Abstract

The scattering properties for both TE and TM modes of an abruptly ended two-layered slab waveguide with anisotropic core and isolated substrate are examined by an improved iteration technique, which is based on the integral equation method with accelerating parameters. The relative dielectric constants of the core for the three Cartesian directions are considered to be different, but cases with isotropic core are also considered. The electric field distribution on the terminal plane and the reflection coefficients of the dominant TE and TM guided modes, as well as the near-field distribution and the far-field radiation pattern, are computed, while numerical results are presented for several cases of the core anisotropy.

© 2007 Optical Society of America

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References

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  1. K. Kitayama and N. Kumagai, "Theory and applications of coupled optical waveguides involving anisotropic or gyrotronic materials," IEEE Trans. Microwave Theory Tech. 25, 567-572 (1977).
    [CrossRef]
  2. D. Marcuse and I. P. Kaminow, "Modes of a symmetric slab optical waveguide in birefringent media. Part II: Slab with coplanar optical axis," IEEE J. Quantum Electron. 15, 92-101 (1979).
    [CrossRef]
  3. L. Torner, J. Recolons, and J. P. Torres, "Guided-to-leaky mode transformation in uniaxial optical slab waveguides," J. Lightwave Technol. 11, 1592-1600 (1993).
    [CrossRef]
  4. A. Knoesen, T. K. Gaylord, and M. G. Moharam, "Hybrid guided modes in uniaxial dielectric planar waveguides," J. Lightwave Technol. 6, 1083-1104 (1988).
    [CrossRef]
  5. S. Sawa, M. Geshiro, and M. Hotta, "Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-40, 338-345 (1992).
    [CrossRef]
  6. D. K. Paul and R. K. Shevgaonkar, "Multimode propagation in anisotropic optical waveguides," Radio Sci. 16, 525-533 (1981).
    [CrossRef]
  7. A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide," Microwave Opt. Technol. Lett. 5, 602-606 (1992).
    [CrossRef]
  8. T. Q. Ho and B. Becker, "Far-field radiation from step junctions in biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 298-301 (1989).
    [CrossRef]
  9. A. B. Manenkov, "Irregular magneto-optical waveguides," IEEE Trans. Microwave Theory Tech. MTT-29, 906-910 (1981).
    [CrossRef]
  10. A. L. Stepanov, "Optical properties of the metal nano-particles synthesized in the polymer by the ion-implantation doping," J. Tech. Phys. 74, 1-12 (2004).
  11. T. Werne, M. Testorf, and U. Gibson, "Local field enhancement in metal dielectric nanocylinders with complex cross sections," J. Opt. Soc. Am. A 23, 2299-2306 (2006).
    [CrossRef]
  12. F. A. Katsriku, B. M. A. Rahman, and K. T. V. Grattan, "Finite element analysis of diffused anisotropic optical waveguides," J. Lightwave Technol. 14, 780-786 (1996).
    [CrossRef]
  13. Y. Tsuji, M. Koshiba, and N. Takimoto, "Finite element beam propagation method for anisotropic optical waveguides," J. Lightwave Technol. 17, 723-728 (1999).
    [CrossRef]
  14. I. V. Lindell and M. I. Oksanen, "Variational method for anisotropic dielectric waveguides," Microwaves RF 22, 145 (1983).
  15. P. Lusse and H. G. Unger, "Finite difference method for anisotropic planar optical waveguides," AEU, Int. J. Electron. Commun. 51, 29-34 (1997).
  16. D. Marcuse, "Coupled-mode theory for anisotropic optical-waveguides," Bell Syst. Tech. J. 54, 985-995 (1975).
  17. B. Becker and T. Q. Ho, "Radiation loss due to step discontinuities in symmetric biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 403-408 (1991).
    [CrossRef]
  18. C. Vassallo, "Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide," J. Opt. Soc. Am. A 5, 1918-1928 (1988).
    [CrossRef]
  19. C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.-J: Optoelectron. 140, 56-61 (1993).
    [CrossRef]
  20. D. N. Chien, M. Tanaka, and K. Tanaka, "Numerical simulation of an arbitrarily ended asymmetrical slab waveguide by guided-mode extracted integral equations," J. Opt. Soc. Am. A 19, 1649-1657 (2002).
    [CrossRef]
  21. K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
    [CrossRef]
  22. P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmodes expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
    [CrossRef]
  23. I. G. Tigelis and A. B. Manenkov, "Analysis of mode scattering from an abruptly ended dielectric slab waveguide by an accelerated iteration technique," J. Opt. Soc. Am. A 17, 2249-2259 (2000).
    [CrossRef]
  24. A. B. Manenkov, G. P. Latsas, and I. G. Tigelis, "Scattering of the transverse magnetic modes from an abruptly ended strongly asymmetrical slab waveguide by an accelerated integral equation technique," J. Opt. Soc. Am. A 18, 3110-3119 (2001).
    [CrossRef]
  25. F. G. Tricomi, Integral Equations (Interscience, 1957).
  26. A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. I: Solution by factorization method," Radiophys. Quantum Electron. 25, 954-960 (1982).
    [CrossRef]
  27. A. B. Manenkov, "Reflection of the surface mode from an abruptly ended W-fibre," IEE Proc.-J: Optoelectron. 139, 101-104 (1992).
    [CrossRef]
  28. M.Abramowitz and I.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972), p. 887.
  29. I. G. Tigelis and A. B. Manenkov, "Scattering from an abruptly terminated asymmetrical slab waveguide," J. Opt. Soc. Am. A 16, 523-532 (1999).
    [CrossRef]
  30. L.Nicolais and G.Carotenuto, eds., Metal-Polymer Nanocomposites (Wiley, 2005).

2006 (1)

2004 (1)

A. L. Stepanov, "Optical properties of the metal nano-particles synthesized in the polymer by the ion-implantation doping," J. Tech. Phys. 74, 1-12 (2004).

2002 (1)

2001 (2)

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmodes expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

A. B. Manenkov, G. P. Latsas, and I. G. Tigelis, "Scattering of the transverse magnetic modes from an abruptly ended strongly asymmetrical slab waveguide by an accelerated integral equation technique," J. Opt. Soc. Am. A 18, 3110-3119 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (1)

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

1997 (1)

P. Lusse and H. G. Unger, "Finite difference method for anisotropic planar optical waveguides," AEU, Int. J. Electron. Commun. 51, 29-34 (1997).

1996 (1)

F. A. Katsriku, B. M. A. Rahman, and K. T. V. Grattan, "Finite element analysis of diffused anisotropic optical waveguides," J. Lightwave Technol. 14, 780-786 (1996).
[CrossRef]

1993 (2)

C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.-J: Optoelectron. 140, 56-61 (1993).
[CrossRef]

L. Torner, J. Recolons, and J. P. Torres, "Guided-to-leaky mode transformation in uniaxial optical slab waveguides," J. Lightwave Technol. 11, 1592-1600 (1993).
[CrossRef]

1992 (3)

S. Sawa, M. Geshiro, and M. Hotta, "Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-40, 338-345 (1992).
[CrossRef]

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide," Microwave Opt. Technol. Lett. 5, 602-606 (1992).
[CrossRef]

A. B. Manenkov, "Reflection of the surface mode from an abruptly ended W-fibre," IEE Proc.-J: Optoelectron. 139, 101-104 (1992).
[CrossRef]

1991 (1)

B. Becker and T. Q. Ho, "Radiation loss due to step discontinuities in symmetric biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 403-408 (1991).
[CrossRef]

1989 (1)

T. Q. Ho and B. Becker, "Far-field radiation from step junctions in biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 298-301 (1989).
[CrossRef]

1988 (2)

A. Knoesen, T. K. Gaylord, and M. G. Moharam, "Hybrid guided modes in uniaxial dielectric planar waveguides," J. Lightwave Technol. 6, 1083-1104 (1988).
[CrossRef]

C. Vassallo, "Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide," J. Opt. Soc. Am. A 5, 1918-1928 (1988).
[CrossRef]

1983 (1)

I. V. Lindell and M. I. Oksanen, "Variational method for anisotropic dielectric waveguides," Microwaves RF 22, 145 (1983).

1982 (1)

A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. I: Solution by factorization method," Radiophys. Quantum Electron. 25, 954-960 (1982).
[CrossRef]

1981 (2)

A. B. Manenkov, "Irregular magneto-optical waveguides," IEEE Trans. Microwave Theory Tech. MTT-29, 906-910 (1981).
[CrossRef]

D. K. Paul and R. K. Shevgaonkar, "Multimode propagation in anisotropic optical waveguides," Radio Sci. 16, 525-533 (1981).
[CrossRef]

1979 (1)

D. Marcuse and I. P. Kaminow, "Modes of a symmetric slab optical waveguide in birefringent media. Part II: Slab with coplanar optical axis," IEEE J. Quantum Electron. 15, 92-101 (1979).
[CrossRef]

1977 (1)

K. Kitayama and N. Kumagai, "Theory and applications of coupled optical waveguides involving anisotropic or gyrotronic materials," IEEE Trans. Microwave Theory Tech. 25, 567-572 (1977).
[CrossRef]

1975 (1)

D. Marcuse, "Coupled-mode theory for anisotropic optical-waveguides," Bell Syst. Tech. J. 54, 985-995 (1975).

Baets, R.

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmodes expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Barbosa, A. M.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide," Microwave Opt. Technol. Lett. 5, 602-606 (1992).
[CrossRef]

Becker, B.

B. Becker and T. Q. Ho, "Radiation loss due to step discontinuities in symmetric biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 403-408 (1991).
[CrossRef]

T. Q. Ho and B. Becker, "Far-field radiation from step junctions in biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 298-301 (1989).
[CrossRef]

Benson, T. M.

C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.-J: Optoelectron. 140, 56-61 (1993).
[CrossRef]

Bienstman, P.

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmodes expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Chien, D. N.

Gaylord, T. K.

A. Knoesen, T. K. Gaylord, and M. G. Moharam, "Hybrid guided modes in uniaxial dielectric planar waveguides," J. Lightwave Technol. 6, 1083-1104 (1988).
[CrossRef]

Geshiro, M.

S. Sawa, M. Geshiro, and M. Hotta, "Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-40, 338-345 (1992).
[CrossRef]

Gibson, U.

Grattan, K. T. V.

F. A. Katsriku, B. M. A. Rahman, and K. T. V. Grattan, "Finite element analysis of diffused anisotropic optical waveguides," J. Lightwave Technol. 14, 780-786 (1996).
[CrossRef]

Hayashi, K.

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

Ho, T. Q.

B. Becker and T. Q. Ho, "Radiation loss due to step discontinuities in symmetric biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 403-408 (1991).
[CrossRef]

T. Q. Ho and B. Becker, "Far-field radiation from step junctions in biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 298-301 (1989).
[CrossRef]

Hotta, M.

S. Sawa, M. Geshiro, and M. Hotta, "Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-40, 338-345 (1992).
[CrossRef]

Kaji, R.

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

Kaminow, I. P.

D. Marcuse and I. P. Kaminow, "Modes of a symmetric slab optical waveguide in birefringent media. Part II: Slab with coplanar optical axis," IEEE J. Quantum Electron. 15, 92-101 (1979).
[CrossRef]

Katsriku, F. A.

F. A. Katsriku, B. M. A. Rahman, and K. T. V. Grattan, "Finite element analysis of diffused anisotropic optical waveguides," J. Lightwave Technol. 14, 780-786 (1996).
[CrossRef]

Kendall, P. C.

C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.-J: Optoelectron. 140, 56-61 (1993).
[CrossRef]

Kitayama, K.

K. Kitayama and N. Kumagai, "Theory and applications of coupled optical waveguides involving anisotropic or gyrotronic materials," IEEE Trans. Microwave Theory Tech. 25, 567-572 (1977).
[CrossRef]

Knoesen, A.

A. Knoesen, T. K. Gaylord, and M. G. Moharam, "Hybrid guided modes in uniaxial dielectric planar waveguides," J. Lightwave Technol. 6, 1083-1104 (1988).
[CrossRef]

Koshiba, M.

Y. Tsuji, M. Koshiba, and N. Takimoto, "Finite element beam propagation method for anisotropic optical waveguides," J. Lightwave Technol. 17, 723-728 (1999).
[CrossRef]

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

Kumagai, N.

K. Kitayama and N. Kumagai, "Theory and applications of coupled optical waveguides involving anisotropic or gyrotronic materials," IEEE Trans. Microwave Theory Tech. 25, 567-572 (1977).
[CrossRef]

Latsas, G. P.

Lindell, I. V.

I. V. Lindell and M. I. Oksanen, "Variational method for anisotropic dielectric waveguides," Microwaves RF 22, 145 (1983).

Lusse, P.

P. Lusse and H. G. Unger, "Finite difference method for anisotropic planar optical waveguides," AEU, Int. J. Electron. Commun. 51, 29-34 (1997).

Manenkov, A. B.

A. B. Manenkov, G. P. Latsas, and I. G. Tigelis, "Scattering of the transverse magnetic modes from an abruptly ended strongly asymmetrical slab waveguide by an accelerated integral equation technique," J. Opt. Soc. Am. A 18, 3110-3119 (2001).
[CrossRef]

I. G. Tigelis and A. B. Manenkov, "Analysis of mode scattering from an abruptly ended dielectric slab waveguide by an accelerated iteration technique," J. Opt. Soc. Am. A 17, 2249-2259 (2000).
[CrossRef]

I. G. Tigelis and A. B. Manenkov, "Scattering from an abruptly terminated asymmetrical slab waveguide," J. Opt. Soc. Am. A 16, 523-532 (1999).
[CrossRef]

A. B. Manenkov, "Reflection of the surface mode from an abruptly ended W-fibre," IEE Proc.-J: Optoelectron. 139, 101-104 (1992).
[CrossRef]

A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. I: Solution by factorization method," Radiophys. Quantum Electron. 25, 954-960 (1982).
[CrossRef]

A. B. Manenkov, "Irregular magneto-optical waveguides," IEEE Trans. Microwave Theory Tech. MTT-29, 906-910 (1981).
[CrossRef]

Marcuse, D.

D. Marcuse and I. P. Kaminow, "Modes of a symmetric slab optical waveguide in birefringent media. Part II: Slab with coplanar optical axis," IEEE J. Quantum Electron. 15, 92-101 (1979).
[CrossRef]

D. Marcuse, "Coupled-mode theory for anisotropic optical-waveguides," Bell Syst. Tech. J. 54, 985-995 (1975).

Moharam, M. G.

A. Knoesen, T. K. Gaylord, and M. G. Moharam, "Hybrid guided modes in uniaxial dielectric planar waveguides," J. Lightwave Technol. 6, 1083-1104 (1988).
[CrossRef]

Oksanen, M. I.

I. V. Lindell and M. I. Oksanen, "Variational method for anisotropic dielectric waveguides," Microwaves RF 22, 145 (1983).

Paiva, C. R.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide," Microwave Opt. Technol. Lett. 5, 602-606 (1992).
[CrossRef]

Paul, D. K.

D. K. Paul and R. K. Shevgaonkar, "Multimode propagation in anisotropic optical waveguides," Radio Sci. 16, 525-533 (1981).
[CrossRef]

Rahman, B. M. A.

F. A. Katsriku, B. M. A. Rahman, and K. T. V. Grattan, "Finite element analysis of diffused anisotropic optical waveguides," J. Lightwave Technol. 14, 780-786 (1996).
[CrossRef]

Recolons, J.

L. Torner, J. Recolons, and J. P. Torres, "Guided-to-leaky mode transformation in uniaxial optical slab waveguides," J. Lightwave Technol. 11, 1592-1600 (1993).
[CrossRef]

Sawa, S.

S. Sawa, M. Geshiro, and M. Hotta, "Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-40, 338-345 (1992).
[CrossRef]

Shevgaonkar, R. K.

D. K. Paul and R. K. Shevgaonkar, "Multimode propagation in anisotropic optical waveguides," Radio Sci. 16, 525-533 (1981).
[CrossRef]

Smartt, C. J.

C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.-J: Optoelectron. 140, 56-61 (1993).
[CrossRef]

Stepanov, A. L.

A. L. Stepanov, "Optical properties of the metal nano-particles synthesized in the polymer by the ion-implantation doping," J. Tech. Phys. 74, 1-12 (2004).

Takimoto, N.

Tanaka, K.

Tanaka, M.

Testorf, M.

Tigelis, I. G.

Topa, A. L.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide," Microwave Opt. Technol. Lett. 5, 602-606 (1992).
[CrossRef]

Torner, L.

L. Torner, J. Recolons, and J. P. Torres, "Guided-to-leaky mode transformation in uniaxial optical slab waveguides," J. Lightwave Technol. 11, 1592-1600 (1993).
[CrossRef]

Torres, J. P.

L. Torner, J. Recolons, and J. P. Torres, "Guided-to-leaky mode transformation in uniaxial optical slab waveguides," J. Lightwave Technol. 11, 1592-1600 (1993).
[CrossRef]

Tricomi, F. G.

F. G. Tricomi, Integral Equations (Interscience, 1957).

Tsuji, Y.

Y. Tsuji, M. Koshiba, and N. Takimoto, "Finite element beam propagation method for anisotropic optical waveguides," J. Lightwave Technol. 17, 723-728 (1999).
[CrossRef]

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

Unger, H. G.

P. Lusse and H. G. Unger, "Finite difference method for anisotropic planar optical waveguides," AEU, Int. J. Electron. Commun. 51, 29-34 (1997).

Vassallo, C.

Werne, T.

Yoneta, S.

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

AEU, Int. J. Electron. Commun. (1)

P. Lusse and H. G. Unger, "Finite difference method for anisotropic planar optical waveguides," AEU, Int. J. Electron. Commun. 51, 29-34 (1997).

Bell Syst. Tech. J. (1)

D. Marcuse, "Coupled-mode theory for anisotropic optical-waveguides," Bell Syst. Tech. J. 54, 985-995 (1975).

IEE Proc.-J: Optoelectron. (2)

C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.-J: Optoelectron. 140, 56-61 (1993).
[CrossRef]

A. B. Manenkov, "Reflection of the surface mode from an abruptly ended W-fibre," IEE Proc.-J: Optoelectron. 139, 101-104 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Marcuse and I. P. Kaminow, "Modes of a symmetric slab optical waveguide in birefringent media. Part II: Slab with coplanar optical axis," IEEE J. Quantum Electron. 15, 92-101 (1979).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

S. Sawa, M. Geshiro, and M. Hotta, "Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-40, 338-345 (1992).
[CrossRef]

A. B. Manenkov, "Irregular magneto-optical waveguides," IEEE Trans. Microwave Theory Tech. MTT-29, 906-910 (1981).
[CrossRef]

K. Kitayama and N. Kumagai, "Theory and applications of coupled optical waveguides involving anisotropic or gyrotronic materials," IEEE Trans. Microwave Theory Tech. 25, 567-572 (1977).
[CrossRef]

J. Lightwave Technol. (5)

F. A. Katsriku, B. M. A. Rahman, and K. T. V. Grattan, "Finite element analysis of diffused anisotropic optical waveguides," J. Lightwave Technol. 14, 780-786 (1996).
[CrossRef]

Y. Tsuji, M. Koshiba, and N. Takimoto, "Finite element beam propagation method for anisotropic optical waveguides," J. Lightwave Technol. 17, 723-728 (1999).
[CrossRef]

L. Torner, J. Recolons, and J. P. Torres, "Guided-to-leaky mode transformation in uniaxial optical slab waveguides," J. Lightwave Technol. 11, 1592-1600 (1993).
[CrossRef]

A. Knoesen, T. K. Gaylord, and M. G. Moharam, "Hybrid guided modes in uniaxial dielectric planar waveguides," J. Lightwave Technol. 6, 1083-1104 (1988).
[CrossRef]

K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Tech. Phys. (1)

A. L. Stepanov, "Optical properties of the metal nano-particles synthesized in the polymer by the ion-implantation doping," J. Tech. Phys. 74, 1-12 (2004).

Microwave Opt. Technol. Lett. (3)

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide," Microwave Opt. Technol. Lett. 5, 602-606 (1992).
[CrossRef]

T. Q. Ho and B. Becker, "Far-field radiation from step junctions in biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 298-301 (1989).
[CrossRef]

B. Becker and T. Q. Ho, "Radiation loss due to step discontinuities in symmetric biaxially anisotropic slab waveguides," Microwave Opt. Technol. Lett. 4, 403-408 (1991).
[CrossRef]

Microwaves RF (1)

I. V. Lindell and M. I. Oksanen, "Variational method for anisotropic dielectric waveguides," Microwaves RF 22, 145 (1983).

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmodes expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Radio Sci. (1)

D. K. Paul and R. K. Shevgaonkar, "Multimode propagation in anisotropic optical waveguides," Radio Sci. 16, 525-533 (1981).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. I: Solution by factorization method," Radiophys. Quantum Electron. 25, 954-960 (1982).
[CrossRef]

Other (3)

M.Abramowitz and I.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972), p. 887.

F. G. Tricomi, Integral Equations (Interscience, 1957).

L.Nicolais and G.Carotenuto, eds., Metal-Polymer Nanocomposites (Wiley, 2005).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Dispersion relation of the dominant TE and TM guided modes for several cases of anisotropy and ϵ 1 = 6.3504 .

Fig. 3
Fig. 3

Power reflectivity of the dominant TE guided mode for several cases of ϵ 2 , y and ϵ 1 = 6.3504 .

Fig. 4
Fig. 4

Power reflectivity of the dominant TM guided mode for several cases of anisotropy and ϵ 1 = 6.3504 .

Fig. 5
Fig. 5

Electric field magnitude E y ( x ) for a slab waveguide with D = 0.15 μ m and ϵ 1 = 6.3504 (TE case).

Fig. 6
Fig. 6

Electric field magnitude E x ( x ) for a slab waveguide with D = 0.15 μ m and ϵ 1 = 6.3504 (TM case).

Fig. 7
Fig. 7

Magnitude of E y ( x , z ) for a slab waveguide with ϵ 2 , y = 12.96 , D = 0.15 μ m , and ϵ 1 = 6.3504 (TE case).

Fig. 8
Fig. 8

Same as Fig. 7, but for a slab waveguide with ϵ 2 , y = 9.072 (TE case).

Fig. 9
Fig. 9

Normalized far-field radiation pattern for the dominant TE guided mode for a slab waveguide with D = 0.15 μ m and ϵ 1 = 6.3504 .

Fig. 10
Fig. 10

Normalized far-field radiation pattern for the dominant TM guided mode for a slab waveguide with D = 0.15 μ m and ϵ 1 = 6.3504 .

Equations (46)

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U g ( x ) = A g { sin ( h 2 D ) exp [ h 1 ( x D ) ] , x > D sin ( h 2 x ) , 0 x D } ,
Ψ ( x , ρ ) = B ( ρ ) { sin ( σ D ) cos [ ρ ( x D ) ] + σ ρ cos ( σ D ) sin [ ρ ( x D ) ] , x > D sin ( σ x ) , 0 x D } ,
0 + U g ( x ) Ψ ( x , ρ ) d x = 0 ,
U g ( x ) U g ( x ) + 0 + Ψ ( x , ρ ) Ψ ( x , ρ ) d ρ = δ ( x x ) .
E y I ( x , z ) = U g ( x ) [ exp ( j β g z ) + R g exp ( + j β g z ) ] + 0 + R ( ρ ) Ψ ( x , ρ ) exp [ + j β ( ρ ) z ] d ρ ,
E y II ( x , z ) = 0 + T ( s ) ϕ ( x , z ) exp [ j γ ( s ) z ] d s ,
0 + ϕ ( x , s ) ϕ ( x , s ) d x = δ ( s s ) ,
0 + ϕ ( x , s ) ϕ ( x , s ) d s = δ ( x x ) .
E ( x ) = E 0 ( x ) + 0 + E ( x ) K ( x , x ) d x ,
E 0 ( x ) = 2 β g β ¯ + γ ¯ U g ( x ) ,
K ( x , x ) = 1 ( β ¯ + γ ¯ ) { ( β ¯ β g ) U g ( x ) U g ( x ) + 0 + [ β ¯ β ( ρ ) ] Ψ ( x , ρ ) Ψ ( x , ρ ) d ρ + 0 + [ γ ¯ γ ( s ) ] ϕ ( x , s ) ϕ ( x , s ) d s } ,
β ¯ = β g , γ ¯ = 0 + γ ( s ) U ϕ ( s ) 2 d s ,
E 1 ( x ) = E 0 ( x ) + 2 β g ( β ¯ + γ ¯ ) 2 0 + [ γ ¯ γ ( s ) ] U ϕ ( s ) ϕ ( x , s ) d s ,
E 2 ( x ) = E 1 ( x ) + 2 β g ( β ¯ + γ ¯ ) 3 { 0 + d ρ [ β ¯ β ( ρ ) ] Ψ ( x , ρ ) × 0 + [ γ ¯ γ ( s ) ] U ϕ ( s ) Ψ ϕ ( ρ , s ) d s + 0 + [ γ ¯ γ ( s ) ] 2 U ϕ ( s ) ϕ ( x , s ) d s } .
R g ( 0 ) = 1 + 2 β g β ¯ + γ ¯ ,
T ( 0 ) ( s ) = 2 β g β ¯ + γ ¯ U ϕ ( s ) .
R g ( 1 ) = R g ( 0 ) ,
T ( 1 ) ( s ) = T ( 0 ) ( s ) + 2 β g ( β ¯ + γ ¯ ) 2 [ γ ¯ γ ( s ) ] U ϕ ( s ) .
R g ( 2 ) = R g ( 1 ) + 2 β g ( β ¯ + γ ¯ ) 3 0 + [ γ ¯ γ ( s ) ] 2 U ϕ ( s ) 2 d s ,
T ( 2 ) ( s ) = T ( 1 ) ( s ) + 2 β g ( β ¯ + γ ¯ ) 3 0 + d s [ γ ¯ γ ( s ) ] U ϕ ( s ) × { 0 + [ β ¯ β ( ρ ) ] Ψ ϕ ( ρ , s ) Ψ ϕ ( ρ , s ) d ρ + [ γ ¯ γ ( s ) ] U ϕ ( s ) δ ( s s ) } .
U g ( x ) = A g { cos ( h 2 D ) exp [ h 1 ( x D ) ] , x > D cos ( h 2 x ) , 0 x D } ,
0 + U g , m ( x ) U g , n ( x ) ϵ d x = δ m n ,
ϵ = { ϵ 1 , x > D ϵ 2 , x , 0 x D } ,
Ψ ( x , ρ ) = B ( ρ ) { cos ( σ D ) cos [ ρ ( x D ) ] ϵ 1 ϵ 2 , z σ ρ sin ( σ D ) sin [ ρ ( x D ) ] , x > D cos ( σ x ) , 0 x D } ,
0 + Ψ ( x , ρ ) Ψ ( x , ρ ) ϵ d x = δ ( ρ ρ ) ,
ϵ = { ϵ 1 , x > D ϵ 2 , x , 0 x D } .
U g ( x ) U g ( x ) ϵ + 0 + Ψ ( x , ρ ) Ψ ( x , ρ ) ϵ d ρ = δ ( x x ) ,
ϵ = { ϵ 1 , x > D ϵ 2 , x , 0 x D } .
0 + ϕ ( x , s ) ϕ ( x , s ) d x = ϵ 0 δ ( s s ) ,
0 + ϕ ( x , s ) ϕ ( x , s ) d s = ϵ 0 δ ( x x ) .
E 0 ( x ) = 2 U g ( x ) p ( x ) ,
E 1 ( x ) = E 0 ( x ) + 2 p ( x ) { 0 + [ 1 β ¯ 1 β ( ρ ) ] Ψ ( x , ρ ) U g Ψ ( ρ ) p ( x ) d ρ + 0 + [ 1 γ ¯ 1 γ ( s ) ] ϕ ( x , s ) U g ϕ ( s ) p ( x ) d s } ,
E 2 ( x ) = E 1 ( x ) + 2 p ( x ) { 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) × 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] Ψ ( x , ρ ) Ψ Ψ ( ρ , ρ ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] ϕ ( x , s ) Ψ ϕ ( ρ , s ) p ( x ) × 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] Ψ ( x , ρ ) Ψ ϕ ( ρ , s ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) 0 + d s [ 1 γ ¯ 1 γ ( s ) ] ϕ ( x , s ) ϕ ϕ ( s , s ) p ( x ) } ,
p ( x ) = ϵ β ¯ + ϵ 0 γ ¯ .
β ¯ = β g , γ ¯ = 0 + d s U g ϕ ( s ) q ( x ) 2 0 + d s 1 γ ( s ) U g ϕ ( s ) q ( x ) 2 ,
q ( x ) = ϵ β g + ϵ 0 k 0 ϵ 0 .
R g ( 0 ) = 1 2 β g U g U g p ( x ) ,
T ( 0 ) ( s ) = 2 γ ( s ) U g ϕ ( s ) p ( x ) .
R g ( 1 ) = R g ( 0 ) 2 β g { 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) 2 + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g Ψ ( s ) p ( x ) 2 } ,
T ( 1 ) ( s ) = T ( 0 ) ( s ) + 2 γ ( s ) { 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] × U g Ψ ( ρ ) p ( x ) Ψ ϕ ( ρ , s ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) ϕ ϕ ( s , s ) p ( x ) } .
R g ( 2 ) = R g ( 1 ) 2 β g { 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) × 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) Ψ Ψ ( ρ , ρ ) p ( x ) + 2 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) Ψ ϕ ( ρ , s ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) ϕ ϕ ( s , s ) p ( x ) } ,
T ( 2 ) ( s ) = T ( 1 ) ( s ) + 2 γ ( s ) { 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) × 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] Ψ Ψ ( ρ , ρ ) p ( x ) Ψ ϕ ( ρ , s ) p ( x ) + 0 + d ρ [ 1 β ¯ 1 β ( ρ ) ] U g Ψ ( ρ ) p ( x ) 0 + d s [ 1 γ ¯ 1 γ ( s ) ] Ψ ϕ ( ρ , s ) p ( x ) ϕ ϕ ( s , s ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ϕ ( s ) p ( x ) 0 + d ρ [ 1 β ¯ 1 β ( p ) ] Ψ ϕ ( ρ , s ) p ( x ) Ψ ϕ ( ρ , s ) p ( x ) + 0 + d s [ 1 γ ¯ 1 γ ( s ) ] U g ψ ( s ) p ( x ) 0 + d s [ 1 γ ¯ 1 γ ( s ) ] ϕ ϕ ( s , s ) p ( x ) ϕ ϕ ( s , s ) p ( x ) } .
1 R g ( υ ) 1 + R g ( υ ) = 0 E g , H s ( f ) 2 d s ,
E g , H s ( f ) = + [ E g × H s ( f ) ] e z d x .
E g , H g = 1 ,
U ( θ ) = cos ( θ ) T ( k 0 n 0 sin ( θ ) ) 2 ,

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