Abstract

We explore the use of air trenches to achieve compact high efficiency 90° waveguide bends and beamsplitters for waveguide material systems that have low refractive index and low refractive index contrast between the core and clad materials. For a single air interface, simulation results show that the optical efficiency of a waveguide bend can be increased from 78.4% to 99.2% by simply decreasing the bend angle from 90° to 60°. This can be explained by the angular spectrum of the waveguide mode optical field. For 90° bends we use a micro-genetic algorithm (µGA) with a 2-D finite difference time domain (FDTD) method to rigorously design high efficiency waveguide bends composed of multiple air trenches. Simulation results show an optical efficiency of 97.2% for an optimized bend composed of three air trenches. Similarly, a single air trench can be designed to function as a 90° beamsplitter with 98.5% total efficiency.

© 2003 Optical Society of America

Full Article  |  PDF Article
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References

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  1. K. K. Lee, D. R. Lim, L. C. Kimmerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 261888 (2001).
    [Crossref]
  2. A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
    [Crossref]
  3. C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
    [Crossref]
  4. R.L. Espinola, R.U. Ahmad, F. Pizzuto, M.J. Steel, and R.M. Osgood, Jr., “A study of high-index-contrast 90° waveguide bend structures,” Opt. Express,  8517–528, 23 April (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517
    [Crossref] [PubMed]
  5. R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electron. 271971 (1991).
    [Crossref]
  6. R. A. Soref, “Silicon-based optoelectronics,” IEEE Proc. 811687 (1993).
    [Crossref]
  7. U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
    [Crossref]
  8. Y. Z. Tang and W. H. Wang, etc., “Integrated waveguide turning mirror in silicon-on insulator,” Phot. Techn. Lett,  1468–70, Jan. (2002).
    [Crossref]
  9. R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
    [Crossref]
  10. John E. Johnson and C.L. Tang, “Precise determination of turning mirror loss using GaAs/AlGaAs lasers with up to ten 90° intracavity turning mirrors,” Phot. Techn. Lett. 424–26 (1992).
    [Crossref]
  11. P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
    [Crossref]
  12. Chulhun Seo and Jerry C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol,  142255–2259 (1996).
    [Crossref]
  13. L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” J. Sel. Top. Quantum Electron. 654 (2000).
    [Crossref]
  14. K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.
  15. M. V. Klein and T. E. Furtak, Optics, 2nd Ed. (John Wiley and Sons, New York, 1986).
  16. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass.,1995).
  17. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [Crossref]
  18. J. Jiang and G. Nordin, “A rigorous unidirectional method for designing finite aperture diffractive optical elements,” Opt. Express,  7237–242 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-6-237
    [Crossref] [PubMed]

2002 (1)

Y. Z. Tang and W. H. Wang, etc., “Integrated waveguide turning mirror in silicon-on insulator,” Phot. Techn. Lett,  1468–70, Jan. (2002).
[Crossref]

2001 (2)

2000 (2)

1999 (1)

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

1997 (1)

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
[Crossref]

1996 (3)

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

Chulhun Seo and Jerry C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol,  142255–2259 (1996).
[Crossref]

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

1995 (1)

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

1993 (1)

R. A. Soref, “Silicon-based optoelectronics,” IEEE Proc. 811687 (1993).
[Crossref]

1992 (1)

John E. Johnson and C.L. Tang, “Precise determination of turning mirror loss using GaAs/AlGaAs lasers with up to ten 90° intracavity turning mirrors,” Phot. Techn. Lett. 424–26 (1992).
[Crossref]

1991 (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electron. 271971 (1991).
[Crossref]

Agarwal, A. M.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

Ahmad, R.U.

Akiyama, S.

K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.

Arndt, F.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

Black, M. R.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

Cerrina, F.

Chen, Jerry C.

Chulhun Seo and Jerry C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol,  142255–2259 (1996).
[Crossref]

Duan, X.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

Eldada, L.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” J. Sel. Top. Quantum Electron. 654 (2000).
[Crossref]

Espinola, R.L.

Fan, S.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

Fischer, U.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

Foresi, J. S.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

Furtak, T. E.

M. V. Klein and T. E. Furtak, Optics, 2nd Ed. (John Wiley and Sons, New York, 1986).

Haus, H. A.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.

Jiang, J.

Joannopoulus, J. D.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

Johnson, John E.

John E. Johnson and C.L. Tang, “Precise determination of turning mirror loss using GaAs/AlGaAs lasers with up to ten 90° intracavity turning mirrors,” Phot. Techn. Lett. 424–26 (1992).
[Crossref]

Johnson, S.G.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

Kimmerling, L. C.

K. K. Lee, D. R. Lim, L. C. Kimmerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 261888 (2001).
[Crossref]

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

Kimmet, J. S.

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

Klein, M. V.

M. V. Klein and T. E. Furtak, Optics, 2nd Ed. (John Wiley and Sons, New York, 1986).

Koster, A.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
[Crossref]

Kropp, J.-R.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

Laval, S.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
[Crossref]

Lee, K. K.

Liao, L.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

Lim, D. R.

Manolatou, C.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

Michel, J.

K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.

Michlak, R. J.

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

Nordin, G.

Orobtchouk, R.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
[Crossref]

Osgood, Jr., R.M.

Parker, M. A.

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

Pascal, D.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
[Crossref]

Petermann, K.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electron. 271971 (1991).
[Crossref]

Pizzuto, F.

Popovic, M.

K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.

Schmidtchen, J.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electron. 271971 (1991).
[Crossref]

Seo, Chulhun

Chulhun Seo and Jerry C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol,  142255–2259 (1996).
[Crossref]

Shacklette, L. W.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” J. Sel. Top. Quantum Electron. 654 (2000).
[Crossref]

Shin, J.

Shire, D. B.

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

Soref, R. A.

R. A. Soref, “Silicon-based optoelectronics,” IEEE Proc. 811687 (1993).
[Crossref]

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electron. 271971 (1991).
[Crossref]

Steel, M.J.

Swanson, P. D.

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass.,1995).

Tang, C. L.

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

Tang, C.L.

John E. Johnson and C.L. Tang, “Precise determination of turning mirror loss using GaAs/AlGaAs lasers with up to ten 90° intracavity turning mirrors,” Phot. Techn. Lett. 424–26 (1992).
[Crossref]

Tang, Y. Z.

Y. Z. Tang and W. H. Wang, etc., “Integrated waveguide turning mirror in silicon-on insulator,” Phot. Techn. Lett,  1468–70, Jan. (2002).
[Crossref]

Villeneuve, P.R.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

Wada, K.

K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.

Wang, W. H.

Y. Z. Tang and W. H. Wang, etc., “Integrated waveguide turning mirror in silicon-on insulator,” Phot. Techn. Lett,  1468–70, Jan. (2002).
[Crossref]

Zinke, T.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

IEEE Proc. (1)

R. A. Soref, “Silicon-based optoelectronics,” IEEE Proc. 811687 (1993).
[Crossref]

J. Appl. Phys. (1)

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimmerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 806120 (1996).
[Crossref]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

J. Lightwave Technol (1)

Chulhun Seo and Jerry C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol,  142255–2259 (1996).
[Crossref]

J. Lightwave Technol. (1)

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, “Analysis of Integrated Optical Waveguide Mirrors,” J. Lightwave Technol. 15815–820 (1997).
[Crossref]

J. of Lightwave Technol. (1)

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H. A. Haus, and J. D. Joannopoulus, “High-Density Integrated Optics,” J. of Lightwave Technol.,  171682–1692 Sept. (1999).
[Crossref]

J. Quantum Electron. (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electron. 271971 (1991).
[Crossref]

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

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” J. Sel. Top. Quantum Electron. 654 (2000).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phot. Techn. Lett (1)

Y. Z. Tang and W. H. Wang, etc., “Integrated waveguide turning mirror in silicon-on insulator,” Phot. Techn. Lett,  1468–70, Jan. (2002).
[Crossref]

Phot. Techn. Lett. (3)

John E. Johnson and C.L. Tang, “Precise determination of turning mirror loss using GaAs/AlGaAs lasers with up to ten 90° intracavity turning mirrors,” Phot. Techn. Lett. 424–26 (1992).
[Crossref]

P. D. Swanson, D. B. Shire, C. L. Tang, M. A. Parker, J. S. Kimmet, and R. J. Michlak, “Electron-cyclotron resonance etching of mirrors for ridge-guided lasers,” Phot. Techn. Lett. 7605–607 (1995).
[Crossref]

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” Phot. Techn. Lett. 8647 (1996).
[Crossref]

Other (3)

K. Wada, M. Popovic, S. Akiyama, H. A. Haus, and J. Michel, “Micron-size bending radii in silica-based waveguides,” Advanced Semiconductor Lasers and Applications/ Ultraviolet and Blue Lasers and Their Applications /Ultralong Haul DWDM Transmission and Networking/WDM Components, 2001. Digest of the LEOS Summer Topical Meetings, (Copper Mountain, CO USA, 2001), 13–14.

M. V. Klein and T. E. Furtak, Optics, 2nd Ed. (John Wiley and Sons, New York, 1986).

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass.,1995).

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Figures (8)

Fig.1.
Fig.1.

Schematic diagram of bend angle definition and a 90° waveguide bend formed by an air interface.

Fig. 2.
Fig. 2.

FDTD simulation result for a 90° bend. The colormap is the same for Figs. 4, 5, and 8(a).

Fig. 3.
Fig. 3.

(a) Waveguide mode profile and (b) its angular spectrum.

Fig. 4.
Fig. 4.

FDTD simulation results for (a) 80° and (b) 60° bends.

Fig. 5.
Fig. 5.

Micro-genetic algorithm-optimized air-trench structures for (a) one, (b) two, and (c) three layers.

Fig. 6.
Fig. 6.

Bend efficiency dependence on wavelength for the 90° air-trench bends of Fig. 5.

Fig. 7.
Fig. 7.

Air-trench beamsplitter. (a) Time-average square magnitude of electric field (monochromatic source at 1.55 µm) and (b) temporal snapshot of the electric field for a pulsed source.

Fig. 8.
Fig. 8.

Air-trench beamsplitter transmission and reflection efficiency.

Tables (1)

Tables Icon

Table 1. Geometry and performance of air-trench 90° bends.

Metrics