Abstract

We theoretically investigate the lateral leakage in fully symmetric horizontal rib-type slot waveguides caused by coupling between the TM-like slot mode and a TE slab mode. The leakage mechanism is described and the dependence on the geometry parameters is studied using the variational mode-matching method. In addition, the effective-index method to solve the transcendent eigenmode equation of rib-type slot waveguides is applied and compared with the aforementioned rigorous numerical method. We show that this semi-analytical approach yields results with sufficiently high accuracy. For design purposes the influence of structural deviations caused by the fabrication process is studied. We show that the usable range of the geometry parameters can be widely extended by exploiting leakage suppressing mechanisms.

©2008 Optical Society of America

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References

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  1. 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] [PubMed]
  2. Q. Xu, A. R. Vilson, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index-matrial,” Opt. Lett. 29, 1626–1628 (2004).
    [Crossref] [PubMed]
  3. T. Baehr-Jones, M. Hochberg, G. Wang, R. Lawson, Y. Liao, P. A. Sullivan, L. Dalton, A. K.-Y Jen, and A. Scherer, “Optical modulation and detection in slotted silicon waveguides,” Opt. Express 13, 5216–5226 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-14-5216.
    [Crossref] [PubMed]
  4. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15, 4977–4993 (2007),http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-4977.
    [Crossref] [PubMed]
  5. T. Fujisawa and M. Koshiba, “Guided modes of nonlinear slot waveguides,” IEEE Photon. Technol. Lett. 18, 1530–1532 (2006).
    [Crossref]
  6. M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
    [Crossref]
  7. P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
    [Crossref]
  8. C. A. Barrios, K. B. Gylfason, B. Sanchez, A. Griol, H. Sohlstroem, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32, 3080–3082 (2007).
    [Crossref] [PubMed]
  9. T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B 23, 684–691 (2006).
    [Crossref]
  10. K. K. McLauchlan and S. T. Dunham, “Analysis of a compact modulator incorporating a hybrid silicon/electro-optic polymer waveguide,” IEEE J. Sel. Top. Quantum Electron. 12, 1455–1460 (2006).
    [Crossref]
  11. C. A. Barrios, “Ultrasensitive nanomechanical photonic sensor based on horizontal slot-waveguide resonator,” IEEE Photon. Technol. Lett. 18, 2419–2421 (2006).
    [Crossref]
  12. A. P. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9197.
    [Crossref] [PubMed]
  13. P. Muellner and R. Hainberger, “Structural optimization of Silicon-On-Insulator Slot waveguides,” IEEE Photon. Technol. Lett. 18, 2557–2559 (2006).
    [Crossref]
  14. C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express 13, 10092–10101 (2005), http://www.opticsexpress.org/abstract.cfm?id=86450.
    [Crossref] [PubMed]
  15. A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2211–233 (1993).
    [Crossref]
  16. A. 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]
  17. N. Finger, C. Pacher, and W. Boxleitner, “Simulation of guided-wave photonic devices with variational mode-matching,” AIP Conference Proceedings 893, pp. 1493–1494 (2007).
  18. A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
    [Crossref]
  19. M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
    [Crossref]
  20. R. Hainberger and P. Muellner, “Modal behavior of SOI slot waveguides,” Proceedings of the Symposium on Photonics Technologies for 7th Framework Program, pp. 282–285, Wroclaw, Poland, 12–14 October 2006, http://www.opera2015.org/deliverables/D_4_3 CD-ROM_Wroclaw Nieuw/6_Proceedings/57_Hainberger.pdf.
  21. V. Ramaswamy, “Strip loaded film waveguide,” Bell Syst. Tech. J. 53, 697–705 (1974).

2007 (4)

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
[Crossref]

C. A. Barrios, K. B. Gylfason, B. Sanchez, A. Griol, H. Sohlstroem, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32, 3080–3082 (2007).
[Crossref] [PubMed]

F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15, 4977–4993 (2007),http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-4977.
[Crossref] [PubMed]

M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
[Crossref]

2006 (7)

T. Fujisawa and M. Koshiba, “Guided modes of nonlinear slot waveguides,” IEEE Photon. Technol. Lett. 18, 1530–1532 (2006).
[Crossref]

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B 23, 684–691 (2006).
[Crossref]

K. K. McLauchlan and S. T. Dunham, “Analysis of a compact modulator incorporating a hybrid silicon/electro-optic polymer waveguide,” IEEE J. Sel. Top. Quantum Electron. 12, 1455–1460 (2006).
[Crossref]

C. A. Barrios, “Ultrasensitive nanomechanical photonic sensor based on horizontal slot-waveguide resonator,” IEEE Photon. Technol. Lett. 18, 2419–2421 (2006).
[Crossref]

A. P. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9197.
[Crossref] [PubMed]

P. Muellner and R. Hainberger, “Structural optimization of Silicon-On-Insulator Slot waveguides,” IEEE Photon. Technol. Lett. 18, 2557–2559 (2006).
[Crossref]

2005 (2)

2004 (2)

1994 (1)

A. 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]

1993 (1)

A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2211–233 (1993).
[Crossref]

1981 (1)

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
[Crossref]

1974 (1)

V. Ramaswamy, “Strip loaded film waveguide,” Bell Syst. Tech. J. 53, 697–705 (1974).

Almeida, V. R.

Anderson, A. P.

Andreani, L. C.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Baehr-Jones, T.

Barrios, C. A.

Blasco, J.

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
[Crossref]

Boxleitner, W.

N. Finger, C. Pacher, and W. Boxleitner, “Simulation of guided-wave photonic devices with variational mode-matching,” AIP Conference Proceedings 893, pp. 1493–1494 (2007).

Canino, A.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Casquel, R.

Dalton, L.

Dell’Olio, F.

Dunham, S. T.

K. K. McLauchlan and S. T. Dunham, “Analysis of a compact modulator incorporating a hybrid silicon/electro-optic polymer waveguide,” IEEE J. Sel. Top. Quantum Electron. 12, 1455–1460 (2006).
[Crossref]

Finger, N.

N. Finger, C. Pacher, and W. Boxleitner, “Simulation of guided-wave photonic devices with variational mode-matching,” AIP Conference Proceedings 893, pp. 1493–1494 (2007).

Fujisawa, T.

T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B 23, 684–691 (2006).
[Crossref]

T. Fujisawa and M. Koshiba, “Guided modes of nonlinear slot waveguides,” IEEE Photon. Technol. Lett. 18, 1530–1532 (2006).
[Crossref]

Galli, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Gerace, D.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Griol, A.

Gylfason, K. B.

Hainberger, R.

P. Muellner and R. Hainberger, “Structural optimization of Silicon-On-Insulator Slot waveguides,” IEEE Photon. Technol. Lett. 18, 2557–2559 (2006).
[Crossref]

R. Hainberger and P. Muellner, “Modal behavior of SOI slot waveguides,” Proceedings of the Symposium on Photonics Technologies for 7th Framework Program, pp. 282–285, Wroclaw, Poland, 12–14 October 2006, http://www.opera2015.org/deliverables/D_4_3 CD-ROM_Wroclaw Nieuw/6_Proceedings/57_Hainberger.pdf.

Hochberg, M.

Holgado, M.

Hsu, T.-I.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
[Crossref]

Irrera, A.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Jen, A. K.-Y

Koch, A.

M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
[Crossref]

Koshiba, M.

T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B 23, 684–691 (2006).
[Crossref]

T. Fujisawa and M. Koshiba, “Guided modes of nonlinear slot waveguides,” IEEE Photon. Technol. Lett. 18, 1530–1532 (2006).
[Crossref]

Lawson, R.

Liao, Y.

Lipson, M.

Liscidini, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Lo Savi, R.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Marti, J.

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
[Crossref]

Martinez, A.

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
[Crossref]

McLauchlan, K. K.

K. K. McLauchlan and S. T. Dunham, “Analysis of a compact modulator incorporating a hybrid silicon/electro-optic polymer waveguide,” IEEE J. Sel. Top. Quantum Electron. 12, 1455–1460 (2006).
[Crossref]

Miritello, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Mitchell, A.

M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
[Crossref]

Muellner, P.

P. Muellner and R. Hainberger, “Structural optimization of Silicon-On-Insulator Slot waveguides,” IEEE Photon. Technol. Lett. 18, 2557–2559 (2006).
[Crossref]

R. Hainberger and P. Muellner, “Modal behavior of SOI slot waveguides,” Proceedings of the Symposium on Photonics Technologies for 7th Framework Program, pp. 282–285, Wroclaw, Poland, 12–14 October 2006, http://www.opera2015.org/deliverables/D_4_3 CD-ROM_Wroclaw Nieuw/6_Proceedings/57_Hainberger.pdf.

Oliner, A. A.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
[Crossref]

Pacher, C.

N. Finger, C. Pacher, and W. Boxleitner, “Simulation of guided-wave photonic devices with variational mode-matching,” AIP Conference Proceedings 893, pp. 1493–1494 (2007).

Pafchek, R. M.

M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
[Crossref]

Panepucci, R. R.

Passaro, V. M. N.

Patrini, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Peng, S.-T.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
[Crossref]

Politi, A.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Priolo, F.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Ramaswamy, V.

V. Ramaswamy, “Strip loaded film waveguide,” Bell Syst. Tech. J. 53, 697–705 (1974).

Sanchez, A.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
[Crossref]

Sanchez, B.

Sanchis, P.

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
[Crossref]

Scherer, A.

Schmidt, B. S.

Sohlstroem, H.

Sudbo, A. S.

A. 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]

A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2211–233 (1993).
[Crossref]

Sullivan, P. A.

Vilson, A. R.

Wang, G.

Webster, M. A.

M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
[Crossref]

Xu, Q.

Appl. Phys. Lett. (1)

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savi, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Bell Syst. Tech. J. (1)

V. Ramaswamy, “Strip loaded film waveguide,” Bell Syst. Tech. J. 53, 697–705 (1974).

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

K. K. McLauchlan and S. T. Dunham, “Analysis of a compact modulator incorporating a hybrid silicon/electro-optic polymer waveguide,” IEEE J. Sel. Top. Quantum Electron. 12, 1455–1460 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (4)

C. A. Barrios, “Ultrasensitive nanomechanical photonic sensor based on horizontal slot-waveguide resonator,” IEEE Photon. Technol. Lett. 18, 2419–2421 (2006).
[Crossref]

P. Muellner and R. Hainberger, “Structural optimization of Silicon-On-Insulator Slot waveguides,” IEEE Photon. Technol. Lett. 18, 2557–2559 (2006).
[Crossref]

T. Fujisawa and M. Koshiba, “Guided modes of nonlinear slot waveguides,” IEEE Photon. Technol. Lett. 18, 1530–1532 (2006).
[Crossref]

M. A. Webster, R. M. Pafchek, A. Mitchell, and A. Koch, “Width dependence of inherent TM-mode lateral leakage loss in Silicon-On-Insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19, 429–431 (2007).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II-New physical effects,” IEEE Trans. Microwave Theory Tech. 29, 855–869 (1981).
[Crossref]

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

Journal of Lightwave Technology (1)

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” Journal of Lightwave Technology 25, 1298–1305 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Pure Appl. Opt. (2)

A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2211–233 (1993).
[Crossref]

A. 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]

Other (2)

N. Finger, C. Pacher, and W. Boxleitner, “Simulation of guided-wave photonic devices with variational mode-matching,” AIP Conference Proceedings 893, pp. 1493–1494 (2007).

R. Hainberger and P. Muellner, “Modal behavior of SOI slot waveguides,” Proceedings of the Symposium on Photonics Technologies for 7th Framework Program, pp. 282–285, Wroclaw, Poland, 12–14 October 2006, http://www.opera2015.org/deliverables/D_4_3 CD-ROM_Wroclaw Nieuw/6_Proceedings/57_Hainberger.pdf.

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Figures (5)

Fig. 1.
Fig. 1. (a) Cross section of a rib-type slot waveguide, (b) overall optical power (contour) and electric field (arrows) distribution of the TM-like slot mode, (c) minor (TE) components.
Fig. 2.
Fig. 2. Effective indices of the TM-like slot mode, and the even and odd TE slab modes as a function of the relative slab thickness h/H for H=137 nm, w=400 nm and for two slot thicknesses, (a) S=150 nm and (b) S=50 nm at λ=1.55 µm; (c) and (d) show the lateral leakage losses of geometries with corresponding w and S, and the leakage criteria obtained numerically from the real part of the effective indices of the VMM simulation (upwardpointing triangles) and using the effective index method (downward-pointing triangles). The vertical dashed lines indicate the thickness used for the computation of the effective indices in (a) and (b).
Fig. 3.
Fig. 3. Leakage loss of rib-type slot waveguides with thickness variations of ±5 nm in the upper rib structure for (a) S=150 nm and (b) S=50 nm at λ=1.55 µm. The semi-analytical leakage criteria for odd (upward-pointing triangles) and even (downward-pointing triangles) TE slab modes are calculated for the most critical structure H′=H-5 nm and h′=h+5 nm. The crosses represent the leakage criteria of a perfectly symmetric system.
Fig. 4.
Fig. 4. (a) Influence of the slot thickness S at w=700 nm, and (b) of the rib width w at S=50 nm on the the leakage criteria for coupling to the even (dashed lines) and odd (solid lines) TE slab modes.
Fig. 5.
Fig. 5. Resonant cancellation of the leakage to the odd TE slab mode in region I (a) and the even TE mode in region II (b). The dashed lines indicate the waveguide widths calculated semi-analytically for the perfectly symmetric structures, i.e., H′=H and h′=h, at which resonances occur for odd and even TE modes, respectively.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

N eff , T M = n eff , T E , odd ( slab ) .
N eff , T M = n eff , T E , even ( slab ) .
w even = m · λ [ ( n eff , T E , even ( Core ) ) 2 ( N eff , T M ) 2 ] 1 2
w odd = m · λ [ ( n eff , T E , odd ( Core ) ) 2 ( N eff , T M ) 2 ] 1 2 ,

Metrics