 11, 1559–1564 (1993).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Haus, H. A.

W. Huang and H. A. Haus, “A simple variational approach to optical rib waveguides,” J. Lightwave Technol. 9, 56–61 (1991).
[CrossRef]

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef]

Hojjat, N.

M. Shahabadi, S. Atakaramians, and N. Hojjat, “Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals,” IEE Proc. Sci. Measure. Tech. 151, 327–334 (2004).
[CrossRef]

Z. G. Kashani, N. Hojjat, and M. Shahabadi, “Full-wave analysis of coupled waveguides in a two-dimensional photonic crystal,” Prog. Electromagn. Res. 49, 291–307 (2004).
[CrossRef]

Huang, C. C.

Huang, W.

W. Huang and H. A. Haus, “A simple variational approach to optical rib waveguides,” J. Lightwave Technol. 9, 56–61 (1991).
[CrossRef]

Huang, W. P.

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method-analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[CrossRef]

Kashani, Z. G.

Z. G. Kashani, N. Hojjat, and M. Shahabadi, “Full-wave analysis of coupled waveguides in a two-dimensional photonic crystal,” Prog. Electromagn. Res. 49, 291–307 (2004).
[CrossRef]

Kendall, P. C.

M. S. Stern, P. C. Kendall, and P. W. A. Mcllroy, “Analysis of the spectral index method for vector modes of rib waveguides,” IEE Proc. J. Optoelectron. 137, 21–26 (1990).
[CrossRef]

Khorasani, S.

Lagasse, P. E.

N. Mabaya and P. E. Lagasse, “Finite element analysis of optical waveguides,” IEEE Trans. Microwave Theory Tech. 29, 600–605 (1981).
[CrossRef]

Lanczos, C.

C. Lanczos, Applied Analysis, (Prentice Hall, 1956).

Lee, P. C.

P. C. Lee and E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1994).
[CrossRef]

Lipson, M.

Lohmeyer, M.

M. Lohmeyer, “Vectorial wave-matching mode analysis of integrated optical waveguides,” Opt. Quantum Electron. 30, 385–396 (1998).
[CrossRef]

M. Lohmeyer, “Wave-matching method for mode analysis of dielectric waveguides,” Opt. Quantum Electron. 29, 907–922 (1997).
[CrossRef]

Mabaya, N.

N. Mabaya and P. E. Lagasse, “Finite element analysis of optical waveguides,” IEEE Trans. Microwave Theory Tech. 29, 600–605 (1981).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).

Marcuse, D.

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J. Quantum Electron. 28, 459–465 (1992).
[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic Press, 1991).

Mcllroy, P. W. A.

M. S. Stern, P. C. Kendall, and P. W. A. Mcllroy, “Analysis of the spectral index method for vector modes of rib waveguides,” IEE Proc. J. Optoelectron. 137, 21–26 (1990).
[CrossRef]

Mehrany, K.

Muraki, M.

Nakano, H.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, 2006).

Panepucci, R. R.

V. R. Almeida, Q. Xu, R. R. Panepucci, C. A. Barrios, and M. Lipson, “Light guiding in low index materials using high-index-contrast waveguides,” Mater. Res. Soc. Symp. Proc. 797, W6.10.1–W6.10.6 (2004).

Petracek, A.

S. Selleri and A. Petracek, “Modal analysis of rib waveguide through finite element and mode matching methods,” Opt. Quantum Electron. 33, 373–386 (2001).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

U. Rogge, and R. Pregla, “Method of lines for the analysis of dielectric waveguides,” J. Lightwave Technol. 11, 2015–2020 (1993).
[CrossRef]

U. Rogge and R. Pregla, “Method of lines for the analysis of strip-loaded optical waveguides,” J. Opt. Soc. Am. B 8, 459–463 (1991).
[CrossRef]

Rahman, B. M. A.

B. M. A. Rahman and J. B. Davies, “Finite-element analysis of optical and microwave waveguide problems,” IEEE Trans. Microwave Theory Tech. 32, 20–28 (1984).
[CrossRef]

Rashidian, B.

Rogge, U.

U. Rogge, and R. Pregla, “Method of lines for the analysis of dielectric waveguides,” J. Lightwave Technol. 11, 2015–2020 (1993).
[CrossRef]

U. Rogge and R. Pregla, “Method of lines for the analysis of strip-loaded optical waveguides,” J. Opt. Soc. Am. B 8, 459–463 (1991).
[CrossRef]

Satpathy, S.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Schulz, N.

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguides by a new finite difference method,” J. Lightwave Technol. 34, 1104–1113 (1986).

Selleri, S.

S. Selleri and A. Petracek, “Modal analysis of rib waveguide through finite element and mode matching methods,” Opt. Quantum Electron. 33, 373–386 (2001).
[CrossRef]

Shahabadi, M.

N. Dabidian, M. Shahabadi, and A. Tavakoli, “Diffraction analysis of photonic metamaterials using a transmission line formulation,” Proc. SPIE 6581, 658111 (2007).
[CrossRef]

M. Ahmadi-Boroujeni and M. Shahabadi, “Full-wave analysis of lossy anisotropic optical waveguides using a transmission line approach based on a Fourier method,” J. Opt. A 8, 1080–1087 (2006).
[CrossRef]

M. Ahmadi-Boroujeni and M. Shahabadi, “Modal analysis of multilayer planar lossy anisotropic optical waveguides,” J. Opt. A 8, 856–863 (2006).
[CrossRef]

Z. G. Kashani, N. Hojjat, and M. Shahabadi, “Full-wave analysis of coupled waveguides in a two-dimensional photonic crystal,” Prog. Electromagn. Res. 49, 291–307 (2004).
[CrossRef]

M. Shahabadi, S. Atakaramians, and N. Hojjat, “Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals,” IEE Proc. Sci. Measure. Tech. 151, 327–334 (2004).
[CrossRef]

Shibayama, J.

Shimabukuro, F. I.

C. Yeh and F. I. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef]

Stern, M. S.

M. S. Stern, P. C. Kendall, and P. W. A. Mcllroy, “Analysis of the spectral index method for vector modes of rib waveguides,” IEE Proc. J. Optoelectron. 137, 21–26 (1990).
[CrossRef]

M. S. Stern, “Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles,” IEE Proc. J. Optoelectron. 135, 56–63 (1988).
[CrossRef]

Sudbo, S.

S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” Pure Appl. Opt. 3, 381–388 (1994).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tavakoli, A.

N. Dabidian, M. Shahabadi, and A. Tavakoli, “Diffraction analysis of photonic metamaterials using a transmission line formulation,” Proc. SPIE 6581, 658111 (2007).
[CrossRef]

Vassallo, C.

C. Vassallo, “1993-1995 optical mode solvers,” Opt. Quantum Electron. 29, 95–114 (1997).
[CrossRef]

Voges, E.

P. C. Lee and E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1994).
[CrossRef]

Xu, C. L.

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method-analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[CrossRef]

Xu, Q.

Yamauchi, J.

Yeh, C.

C. Yeh and F. I. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008).

Zhang, Z.

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Figures (12)

Fig. 1.
Fig. 1.

Cross-section of a silicon-photonics strip-based slot waveguide.

Fig. 2.
Fig. 2.

Periodization of the original waveguide shown in Fig. 1 with period Lx along the x-axis. w=2wH+wS.

Fig. 3.
Fig. 3.

Refractive-index profile of the dielectric strip-based slot waveguide in layer #2 with wH=218nm, wS=101nm, nH=3.48, nC=1.46, and nS=1. The solid line curve represents the result of Fourier expansion approximation with Lx=3w and M=40 in (a) and M=150 in (b); the dashed line represents the exact profile.

Fig. 4.
Fig. 4.

Refractive-index profile of the dielectric strip-based slot waveguide in layer #2 with wH=218nm, wS=101nm, nH=3.48, nC=1.46, and nS=1. The solid line curve represents the result of Lanczos–Fourier expansion approximation with Lx=3w and M=40 in (a) and M=150 in (b); the dashed line represents the exact profile.

Fig. 5.
Fig. 5.

Flow-chart of the proposed algorithm for finding the optimum values Lx,opt and Mopt applied in the Lanczos–Fourier expansion and calculation of the dispersion and field parameters.

Fig. 6.
Fig. 6.

Cross-section of an optical strip waveguide. In channel waveguides, nC=nB.

Fig. 7.
Fig. 7.

Simulated dispersion diagram of quasi-TE and quasi-TM modes for the STRIP. The solid curves represent the results of present analysis for Lx=6wH and M=90. The circle and square markers respectively represent Marcatili’s planar approximate and Goell’s circular harmonic expansion methods presented in [24]. Goell’s results are presented only for E11, E12, E21, and E22 modes; additionally, Goell’s and Marcatili’s results in the E22 mode are same.

Fig. 8.
Fig. 8.

Three-dimensional distribution of (a) normalized |Ex|, (b) normalized |Ey|, (c) normalized |Ez|, and (d) normalized transverse electric field of the fundamental quasi-TE mode for the STRIP at λ0=1.5μm with Lx=6wH and M=90. Dispersion parameters obtained for this mode are neff=1.00378108 and b=0.18753616.

Fig. 9.
Fig. 9.

Transverse electric fields for fundamental quasi-TE mode of the CHANNEL 1 at λ0=1550nm. (a) and (b) are based on Fourier expansion with Lx=4wH and M=200; while (c) and (d) are based on Lanczos–Fourier expansion with Lx=4wH and M=200. Vertical dashed lines represent the core-cladding interfaces. Effective refractive-indices obtained for this mode are neff=2.42457251 and neff=2.42601406, respectively, based on pure Fourier and Lanczos–Fourier expansions. In [38], neff2.43.

Fig. 10.
Fig. 10.

Three-dimensional normalized transverse electric field distribution of (a) fundamental quasi-TE mode and (b) fundamental quasi-TM mode for CHANNEL 2 at λ0=1550nm with Lx,opt=5wH and Mopt=500. Dispersion parameters obtained for quasi-TE mode are neff=2.59592747, b=0.46170275, and kz=10.52302797μm1, and for the quasi-TM mode they are neff=2.01774952, b=0.19438340, and kz=8.17928654μm1.

Fig. 11.
Fig. 11.

Dispersion diagrams of quasi-TE and quasi-TM modes in the channel and strip-based slot waveguides. (a) SLOT with Lx=5w and M=500. Results of FVFD method are from [38]. (b) SLOT with Lx=5w and M=500. Experimental results are from [38]. (c) SLOT with Lx=5w and M=500, and CHANNEL 1 with Lx=5wH and M=500. (d) SLOT with Lx=5w and M=500, and CHANNEL 2 with Lx=5wH and M=500.

Fig. 12.
Fig. 12.

(a) Three-dimensional and (b) Two-dimensional, normalized transverse electric field distribution of the fundamental quasi-TE mode for SLOT at λ0=1550nm with Lx,opt=5w and Mopt=500. Dispersion parameters obtained for quasi-TE mode are neff=1.62058096, b=0.04957336, and kz=6.56929710μm. Level step|(b)=0.005.

Tables (4)

Tables Icon

Table 1. Dispersion Analysis of the Fundamental Quasi-TE Mode and Determination of Lx,opt and Mopt for the CHANNEL 1. Wavelengths are in μm and δneff=5×104

Tables Icon

Table 2. Dispersion Analysis of the Fundamental Quasi-TM Mode and Determination of Lx,opt and Mopt for the CHANNEL 1. Wavelengths are in μm and δneff=5×104

Tables Icon

Table 3. Dispersion Analysis of the Fundamental Quasi-TM Mode and Determination of Lx,opt and Mopt for the SLOT. Wavelengths are in μm and δneff=2×104

Tables Icon

Table 4. Dispersion Analysis of the Fundamental Quasi-TE Mode and Determination of Lx,opt and Mopt for the SLOT. Wavelengths are in μm and δneff=5×103

Equations (7)

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E(r)=limMm=MMEm(y)exp(jαmx)exp(jkzz),
H(r)=limMm=MMHm(y)exp(jαmx)exp(jkzz),
εr(r)=limMm=MMεm(y)exp(jαmx),
εr(r)=limMm=MMσmεm(y)exp(jαmx),
Lx=3wmax,M=6forwmax<λmax;Lx=2wmax,M=4forwmax>λmax.
Lx=3wmax,M=6forΔn<1;Lx=2wmax,M=4forΔn>1.
Lx=3wmax,M=6forwmax<λmaxandΔn<1;Lx=3wmax,M=6forwmax<λmaxandΔn>1;Lx=3wmax,M=6forwmax>λmaxandΔn<1;Lx=2wmax,M=4forwmax>λmaxandΔn>1.

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