Abstract

A rigorous full-vector analysis based on the finite-difference mode-matching method is presented for three-dimensional optical wave propagation problems. The computation model is facilitated by a perfectly matched layer (PML) terminated with a perfectly reflecting boundary condition (PRB). The complex modes including both the guided and the radiation fields of the three-dimensional waveguide with arbitrary index profiles are computed by a finite-difference scheme. The method is applied to and validated by the analysis of the facet reflectivity of a buried waveguide and the power exchange of a periodically loaded dielectric waveguide polarization rotator.

© 2008 Optical Society of America

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  1. S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
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    [CrossRef]
  5. T. E. Murphy, J. T. Hastings, and H. I. Smith, "Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides," J. Lightwave Technol. 19, 1938-1942 (2001).
    [CrossRef]
  6. O. Limon, A. Rudnitsky, Z. Zalevsky, M. Nathan, L. Businaro, D. Cojoc, and A. Gerardino, "All-optical nano modulator on a silicon chip," Opt. Express 15, 9029-9039 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-14-9029.
    [CrossRef] [PubMed]
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  9. A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. 9, 919-933 (1973).
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  10. A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
    [CrossRef]
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    [CrossRef]
  13. P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
    [CrossRef]
  14. S. F. Helfert, A. Barcz, and R. Pregla, "Three-dimensional vectorial analysis of waveguide structures with the method of lines," Opt. Quantum Electron. 35, 381-394 (2003).
    [CrossRef]
  15. T. E. Rozzi, "Rigorous Analysis of Step Discontinuity in a Planar Dielectric Waveguide," IEEE Trans. Microwave Theory Tech. 26, 738-746 (1978).
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  16. H. Shigesawa and M. Tsuji, "Mode Propagation through a Step Discontinuity in Dielectric Planar Wave-Guide," IEEE Trans. Microwave Theory Tech. 34, 205-212 (1986).
    [CrossRef]
  17. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001).
    [CrossRef]
  18. C. Vassallo, "Finite-difference derivation of the reflectivity at output facets of dielectric waveguides with a highly diverging output beam," J. Opt. Soc. Am. A 15, 717-726 (1998).
    [CrossRef]
  19. H. Derudder, D. De Zutter, and F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
    [CrossRef]
  20. H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
    [CrossRef]
  21. K. Jiang and W. P. Huang, "Finite-difference-based mode-matching method for 3-D waveguide structures under semivectorial approximation," J. Lightwave Technol. 23, 4239-4248 (2005).
    [CrossRef]
  22. Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
    [CrossRef]
  23. T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
    [CrossRef]
  24. F. J. Mustieles, E. Ballesteros, and F. Hernandezgil, "Multimodal Analysis Method for the Design of Passive Te/Tm Converters in Integrated Wave-Guides," IEEE Photon. Technol. Lett. 5, 809-811 (1993).
    [CrossRef]
  25. W. P. Huang and C. L. Xu, "Simulation of 3-Dimensional Optical Wave-Guides by a Full-Vector Beam-Propagation Method," IEEE J. Quantum Electon. 29, 2639-2649 (1993).
    [CrossRef]
  26. W. C. Chew, J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett. 15, 363-369 (1997).
    [CrossRef]
  27. L. F. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
    [CrossRef]
  28. L. F. Li, "Multilayer Modal Method for Diffraction Gratings of Arbitrary Profile, Depth, and Permittivity," J. Opt. Soc. Am. A 10, 2581-2591 (1993).
    [CrossRef]
  29. P. L. Ho and Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).
    [CrossRef]
  30. H. A. Jamid and M. Z. M. Khan, "3-D full-vectorial analysis of strong optical waveguide discontinuities using Pade approximants," IEEE J. Quantum Electron. 43, 343-349 (2007).
    [CrossRef]
  31. K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
    [CrossRef]

2007 (2)

H. A. Jamid and M. Z. M. Khan, "3-D full-vectorial analysis of strong optical waveguide discontinuities using Pade approximants," IEEE J. Quantum Electron. 43, 343-349 (2007).
[CrossRef]

O. Limon, A. Rudnitsky, Z. Zalevsky, M. Nathan, L. Businaro, D. Cojoc, and A. Gerardino, "All-optical nano modulator on a silicon chip," Opt. Express 15, 9029-9039 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-14-9029.
[CrossRef] [PubMed]

2006 (1)

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

2005 (3)

2004 (1)

G. T. Reed, "Device physics - The optical age of silicon," Nature 427, 595-596 (2004).
[CrossRef] [PubMed]

2003 (1)

S. F. Helfert, A. Barcz, and R. Pregla, "Three-dimensional vectorial analysis of waveguide structures with the method of lines," Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

2002 (2)

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

P. L. Ho and Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).
[CrossRef]

2001 (5)

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001).
[CrossRef]

T. E. Murphy, J. T. Hastings, and H. I. Smith, "Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides," J. Lightwave Technol. 19, 1938-1942 (2001).
[CrossRef]

H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
[CrossRef]

P. L. Ho and Y. Y. Lu, "A stable bidirectional propagation method based on scattering operators," IEEE Photon. Technol. 13, 1316-1318 (2001).
[CrossRef]

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

2000 (1)

A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
[CrossRef]

1999 (1)

1998 (3)

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

C. Vassallo, "Finite-difference derivation of the reflectivity at output facets of dielectric waveguides with a highly diverging output beam," J. Opt. Soc. Am. A 15, 717-726 (1998).
[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
[CrossRef]

1997 (1)

W. C. Chew, J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett. 15, 363-369 (1997).
[CrossRef]

1996 (1)

1993 (3)

L. F. Li, "Multilayer Modal Method for Diffraction Gratings of Arbitrary Profile, Depth, and Permittivity," J. Opt. Soc. Am. A 10, 2581-2591 (1993).
[CrossRef]

F. J. Mustieles, E. Ballesteros, and F. Hernandezgil, "Multimodal Analysis Method for the Design of Passive Te/Tm Converters in Integrated Wave-Guides," IEEE Photon. Technol. Lett. 5, 809-811 (1993).
[CrossRef]

W. P. Huang and C. L. Xu, "Simulation of 3-Dimensional Optical Wave-Guides by a Full-Vector Beam-Propagation Method," IEEE J. Quantum Electon. 29, 2639-2649 (1993).
[CrossRef]

1991 (1)

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

1986 (1)

H. Shigesawa and M. Tsuji, "Mode Propagation through a Step Discontinuity in Dielectric Planar Wave-Guide," IEEE Trans. Microwave Theory Tech. 34, 205-212 (1986).
[CrossRef]

1978 (1)

T. E. Rozzi, "Rigorous Analysis of Step Discontinuity in a Planar Dielectric Waveguide," IEEE Trans. Microwave Theory Tech. 26, 738-746 (1978).
[CrossRef]

1977 (1)

W. Streifer, D. Scifres, and R. Burnham, "Coupled wave analysis of DFB and DBR lasers," IEEE J. Quantum Electron. 13, 134-141 (1977).
[CrossRef]

1973 (1)

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

Alferness, R.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Ando, T.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

Baets, R.

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

Ballesteros, E.

F. J. Mustieles, E. Ballesteros, and F. Hernandezgil, "Multimodal Analysis Method for the Design of Passive Te/Tm Converters in Integrated Wave-Guides," IEEE Photon. Technol. Lett. 5, 809-811 (1993).
[CrossRef]

Barcz, A.

S. F. Helfert, A. Barcz, and R. Pregla, "Three-dimensional vectorial analysis of waveguide structures with the method of lines," Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

Bienstman, P.

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

Burnham, R.

W. Streifer, D. Scifres, and R. Burnham, "Coupled wave analysis of DFB and DBR lasers," IEEE J. Quantum Electron. 13, 134-141 (1977).
[CrossRef]

Businaro, L.

Cao, Q.

Cheben, P.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Chew, W. C.

W. C. Chew, J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett. 15, 363-369 (1997).
[CrossRef]

Cojoc, D.

Dalacu, D.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

De Zutter, D.

H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
[CrossRef]

Delage, A.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Densmore, A.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Derudder, H.

H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
[CrossRef]

Fan, S. H.

Franck, T.

Gerardino, A.

Hastings, J. T.

Hasumi, Y.

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

Haus, H. A.

Helfert, S. F.

S. F. Helfert, A. Barcz, and R. Pregla, "Three-dimensional vectorial analysis of waveguide structures with the method of lines," Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

Hernandezgil, F.

F. J. Mustieles, E. Ballesteros, and F. Hernandezgil, "Multimodal Analysis Method for the Design of Passive Te/Tm Converters in Integrated Wave-Guides," IEEE Photon. Technol. Lett. 5, 809-811 (1993).
[CrossRef]

Ho, P. L.

P. L. Ho and Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).
[CrossRef]

P. L. Ho and Y. Y. Lu, "A stable bidirectional propagation method based on scattering operators," IEEE Photon. Technol. 13, 1316-1318 (2001).
[CrossRef]

Hodge, D.

Hong, J.

A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
[CrossRef]

Huang, W. P.

K. Jiang and W. P. Huang, "Finite-difference-based mode-matching method for 3-D waveguide structures under semivectorial approximation," J. Lightwave Technol. 23, 4239-4248 (2005).
[CrossRef]

A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
[CrossRef]

W. P. Huang and C. L. Xu, "Simulation of 3-Dimensional Optical Wave-Guides by a Full-Vector Beam-Propagation Method," IEEE J. Quantum Electon. 29, 2639-2649 (1993).
[CrossRef]

Hugonin, J. P.

Jamid, H. A.

H. A. Jamid and M. Z. M. Khan, "3-D full-vectorial analysis of strong optical waveguide discontinuities using Pade approximants," IEEE J. Quantum Electron. 43, 343-349 (2007).
[CrossRef]

Janz, S.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Jiang, K.

Jin, J. M.

W. C. Chew, J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett. 15, 363-369 (1997).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kawano, K.

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

Keil, U. D.

Khan, M. Z. M.

H. A. Jamid and M. Z. M. Khan, "3-D full-vectorial analysis of strong optical waveguide discontinuities using Pade approximants," IEEE J. Quantum Electron. 43, 343-349 (2007).
[CrossRef]

Kitoh, T.

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

Koch, T.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Kohtoku, M.

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

Koren, U.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Lalanne, P.

Lamontagne, B.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Li, L. F.

Li, X.

A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
[CrossRef]

Liao, L.

Limon, O.

Lipson, M.

Liu, A. S.

Lu, Y. Y.

P. L. Ho and Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).
[CrossRef]

P. L. Ho and Y. Y. Lu, "A stable bidirectional propagation method based on scattering operators," IEEE Photon. Technol. 13, 1316-1318 (2001).
[CrossRef]

Manolatou, C.

Michielssen, E.

W. C. Chew, J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett. 15, 363-369 (1997).
[CrossRef]

Miller, B. I.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Morse, M.

Murata, T.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

Murphy, T. E.

Mustieles, F. J.

F. J. Mustieles, E. Ballesteros, and F. Hernandezgil, "Multimodal Analysis Method for the Design of Passive Te/Tm Converters in Integrated Wave-Guides," IEEE Photon. Technol. Lett. 5, 809-811 (1993).
[CrossRef]

Nakano, H.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

Nakayama, H.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

Nathan, M.

Olyslager, F.

H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
[CrossRef]

Oron, M.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Picard, M. J.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Post, E.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Pregla, R.

S. F. Helfert, A. Barcz, and R. Pregla, "Three-dimensional vectorial analysis of waveguide structures with the method of lines," Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

Reed, G. T.

G. T. Reed, "Device physics - The optical age of silicon," Nature 427, 595-596 (2004).
[CrossRef] [PubMed]

Rozzi, T. E.

T. E. Rozzi, "Rigorous Analysis of Step Discontinuity in a Planar Dielectric Waveguide," IEEE Trans. Microwave Theory Tech. 26, 738-746 (1978).
[CrossRef]

Rubin, D.

Rudnitsky, A.

Samara-Rubio, D.

Schmid, J. H.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Scifres, D.

W. Streifer, D. Scifres, and R. Burnham, "Coupled wave analysis of DFB and DBR lasers," IEEE J. Quantum Electron. 13, 134-141 (1977).
[CrossRef]

Shams-Zadeh-Amiri, A. M.

A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
[CrossRef]

Shani, Y.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Shigesawa, H.

H. Shigesawa and M. Tsuji, "Mode Propagation through a Step Discontinuity in Dielectric Planar Wave-Guide," IEEE Trans. Microwave Theory Tech. 34, 205-212 (1986).
[CrossRef]

Silberstein, E.

Smith, H. I.

Streifer, W.

W. Streifer, D. Scifres, and R. Burnham, "Coupled wave analysis of DFB and DBR lasers," IEEE J. Quantum Electron. 13, 134-141 (1977).
[CrossRef]

Takeshita, T.

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

Tsuji, M.

H. Shigesawa and M. Tsuji, "Mode Propagation through a Step Discontinuity in Dielectric Planar Wave-Guide," IEEE Trans. Microwave Theory Tech. 34, 205-212 (1986).
[CrossRef]

Van den Berghe, S.

H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
[CrossRef]

Vassallo, C.

Villeneuve, P. R.

Waldron, P.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Xu, C. L.

W. P. Huang and C. L. Xu, "Simulation of 3-Dimensional Optical Wave-Guides by a Full-Vector Beam-Propagation Method," IEEE J. Quantum Electon. 29, 2639-2649 (1993).
[CrossRef]

Xu, D. X.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Yamauchi, J.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

Yap, K. P.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Yariv, A.

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

Ye, W. N.

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

Young, M. G.

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Zalevsky, Z.

Appl. Phys. Lett. (1)

Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, "Polarization Rotation in Asymmetric Periodic Loaded Rib Wave-Guides," Appl. Phys. Lett. 59, 1278-1280 (1991).
[CrossRef]

Electron. Lett. (1)

H. Derudder, D. De Zutter, and F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
[CrossRef]

IEEE J. Quantum Electon. (1)

W. P. Huang and C. L. Xu, "Simulation of 3-Dimensional Optical Wave-Guides by a Full-Vector Beam-Propagation Method," IEEE J. Quantum Electon. 29, 2639-2649 (1993).
[CrossRef]

IEEE J. Quantum Electron. (4)

W. Streifer, D. Scifres, and R. Burnham, "Coupled wave analysis of DFB and DBR lasers," IEEE J. Quantum Electron. 13, 134-141 (1977).
[CrossRef]

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

A. M. Shams-Zadeh-Amiri, J. Hong, X. Li, and W. P. Huang, "Second- and higher order resonant gratings with gain or loss - Part I: Green's function analysis," IEEE J. Quantum Electron. 36, 1421-1430 (2000).
[CrossRef]

H. A. Jamid and M. Z. M. Khan, "3-D full-vectorial analysis of strong optical waveguide discontinuities using Pade approximants," IEEE J. Quantum Electron. 43, 343-349 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Janz, P. Cheben, D. Dalacu, A. Delage, A. Densmore, B. Lamontagne, M. J. Picard, E. Post, J. H. Schmid, P. Waldron, D. X. Xu, K. P. Yap, and W. N. Ye, "Microphotonic elements for integration on the silicon-on-insulator waveguide platform," IEEE J. Sel. Top. Quantum Electron. 12, 1402-1415 (2006).
[CrossRef]

IEEE Photon. Technol. (1)

P. L. Ho and Y. Y. Lu, "A stable bidirectional propagation method based on scattering operators," IEEE Photon. Technol. 13, 1316-1318 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

P. L. Ho and Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).
[CrossRef]

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide," IEEE Photon. Technol. Lett. 14, 1288-1290 (2002).
[CrossRef]

F. J. Mustieles, E. Ballesteros, and F. Hernandezgil, "Multimodal Analysis Method for the Design of Passive Te/Tm Converters in Integrated Wave-Guides," IEEE Photon. Technol. Lett. 5, 809-811 (1993).
[CrossRef]

IEEE Photon.Technol. Lett. (1)

K. Kawano, T. Kitoh, M. Kohtoku, T. Takeshita, and Y. Hasumi, "3-D semivectorial analysis to calculate facet reflectivities of semiconductor optical waveguides based on the bi-directional method of line BPM (MoL-BPM)," IEEE Photon.Technol. Lett. 10, 108-110 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

H. Derudder, F. Olyslager, D. De Zutter, and S. Van den Berghe, "Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers," IEEE Trans. Antennas Propag. 49, 185-195 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

T. E. Rozzi, "Rigorous Analysis of Step Discontinuity in a Planar Dielectric Waveguide," IEEE Trans. Microwave Theory Tech. 26, 738-746 (1978).
[CrossRef]

H. Shigesawa and M. Tsuji, "Mode Propagation through a Step Discontinuity in Dielectric Planar Wave-Guide," IEEE Trans. Microwave Theory Tech. 34, 205-212 (1986).
[CrossRef]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. A (4)

Microwave Opt. Technol. Lett. (1)

W. C. Chew, J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett. 15, 363-369 (1997).
[CrossRef]

Nature (1)

G. T. Reed, "Device physics - The optical age of silicon," Nature 427, 595-596 (2004).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Quantum Electron. (2)

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

S. F. Helfert, A. Barcz, and R. Pregla, "Three-dimensional vectorial analysis of waveguide structures with the method of lines," Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

Other (1)

A. Taflove, and S. C. Hagness, Computational Electrodynamics : the finite-difference time-domain method (Artech House, Boston, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Buried waveguide

Fig. 2.
Fig. 2.

Calculated modal reflectivities of quasi-TE and quasi-TM modes. Solid triangles: full vector mode matching method; solid circles: full vector beam propagation method [30]; solid squares: semi –vector beam propagation method [31].

Fig. 3.
Fig. 3.

Facet modal reflectivity as a function of mode numbers.

Fig. 4.
Fig. 4.

Schematic representation of a periodically loaded waveguide. (a) Top view (b) cross-section.

Fig. 5.
Fig. 5.

The Power exchange between quasi-TE and quasi-TM modes as the functions of loading numbers (h=2mm). Solid line: Quasi-TE from MMM; dot line: Quasi-TM from MMM; circle: Quasi-TE from experiments [23]; square: Quasi-TM from experiments [23].

Fig. 6.
Fig. 6.

The Power exchange between quasi-TE and quasi-TM modes as the functions of loading numbers (h=3mm). Solid line: Quasi-TE from MMM; dot line: Quasi-TM from MMM; circle: Quasi-TE from experiments [23]; square: Quasi-TM from experiments [23].

Equations (42)

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[ P xx P xy P yx P yy ] [ E x E y ] = β 2 [ E x E y ] ,
P xx E x = x [ 1 n 2 x ( n 2 E x ) ] + 2 E x y 2 + n 2 k 0 2 E x ,
P xy E y = x [ 1 n 2 y ( n 2 E y ) ] 2 E y y x ,
P yy E y = y [ 1 n 2 y ( n 2 E y ) ] + 2 E y x 2 + n 2 k 0 2 E y ,
P yx E x = y [ 1 n 2 x ( n 2 E x ) ] 2 E x x y .
ζ ˜ = 0 ζ s ζ ( ζ ) d ζ ,
s ζ ( ζ ) = ( 1 j σ ζ ( ζ ) ω ε 0 n 2 , PML region 1 , elsewhere ,
σ ζ ( ζ ) = σ ζ max ( ζ ζ 0 d ) m .
σ max = c ε 0 n 2 d [ ( m + 1 ) ln 1 R ] ,
H x = Y 0 N eff E y + Y 0 N eff k 0 2 { y [ 1 n 2 y ( n 2 E y ) ] + y [ 1 n 2 x ( n 2 E x ) ] } ,
H y = + Y 0 N eff E y Y 0 N eff k 0 2 { x [ 1 n 2 x ( n 2 E x ) ] + x [ 1 n 2 y ( n 2 E y ) ] } ,
1 4 Entire region ( E tk × H tk * + E tk * × H tk ) · z ̂ ds = 1 ,
1 2 Entire region ( E tk × H tk ) · z ̂ ds = 1
1 4 ( E tm * × H tk + E tk × H tm * ) · z ̂ ds = δ mk
1 2 ( E tm × H tk ) · z ̂ da = P n δ mk
δ mn = { 1 m = k 0 m k ,
E t A = i = 1 N ( a i + e j β i A z + a i e j β i A z ) e ti A ,
H t A = i = 1 N ( a i + e j β i A z a i e j β i A z ) h ti A ,
E t B = k = 1 N ( b k + e j β k B z + b k e j β k B z ) e tk B ,
H t B = k = 1 N ( b k + e j β k B z b k e j β k B z ) h tk B .
i = 1 N ( a i + + a i ) e ti A = k = 1 N ( b k + + b k ) e tk B ,
i = 1 N ( a i + a i ) h ti A = k = 1 N ( b k + b k ) h tk B .
b k + = i = 1 N a i + [ < e ti A , h tk B > + < e tk B , h ti A > 2 < e tk B , h tk B > ] + i = 1 N a i [ < e ti A , h tk B > < e tk B , h ti A > 2 < e tk B , h tk B > ] ,
b k = i = 1 N a i + [ < e ti A , h tk B > < e tk B , h ti A > 2 < e tk B , h tk B > ] + i = 1 N a i [ < e ti A , h tk B > < e tk B , h ti A > 2 < e tk B , h tk B > ] ,
( p + p ) = ( T 11 AB T 12 AB T 21 AB T 22 AB ) ( q + q ) = T AB · ( q + q ) ,
( q + p ) = ( T A , B R B , A R A , B T B , A ) ( p + q ) = S AB × ( q + q )
T A , B = T 11 AB T 12 AB · T 22 AB 1 · T 21 AB
R B , A = T 12 AB · T 22 AB 1
R A , B = T 22 AB 1 · T 21 AB
T B , A = T 22 AB 1
P B = ( e j β 1 B Λ b 0 0 e j β N B Λ b ) ,
T A , B u = P B · T A , B ,
R B , A u = P B · R B , A · P B ,
R A , B u = R A , B ,
T B , A u = T B , A · P B ,
[ p m 1 + p 1 ] = [ T 1 , m 1 R m 1 , 1 R 1 , m 1 T m 1 , 1 ] [ p 1 + p m 1 ] ,
[ p m + p m 1 ] = [ T m 1 , m R m , m 1 R m 1 , m T m , m 1 ] [ p m 1 + p m ] ,
[ p m + p 1 ] = [ T 1 , m R m , 1 R 1 , m T m , 1 ] [ p 1 + p m ] ,
T 1 , m = T m 1 , m ( I R m 1 , 1 R m 1 , m ) 1 T 1 , m 1 ,
R m , 1 = T m 1 , m ( I R m 1 , 1 R m 1 , m ) 1 R m 1 , 1 T m , m 1 + R m , m 1 ,
R 1 , m = T m 1 , 1 ( I R m 1 , m R m 1 , m ) 1 R m 1 , m T 1 , m 1 + R 1 , m 1 ,
T m , 1 = T m 1 , 1 ( I R m 1 , m R m 1 , 1 ) 1 T m , m 1 .

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